Using Computational Methods to Teach Chemical Principles 2019006545, 2019015021, 9780841234178, 9780841234208, 0841234175

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Using Computational Methods To Teach Chemical Principles

ACS SYMPOSIUM SERIES 1312

Using Computational Methods To Teach Chemical Principles Alexander Grushow, Editor Department of Chemistry, Biochemistry, and Physics Rider University Lawrenceville, New Jersey, United States

Melissa S. Reeves, Editor Department of Chemistry Tuskegee University Tuskegee, Alabama, United States

Sponsored by the ACS Division of Chemical Education

American Chemical Society, Washington, DC

Library of Congress Cataloging-in-Publication Data Names: Grushow, Alexander, editor. | Reeves, Melissa Setsuko, 1966- editor. | American Chemical Society. Division of Chemical Education. | American Chemical Society. Meeting (254th : 2017 : Washington, D.C.) Title: Using computational methods to teach chemical principles / Alexander Grushow, editor (Department of Chemistry, Biochemistry, and Physics, Rider University, Lawrenceville, New Jersey, United States), Melissa S. Reeves, editor (Department of Chemistry, Tuskegee University, Tuskegee, Alabama, United States) ; sponsored by the ACS Division of Chemical Education. Description: Washington, DC : American Chemical Society, [2019] | Series: ACS symposium series ; 1312 | Based on the 254th American Chemical Society national meeting, held in 2017, in Washington, DC. | Includes bibliographical references and index. | Description based on print version record and CIP data provided by publisher; resource not viewed. Identifiers: LCCN 2019006545 (print) | LCCN 2019015021 (ebook) | ISBN 9780841234178 (ebook) | ISBN 9780841234208 (alk. paper) Subjects: LCSH: Chemistry--Study and teaching--Congresses. Classification: LCC QD40 (ebook) | LCC QD40 .U845 2019 (print) | DDC 540.71--dc23 LC record available at https://lccn.loc.gov/2019006545

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Foreword The purpose of the series is to publish timely, comprehensive books developed from the ACS sponsored symposia based on current scientific research. Occasionally, books are developed from symposia sponsored by other organizations when the topic is of keen interest to the chemistry audience. Before a book proposal is accepted, the proposed table of contents is reviewed for appropriate and comprehensive coverage and for interest to the audience. Some papers may be excluded to better focus the book; others may be added to provide comprehensiveness. When appropriate, overview or introductory chapters are added. Drafts of chapters are peer-reviewed prior to final acceptance or rejection. As a rule, only original research papers and original review papers are included in the volumes. Verbatim reproductions of previous published papers are not accepted. ACS Books Department

Contents 1. Using Computational Methods To Teach Chemical Principles: Overview . . . . . . . . . . . . . . . . . .  Alexander Grushow and Melissa S. Reeves

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2. Molecular Dynamics Simulations in First-Semester General Chemistry: Visualizing Gas Particle Motion and Making Connections to Mathematical Gas Law Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11 C. D. Bruce 3. Using Electronic Structure Calculations To Investigate the Kinetics of Gas-Phase Ammonia Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21 Kelsey M. Stocker 4. Modeling Reaction Energies and Exploring Noble Gas Chemistry in the Physical Chemistry Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33 James A. Phillips 5. How Can You Measure a Reaction Enthalpy without Going into the Lab?. . . . . . . . . . . . . . . . . . .  51 Melissa S. Reeves, H. Laine Berghout, Mark J. Perri, Steven M. Singleton, and Robert M. Whitnell 6. Process Oriented Guided Inquiry Learning Computational Chemistry Experiments: Revisions and Extensions Based on Lessons Learned from Implementation . . . . . . . . . . . . . . .  65 Robert M. Whitnell and Melissa S. Reeves 7. Chem Compute Science Gateway: An Online Computational Chemistry Tool . . . . . . . . . . .  79 Mark J. Perri, Mary Akinmurele, and Matthew Haynie 8. Using Computational Chemistry to Extend the Acetylene Rovibrational Spectrum to C2T2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  93 William R. Martin and David W. Ball 9. Introducing Quantum Calculations into the Physical Chemistry Laboratory . . . . . . . . . . . . .  109 Thomas C. DeVore 10. Learning by Computing: A First Year Honors Chemistry Curriculum . . . . . . . . . . . . . . . . . . . . . . . .  127 Arun K. Sharma and Lukshmi Asirwatham 11. Integrating Computational Chemistry into an Organic Chemistry Laboratory Curriculum Using WebMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  139 Brian J. Esselman and Nicholas J. Hill

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12. Computational Narrative Activities: Combining Computing, Context, and Communication To Teach Chemical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  163 Steven M. Singleton 13. Computational Chemistry as a Course for Students Majoring in the Sciences . . . . . . . . . . . .  183 Lorena Tribe 14. Beyond the Analytical Solution: Using Mathematical Software To Enhance Understanding of Physical Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  195 Ashley Ringer McDonald and John P. Hagen 15. A Lab Course in Computational Chemistry Is Not About Computers . . . . . . . . . . . . . . . . . . . . . . . . .  211 Alexander Grushow 16. Discovery-Based Computational Activities in the Undergraduate Chemistry Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  227 Yana Kholod and Dmytro Kosenkov 17. Using the Hydrogen Bond as a Platform for the Enhancement of Integrative Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  245 Harry L. Price Editors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  259 Indexes Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  263 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  265

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Chapter 1

Using Computational Methods To Teach Chemical Principles: Overview Alexander Grushow*,1 and Melissa S. Reeves*,2 1Department of Chemistry, Biochemistry & Physics, Rider University,

Lawrenceville, New Jersey 08648, United States

2Department of Chemistry, Tuskegee University,

Tuskegee, Alabama 36088, United States *E-mail: [email protected] (A.G.). *E-mail: [email protected] (M.S.R.).

While computational chemistry methods are usually a research topic of their own, even in the undergraduate curriculum, many methods are becoming mainstream and can be used to appropriately compute chemical parameters that are not easily measured in the undergraduate laboratory. These calculations can be used to help students explore and understand chemical principles and properties. Visualization and animation of structures and properties are also aids in students’ exploration of chemistry. The ubiquity of personal computing devices capable of running calculations and the user-friendliness of software to fully optimize small and medium molecules using graphical interfaces and drop-down control menus has made it possible to readily use computational chemistry tools in most chemistry courses in the undergraduate curriculum. This book will focus on the use of computational chemistry as a tool in the classroom and laboratory to teach chemical principles.

Introduction The chapters in this book are the result of the growing ubiquity of theoretical and computational methods in all facets of chemistry education. For better or worse, the days of hand calculating solutions to Schrödinger equations are long gone. The ability to use a computer to solve thousands of equations in the blink of an eye makes it possible to pursue computations that generate meaningful results in a very short time. Whether those computations are quantum mechanical, statistical mechanics or examining molecular dynamics, the even greater power of modern computational chemistry is the ability to visualize the results of these calculations in ways that provide real chemical insight to both experts and novices. It is the latter group that the authors within this book serve. © 2019 American Chemical Society

Herein are described many different uses of computers, from high level quantum mechanical calculations, through molecular dynamics simulations to the use of mathematical engines to model chemical systems. All of this computing power however is targeted at teaching students about chemistry. Along the way students will likely learn some other computer-based techniques, but the goal is to learn about chemistry. The symposium that resulted in this book was held at the 254th ACS National Meeting held in Washington, DC. Many of the authors in this book presented talks during that symposium, which also was highlighted by an extended afternoon break for participants to go outside and witness the solar eclipse of 2017. Other chapters represent the work of authors who could not participate in the symposium, but provide valuable insight into ways computational chemistry can be used to teach chemical principles. We are emphasizing the idea that the focus can now be on learning chemistry and not on the theoretical methods themselves. While we are not diminishing the importance of the theoretical background, we wanted to document the myriad of ways to teach chemistry using computational methods. The objective of this book is to provide the reader with examples of the use of computational methods in the classroom and laboratory in various institutional settings. While the use of computational methods has been developing for years, we felt that the work of the authors was important to present even though we have not had the opportunity to systematically assess the outcomes of these innovations. We expect that research will be done to explore the effectiveness of computational methods in the teaching of chemical concepts as computational methods become more mainstream. Wherever possible we have asked authors to comment on their experiences, challenges, and successes, including student feedback when available, but our primary focus has been to publicize what various instructors have done to promote the use of computational methods in the teaching of chemistry. In the meantime, we hope that you will find some use in learning about the current innovations and about the successes and challenges that the authors have experienced in bringing computational methods to bear in the teaching of chemistry.

History of Computational in Chemistry in Our Classes When we first started our teaching careers, desktop computers were just starting to be regularly used to perform ab initio or semi-empirical quantum mechanical calculations. More often than not however, the software was limited to a single or small number of available licenses. And examination of anything more than a few heavy atoms took longer than the typical undergraduate student attention span. As a result, these packages were usually used in research situations or on a very limited basis in the undergraduate curriculum to provide a single example of computational methods. Molecular mechanics and dynamics could also be performed on small systems using a desktop computer, but the limitation with this type of computation was that commercial packages were often costly and the low cost (and free) applications often did not come with a useful graphical interface. While we are both physical chemists and had used computational resources in our own research, bringing it into the classroom was fraught with many difficulties. Most of the time students needed to learn new computer constructs, such as coding and command-line instructions. While we did feel that these kinds of experiences were important for our undergraduates to engage in, because of the value of computational methods used in professional research situations in chemistry, many of the early exercises expended much more effort in computer programming and less time thinking about the chemistry questions.

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As indicated by a number of authors in this book, there has been a great development of computational tools to both quickly calculate and easily visualize results of calculations on many types of chemical systems. These developments have changed our questions from “how do I get students to learn how to use computational software?” to “what chemical questions can we explore using this relatively easy tool?” Within this book, you will find chapters that explore chemistry questions that utilize tools such as high-level quantum computational chemistry, molecular dynamics simulations, and computational engines to visualize complex mathematical functions used in physical chemistry. The material, however is not just for the physical chemist, as we have contributions from organic chemistry and general chemistry as well.

Selected Landmarks in Computational Chemistry Education Computational chemistry has been part of the undergraduate curriculum for decades (1), but has stubbornly remained in isolated pockets of particular departments. Despite the optimistic J. Chem. Ed. editorial “Computational Chemistry for the Masses (2)” from 1996, computational chemistry did not spread to the masses. As recently as 2015, Fortenberry, et al., argued that computational chemistry had still not entered the standard undergraduate chemistry curriculum (3) [emphasis added]. The same argument has been made by Johnson and Engel (4). Most purveyors of computational chemistry have made sincere efforts to woo the undergraduate education market with specialized packages, books (5–7), and even workshops for professors. One large barrier has been the expense of equipping a computer classroom and purchasing the license to a suite of software; a second barrier is the regular maintenance and upgrades needed for hardware and software. Finally, the professor running the course has to have a plan, curricular materials, and the expertise to use the computational tools within the curriculum. A coarse timeline of “landmark” events in the last 25 years of computational chemistry education here begins in 1993 (see Figure 1) with the publication of the Schwenz and Moore Physical Chemistry: Developing a Dynamic Curriculum (8). Three of the 31 chapters were computationally oriented, covering ab initio calculations (9), Hückel calculations (10), and using Monte Carlo calculations to simulate kinetic data (11). That same year, a review by Casanova covered molecular modeling in education up to that date (1). Coincidentally, 1993 was also the debut of Mosaic, the first web browser for general users. The 90s saw a rise in the graphical user interface (GUI) and software designed for the desktop computer. For example, Gaussian was released for the Windows-based PCs in 1994, and Spartan for Mac (1994) and Windows (1995) were released. Gaussview (the Gaussian GUI) was first available in 1997. Many efforts were made by commercial software companies to produce educational materials in this period (5–7). Gaussview/Gaussian and Spartan remain highly popular today. In 1998, a paper detailed the “Integration of Computational Chemistry in the Chemistry Curriculum (12)” at UNC Wilmington; computational chemistry was incorporated in six courses there, including Organic 1 and 2. Other papers detailed single courses (13) or single experiments (14–16) utilizing computational chemistry. There was a sea change in 2000: the initial release of WebMO (17, 18) and the rise of webbased computational chemistry. Growth was burgeoning in educational use as well in 2001 there was both an ACS Symposium “Teaching Chemistry in the New Century: Physical Chemistry (19)” which listed 6 computational presentations out of 18, including talks on molecular dynamics and using symbolic math programs and also a full day symposium at the fall ACS meeting entitled “Computational Chemistry in the Undergraduate Curriculum.” These were emblematic of the 3

incursions of computational chemistry into education. These incursions continued with a number of symposia, usually about physical chemistry education, that would include aspects of computational chemistry. While computational chemistry is often used as a synonym for ab initio electronic structure calculations, many of the symposia included a broader view, as we have done in this book, to include other types of computation such as molecular mechanics and dynamics, kinetics simulators and the use of symbolic math programs.

Figure 1. Timeline of landmark events in computational chemistry education. The top row is about technology, the middle row about software, and the bottom row is published works. The rise of the smartphone, tablet and low cost laptop may have finally broken the cost barrier. We will date this landmark at the advent of the iPhone in 2007. Essentially all college students now arrive at the classroom with a 1990s supercomputer in their back pocket; they are pre-equipped to do high level computation and visualization (20). After hardware costs, the next largest barrier (for the masses) is the purchase and maintenance of software. Freely distributed packages have long been available, such as PSI4 (21, 22) and GAMESS (23, 24) for electronic structure calculations and TINKER (25, 26) for molecular dynamics. However, the technical issues with downloading packages, installing them, and maintaining them are nonneglible. These barriers, too, may be falling with freely available software packages such as WebMO as a web client-based front end to freely distributed packages such as GAMESS and PSI4 (and the WebMO app (27, 28) as the front end to the front end). There are also freely accessible web servers such as Chem Compute (29). This brings us to the present time and the final barrier, which is that professors interested in using the computational tools may be uncertain how to use them in the classroom or lab because of a lack of training. At some point, we envision that there will be a computational experiment in every lab manual from General Chemistry on up to Physical Chemistry, but that point has not yet been reached. The chemical education literature now has a number of computational experiments, some of which have already been referenced and others which are described in other chapters in this book. PSI4 Education (3) is a recent project to build a library of freely available curricular materials. The POGIL-PCL project (30, 31) has developed and tested three guided inquiry computational experiments. Another recent ACS Symposium Series book (32) also has a couple of examples of physical chemistry experiments in computational chemistry or with computational components. Since the American Chemical Society Committee on Professional Training issued the guidelines allowing advanced courses to replace the traditional two-semester sequences of organic and physical chemistry (33) it has become possible to have a course entirely about computational chemistry as

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part of the undergraduate major. There is certainly space in the curriculum to use computational chemistry.

Balancing Theory and Application Clearly the tools are available and there is more room in the curriculum to include computational methods in a course or a lab. The question is, how to implement? As with the utilization of complex instrumentation, the use of computational methods in chemistry laboratories also raises the question of how much a student needs to understand about the inner workings of the tools they are using to learn chemistry. In the world of laboratory instrumentation, for example, there is the still open question “Does a student need to understand the nuclear relaxation phenomenon to use an NMR instrument?” Or do students need to know how to shim a magnetic field in an NMR instrument? Does a student need to fully understand population inversions and how lasers work in order use a laser-based spectrometer? There has long been an interest in examining how instruments are used in the chemistry curriculum (34) but only recently has there been some examination into how use of instrumentation in the chemistry laboratory impacts student learning (35). However, the definitive answer of how much students need to understand about those instruments has not appeared in the educational literature. On the other hand, the instrumentation technology and automation has rendered the question moot, as it is often counterproductive to get “under the hood” for many instruments. At the undergraduate level, the goal is often to provide students the experience of using instrumentation and learning how to interpret the resulting data. The advanced work of understanding how instrumentation works and its limitation is often left to advanced courses, independent research or graduate studies. The similar question in computational chemistry is, how much do students need to understand about the methods they use? In a molecular dynamics simulation do students need to understand the application of force fields from all the nuclei or molecules in the system? When performing an ab initio calculation, does a student need to understand how thousands of integrals are evaluated to generate the matrix elements that will then be manipulated to form a single iteration of a structure minimization? We think, at this point in the technological development, the answer is no (see Figure 2). The use of computational tools has permeated the practice of chemistry such that their inclusion should be as mundane as obtaining an NMR spectrum. Students can learn to recognize from experience that use of a particular deuterated solvent in NMR spectroscopy might be preferred over another, without necessarily understanding why. Similarly, students can begin to recognize that HF/ STO-3G calculations are fast, but MP2/6-31G* and B3LYP/6-311+G** will improve the energy and vibrational frequencies. As stated above, both authors have engaged students in computational methods early in our teaching careers. In those early days, we had students actively coding, developing scripts and creating their own visualizations. In large part, we did this because we had to. The tools were not available to provide students the ability to answer even simple chemical questions without some work developing the computational tools. We did have students develop scripts, learn how integrals were calculated, and port output files from a computational program to some sort of graphical output. This kind of activity could take up to an entire 3-hour lab period. Now it can be done automatically in a few minutes. By using the tools to answer a chemistry question, students can explore their chosen discipline, and if they become interested in the details of the computational methodology, they can pursue that understanding in advanced coursework or independent research.

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We feel that including computational tools to explore chemical questions should be part of our goal to teach students about chemical concepts. Yet, it is clear from some of the chapters in this volume that there is still room to discuss how to use computational methods in the classroom. It really does depend on the goals for one’s course or curriculum. We could also envision a course that is designed to teach chemistry students the tools and techniques of computer programming and coding. This would be very much a course that goes “under the hood” of computational methods. On the other hand, the amount of material to potentially teach in computational methods is expansive and would likely take more than even two semesters to do it all justice at the undergraduate level.

Figure 2. In their undergraduate teaching, the authors are weighing heavily on time for application over time spent on details of the theory. In the end, it comes down to the instructor’s preference and course goals. As you read the chapters in this book, please take some time to think about how you might implement the ideas that are described within. Some of them require deep exploration of computational methods, while others use the computational tools to develop chemical understanding without seeking to understand how the tools work. Other chapters are found in between these two extremes. The reader is cautioned to make sure they understand the requirements for utilizing the tools and methods described in each chapter before adopting a particular activity.

Overview of the Chapters The original ACS symposium in Washington, D.C. was divided roughly in half between single experiments and collections of activities or full courses. We have kept a similar division in this book. The authors were encouraged to provide their personal stories as they developed their materials in computational chemistry. As a result, many of the chapters seem conversational because they are a description the process of development of these activities. In so doing the authors also provide insight into what has worked and what has not. 6

In the first half of this book, the chapters describe one or a couple of computational activities. In the chapter following this one (Chapter 2), Bruce explains how computational methods can be used to provide theoretical context and visualization of kinetic molecular theory. Chapters 3, 4, and5 provide development of multi-faceted computational experiments that provide chemical insight without performing multiple laboratory experiments, many of which would be dangerous or difficult to set-up in the undergraduate laboratory. Stocker describes a series of activities that explore the energetics for the reaction pathway for the formation of ammonia. Phillips has developed a couple of activities that stem from computations on the insertion of an argon atom into the HF molecule. This experiment has a couple of avenues for additional exploration of chemistry that would not be readily available in the undergraduate laboratory. Reeves, et al., describe an experiment for exploring computational thermochemistry on halogenated compounds, showing how useful computational chemistry can be to examine potentially toxic and hazardous compounds. This group is followed by Chapter 6 in which Whitnell and Reeves explore the process of developing and testing computational experiments within a guided inquiry framework. In Chapter 7, Perri, Akinmurele and Haynie describe the computational tools that have been made available through a browser-based platform, increasing the accessibility of high-performance computing to educators everywhere. Finally, there are two chapters that explore the use of computational chemistry to extend chemical understanding developed in the physical chemistry laboratory. Chapter 8 is a single module by Martin and Ball that extends the spectroscopic study of acetylene to a computation of tritiated acetylene what is not easily obtained in an undergraduate laboratory. The final chapter (Chapter 9) in this section by DeVore describes a couple of different computational extensions to the physical chemistry laboratory from infrared spectroscopy to the Aufbau principle. In the second half of the book, the chapters cover collections of activities or full courses. Chapter 10, by Sharma and Asirwatham, details use of computational activities in an Honors General Chemistry course. This chapter is significant for its use of computation in multiple applications and topical settings throughout that foundational semester. Several freely accessible software packages are discussed. Esselman and Hill describe in Chapter 11 the integration of ab initio calculations into Organic Chemistry lab. Their work combining wet labs with insight from computations is aimed at improving students’ rationalizations of chemical phenomena. In Chapters 12, 13, and 14, different uses of computation in the Physical Chemistry sequence are described. Singleton uses Jupyter notebooks to create “computational narratives,” which combine complex calculations with written interpretations. Tribe emphasizes student programming assignments to expand student comprehension of the inner workings of computational programs. In Chapter 14, McDonald and Hagan detail using MATLAB assignments throughout Physical Chemistry to build students’ computational thinking and expertise. In Chapter 15, Grushow details a standalone laboratory course on teaching chemistry with computational chemistry intended to follow a course on the fundamentals of Physical Chemistry. The final two chapters have discussions of activities which cover a span of courses. Kholod and Kosenkov (Chapter 16) discuss using computational chemistry to add research experiences in the curriculum to a variety of levels of courses. Lastly, Price (Chapter 17) has a plan to unify multiple courses (as well as de-compartmentalize student thinking) with a study of a single unifying chemical concept: the hydrogen bond.

7

Conclusion The use of computational chemistry to explore chemistry through visualization and quantification of difficult or impossible to measure properties makes it invaluable as a teaching tool. The chapters in this book provide some interesting ideas and practical insight for the instructor who wants to include more computational and theoretical lessons into their chemistry curriculum. The smart phone combined with web interfaces have brought us to a time when “bring your own device” is feasible. We have not reached the stage where every lab manual (beginning in General Chemistry) includes a computational experiment, but we are heading in that direction. The next key step will be to make computational methods more accessible for instructors who have not been previously trained in using them for chemistry instruction.

References 1.

Casanova, J. Computer-Based Molecular Modeling in the Curriculum. J. Chem. Educ. 1993, 70, 904. 2. JCE staff. Computational Chemistry for the Masses. J. Chem. Educ. 1996, 73, 104. 3. Fortenberry, R. C.; McDonald, A. R.; Shepherd, T. D.; Kennedy, M.; Sherrill, C. D. PSI4Education: Computational Chemistry Labs Using Free Software. In The Promise of Chemical Education: Addressing our Students Needs; ACS Symposium Series 1193; American Chemical Society, 2015; pp 85–98. 4. Johnson, L. E.; Engel, T. Integrating Computational Chemistry into the Physical Chemistry Curriculum. J. Chem. Educ. 2011, 88, 569–573. 5. Foresman, J. B.; Frisch, A. Exploring Chemistry With Electronic Structure Methods: A Guide to Using Gaussian, 2nd ed.; Gaussian: Pittsburgh, PA, 1996. 6. Hehre, W. J. Introducing Molecular Modeling into the Undergraduate Chemistry Curriculum; Wavefunction: Irvine, CA, 1997. 7. Viste, A. Laboratory Exercises Using HyperChem (Caffery, Mary L.; Dobosh, Paul A.; Richardson, Diane M.). J. Chem. Educ. 1999, 76, 1065. 8. Physical Chemistry: Developing a Dynamic Curriculum; Schwenz, R. W., Moore, R. J., Eds.; American Chemical Society: Washington, DC, 1993. 9. Brown, F. B. Computational Chemistry in the Physical Chemistry Laboratory: Ab Initio Molecular Orbital Calculations. In Physical Chemistry: Developing a Dynamic Curriculum; Schwenz, R. W., Moore, R. J., Eds.; American Chemical Society: Washington, D.C., 1993; pp 2–13. 10. Moog, R. S. Hückel Molecular Orbitals. In Physical Chemistry: Developing a Dynamic Curriculum; Schwenz, R. W., Moore, R. J., Eds.; American Chemical Society: Washington, D.C., 1993; pp 280–291. 11. Bluestone, S. A Monte Carlo Method for Chemical Kinetics. In Physical Chemistry: Developing a Dynamic Curriculum; Schwenz, R. W., Moore, R. J., Eds.; American Chemical Society: Washington, D.C., 1993; pp 434–461. 12. Martin, N. H. Integration of Computational Chemistry into the Chemistry Curriculum. J. Chem. Educ. 1998, 75, 241.

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13. Holme, T. Teaching Computational Chemistry in the Undergraduate and Graduate Chemistry Curriculum. J. Mol. Graph. Model. 1999, 17, 244–247. 14. Ringan, N. S.; Grayson, L. Molecular Modelling in the Undergraduate Chemistry Curriculum: The Use of Beta-Lactams as a Case Study. J. Chem. Educ. 1994, 71, 856. 15. Saiz, E.; Tarazona, M. P. Molecular Dynamics and the Water Molecule: An Introduction to Molecular Dynamics for Physical Chemistry Students. J. Chem. Educ. 1997, 74, 1350–1354. 16. Salter, C.; Foresman, J. B. Naphthalene and Azulene I: Semimicro Bomb Calorimetry and Quantum Mechanical Calculations. J. Chem. Educ. 1998, 75, 1341. 17. Schmidt, J. R.; Polik, W. F. WebMO; WebMO LLC: Holland, MI, 2018. 18. WebMO - Computational Chemistry on the WWW https://www.webmo.net/(accessed Oct 25, 2018). 19. Zielinski, T. J.; Schwenz, R. W. Teaching Chemistry in the New Century: Physical Chemistry. J. Chem. Educ. 2001, 78, 1173. 20. Williams, A. J.; Pence, H. E. Smart Phones, a Powerful Tool in the Chemistry Classroom. J. Chem. Educ. 2011, 88, 683–686. 21. Parrish, R. M.; Burns, L. A.; Smith, D. G. A.; Simmonett, A. C.; DePrince, A. E.; Hohenstein, E. G.; Bozkaya, U.; Sokolov, A. Y.; Di Remigio, R.; Richard, R. M.; Gonthier, J. F.; James, A. M.; McAlexander, H. R.; Kumar, A.; Saitow, M.; Wang, X.; Pritchard, B. P.; Verma, P.; Schaefer, H. F., III; Patkowski, K.; King, R. A.; Valeev, E. F.; Evangelista, F. A.; Turney, J. M.; Crawford, T. D.; Sherrill, C. D. Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability. J. Chem. Theory Comput. 2017, 13, 3185–3197. 22. Psi4: Open-Source Quantum Chemistry; http://www.psicode.org/(accessed Oct 25, 2018). 23. Gordon, M. S.; Schmidt, M. W. Advances in Electronic Structure Theory: GAMESS a Decade Later. In Theory and Applications of Computational Chemistry; Dykstra, C. E., Frenking, G., Kim, K. S., Scuseria, G. E., Eds.; Elsevier: Amsterdam, 2005; Chapter 41, pp 1167–1189. 24. Gordon Group/GAMESS Homepage; https://www.msg.chem.iastate.edu/gamess/(accessed Oct 25, 2018). 25. Xie, Q.; Tinker, R. Molecular Dynamics Simulations of Chemical Reactions for Use in Education. J. Chem. Educ. 2006, 83, 77. 26. Tinker Molecular Modeling Package; https://dasher.wustl.edu/tinker/(accessed Oct 25, 2018). 27. WebMO Molecule Editor; https://itunes.apple.com/gh/app/webmo-molecule-editor/ id797898095?mt=8 (accessed Oct 25, 2018). 28. WebMO - Apps on Google Play; https://play.google.com/store/apps/details?id=net.webmo. android.moledit&hl=en_US (accessed Oct 25, 2018). 29. Perri, M. J.; Weber, S. H. Web-Based Job Submission Interface for the GAMESS Computational Chemistry Program. J. Chem. Educ. 2014, 91, 2206–2208. 30. Hunnicutt, S. S.; Grushow, A.; Whitnell, R. Guided-Inquiry Experiments for Physical Chemistry: The POGIL-PCL Model. J. Chem. Educ. 2015, 92, 262–268. 31. Reeves, M. S.; Whitnell, R. M. New Computational Physical Chemistry Experiments: Using POGIL Techniques with Ab Initio and Molecular Dynamics Calculations. In Addressing the Millennial Student in Undergraduate Chemistry; ACS Symposium Series 1180; American Chemical Society, 2014; pp 71–90. 9

32. Engaging Students in Physical Chemistry, Teague, C. M.; Garder, D. E., Eds.; ACS Symposium Series 1297; American Chemical Society, 2018. 33. Committee on Professional Training. ACS Guidelines and Evaluation Procedures for Bachelor’s Degree Programs; American Chemical Society, 2015. https://www.acs.org/content/dam/acsorg/ about/governance/committees/training/2015-acs-guidelines-for-bachelors-degreeprograms.pdf (accessed July 18, 2018) 34. Pickral, G. M. The Laboratory Use of Chemical Instrumentation in the Undergraduate Chemistry Curriculum. J. Chem. Educ. 1983, 60, A338. 35. Warner, D. L.; Brown, E. C.; Shadle, S. E. Laboratory Instrumentation: An Exploration of the Impact of Instrumentation on Student Learning. J. Chem. Educ. 2016, 93, 1223–1231.

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Chapter 2

Molecular Dynamics Simulations in First-Semester General Chemistry: Visualizing Gas Particle Motion and Making Connections to Mathematical Gas Law Relationships C. D. Bruce* John Carroll University, 1 John Carroll Blvd., University Heights, Ohio 44118, United States *E-mail: [email protected].

Implementation of a freely available molecular dynamics (MD) software program in a general chemistry class to assist students in learning the relationship among particle motion, macroscopic properties, and mathematical gas laws is described. In this activity, students acquire skills in data analysis while developing a deeper understanding of the origin of macroscopic physical properties of gases. The activity is easy to implement and does not require significant expertise in computational chemistry on the part of the instructor.

Introduction The transition from novice to professional chemist requires not only acquisition of content knowledge but also development of chemical intuition grounded in that content knowledge. Visualization of atomic and molecular level processes is a valuable tool in a instructor’s toolbox for helping students at all levels acquire content knowledge and use that knowledge to develop accurate chemical intuition (1). Many types of visualizations exist, ranging from interactive laboratory simulations to mathematically accurate computational techniques (2–6). The former are traditionally used in introductory level courses while the latter are often reserved for higher-level courses after students have additional subject-specific content knowledge. This chapter will argue that students at the General Chemistry level can benefit from introduction to and use of mathematically accurate models of chemical behavior to develop a better understanding of molecular-level behavior via both visualization of particle motion and confirmation of mathematical relationships typically taught in the General Chemistry curriculum. Readers of this book are likely already aware of the value of using computational techniques in the curriculum, but for some instructors, the barrier to introducing a new technology, particularly one not in their area of expertise, is too great. The activity described in this chapter is accessible for students and instructors at all knowledge levels. At the introductory level, the addition of computational tools to the course provides another mechanism for students to learn the required © 2019 American Chemical Society

content in a way that appeals to visual learners and to those who are ready for more advanced understanding of molecular-level behavior. Many students, even those at the upper-level, consider molecules to be stationary images of Lewis structures they learn to draw in general chemistry. Early introduction to molecular motion helps students with topics such as kinetics and reaction mechanisms in a way that stationary images cannot. Visualization Activities In each semester of my general chemistry lecture course of approximately thirty students, I assign students five “Visualization” activities, one of which is described in this chapter. The Visualization assignments are independent of each other, vary in complexity and technique, and often make use of PhET (7) or Jmol (8) resources. The primary objective is to help students understand molecularlevel phenomena, so I select activities that allow students to visualize concepts such as dissociation (comparing electrolytes and nonelectrolytes as well as building skills for understanding spectator ions) (9), molecular geometry (10), and crystal structures (11). Many students report that the Visualization activities are the most helpful assignments for learning chemistry (more than homework, weekly quizzes, daily on-the-fly clicker questions, or daily warm-up questions). I use the freeware Virtual Substance molecular dynamics simulation software (12) as one of the Visualization assignment to teach gas laws, data analysis, and relationships between kinetic energy and temperature. Other software programs can be used to accomplish the same goals depending on access (purchased from companies such as Wavefunction (13)) or instructor familiarity (other freeware such as NAMD (14)). Using Molecular Dynamics Software To Aid Student Learning With the complementary goals of improving content knowledge and assisting students in the transition from novice to professional chemists, I have implemented assignments using the molecular dynamics (MD) software package Virtual Substance (12) in both my General Chemistry and Physical Chemistry courses. I have written about using the software in the Physical Chemistry curriculum on the first day of the lecture course (15) and in a lab situation (16) where students develop mathematical relationships that describe the physical behavior of real and ideal gases. In this chapter, I describe how I have used an activity in the General Chemistry course where students conduct MD simulations on ideal gases, collect data on the physical properties (Temperature, Pressure, Volume, Kinetic Energy, and Potential Energy) of the system during the simulation, and use spreadsheet software (Excel, for example) to understand the relationships among these properties by plotting their data and using the trendline feature to determine physical constants. This activity addresses a number of course learning goals including understanding mathematical relationships among physical properties of ideal gases, representing and interpreting data graphically, and relating kinetic energy to temperature and particle motion. These learning goals are three of the most difficult for novice students. They can easily memorize and grind through the ideal gas law, but they do not really understand the origin of these physical properties at the atomic or molecular level. They also struggle with interpreting data graphically as well as using a spreadsheet program to clearly represent the data they have collected, particularly if this is the first time they are asked to do so. There are a number of places in the general chemistry curriculum where data analysis skills can be developed, particularly in the laboratory component of the course. Students frequently collect, plot, and analyze data. Performing a similar activity in the lecture course further cements the importance of graphical analysis and interpretation of data, skills students need on their path from 12

novice to professional chemist. This connection may be particularly valuable when students have different instructors for the lecture and lab components of the course. As students are somewhat familiar with the application of these skills, and explicit instructions for constructing plots can be provided, it is somewhat more challenging for students to understand that particle interactions determine macroscopic physical properties and the mathematical relationships between those properties. Molecular dynamics simulations provide a perfect opportunity for students to learn each of these content topics and skills.

Implementation and Results Keeping in mind that the purpose of the activity is student learning, students at the general chemistry level do not need to understand how an MD simulation works beyond knowing that the particles are following the laws of physics that govern their motion. These topics can be adequately explained at the instructor’s discretion as the Virtual Substance (16) MD software program is introduced and the activity to be completed is distributed. The first steps in using the software require selecting the substance to use (He, Ne, Ar, Kr, Xe, or user defined), the type of boundary conditions (Fixed Walls or Periodic Boundary Conditions), and the Potential Model (No potential = ideal gas, soft sphere, Lennard-Jones, and options for adding finite extensible nonlinear elastic models for treating polymers) as seen in Figure 1.

Figure 1. Screenshot of Virtual Substance initial set up for 128 Argon atoms treated as an ideal gas and using periodic boundary conditions. Depending on the goals of the instructor for use of this activity, these selections can be explained fully or minimally. My preference is that the students understand that periodic boundary conditions are a mechanism for replicating the box in all dimensions, therefore mimicking bulk-like behavior by allowing particles to pass through one edge of the box and reappear on the other side as if the boundary did not exist. I also explain that the other Potential Models in the software allow modeling of real gas behavior and how real gases differ from ideal gases on a general chemistry level, i.e. real gases have volume and experience intermolecular forces. Beyond that, I do not discuss in detail the different options for real gas potential models. Once the Virtual Substance is built using the process outlined in the previous paragraph, the next step is to run the simulation. Once again, the instructor can choose how much or how little detail is necessary for the student to understand the simulation. The user must select the type of simulation (constant energy, constant volume and temperature, or constant temperature and pressure), targets for that selected simulation type, time step (0.5, 1.0, 2.0, 5.0, or 10.0 fs), number of steps (500, 1000, 2000, 5000, 10000, 20000), and how frequently the calculations should be reported to the user. After building the Virtual Substance and selecting the simulation settings, the user selects Run Simulation, and the data appears in an output screen (Figure 2a) while the movement of the substance is observed in another part of the screen (Figure 2b). A typical simulation of an ideal gas on a personal computer will take under a minute. 13

Figure 2. Screenshot of Virtual Substance a) simulation parameters for 128 Argon gas particles treated as an ideal gas with periodic boundary conditions after 120 ps of Molecular Dynamics Simulation under conditions of constant volume (1.0 L/mol) and temperature (298 K) and b) static image at the conclusion of the simulation. Instantaneous and average values of the temperature, pressure, volume, and total, kinetic, and potential energy are reported. In the assigned activity, all students are required to run five separate simulations at a fixed temperature and a series of molar volumes. They are then required to prepare Pressure versus molar Volume, Vm, (see Figure 3) and Pressure vs Vm-1 plots and determine the value of the gas constant, R. I do not tell them how to numerically determine R, which results in guided discussion in class as students ask about that part of the assignment. How to proceed after making plots is not immediately obvious to many students. After our in-class discussion, students typically choose to use a linear fit of their Pressure vs Vm-1 plot to determine R (the slope of the trendline is RT), but some students will perform a fit to the curve from their Pressure vs Vm-1 plot and determine R from the equation of that fit. For example, in Figure 3, the fit yields P = (24.375) Vm(-1.003) for simulations conducted at 298 K. Using P = RT/Vm, the calculated value of R would be 0.0818 L atm mol-1 K-1, an error of less than 1% from the accepted value of 0.0821 L atm mol-1 K-1. This level agreement is the norm, which does give students some comfort that they are on the right track. Students are subsequently asked to perform additional simulations of argon gas at either a fixed volume and a series of temperatures (still using a constant volume and temperature simulation) or a fixed pressure and a series of temperatures (using a constant pressure and temperature simulation). In both cases, students are again asked to determine the gas constant, R. In addition, students are required to plot the average kinetic energy as a function of temperature. See Figure 4. If appropriate to the class, instructors could point out that the slope of the energy vs temperature plot is 3/2 R and discuss the equipartition theorem demonstrating the three translation degrees of freedom each contributing 1/2 R. Students are also asked to submit a coherent paragraph that includes their observations of the gas motion, how visualizing this motion impacted their understanding of gas behavior, an interpretation of their results (are they consistent with what was expected), and any unusual results. The paragraph was evaluated holistically for patterns of both clarity and misunderstandings. 14

Figure 3. Student-submitted plot for Virtual Substance simulation of Argon at 298 K and a series of molar volumes. The line, which is the best fit by least squares regression, is y = 24.375x-1.003, where y is pressure in atmospheres and x is volume in L/mol, with correlation coefficient 0.9999.

Figure 4. Student-submitted plot for Virtual Substance simulation of Argon at fixed pressure and a series of temperatures. The line, which is the best fit by least squares regression, is y = 12.372x + 12.535, where y is average kinetic energy in J mol-1 and x is temperature in Kelvin, with correlation coefficient 0.9999.

Conclusions Impact on Student Learning Student learning was evaluated using three measures: 1) the submitted assignments, 2) a pre/ post set of 6 clicker questions (see Table 1), and 3) relevant questions on the final exam. The results showed distinct improvements in students’ understanding of gas motion and the connection between that motion and the physical properties of pressure, temperature, volume, and kinetic 15

energy. There were clearly areas where student misconceptions were still evident even after the visualization activity, however. In the submitted assignments, students were able to collect the appropriate data and generate the requested plots (representative plots shown in Figures 3 and 4). They were able to follow the instructions in the assignment sheet easily. In their summary paragraph, many students stated that they were able to understand and make connections more clearly as a result of visualizing gas particle behavior and the relationship between physical properties. Representative statements from students include the following • “Being able to watch the simulations enhanced my ability to understand the concepts behind the math associated with the ideal gas law.” • “It was helpful to me because I am a visual learner and when I see things it makes me understand them more thoroughly.” • “The visualization of the movement of gasses showed the random nature of the movement of the gases in a way that describing it does not.” • “I could see the relationships in the gas law physically in action which helped me to form more realistic connections in understanding the material.” In the post-activity clicker questions, most students were able to identify the correct static image of gas particles distributed throughout a container, select the correct relationships between volume and pressure (inversely proportional) and volume and temperature (directly proportional), and relate pressure to macroscopic and molecular-level relationships. In the 2017 class, 65% of students showed improved scores on the clicker questions after completing the MD activity. As shown in Table 1, improved scores were primarily due to increased understanding of relationships between gas properties. Parts of their paragraphs describing their observations along with the questions they answered incorrectly on the post-activity clicker questions highlighted their continued misunderstandings on some of the important physical relationships, particularly among kinetic energy, average velocity, and temperature. While they were able to make a plot showing that kinetic energy and temperature are directly proportional (Figure 4), they did not understand that kinetic energy was related to particle velocity. We had not yet studied the Maxwell-Boltzmann distribution relating particle velocity to temperature, and some students made incorrect statements that the particles were moving faster or slower when pressure or volume changed while temperature was held constant. These statement are, of course, incorrect. Perhaps the computer was refreshing less frequently or they felt that they were seeing the particles move more slowly, but the average kinetic energy at constant temperature was constant, so their perceptions were incorrect. This misconception was very enlightening to me as an instructor. When we arrived at kinetic-molecular theory and the Maxwell-Boltzmann distribution, I opened the Virtual Substance program and ran a simulation for the entire class. We talked about the distribution of particle speeds and how that depended solely on temperature for an ideal gas. They had a context for understanding the new material, which is always helpful for learning and retaining knowledge.

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Table 1. Clicker Question Summary. Note that this clicker set allows multiple selections per question.

Extensions and Challenges While my classes are relatively small, this activity can easily be used with larger classes. Most of the work is performed independently. The instructor will need to review student submissions, but there is no additional equipment or preparation required. Variations on data collected and plots prepared are endless depending on the goals of the instructor. As mentioned earlier, other topics at the general chemistry level can be clarified by use of Virtual Substance simulations, for example, how non-zero volume and intermolecular forces (i.e. those in real gases) impact physical properties of pressure and internal energy, or a more explicit understanding of internal energy as the sum of kinetic and potential energy, just to name two. If more insight into how the least squares fit is used to create a trendline, activities such as the Multi-Function Data Flyer (17) could be used. The challenges associated with this activity are the same as those associated with teaching in general: students arrive with preconceived ideas about a topic. Some students are resistant to activities that challenge their preconceived ideas and will continue to cling to those instead. Technical difficulties have been relatively minimal. Access to a PC is required, but the software works on a variety of machines and operating systems, including Windows 10. Installing and running several

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simulations of ideal gases should take less than 30 minutes. Simulations using a Lennard-Jones potential will take longer, and may be better suited to homework assignments or lab activities (16). The activity itself is usually one students enjoy. When I ask what component of the course was most helpful for their learning, the visualization activities are consistently rated very highly. As I hope is clear from the collection of chapters in this book, computational chemistry is just one tool in the arsenal to improve student learning. It is not a magic bullet. It is another way to aid learners in developing a molecular-level understanding of chemical behavior that will serve them well as they move from novice to professional chemist.

References 1.

2.

3.

4.

5.

6. 7.

8. 9. 10. 11. 12. 13. 14.

Mahaffy, P. G.; Holme, T. A.; Martin-Visscher, L.; Martin, B. E.; Versprille, A.; Kirchhoff, M.; McKenzie, L.; Towns, M. Beyond “Inert” Ideas to Teaching General Chemistry from Rich Contexts: Visualizing the Chemistry of Climate Change (VC3). Journal of Chemical Education 2017, 94 (8), 1027–1035. Miorelli, J.; Caster, A.; Eberhart, M. E. Using Computational Visualizations of the Charge Density To Guide First-Year Chemistry Students through the Chemical Bond. Journal of Chemical Education 2017, 94 (1), 67–71. Moore, E. B. ConfChem Conference on Interactive Visualizations for Chemistry Teaching and Learning: Accessibility for PhET Interactive Simulations—Progress, Challenges, and Potential. Journal of Chemical Education 2016, 93 (6), 1160–1161. Smith, G. C.; Hossain, M. M. Visualization of Buffer Capacity with 3-D “Topo” Surfaces: Buffer Ridges, Equivalence Point Canyons and Dilution Ramps. Journal of Chemical Education 2016, 93 (1), 122–130. Wichmann, A.; Timpe, S. Can Dynamic Visualizations with Variable Control Enhance the Acquisition of Intuitive Knowledge? Journal of Science Education and Technology 2015, 24 (5), 709–720. Tay, G. C.; Edwards, K. D. DanceChemistry: Helping Students Visualize Chemistry Concepts through Dance Videos. Journal of Chemical Education 2015, 92 (11), 1956–1959. Perkins, K.; Adams, W.; Dubson, M.; Finkelstein, N.; Reid, S.; Wieman, C.; LeMaster, R. PhET: Interactive Simulations for Teaching and Learning Physics. The Physics Teacher 2006, 44, 18–23. Jmol: An Open-Source Java Viewer for Chemical Structures in 3D. http://www.jmol.org/. Lancaster, K.; Reid, S.; Moore, E.; Chamberlain, J.; Loeblein, T.; Parson, R.; Perkins, K. Sugar and Salt Solutions. https://phet.colorado.edu/en/simulation/sugar-and-salt-solutions. Moore, E. B.; Olson, J.; Lancaster, K.; Chamberlain, J.; Lancaster, K.; Paul, A.; Perkins, K. Molecule Shapes. https://phet.colorado.edu/en/simulation/molecule-shapes. Chaplin, M. Water Structure and Science. http://www1.lsbu.ac.uk/water/ice1hsc.html. Papanikolas, J. Virtual Substance https://www.unc.edu/~jpapanik/VirtualSubstance/ VGMain.htm. Odyssey, Wavefunction, Inc., Irvine, CA. Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable molecular dynamics with NAMD. J Comput Chem 2005, 26 (16), 1781–802. 18

15. Bruce, C. D. Beyond the Syllabus: Using the First Day of Class in Physical Chemistry as an Introduction to the Development of Macroscopic, Molecular-Level, and Mathematical Models. Journal of Chemical Education 2013, 90 (9), 1180–1185. 16. Bruce, C. D.; Bliem, C. L.; Papanikolas, J. M., “Partial Derivatives: Are You Kidding?”: Teaching Thermodynamics Using Virtual Substance. In Advances in Teaching Physical Chemistry; Ellison, M. D., Schoolcraft, T. A.; , Eds.; ACS Symposium Series 973; American Chemical Society, 2007; pp 194−206. 17. Shodor. http://www.shodor.org/interactivate/activities/MultiFunctionDataFly/.

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Chapter 3

Using Electronic Structure Calculations To Investigate the Kinetics of Gas-Phase Ammonia Synthesis Kelsey M. Stocker* Department of Chemistry and Biochemistry, Suffolk University, 8 Ashburton Place, Boston, Massachusetts 02108, United States *E-mail: [email protected].

Computational chemistry techniques are valuable tools for teaching concepts in thermodynamics and chemical kinetics. In this experiment, undergraduate physical chemistry students gain valuable, authentic experience with the tools of computational chemistry and a more “hands-on” interaction with the energy landscape of a chemical reaction. Students use electronic structure calculations to determine the geometry, vibrational frequencies, and energy of the reactants, products, intermediates, and transition states in a four-step gas-phase ammonia synthesis reaction. Using transition state theory, they construct the reaction coordinate diagram and calculate activation energies, rate constants, and equilibrium constants.

Introduction Computational methods can play a valuable role in undergraduate chemistry courses and have been successfully integrated into the curriculum in a variety of courses (1–4). Electronic structure calculations in particular can contribute to student learning by allowing them to gain “hands on” experiences at the atomic level in ways that traditional undergraduate experiments cannot. Electronic structure methods have been used in excellent computational experiments on reaction mechanisms for use in undergraduate organic or physical chemistry courses (5–11). I developed this lab to fit into the Advanced Theories of Reaction Rates module of my secondsemester 400-level physical chemistry course. At this point in the course, my students have learned about the laws of thermodynamics, physical and chemical equilibria, reaction mechanisms, rate laws, and potential energy surfaces. I wrote this lab to give my students the experience of studying the kinetics of a realistic, multi-step reaction mechanism using reaction coordinate diagrams and transition state theory. There are five primary learning goals associated with this experiment: © 2019 American Chemical Society

• • • • •

Perform authentic electronic structure calculations Construct a reaction coordinate diagram for a multi-step reaction Apply the thermodynamic formulation of transition state theory Calculate activation energies, rate constants, and equilibrium constants Use kinetics data to evaluate plausibility of reaction mechanism

Throughout this chapter I have noted possible adaptations and extensions that can be used to make the experiment appropriate for a variety of courses. I have also attempted to make the description of the procedure general enough that it can be used with various electronic structure programs and interface packages. I teach a “quantum first” approach, so by the time we conduct this experiment my students have been exposed to partition functions, statistical mechanics, and computational chemistry techniques. However, the experiment utilizes the thermodynamic formulation of transition state theory so it could easily be used in a “thermo first” course design (12).

Why Ammonia Synthesis? The formation of ammonia is a vitally important process made up of structurally simple species, which makes it an ideal reaction for a computational kinetics experiment (13). After investigating the kinetics of the multi-step gas-phase mechanism, students have a deeper appreciation for the importance of heterogeneous catalysis in industrial processes. The reaction may look harmless enough on paper, but it turns out to be so devilishly difficult to carry out that the first industrially viable process yielded two separate Nobel Prizes in Chemistry: Fritz Haber in 1918 and Carl Bosch in 1931 (14, 15). I typically can’t resist including a brief synopsis of Fritz Haber’s story in the rest of my pre-lab lecture (16). The synthesis of ammonia has history. But it’s not old news by a longshot considering that new, more efficient catalysts remain an area of active research (17). Even the gas-phase reaction, while not industrially viable, was still being investigated nearly a century after the Haber-Bosch process was developed. The energetics of the gasphase mechanism used in this lab weren’t fully mapped until 2003 (18). Reaction Mechanism In their computational study of several potential gas-phase mechanisms, Hwang and Mebel identified the following four-step pathway as the most favorable (18):

The overall reaction is

Conveniently, this mechanism does not include any ions or radical species. The reaction coordinate diagram includes nine distinct stages: five minima (reactants, intermediates, or products) and four maxima (transition states). 22

Experimental Procedure The calculations for this lab follow the general procedure shown in Figure 1 and are completed within a single four-hour laboratory period.

Figure 1. Simplified workflow for calculations. To cover all species included in the reaction mechanism, students must perform six geometry optimizations (N2, H2, NNH2, H2NNH2, HNNH3, and NH3), four transition state optimizations (TS1, TS2, TS3, and TS4), and ten vibrational frequency analyses (all species). Computational Details Our lab computers are equipped with Gaussian 09, which is linked to an installation of WebMO version 16.1 (19, 20). All calculations were done using the PBE0 level of theory and the “Routine: 6-31G(d)” basis set. I selected the combination of theory and basis set that gave results for ΔH°rxn (-90.35 kJ mol-1), ΔS°rxn (-197.77 J mol-1 K-1), and ΔG°rxn (-31.40 kJ mol-1) that were closest to the values computed from standard back-of-the-textbook thermodynamic tables (-91.88 kJ mol-1, 198.11 J mol-1 K-1, and -32.80 kJ mol-1, respectively) (21). A thorough discussion of the shortcomings of density functional theory is beyond the scope of my course so I prioritized matching experimental data when choosing a level of theory. I find it also has the added benefit of increasing students’ confidence in computational methods, which can be helpful if you plan to do additional computational labs later in the course. However, the vast majority of other levels of theory and basis sets will still produce reaction coordinate diagrams that are qualitatively similar to the results shown here, so you can use whatever works best for your class. Optimization of Reactants, Products, and Intermediate Species Students build all stable species (non-transition states) in the WebMO molecule editor. I assign pre-lab work that includes drawing Lewis structures of all reactants, products, and intermediates. Students are then equipped to determine the total charge and spin multiplicity of all species when setting up their WebMO jobs. They all turn out to be neutral molecules in the singlet state, which are 23

the default settings for WebMO jobs, so you could omit any discussion of charge or spin multiplicity and have students ignore those options when submitting jobs. WebMO has the option to perform a geometry optimization and frequency analysis in a single job. However, there is not an option for a combined transition state optimization and frequency analysis. For ease of instruction and to avoid confusion, I have students do all structure optimizations separately from frequency analyses. Once the structure optimization completes successfully, students can view the results from the Job Manager and select “New Job Using This Geometry” to continue on to the frequency analysis. Optimization of Transition States There are several options for obtaining the transition state structures. You can adapt the transition state optimizations to suit available computational resources, length of lab period, and course level. Import Coordinates Importing coordinates is the fastest and most frustration-free option for students. You can provide the transition state coordinates in XYZ format or as a Gaussian input file. The XYZ coordinates of all four transition states are provided in Tables 1-4. To avoid a “plug and chug” effect, consider asking students to predict the general structure of the transition state based on the reactants and products; this could be assigned as pre-lab work or as part of an in-class discussion. A transition state optimization should still be performed on each structure (which should finish very quickly) before moving on. Table 1. Transition state 1 XYZ coordinates Atom

X (Å)

Y (Å)

Z (Å)

N

0.000000

0.000000

0.000000

N

0.000000

-1.141238

0.000000

H

0.019343

1.011376

0.000000

H

-1.489645

0.955365

0.000000

Table 2. Transition state 2 XYZ coordinates Atom

X (Å)

Y (Å)

Z (Å)

N

0.000000

0.000000

0.000000

N

1.242512

0.347714

-0.117104

H

1.767858

0.109792

-0.953584

H

1.689979

1.010050

0.512958

H

-0.914832

1.024244

-0.816374

H

-0.730331

1.000708

0.092843

24

Table 3. Transition state 3 XYZ coordinates Atom

X (Å)

Y (Å)

Z (Å)

N

0.000000

0.000000

0.000000

N

-1.603532

-0.136164

-0.083991

H

-1.844272

0.863625

-0.139143

H

0.415124

-0.758790

-0.527432

H

0.404776

0.906456

-0.205203

H

-0.556551

-0.186787

0.911039

Table 4. Transition state 4 XYZ coordinates Atom

X (Å)

Y (Å)

Z (Å)

N

0.000000

0.000000

0.000000

N

1.911251

-0.071020

0.060975

H

2.072585

0.925068

-0.018935

H

2.326204

-0.540188

-0.737908

H

2.331892

-0.411310

0.920272

H

-0.053464

-1.022976

0.140798

H

-1.686696

-0.084442

-0.203073

H

-1.316616

0.156347

0.502845

Draw Structures A more advanced option is to have students draw the transition states in the WebMO molecular editor. This requires you to provide images of the transition states with bond lengths, angles, and/or dihedrals labeled. An example of this is shown in Figure 2. This approach is much more successful if students have a moderate amount of experience with the WebMO interface. The optimization of TS4 in particular is very sensitive to dihedral angles, so ideally students are comfortable manipulating molecular structures in three dimensions. Transition State Search The most authentic method for locating the transition states is performing a transition state search, or saddle calculation. This calculation requires two structures on either side of the saddle point to be specified and interpolates between them to produce a structure that is close to the transition state. The resulting structure should then be used as input for a transition state optimization before continuing. I have not yet implemented this procedure in my class, primarily due to concerns about time constraints. Additional considerations to keep in mind are that the two input structures must have the same atomic numbering scheme, so students must be especially careful when creating the inputs. 25

Figure 2. Transition state structures with interatomic distances in Angstrom. For some transition states, you can approximate a saddle calculation by performing a coordinate scan. To reach TS1, start with the NNH2 structure and perform a coordinate scan over one of the HN-N bond angles, with a maximum angle of 179.9° (extending to 180° will cause the Gaussian job to fail). Optimize the highest energy structure along the coordinate scan as a transition state. Verifying Transition States Regardless of the method chosen to locate and optimize a transition state, the structures should be verified as such. This can be accomplished by a vibrational frequency analysis or an intrinsic reaction coordinate calculation. Aside from verifying a transition state, the results of the vibrational frequency analyses are the source of all thermodynamic data that students record and use later in their calculations. Vibrational Frequencies For each transition state, I have students perform a vibrational analysis to confirm that the structure represents a saddle point on the potential energy surface. The simplest analysis is to record any imaginary (negative) frequencies in the results. There should not be any such frequencies for reactants, products, or intermediates, but there should be exactly one for a transition state. In particular, TS3 and TS4 can be tricky to locate and my students appreciate the straightforward validation that they “got it right”. WebMO also has the ability to animate each vibrational mode. Animation of the transition state imaginary frequency is a helpful tool for demonstrating the simultaneous bond formation and dissociation that occurs along the reaction coordinate. Students also find it fairly entertaining, especially if the structure resembles a stick figure human in any way. Intrinsic Reaction Coordinate An intrinsic reaction coordinate (IRC calculation in WebMO) takes the input transition state structure and moves along the reaction coordinate. The IRC is calculated in both the forward and reverse directions by default. If the transition state structure is correct, the IRC should arrive at the structure of the expected products when moving in one direction, and should arrive at the structure of the expected reactants when moving in the opposite direction. 26

The reaction coordinate path can be animated in WebMO and very clearly demonstrates reactants progressing through the transition state to become products. Students can optimize the structures that result from the forward and reverse IRC calculation and compare their geometries to the expected reactant and product species that they have already optimized individually.

Data Analysis and Results The internal energy, enthalpy, and entropy of each species should be recorded from the vibrational frequencies calculation. I structure the data analysis prompts in the lab handout to guide them through a sensible spreadsheet design; it also happens to make it much easier to track down errors when the intermediate values are tabulated and turned in. While I provide the four-step mechanism shown in Reactions 1-4, I ask students to re-write each reaction stage to be stoichiometrically balanced with the end product (2 NH3). The stoichiometrically balanced mechanism steps are

I ask students to get at least this far in their analysis and check in with me before leaving lab. The most common error is adding too many H2 molecules to the transition state stages, essentially forgetting that one has been “used up” to form the transition state. Once all reaction stages have been balanced correctly, they use their data for the individual species to create a table of calculated thermodynamic quantities, as shown in Table 5. The convention of reporting values relative to the first stage is not mandatory, but can make it easier to get an initial sense of the energy landscape. Table 5. Calculated thermodynamic quantities relative to first reaction stage Reaction Stage

Enthalpy (kJ mol-1)

Entropy (J mol-1 K-1)

Internal Energy (kJ mol-1)

0.000

0.00

0.000

TS1 + 2 H2

500.491

-94.73

502.967

NNH2 + 2 H2

261.581

-98.13

264.057

TS2 + H2

369.571

-213.10

374.528

65.094

-222.34

70.051

TS3 + H2

347.593

-211.07

352.549

HNNH3 + H2

265.740

-216.58

270.694

TS4

354.232

-311.81

361.665

2 NH3

-90.354

-197.77

-85.397

N2 + 3 H2

H2NNH2 + H2

27

Reaction Coordinate Diagram The reaction coordinate diagram is constructed using the relative internal energy of each reaction stage, as shown in Figure 3.

Figure 3. Reaction coordinate diagram based on internal energy of each reaction stage relative to reactants. I ask students to label each stage in the diagram and discuss the major features of the energy landscape. This part of the analysis helps students to grasp the concept of a potential energy surface and its connection to reaction rate. Students’ discussion of their reaction coordinate diagrams are often phrased in terms of hikers, hills, and valleys. This type of framework helps students to rationalize how something that would provide a less hilly path from reactants to products (a catalyst) would be advantageous. Transition State Theory My students make tables showing the calculated enthalpy of activation (ΔH°‡), entropy of activation (ΔS°‡), and change in molecularity (Δn‡) for each step in the forward and reverse directions. These quantities are shown in Tables 6 and 7, respectively. Table 6. Transition state theory values for forward reactions ΔH°‡ (kJ mol-1)

(J mol-1 K-1)

ΔS°‡

Δn‡

1

500.491

-94.73

-1

2

107.989

-114.96

-1

3

282.499

11.28

0

4

88.492

-95.23

-1

Reaction Step

Table 7. Transition state theory values for reverse reactions ΔH°‡ (kJ mol-1)

(J mol-1 K-1)

ΔS°‡

Δn‡

1

238.910

3.40

0

2

304.477

9.25

0

3

81.853

5.51

0

4

444.586

-114.03

-1

Reaction Step

28

Interestingly, the change in molecularity has been the most error-prone quantity in students’ lab reports. Even when they’re clear on the concept, students often easily default to “products minus reactants” when computing a delta quantity. Perhaps because the number of reactant and product molecules is easier to visualize, they struggled with this concept more than with the enthalpy or entropy of activation. Activation Energy The activation energy, Ea, of each reaction step can be calculated from the enthalpy of activation and change in molecularity:

where R is the gas constant and T is temperature. The activation energies in the forward direction are 505.449, 112.947, 284.977, and 93.450 kJ/mol. I ask for tabulated values, but the activation energy of each step can also be labeled on the reaction coordinate diagram. Students should be able to easily identify the step with the largest activation energy and predict that this step should also be rate-limiting (i.e., have the smallest forward rate constant). You can also provide students with the mechanism and ask them to predict the rate-limiting step as part of the pre-lab assignment. This provides an opportunity for them to apply their previous knowledge of the stability and bond strength of molecular nitrogen in order to predict that the activation of nitrogen is the rate-limiting step. Rate Constants Forward and reverse rate constants are calculated using the thermodynamic formulation of transition state theory (12):

where kB is the Boltzmann constant, R is the gas constant, T is temperature, h is Planck’s constant, and c° is standard concentration. Calculated values for the rate constant of each step in the forward and reverse direction are shown in Table 8. Table 8. Calculated rate constants in the forward (kf) and reverse (kr) directions Step

kf

kr

1

a1.438 × 10-80

b1.298 × 10-29

2

a7.378 × 10-13

b8.537 × 10-41

3

b7.725 × 10-37

b5.500 × 10-2

4

a2.063 × 10-8

a8.790 × 10-72

a Units of M-1 s-1.

b Units of s-1.

Note that I have conserved step numbers in the forward and reverse directions: Step 1 is always step 1, the only difference is whether it proceeds as N2 + 3 H2 → [TS1]‡ + 2 H2 → NNH2 + 2 H2 (forward) or NNH2 + 2 H2 → [TS1]‡ + 2 H2 → N2 + 3 H2 (reverse). Several students inverted the 29

entire mechanism when looking at the reverse direction, so what was originally step 4 was relabeled step 1. This doesn’t affect their raw rate constant values, but the equilibrium constants (ratios of forward and reverse rate constants) are affected. In the next iteration of this lab, I plan to be more explicit about the step numbering scheme in my pre-lab lecture, or perhaps adopt a different labeling scheme (e.g., step A, B, C, and D). Equilibrium Constants Once the system has established a dynamic equilibrium, the equilibrium constant is the ratio of the forward and reverse rate constants:

The forward equilibrium constants are 1.108 × 10-51, 8.643 × 1027, 1.405 × 10-35, and 2.348 × 1063. The relatively large equilibrium constant of step 2 makes for an interesting discussion question. The product of step two is the rocket propellant hydrazine (H2NNH2), which is a comparatively stable intermediate compared to its precursor 1,1-diazine (NNH2). Perceptive students will draw connections between the equilibrium constant values and the relative depths of the valleys in the reaction coordinate diagram by drawing upon their prior knowledge of chemical equilibria.

Conclusions In my experience, the major challenges when creating an experiment using electronic structure calculations are maintaining an authentic experience without being too tedious, and communicating the relevance of the experiment to the students. If students have not been previously exposed to computational methods, they may not immediately view their results as “real data” or fully understand how computational tools contribute to our understanding of chemical systems. This experiment uses realistic electronic structure calculations to study the mechanism of a reaction that is connected to one of the most important industrial processes in modern life. Students use their knowledge of thermodynamics, equilibria, and kinetics to discuss their findings, effectively retracing a path throughout the physical chemistry thermodynamics curriculum.

References 1. 2. 3. 4.

5.

Martini, S. R.; Hartzell, C. J. Integrating Computational Chemistry into a Course in Classical Thermodynamics. J. Chem. Educ. 2015, 92, 1201–1203. Esselman, B. J.; Hill, N. J. Integration of Computational Chemistry into the Undergraduate Organic Chemistry Laboratory Curriculum. J. Chem. Educ. 2016, 93, 932–936. Johnson, L. E.; Engel, T. Integrating Computational Chemistry into the Physical Chemistry Curriculum. J. Chem. Educ. 2011, 88, 569–573. Karpen, M. E.; Henderleiter, J.; Schaertel, S. A. Integrating Computational Chemistry into the Physical Chemistry Laboratory Curriculum: A Wet Lab/Dry Lab Approach. J. Chem. Educ. 2004, 81, 475–477. Halpern, A. M. Computational Studies of Chemical Reactions: The HNC-HCN and CH3NHCH3CN Isomerizations. J. Chem. Educ. 2006, 83, 69–76.

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Hessley, R. K. Computational Investigations for Undergraduate Organic Chemistry: Predicting the Mechanism of the Ritter Reaction. J. Chem. Educ. 2000, 77, 202–203. Montgomery, C. D. Factors Affecting Energy Barriers for Pyramidal Inversion in Amines and Phosphines: A Computational Chemistry Lab Exercise. J. Chem. Educ. 2013, 90, 661–664. Csizmar, C. M.; Daniels, J. P.; Davis, L. E.; Hoovis, T. P.; Hammond, K. A.; McDougal, O. M.; Warner, D. L. Modeling SN2 and E2 Reaction Pathways and Other Computational Exercises in the Undergraduate Organic Chemistry Laboratory. J. Chem. Educ. 2013, 90, 1235–1238. Marzzacco, C. J.; Baum, J. C. Computational Chemistry Studies on the Carbene Hydroxymethylene. J. Chem. Educ. 2011, 88, 1667–1671. Galano, A.; Alvarez-Idaboy, J. R.; Vivier-Bunge, A. Computational Quantum Chemistry: A Reliable Tool in the Understanding of Gas-Phase Reactions. J. Chem. Educ. 2006, 83, 481–487. Albrecht, B. Computational Chemistry in the Undergraduate Laboratory: A Mechanistic Study of the Wittig Reaction. J. Chem. Educ. 2014, 91, 2182–2185. Chang, R. Physical Chemistry for the Chemical and Biological Sciences, 3rd ed.; University Science Books: Mill Valley, CA, 2000; pp 476−479. United States Geological Survey. Minerals Information: Nitrogen Statistics and Information. https://minerals.usgs.gov/minerals/pubs/commodity/nitrogen/ (accessed July 22, 2018). Nobelprize.org. Fritz Haber – Facts. https://www.nobelprize.org/nobel_prizes/chemistry/ laureates/1918/haber-facts.html (accessed July 22, 2018). Nobelprize.org. Carl Bosch – Facts. https://www.nobelprize.org/nobel_prizes/chemistry/ laureates/1931/bosch-facts.html (accessed July 22, 2018). Everts, S. Who Was Fritz Haber? Chem. Eng. News 2015, 93 (8), 18–23. http://chemicalweapons.cenmag.org/who-was-the-father-of-chemical-weapons/ (accessed July 22, 2018). Kitano, M.; Inoue, Y.; Sasase, M.; Kishida, K.; Kobayashi, Y.; Nishiyama, K.; Tada, T.; Kawamura, S.; Yokoyama, T.; Hara, M.; Hosono, H. Self-Organized Ruthenium-Barium Core-Shell Nanoparticles on a Mesoporous Calcium Amide Matrix for Efficient LowTemperature Ammonia Synthesis. Angew. Chem. Int. Ed. 2018, 57, 2648–2652. Hwang, D.- Y.; Mebel, A. M. Reaction Mechanism of N2/H2 Conversion to NH3: A Theoretical Study. J. Phys. Chem. A. 2003, 107, 2865–2874. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg,

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J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. 20. Schmidt, J. R.; Polik, W. F. WebMO, version 16.1; WebMO LLC: Holland, MI, 2013. 21. Ball, D. W. Physical Chemistry, 2nd ed.; Cengage Learning: Stamford, CT, 2015; p 808.

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Chapter 4

Modeling Reaction Energies and Exploring Noble Gas Chemistry in the Physical Chemistry Laboratory James A. Phillips* Department of Chemistry, University of Wisconsin – Eau Claire, 105 Garfield Ave., Eau Claire, Wisconsin 54701, United States *E-mail: [email protected].

A two-part computational chemistry module for a physical chemistry lab course is described. The first part is concerned with the characterization of argon hydrofluoride (HArF), and the primary intent is to assess its energy relative to Ar and HF. The charge distribution is also considered, and the Ar-H and ArF distances are compared to those expected for bonding and non-bonding interactions. The second part involves a student-driven exploration of other noble gas compounds. The goal here is to cultivate literature proficiency and creative thinking skills within an accessible intellectual context. Ultimately, this endeavor illustrates how chemical computations enable a completely safe, open-ended scholarly project that provides original and substantive material for the introduction and discussion sections of a lab report. The extent to which the skills cultivated via this module manifest students’ ability to design and execute a subsequent calorimetry project is also considered.

Overview and Context This chapter describes the design and implementation of a two-part computational lab module for a physical chemistry lab course, and the motivation for doing so. As a whole, this exercise emphasizes underlying chemical concepts and how quantum chemistry can illuminate these, as opposed to the underlying theory of the theoretical models themselves. Part 1 is concerned with modeling the formation of argon hydrofluoride (HArF), the only known compound containing the element argon. Part 2 is a student-driven exploration of the design and characterization of other noble gas compounds.

© 2019 American Chemical Society

Beyond providing some practical experience with computations, this module targets several specific learning outcomes, specifically: Connecting macroscopic thermochemical quantities (e.g., ΔrH°) to specific, microscopic contributions to the molecular energy (Emolec). ii) Learning to navigate chemical literature databases, finding relevant research articles, and critically reading them to extract key information and insight. iii) Developing chemical creativity; asking meaningful research questions, and/or generating sound hypotheses. iv) Collecting relevant data, and using it to address hypotheses, and making meaningful, effective comparisons between chemical systems. i)

Since its initial inception in the early 2000’s, I have used this module in three different courses, though the goal has always been to address the same general objectives, despite a slightly different context in each case. In addition, though both computational methods and accessible computing speed have changed dramatically over the ensuing time period, the first part of module has changed but very little, and while the results obtained by the students are now much more consistent with those in the original research manuscript (1, 2), this has had no real effect on the educational impact. Originally, I taught this as the first lab in my physical chemistry I (thermodynamics and kinetics) course, with a goal of initiating and/or and reinforcing a conversation about microscopic molecular energies, in addition to providing students with the tools to theoretically model calorimetry results later in the term. Falling short of any rigorous treatment of statistical mechanics in my thermodynamics course, I still attempt to provide a microscopic rationale for various concepts (e.g., heat capacities of ideal gases, ΔvapS values, etc.), which mandates some understanding of how individual molecules store energy and interact. One advantage of approaching this issue in the lab setting is to provide a hands-on exercise that enables two-way interactions between student and instructor. Students’ ability to correctly answer questions related to outcome (i) stated above provides at least some indication that this module has been effective in achieving that stated learning goal. In addition, the fact that they can effectively apply these skills to calorimetry projects later in the term indicates that the practical experience gives them some confidence in using these theoretical tools, even if most students need some guidance in extending them to slightly more complicated reactions. I have also used this module as a first lab in the physical chemistry II (quantum) course, and for the last decade, after a consolidation of our physical chemistry and instrumental analysis labs, we have used it as one of the initial modules in our “physical-analysis laboratory” course, which runs in parallel with physical chemistry II lecture. Students in this course are in one of three cohorts: i) taking quantum chemistry in parallel to the integrated lab, ii) enrolled in our ACS certified biochemistry major which does not require physical chemistry II (as of yet), or iii) took the physical chemistry lecture sequence the previous year. The latter cohort is very much the minority of this group, and as such, the student population has little experience with quantum mechanics prior to this lab module. For the first cohort, this exercise seems to facilitate the transition between physical chemistry I and II (macroscopic to microscopic). For the latter, it is an effective overview of concepts that stream through both semesters of the yearlong sequence. It is worth noting that neither the inhomogeneity of the student population nor limited experience with quantum chemistry has ever significantly inhibited the implementation of this module.

34

Methods Though there are numerous options for software platforms, and the choice is strictly a matter of taste, I have exclusively used various versions of Spartan in the classroom (details below). The advantages are ease of use, visual quality, and I have found that the menu-driven/dialog box structure of Spartan is rather effective in terms of highlighting the essential elements of a quantum-chemical computation for first-time users. The molecules are built (i.e., starting nuclear coordinates specified), by simply by clicking the mouse on a “builder” palette, a process much like using a chemistry desktop publishing application. In turn, the calculation is set up and executed using a series of drop-down menus in a single dialog box. There is no coding involved to run these jobs in Spartan (though some calculation parameters can be customized using optional keyword inputs). On the other hand, there are numerous software alternatives that are free or significantly less expensive, and many of colleagues with more experience in computational chemistry prefer these. The results presented herein come from two specific sources. The B3LYP (3) results obtained with the 6-31G* (aka 6-31G(d)) (4, 5) were obtained using Spartan student version 5.0.1 (6), with the default calculation parameters (i.e., no modifying keywords were used). These results, which replicate those initially generated by students, are emphasized in Part 1, and the atomic charges are Mulliken charges (see below) (3). Interestingly, the B3LYP/6-31G* results are incredibly (and fortuitously) accurate, can be obtained with the reasonably inexpensive student version of Spartan, and the jobs completed in less than one minute on an older desktop PC. (Some specific clocktime data: A B3LYP/6-31G* optimization of HArF took 41 seconds to complete, a subsequent B3LYP/6-311+G** (3–5) optimization of that geometry took 51 seconds.) The remainder of the results, obtained from methods including HF, B3LYP, MP2, and M06 (7), with the 6-31G(d), 6311+G(2df,2pd), aug-cc-pVTZ, and aug-cc-pV5Z basis sets (3–5) were obtained using Gaussian09 (G09) version B.0.1 (8), with coordinates and input files generated using GaussView version 5.0. Beyond exploring method performance (Table 2), which may be of interest to potential adopters of this module, a higher level of theory and greater control over the calculations were sought for the compounds described in Part 2, as to ensure reliability of these “published” results. If one is familiar with coding Gaussian files, running G09 is arguably a more convenient means of changing the parameters that dictate how the calculations are executed. Accordingly, the G09 results here were obtained using more stringent calculation parameters; an ultrafine integration grid (“int=ultrafine”) and tight geometry convergence criteria (“opt=tight”). Such settings are often desirable for quasistable systems, though omitting these settings in Spartan calculations has not led to any issues for students. Charges displayed with these latter results are from a Natural Population Analysis (NPA) (3, 9). Also note that because of the Gaussian calculation settings differ, the duplicate (B3LYP/631G(d)) results for HArF do exhibit some trivial differences from those obtained via Spartan (Table 1 vs. Table 2).

Part 1: Modeling the Formation of Argon Hydrofluoride (HArF) The first part of this module is taught in an instructional computer lab, in a mode best described as a “workshop”. In this setting, I deliver a few 10 to 15-minute mini-lectures, often interspersed, on various topics including: i) A description of the original experiment in which HArF was produced, identified, and characterized (if not during the preceding lab meeting), ii) an overview of the software program, and iii) a short overview of quantum chemical models and their execution. For the prelab assignment students are instructed to: i) Acquire the primary HArF reference article (1), ii) read it, iii) 35

read some background material on molecular energies (e.g., Atkins Chapter 0) (10), and iv) provide a Lewis structure and VSEPR geometry for HArF. HArF was originally produced in a low-temperature (20 K) argon matrix that had been seeded with HF and irradiated with deep UV photons (130-150 nm) (1, 2). However, we ignore any effects due to solvation by argon on the molecular energies, and model the reaction energy (path independent, solvation notwithstanding) as if it were a simple, direct gas-phase reaction, viz.

The theoretical framework used to compile the various contributions to the molecular energies, and subsequently, the reaction energy at (ΔrE), is described immediately henceforth. This is critical information for students, and is included in the lab manual text and my pre-lab lecture for this project, so it is described in detail here. Note also that the standard state symbol (°) is deliberately excluded; these values are formally not reflective of a standard condition. In compiling these energies, the rotational and translational energies are from some user-specified temperature, but the vibrational energy is from absolute zero (see below). In the reaction above, ΔrE is simply the difference in molecular energy (Emolec) between the products reactants, i.e.

For HArF and HF, the molecular energy (Emolec) is the sum of electronic, vibrational, rotational, and translational terms, viz.

For argon, which lacks vibrational and rotational degrees of freedom, equation 3 reduces to a sum of electronic and translational terms, viz.

The electronic energy (Eelec) is precisely the quantity that the quantum-chemical computations provide, and it dominates all other terms in equations 3 and 4. Similarly, the vibrational energy (Evib) is also obtained from the computations. Though not a primary output, frequencies can be determined from the electronic energies; the force constants are essentially the second derivatives of the electronic energy with respect to each normal coordinate. In this treatment, the total Evib is taken to be the total zero-point energy, equal to half the sum of the vibrational frequencies (ν), i.e.,

Argon, being monatomic, lacks any vibrational degrees of freedom, while HArF and HF, being linear molecules, have 3N-5 vibrational modes (4 and 1, respectively). Non-linear molecules have 3N-6 vibrational modes, and this can be relevant for the second part of this module. For the rotational (Erot) translational (Etrans) energies, we make a classical approximation, and use the equipartition theorem, and thus presume that the average energy of each degree of freedom for a given atom or molecule is equal to ½ RT (in molar energy units). Each reactant and product in 36

equation 1 has three translational degrees of freedom, making the translational energies equal at any given temperature (about 3.7 kJ/mol at 298 K), viz.

For rotational energies, it is essential to properly account for the number of rotational modes. Argon, again being monatomic, lacks any rotational degrees of freedom. For HArF and HF, being linear molecules, each has two rotational degrees of freedom, and thus their rotational energies are equal at any given temperature (approximately 2.5 kJ/mol at 298 K), viz.

Polyatomic molecules have three rotational degrees of freedom, and this underlies the difference in vibrational modes for linear and non-linear molecules, and again, this may warrant consideration in the second part of the module. For example, a bent triatomic has three rotational degrees of freedom and a single bending vibrational mode, whereas a linear triatomic has only two rotational degrees of freedom, and there are two degenerate bending vibrations. The conversion of ΔrE reaction to ΔrH reaction is given by,

in which Δn is the difference in moles of gas between products reactants (Δn = –1, for reaction 1). Alternatively, though I have never done so in my course, one could obtain the standard molar enthalpy values (H°m) of the reactants and products at 298 K, as determined by the values of the molecular partition functions. This approach more accurately accounts for the translational, rotational, and especially the vibrational energy (via contributions from thermally-accessible excited states), and could be critical when dealing with low-frequency vibrations. Moreover, the molar enthalpies are provided directly by most software packages when a frequency calculation is requested, including in Gaussian and Spartan. But in this process, the students do not deal directly with the physical origin of these quantities (unless they were to work through the partition functions as part of the exercise), and there may be issues with some software platforms as far as requesting a frequency calculation on Ar. Gaussian does provide thermodynamic data for Ar in this manner, however. Regardless, with the molar enthalpy data in hand, ΔrH° is simply the difference between the standard molar enthalpy values of the products and reactants, viz.

It is worth noting that the difference between the Hm values for HArF obtained via the method presented above and that obtained via the partition functions (and provided by Spartan) is only about 0.001 kJ/mol. Table 1 displays a set of sample thermochemical results for reaction 1 from B3LYP/6-31G* calculations (3–5). As noted above, these results take oat most a few minutes of clock time (in total) to execute, and as such, I most often use this model chemistry in the classroom for delivering Part 1. The table is constructed in a way that illustrates the various specific energetic contributions to ΔrE and note that Eelec dominates all other contributions. A sample student spreadsheet, essentially identical to that provided in our lab manual, is included as Figure 1. There are three sections: The top is simply a place to paste in raw computational results, the middle section is for planning the formula entries and unit conversions for use in the final reaction energy table, which comprises the 37

lower section (and mimics Table 1 to some extent). The final table computes ΔrE for each specific type of energy as well as the total, and the rotational and translational energies are designed to update for a different reaction temperature. The electronic and vibrational energies are not temperature dependent (within our treatment). As such, this module also provides an opportunity to teach intermediate spreadsheet skills, which are essential throughout our physical analysis lab course.

Figure 1. A sample spreadsheet for organizing student thermochemical calculations.

38

Table 1. Energy Data for Ar, HF, HArF, and Reaction 1a B3LYP/6-31G*

Eelec

Evib

Erotb

Etransb

Ar

-1384995.67

–

–

3.72

-263653.04

23.84

2.48

3.72

(-100.42017)

(1993.3)

-1648071.93

20.90

2.48

3.72

(-627.717625)

(1746.9)

576.8

-2.9

0.0

-3.7

ΔrE d =

570.1

ΔrH e =

567.6

(-527.5171419) HF HArF ΔrEtypec

a kJ/mol

unless otherwise noted; additional Eelec and Evib values noted in parentheses. Eelec values in parentheses are in units of Hartrees or au. Evib values in parentheses are cm-1. The individual HArF frequencies are 463, 709 (2 modes), and 1639 cm-1. b Obtained assuming average energy per mode is ½ RT, with T = 298K. c Reaction energy difference for each type of energy, respectively by column. d Total reaction energy as obtained via the sum of the individual contributions. e Reaction enthalpy as determined from ΔEtot and equation 8.

Table 2 presents a comparison of various model chemistries (methods and basis sets) and the intent here is strictly to aid instructors in model selection; this is not intended as a student exercise. Balancing resources and accuracy is always a key consideration, and in this instance, the B3LYP/ 6-31G(d) results are among the most accurate relative to the high-level CCSD(T)/aug-cc-pV5Z results from the original manuscript (1). However, this is due to a fortuitous cancellation of errors; the discrepancy for B3LYP increases with larger basis sets which suggests a cancellation of model and basis set errors with smaller basis sets. Overall, each method highlighted in Table 2 (except HF) is reasonably accurate, and overall, I have only allocated minimal attention to the issue of model performance in teaching this module. Often, I will have students explore basis sets and the corresponding impact on clock-time. This does provide a first-hand illustration of the variation principle, and also a practical lesson in balancing time and (presumed) accuracy. In the follow-up assignment for Part 1, students are tasked with re-performing these calculations at a higher level of theory, usually M06/6-311+G** (3–5, 7), which is available via the full version of Spartan. I also note that I originally ran this module with the HF/3-21G level of theory (3), and though these results were quite inaccurate, there was little or no pedagogical impact. Note that the HF results in Table 2, even with larger basis sets, are by far the least accurate. One thing to note is the effectiveness of the density functional (DFT) methods (B3LYP (3) and M06 (7)), which are comparable to HF in terms of computational time (roughly twice the clock time), but include the effects of electron correlation, which greatly improves the energy predictions. The MP2 method involves an explicit correction to HF to account for electron correlation, and was used widely prior to the development of accurate DFT methods, but is much more demanding in terms of computational time and resources (6). It is also less accurate with the smallest (6-31G(d)) basis set in Table 2.

39

Table 2. Model Chemistry Comparison for ΔrE (kJ/mol) method

basis set

ΔrEelecb

ΔrE

ΔΔrEelecc

% diff.

HF

6-31G(d)

732.3

731.0

166.3

29.4

6-311+G(2df,2pd)

655.9

653.6

89.9

15.9

6-31G(d)

577.7

571.3

11.7

2.1

6-311+G(2df,2pd)

532.5

527.7

-33.5

5.9

aug-cc-pVTZ

529.5

525.0

-36.5

6.4

6-31G(d)

648.4

640.1

82.4

14.6

6-311+G(2df,2pd)

578.1

574.8

12.1

2.1

aug-cc-pVTZ

560.6

557.7

-5.4

0.9

6-31G(d)

603.2

596.6

37.2

6.6

6-311+G(2df,2pd)

547.4

574.8

-18.6

3.3

aug-cc-pVTZ

546.4

542.3

-19.6

3.5

aug-cc-pV5Z

544.3

540.3

-21.7

3.8

aug-cc-pV5Z

566.0

–

–

–

B3LYP

MP2

M06

CCSD(T)a a Ref.

(1).

bΔ

rE value in terms of only electronic energies; difference in Eelec between product (HArF) and

reactancs (Ar, HF) in equation 1. (1).

c Difference

between the ΔrEelec value and the CCSD(T) value from Ref.

Another element of the follow-up assignment is to answer some discussion questions related to the original manuscript, focusing on the energetic issues and comparing our results wherever possible to those reported in that paper (1). These questions are also included in Table 3, for use with the module. The remaining part of the follow-up assignment is to make a high-quality graphical figure with a descriptive caption, which includes bond lengths, calculated atomic charges, and ΔrE. Proper precision for these data are, 0.1 Å for bond distances, 0.1° for angles, and 0.1 kJ/mol (or kcal/mol). A depiction of the B3LYP/6-31G* structure parameters for HArF, based on an image generated by Spartan, is displayed in Figure 2, with a Lewis structure, per the prelab assignment. One way that this module could be extended is in the extent to which the bonding in HArF is characterized. Alas, I have pursued only a few rather simplistic considerations, but I do take time to highlight the visualization capabilities that Spartan offers, such as maps of the “electron density” and “electrostatic potential” surfaces. Such images are now commonplace in textbooks, but that latter does shed light on one issue discussed in the original manuscript; the extent of ionic bond character in HArF, or stated somewhat differently, the weight of an HAr+/F– resonance structure (HAr+ is isoelectronic with HCl). This consideration leads to a brief discussion of computed atomic charges, and the difficulty of even defining them and thus somehow assigning electrons to a given atom, in light of the complexity of the computer-generated electron distribution. In spite of these potentially complicating issues, I do have students examine computed charges and include values in their figures; non-zero values indicate that the noble gas is taking part in actual bonding interactions. Mulliken charges are displayed in Figure 2; these tend to be reasonable when small basis sets are used (3). Because the results in the next section involve the much larger aug-cc-pVTZ basis set, values therein result from Natural Population Analyses (9). NPA charges are more stable with respect to basis set 40

size, but tend to be larger in magnitude overall than those computed from other models (3). Indeed, they are larger for HArF in Figure 2 (below). Though I tend not to engage in a detailed discussion of charge models with my students, the text by Cramer (3) does offer a thorough and accessible treatment of this topic. Another noteworthy point is that in practice, it is advisable not to indulge in a precise, quantitative interpretation of calculated atomic charges, but rather, trends in charges obtained from identical model chemistries for a series of analogous compounds are physically meaningful (3).

Figure 2. A Lewis structure and B3LYP/6-31G* geometry parameters for HArF, with Mulliken atomic charges. Rcov and Rvdw are distances predicted by summing covalent and van der Waals radii, respectively. One final characterization issue is how we establish that the adjacent atoms are truly bonded to the noble gas, beyond noting those shifts in atomic charges discussed immediately above. To this end, I typically have students consider predictions of bonding or non-bonding distances from sums of covalent (11) and van der Waals radii (12), respectively. In the case of HArF, the Ar-F distance (1.974 Å via B3LYP/6-31G*) is much closer to the sum of the covalent radii (1.68 Å) than to the sum of the van der Waals radii (3.35 Å). The case is more compelling for the Ar-H distance (1.426 Å), for which the sum of the covalent and van der Waals radii are 1.34 Å and 2.98 Å respectively. This is surely an old-fashioned approach perhaps, but nonetheless, I believe senior students should understand the application of bond radii, and internalize some knowledge of typical bond distances. In addition, I also note that these calculations yielded all real frequencies (i.e., no imaginary values); this indicates a true equilibrium structure for HArF. Regardless, a possible extension of this module would be to further characterize the bonding in HArF by a more sophisticated analysis such as Atoms in Molecules (AIM) (13) or Natural Bond Orbitals (NBO) (14). To summarize Part 1 of this module, students will: i)

For prelab: Obtain and read the main reference article and background material, plus draw the Lewis structure and VSEPR geometry for HArF. ii) In lab: Perform computations, build a thermochemical analysis spreadsheet, and undertake some consideration of the bond distances and atomic charges. iii) Follow-up assignment: Re-do the computational analysis using a higher level theory, answer discussion questions, and generate a high-quality figure of HArF with a figure caption that provides a consideration of the bond distances and charge distribution. 41

Table 3. Discussion Questions for Part 1 1) Briefly explain/rationalize the origin of the specific contributions to Erot and Etrans for each species in the net reaction (HF, Ar, and HArF). (Equations are essential.) 2) Our electronic structure calculations are much less sophisticated than those discussed in the HArF paper. Compare your calculated ΔrE to theirs (both B3LYP & M06, converting between units as necessary). What is the % difference in the reaction energy (relative to their highest quality result)? Which of our methods is more accurate (relative to theirs)? 3) What “type” of energy dominates the reaction energy (i.e., what is the biggest term in Equations (3) and (4))? Does the changing the temperature change ΔrE much? Why or why not? 4) Mechanistic Considerations: Formation of HArF. a) What is the source of energy that “drives” the reaction in the experiment (as conducted and described in the paper)? b) What range of energies (in molar energy units) does this source provide? c) Compare it to ΔrE. It is enough to complete the reaction? d) HF bond rupture (upon photo-excitation) is initial step in the formation of HArF. i) How much energy is required to break an HF bond? (Look up the Bond E) ii) How does that compare to the photon energy? (i.e., from your answers to “a” and “b” iii) What happens to the excess energy, i.e., that which is left over after breaking H-F with hν?

Part 2: Exploring New Noble Gas Compounds In Part 2 of this module, students characterize a noble gas compound of their own design, subject to a few guiding constraints. The goal here is to encourage students to ask appropriate and effective “chemical questions”, and thereby facilitate the growth of their creative thinking skills. One challenge associated with these intentions is that quite often, the context for a solid research question takes years of experience to fully comprehend. But in this case, the issue is quite accessible to nearly all chemistry students because it simply challenges well-established dogma: The Group 18 elements are notoriously unreactive, so is it possible to form bonds to them? In fact, there are have been numerous studies of noble gas compounds similar to HArF, with theory often preceding experiment (15–18), and these efforts continue at present (19, 20). A key issue from an educational standpoint is how the computational approach facilitates an open-ended inquiry, for one because it is simply easier to build molecules on a computer screen than to actually synthesize them, and in addition, the safety advantage is noteworthy. One simply could not safely supervise 24 students working with an array of such notoriously unstable compounds. With computational chemistry, however, there are no safety hazards whatsoever, and students can explore a wide range of bizarre and unstable compounds with essentially zero risk. Part 2 starts with a literature workshop that we hold in the library computer lab, and it is taught primarily by the science librarian. The broader goals are to facilitate the use and understanding of various literature databases and also help students grasp the broader scope of the chemical literature (e.g., What are the various types of research articles? Who publishes research journals? What is the scope or audience for a given journal?). More to the point of this project, the specific intent is to cultivate the skills needed to find all the pertinent information available on a noble gas compound of their choosing. Ultimately, the collection of relevant articles they find guides their design, and establishes an intellectual context for their report introduction. The students’ noble gas compounds are subject to a few design constraints. The point is not only to direct their thinking, but also to produce a set of results that are more-or-less comparable 42

across the entire class to illuminate key trends, but also because we award a trophy to the student that designs the highest-energy stable compound. These constraints level the playing field for this contest by establishing a common energetic benchmark. They are as follows: i) The compound must be neutral, ii) The formula can only contain one noble gas atom, and iii) One must be able to form the compound via a reference reaction (akin to equation 1 above) that involves only one equivalent of some stable compound. Also, it is essential that the compound exhibit bona fide chemical bonds to noble gas atoms, though this condition is not always easy to establish completely. As above, we have made this assessment by comparing distances to (sums of) covalent van der Waal’s radii, requiring that the frequencies are real, and noting non-zero values for calculated charges on noble gas atoms. Quite often, the interatomic distances involving the noble gas atom in a “stable” compound are somewhat longer that those predicted from covalent radii. Conversely, they are usually a great deal shorter than those predicted by van der Waals radii, and the truly unstable compounds tend to fragment completely during the geometry optimization (i.e., the noble gas atom gets pushed out to a location several angstroms from the other atoms). So, even on a purely structural basis, the distinction is reasonably clear when the results are viewed through the proper filter – if the distances are significantly shorter than the predicted non-bonded distances it is considered a valid compound for the project. In addition, vibrational frequencies should be real for true minimum-energy structures, but I have on occasion relaxed this requirement. Again, one possible extension of this lab would be to undertake a more a sophisticated analysis of the bonding to make this case. Despite of some degree of variability in the approach that students take to this challenge, the comparisons which most easily facilitate a discussion of noble gas stability tends to follow a simple bond-insertion mechanism, which is essentially a generalization of reaction 1 above, i.e.,

Often students follow this path, and many make a simple substitution relative to HArF (e.g., Kr for Ar, Cl for F, etc.), not only because it is a relatively simple extension, but also it sets up a direct, single-variable comparison to HArF. Other students that pursue more creative options realize at some point that to make a valid comparison, they need to consider a reference compound that differs from theirs by only one parameter (e.g., the noble gas atom or one of the X/Y groups). As such, I often I encourage them to coordinate with a fellow classmate, or just examine a second compound (or a series) so that they can do so, but only after I challenge them as to how they will construct a comparison based on the compound they chose. Students that deviate from the mechanism entirely (e.g., inserting a noble gas into a crown ether, or bonding it with a Lewis acid) sometimes have difficulty making effective comparisons between systems without a great deal of extra effort. Some degree of patience on the part of the instructor is critical, as is a willingness to let students pursue their ideas and encounter roadblocks and unexpected results. The first assignment for Part 2, following the literature session and some time to do their analysis, is a mock group meeting in which each student gives a brief, two- or three-slide presentation on their compound. They are specifically instructed to: i) introduce their compound and the hypothesis or question that led to it, ii) display its structural properties, charge distribution, and its energy value relative to the noble gas and the stable X-Y compound, and iii) make the case using bond radii that there are bona fide bonds to the noble gas atom. Almost always, students assemble a set of results from which stability trends can be deduced during the group discussion that ensues, at least among those 43

that fit the mechanism implied by reaction 10. The assessment of “stability” is based upon ΔrE for equation 10, as it applies to the various compounds. A few apparent trends in these compounds are: 1. Stability Increases with the Size of a Noble Gas Atom. Figure 3 displays structural properties and ΔrEelec values for H-Ar-F, as well as H-Ne-F, and HKr-F. These were obtained via M06/aug-cc-pVTZ, and B3LYP/6-31G(d) energies are also included for comparison. It is worth noting that there are no significant structural differences between the M06/aug-cc-pVTZ and B3LYP/6-31G(d) structures for any of the compounds discussed herein, and all exhibit only real vibrational frequencies. In any event, the ΔrEelec values increase steadily in the manner: HKrF < HArF < HNeF. A simple rationalization of this trend relates to size; because the noble gas must expand its octet to bond, a larger size reduces repulsion between electron pairs about the noble gas. In addition, neon, being a second-row element, is presumably tyrannized by the octet rule with only s and p orbitals in its valence shell, but the HNeF compound is quasi-stable, with distances about the Ne that are still much closer to bonded limit than the non-bonded limit. No compound containing the element neon has ever been observed, however. Another factor that may underlie this trend is the extent of shielding of the valance electrons (i.e., ionization energies decrease in proceeding down a group); charges indicate that the noble gas gives up electron density in every interaction among the compounds discussed herein. Thus, more bonding should ensue when these electrons are held less tightly. A trend in the charge distribution is also apparent, and it reinforces this rationale; the charge on the noble gas increases (Ne < Ar < Kr) with size.

Figure 3. Structure parameters, atomic charges (NPA), and ΔrEelec values, via M06/aug-cc-pVTZ, for HNeF, HArF, and HKrF. Rcov and Rvdw are distances predicted by summing covalent and van der Waals radii, respectively. 44

2. Stability Increases with the Polarity of the X–Y Bond. Two illustrations of this trend are apparent from the results shown in Figure 4, together with the HArF results (Figure 3). In the hydrogen-halide series (H-Ar-X, X=F, Cl, Br), the ΔrEelec values steadily increase with the size of the halogen. Apparently, this reflects the electronegativity of the halogen; a greater tendency for X atom to withdraw electron density from the noble gas seems to stabilize the compounds. An analogous trend is apparent for the 2nd row series (H2N-Ar-H vs. HOAr-H vs. H-Ar-F).

Figure 4. Structure parameters, atomic charges (NPA), and ΔrEelec values, via M06/aug-cc-pVTZ, for HArCl, HArBr, HArOH and HArNH2. Rcov and Rvdw are distances predicted by summing covalent and van der Waals radii, respectively. 45

3. Stability Decreases with X−Y Bond Strength and/or Over Stability of XY. Within the constraint of the bond-insertion mechanism conveyed by equation 10, it would follow that ΔrEelec will increase when the noble gas is inserted into a stronger bond, or otherwise reacts with a more stable (lower energy) compound overall. A good illustration is the fact that ΔrEelec is much higher for HArOH than for HArCl; though the O-H bond is more polar, it is also stronger, and the resulting compound has a higher energy relative to its respective fragments. The highest energy compound ever designed by students is displayed in Figure 5; the result of inserting Ar into the triple bond in N2. A Lewis structure is also included; we found it challenging to draw this during the group meeting in which this compound first arose. The energy is high, and it epitomizes the trend noted immediately above, it a relatively small noble gas (the analogous neon compound is truly stable), and the XY unit has a strong, non-polar bond. The Ar-N distances are actually short relative to the covalent prediction, but the best Lewis structure for NArN has double bonds (it is isoelectronic with SO2). The assignment for Part 2 of the module consists of several parts. First, students must construct a spreadsheet that shows the calculation of the ΔrE, as well as a high-quality graphic with a caption, just as in Part 1 for HArF. In addition, there is a partial lab report. In general, we try to scaffold the development of manuscript writing skills by breaking the process down into parts, so we assign specific sections of partial reports early in the course. In this project, we focus on the introduction, which builds on the literature session they did at the outset of Part 2. I typically suggest a rough outline as to guide them through this process. In addition, they also write a paragraph of discussion in which they compare and contrast their new noble gas compound with at least one analogous compound, and discuss apparent stability trends and their underlying rationale. The broader intent is to guide them in the process of making valid, insightful comparisons, and writing an effective discussion with a genuine chemical content. A computational methods paragraph would be a worthy addition, and will most likely be included in the next revision.

Figure 5. Lewis structure, geometry parameters, atomic charges (NPA), and ΔrE via M06/aug-cc-pVTZ for NArN. The Ar-N distances are actually shorter than the sum of covalent radii (Rcov = 1.72 Å), as is displayed in Figure 4 for H-Ar-NH2. 46

The bigger question perhaps, is whether or not engaging in an open-ended activity such as this actually manifests some enhancement of students’ critical and creative thinking skills. I have never collected any formal assessment data that addresses this issue, and it seems that designing the outcomes and rubrics to try to measure such progress would be more challenging than probing mere “content”. Nonetheless, I’d argue that offering such an opportunity to utilize and develop these skills must have a greater impact than confining the course to “canned” experiments in which all the questions are asked for the students, and the goal is strictly to measure some “value” while discussing only errors and/or experimental shortcomings. In addition, I can say informally that students do engage this process; some are enthusiastic about this freedom from the outset, some are apprehensive. Often, students in the latter group become quickly aware of their shortcomings and embrace the need to develop these skills. The other observations, in regard to the subsequent designbased activity (see below), are: i) Apprehensive students tends to approach the follow-up task with greater confidence, and ii) Overall, nearly all projects are rooted in meaningful, valid questions (after varying degrees of feedback from the instructor). To summarize Part 2 of this module, students will: i) Design a “new” noble gas compound of their choosing, subject to a few design constraints. ii) Search the literature to obtain previous reports on their compound and those closely related to it, as well as possibly refining their hypothesis or target compound accordingly. iii) Characterize the compound via computations, and present their preliminary results in a mock group meeting. iv) Prepare a partial lab report, including: A publication-style graphical figure with a descriptive caption, an introduction that conveys the hypothesis or question that motivated the design of their compound as well as the broader intellectual context, and a discussion paragraph that compares and contrasts their compound with at least one analogous system.

Looking Forward: Modeling and Extending Calorimetry Results Later in the term, physical analysis lab students embark on a major calorimetry project which builds directly on the outcomes targeted in the noble gas module. There are two possible tracks for this project, they either measure ΔrH of a reaction by solution calorimetry or ΔrE (ΔrU in most texts) of some reaction via bomb calorimetry. In both cases, they use computations to extend these results to other reactions or compounds and establish a valid comparison or a consideration of some structure-reactivity relationship. In the case of the bomb calorimetry experiments, most students investigate the difference in combustion energy (or enthalpy) of a pair of structural isomers (e.g., n-butanol and diethylether):

There are two minor complications that must be addressed. One is that O2 has a triplet ground state, which must be specified. In turn, this requires an “unrestricted” calculation (6), and this specification should be applied to all reactants and products. Two, by default, the models reflect gasphase reactants and products. Thus to compare between the measured reaction, which involves H2O (l) and a liquid or solid organic compound, one must appropriately construct a thermochemical cycle to correct the modeled ΔrE or ΔrH value with the ΔvapH value of water and some reference value 47

(or estimate) of the sublimation enthalpy of the organic. Nonetheless, students typically can predict the measured reaction energy to within 10 or 20%, and thus having “validated” their model, they can explore the energy difference between with compound and any structural isomers. Because the products of reaction (11) are identical for any set of structural isomers, the difference in combustion enthalpy (or heat of formation) is nearly equal to the difference in Eelec between the various isomers. Ultimately, students can address this difference directly if they so choose, but either way, they can rationalize the effect of various structural features (e.g., types of bonds, types of unsaturation) on the overall energetic stability of the isomeric compounds. At this point, they are truly exploring chemical ideas with computational chemistry. For solution calorimetry, I usually direct students to a study of strong acid (H3O+)-weak base reactions, for which they will compare the reaction enthalpies for pair or weak bases (e.g., pyridine and 3-chloropyridine). The two complications here are: i) the reactions take place in solution, so they must use the E(aq) values from Spartan for Eelec (which are actually free energies but the entropic contribution is relatively insignificant) (6), and ii) the observed reaction enthalpy (ΔrHmeas) reflects two processes, the heat of solution (or dilution) of the base (ΔsolH), plus the enthalpy change for the acid-base reaction (ΔrHAB), which is the modeled quantity. Thus, to compare their measured and modelled reaction enthalpies and thus validate their computational predictions, they must run a second set of experiments to determine solution/dilution enthalpy of the base, and combine the data as follows.

Once they have established confidence in their theoretical (ΔrHAB) values through favorable comparison to their experimental results (again, agreement to within 10-20% is deemed acceptable), they can compare to another weak base (or two) using the computations. Moreover, the comparison is direct and reflects only the acid-base reaction, free of the potentially obscuring effects of the solution enthalpy. The common theme here is to first “validate” a computational model against an experimental observation (often with a liberal definition of success), and then, with a reliable method in hand, students can explore related reactions and thus make comparisons between compounds without doubling or tripling their experimental work. Moreover, they can also investigate compounds that are otherwise inaccessible due to instability or cost. As such, linking this calorimetry project to the noble gas module not only allows them to utilize their practical experience with computational methods, but also utilize and further develop their critical and creative thinking skills. They are provided with the opportunity to formulate a hypothesis or question and test it, and develop a discussion for their reports that has a truly chemical focus. As noted above, students seem to engage this project with a greater degree of confidence after having sought their own direction in the noble gas compound project. 48

Summary The design and implementation of a computational module for a physical chemistry lab course has been described. It occurs in two parts, the first of which involves an analysis of HArF, and the main intent is assessing the energy relative to Ar and HF. Subsequently, students design their own noble gas compound, and intimately, compare and contrast this system with an appropriate analog. Beyond the practical experience using chemical computations, the module provides the opportunity to build literature proficiency, as well as critical and creative thinking skills. In addition, students employ these skills, both the practical application of computational chemistry techniques, as well as creative and critical thinking, in a subsequent calorimetry project.

References 1. 2. 3.

4.

5.

6. 7.

8.

Khriachtchev, L.; Pettersson, M.; Runeberg, N.; Lundell, J.; Räsänen, M. A Stable Argon Compound. Nature 2000, 406, 874. Frenking, G. Chemistry: Another Noble Gas Compound. Nature 2000, 406, 836. For a description of the methods and basis sets used herein (except M06), see: Cramer, C. J. Essentials of Computational Chemistry, 2nd ed.; John Wiley and Sons: Chichester, U.K., 2004; and references therein. For an accessible discussion of Gaussian basis sets see: Clark, T. A Handbook of Computational Chemistry: A Practical Guide to Chemical Structure and Energy Calculations; Wiley: New York, 1985. A note regarding basis set nomenclature. In Spartan, polarization functions in a basis set such as 6-31G* are denoted by the asterisk; which in this case indicates that d-orbitals have been added to 2nd row atoms (Li-Ne). A more specific and preferred way to specify this basis set is “631G(d)” in which the polarization functions are noted explicitly. For the “6-311+G**” basis set in Spartan, the more specific nomenclature is “6-311+G(d,p)”, and this, in addition to the d-functions for the 2rd row elements, lso indicates that p orbitals have been added to hydrogen (and helium). See references 3 & 4 for a more extended discussion of basis sets. Spartan Student, Version 5.0.1; Wavefunction, Inc.: Irvine, CA, 2012. Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theo. Chem. Accts. 2008, 120, 215. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K. V.; Zakrzewski, G.; Voth, G. A.; Salvador, P.; Dannenberg,

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9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19. 20.

J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. Reed, A. E.; Wienstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, 1997; Chapter 0. Cordero, B.; Gomez, V.; Platero-Prats, A. E.; Reves, M.; Echeverria, J.; Cremades, E.; Barragan, F.; Alvarez, S. Covalent Radii Revisited. Dalton Trans. 2008, 2832. Mantina, M.; Chamberlin, A. C.; Valero, R.; Cramer, C. J.; Truhlar, D. G. Consistent van der Waals Radii for the Whole Main Group. J. Phys. Chem. A 2009, 113, 5806. Bader, R. F. W. Atoms in Molecules. Accts. Chem. Res. 1985, 18, 9. Weinhold, F.; Landis, C. R., Discovering Chemistry with Natural Bond Orbitals; Wiley: Hoboken, NJ, 2012. Berski, S.; Latajka, Z.; Silvi, B.; Lundell, J. Electron Localization Function Studies of the Nature of Binding in Neutral Rare-Gas Containing Hydrides: HKrCN, HKrNC, HXeCN, HXeNC, HXeOH, and HXeSH. J. Chem. Phys. 2001, 114, 4349. Gerber, R. B. Formation of Novel Rare-Gas Molecules in Low-Temperature Matrices. Ann. Rev. Phys. Chem. 2004, 55, 55. McDowell, S. A. C. Studies of Neutral Rare-Gas Compounds and Their Non-Covalent Interactions with Other Molecules. Curr. Org. Chem. 2006, 10, 791. Grochala, W. Atypical Compounds of Gases, Which Have Been Called ‘Noble’. Chem. Soc. Rev. 2007, 36, 1632. Borocci, S.; Giordani, M.; Grandinetti, F. Bonding Motifs of Noble-Gas Compounds as Described by the Local Electron Energy Density. J. Phys. Chem. A 2015, 119, 6528. Chopra, P.; Ghosh, A.; Roy, B.; Ghanty, T. K. Theoretical Prediction of Noble Gas Inserted Halocarbenes: FNgCX (Ng = Kr, and Xe; X = F, Cl, Br, and I). Chem. Phys. 2017, 494, 20.

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Chapter 5

How Can You Measure a Reaction Enthalpy without Going into the Lab? Using Computational Chemistry Data to Draw a Conclusion Melissa S. Reeves,*,1 H. Laine Berghout,2 Mark J. Perri,3 Steven M. Singleton,4 and Robert M. Whitnell5 1Department of Chemistry, Tuskegee University, Tuskegee, Alabama 36088, United States 2Department of Chemistry, Weber State University, Ogden, Utah 84408, United States 3Department of Chemistry, Sonoma State University,

Rohnert Park, California 94928, United States 4Chemistry Department, Coe College, Cedar Rapids, Iowa 52402, United States 5Department of Chemistry, Guilford College,

Greensboro, North Carolina 27410, United States *E-mail: [email protected].

In the experiment “How can you measure a reaction enthalpy without going into the lab?” we have students use computational thermochemistry to explore the properties and reaction thermodynamics of hydrofluoropropanes. This guided inquiry lab was developed under the Process Oriented Guided Inquiry Lab Physical Chemistry Laboratory (POGIL-PCL) project. Students are asked to find the “best” replacement for the hydrofluoropropane CFC-227ea, which has been used in military fire suppression systems. The compound has been known to decompose at high temperatures to produce poisonous HF, resulting in some casualties. Students are asked to choose an alternative compound based upon properties predicted with computational chemistry. The number of possibilities is large enough that a class will have to pool data to make a selection. As part of their study, students are also asked to evaluate calculational methods for speed and accuracy and to cooperatively choose the “best” method for the class’s analysis. The evaluation of methods requires them to compare computational results with experimental values. Finally, students must use their calculational data to rationalize a choice about the “best” fire suppressant molecule.

© 2019 American Chemical Society

Introduction At a workshop for the Process Oriented Guided Inquiry Learning Physical Chemistry Laboratory (POGIL-PCL) (1) project in Richmond, VA, in 2015, the authors sat around a table discussing what would make an interesting experiment using computational thermochemistry. The POGIL-PCL model for a physical chemistry experiment includes a title which is a question, opportunities for students to make experimental design choices, an outcome which is not a priori known to the students, and the necessity for students to collaboratively pool data to answer the question. For a computational experiment, we sought to develop an application where students could make choices about how to proceed even with little or no experience. It also needed to be an experiment where the results were not readily available, either in experimental or computational data. At the conclusion of the discussions, the experiment chosen was “How do you measure a reaction enthalpy without going into the lab?” Students were introduced to the problem through primary literature: the current fire suppression system in U.S. armored vehicles could produce deadly HF gas and injure or kill personnel (2). A short set of initial calculations introduced students to a subset of computational chemistry’s myriad methods and basis set choices. The National Institute of Standards and Technology (NIST) Computational Chemistry Benchmark Database (CCCBDB) (3) was utilized to validate the results from the calculations and guide students’ choices about which method and basis set to use. Students chose alternative chemicals for fire suppression to compare with the current one. Finally, students had to formulate a recommendation based upon the calculational results. After several rounds of development and “alpha testing” with students, we have an experiment which provokes student engagement, guides the students to make well-reasoned design choices, and results in student reasoning from evidence. Using the Chem Compute site (4), even faculty with no software and novice computer expertise can use the experiment. In this chapter, a brief overview of the POGIL-PCL method will be given, the experiment will be described, and the authors’ experiences with classroom use of the experiment will be discussed. Background The POGIL-PCL project was launched in 2011 through an NSF grant obtained by Sally Hunnicutt, Alex Grushow, and Rob Whitnell (1). The goals of the grant were to develop guided inquiry physical chemistry lab experiments as well as to foster a community of physical chemistry professors who would be the developers and users of the experiments. The development of this experiment showcases the epitome of their grant’s goals: five physical chemistry professors, spread across the country, worked together to develop and test this experiment. POGIL-PCL is part of a larger project, the POGIL project (5). POGIL is a student-centered instructional strategy emphasizing small, self-managed student teams working through guided inquiry activities developed to aid them in constructing content knowledge while prompting them to build process skills (often called soft skills). The method has been described previously (6), compared to other inquiry methods (7), and evaluated in different chemistry settings (8, 9). The instructor’s role in POGIL is to facilitate the student teams as they work through activities. An activity typically has three stages: an exploration stage where students examine a model and relate it to previous knowledge, a concept invention stage where students answer questions relating to the model to discover the concept targeted by the activity, and an application stage where students utilize the concept to solve a problem or analyze a new model (10). The POGIL community and library of available activities is particularly strong in General Chemistry and Physical Chemistry. 52

A central part of the POGIL-PCL paradigm is the learning cycle (11). In each experiment, students build deeper and deeper conceptual understanding through successive predict-experimentanalyze cycles. This experiment includes three learning cycles. A typical POGIL-PCL experiment has an initial “quick and dirty” experimental cycle to provide students with familiarity with the experimental setup and a small dataset from which to make more refined predictions. Students also use pooled class data and hence can solve a problem more complex than one or two students working with their own data. There are already two computationally-based POGIL-PCL experiments developed by two of the authors (12). The first is “What makes an electron a valence electron?”, an ab initio experiment designed to explore the orbital structures of first and second row atoms and diatomics. The second is “What factors govern the escapability of a molecule from a liquid?” This experiment is an introduction to molecular dynamics to examine the intermolecular forces governing liquid cohesion. Additional experience with implementing these two experiments is described in a separate chapter in this volume. The experiment described in this chapter is the first POGIL-PCL computational experiment applied to a reaction system. Real Life Setting for a Problem The title of a POGIL-PCL experiment is formulated as a question a student would be interested in answering – this is the first step to engaging the student. For this experiment, the title refers to the general technique of computational thermochemistry rather than a specific application. The strongest appeal to engagement in this experiment is the application: the fire suppressant HFC-227ea (1,1,1,2,3,3,3-heptafluoropropane) was found to have caused deaths of U.S. military personnel in an armored vehicle after a hit from a rocket-propelled grenade (2). Students are guided to explore the properties and reaction enthalpies of various fluoropropanes (there are 27 possibilities) to determine whether they can suggest an alternative fire suppressant. The opportunity to use chemistry to potentially save lives increases engagement, at least anecdotally, for most of the students. A convenient feature of this experiment is that, at this time, the experimental and computational results for these compounds are unavailable in the literature. This experiment cannot be termed an exercise of “confirm the known results.” The fluoropropane HFC-227ea, also known as FM-200, is the replacement for halon 1301 whose production was banned in 1994. The mechanism of fire suppression by HFC-227ea is a combination of a high heat capacity and some ability to react with the free radicals in combustion (13). The scavenging of free radicals can lead to toxic HF production; this mechanism can be reduced by adding particulate NaHCO3 in the formulation. At high temperatures, HFC-227ea can decompose by elimination to produce a fluoropropene and HF (see Figure 1). This reaction has an experimentally determined activation barrier of 291 kJ mol-1 at 1200 K (14) and an enthalpy of reaction of 126 kJ mol-1 at 298 K (15). Theoretical calculations put the transition state energy at 333 kJ mol-1 and the reaction enthalpy at 146 kJ mol-1 (16). Analogs of the reaction in Figure 1 with various fluoropropanes substituted for the HFC-227ea are the subject of the computational studies performed by the students. With 27 choices, from the three mono-substituted fluoropropanes to the other heptasubstituted fluoropropane, it is unlikely that a class will explore all the choices. There are also enough choices that each team can explore multiple fluoropropanes.

53

Figure 1. Elimination of HF from HFC-227ea. Computational Chemistry as a Tool, Not a Topic While this experiment utilizes ab initio computational chemistry methods, it is intended as a thermodynamics experiment. The prerequisite quantum knowledge is at the general chemistry level; that is, students are expected to know what atomic and molecular orbitals are. The comparison of methods and basis sets does not require additional background for the students. The goal was to use computational chemistry to answer a question, in a manner we imagine many chemists (who are not computational chemists) would approach the use of these tools. There are many instances of computational thermochemistry lab experiments in the literature. Barbiric, Tribe, and Soriano used computational chemistry to estimate calories in food, although at the general chemistry level (17). Martini and Hartzell report including computational chemistry into a full course in classical thermodynamics (18). Lever, Howe, and Whisnant applied computational chemistry to the spontaneity of stratospheric ozone reactions with Cl2O4 (19). Bumpus, et al., used computational chemistry at various levels to assess thermochemistry of various explosives (20). Finally, the popular (but apparently out of print) Physical Chemistry lab textbook by Halpern and McBane has an experiment studying the 2 NO2 ⇌ N2O4 reaction at high levels of theory (21). Using Data To Make a Decision Another feature of POGIL-PCL is promotion of higher-order learning (analysis, evaluation and synthesis). In this experiment, students choose and justify choices of computational method and molecules to target. Then, after pooling class data, students make a recommendation from the results about which molecule would serve as a preferred fire suppressant compound. Data analysis must lead, in this experiment, to an appropriately justified, recommended compound.

The Experiment Objectives and Prerequisites All POGIL-PCL labs have a combination of content and process learning objectives. “How do you measure a reaction enthalpy without going into the lab?” has four listed content objectives, the first of which is to obtain thermochemical quantities from electronic structure calculations. The other content objectives relate to the difference in zeroes of energy between enthalpy of formation and electronic structure, when calculations can be useful in the absence of experimental data, and how to use the specific results of this experiment to choose the best fire suppressant. Process learning objectives are an essential feature in the POGIL method. The “official” process goals include oral and written communication, problem solving, and critical thinking among others (22). Most of the POGIL-PCL lab experiments include those four process skills, but in addition have lab-oriented process learning objectives. The process learning objectives for this experiment are to develop approaches to quantum chemistry calculations which maximize accuracy while utilizing 54

computational resources effectively and to use available databases to make comparisons among the students’ calculations and known computational and experimental data. The experiment would be most appropriate in the thermodynamics semester of Physical Chemistry. It does not require quantum mechanics or thermodynamics preparation beyond what students receive in General Chemistry. Bond enthalpies are used for an early calculation. The POGIL-PCL philosophy is to have students build concepts; hence, they are designed to be used without a tight relationship to the lecture. This is especially helpful at larger schools using round robin methods in the laboratory. As with other POGIL-PCL experiments, the student handout, Instructor’s Handbook with answers and facilitation notes, and supplemental information are available upon request. Pre-Experiment Questions Pre-experiment questions are used in a POGIL-PCL lab to prompt students to remember what they already know about the concepts in the experiment, to have students look up and record needed data, and to encourage students to organize that information to make a prediction relevant to the experiment. In this experiment, students are first asked to read the Zierold and Chauviere paper and determine the fire suppressant molecule’s identity and structure. They predict the enthalpy of the elimination reaction in Figure 1 using standard general chemistry bond enthalpies. Then students are directed to construct Hess’s Law diagrams relating to the standard enthalpy change and for an electronic energy calculation; these two diagrams differ primarily in the zero of energy (see Figure 2). The thermochemical convention for enthalpies is that the zero of energy is for elements in their standard states, and is usually tabulated for 298.15 K. For electronic energies, however, the zero of energy is for infinitely separated nuclei and electrons at 0 K. Our experience is that, even with these examples, students require guidance to create a correct diagram. Finally, students make an initial prediction about which fluoropropane may be a suitable replacement for HFC-227ea. Facilitating the POGIL-PCL experiments is an art, and faculty workshops have included training in facilitation. The prelab questions are generally not a source of discussion in the Physical Chemistry lab, but POGIL-PCL has team and class discussion prior to the experimentation phase. The final prelab question where students make a prediction requires class facilitation: putting the team consensus predictions on the board or some other visible place is important. Revisions of the predictions will occur in the successive experimental cycles, and students gain an appreciation for the new information as it is juxtaposed against previous decisions. Cycle 1 and Properties Calculations In the first experimental cycle, the class is divided into teams which perform HF/6-31G* calculations on either CH3F or CHF3. The teams compare results to ensure everyone has completed the calculations successfully. Then the results of electronic energy, geometry, vibrational frequencies, and heat capacities are compared and contrasted between the two molecules. Neither molecule takes long (less than 20 cpuseconds on a single node of Chem Compute), so the first cycle should be done relatively quickly.

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Figure 2. Hess’s Law diagrams similar to templates presented for students to revise. These diagrams show an example of an exothermic reaction although the bond enthalpy calculation for HF elimination gives an endothermic result. In (a), the diagram is for standard enthalpy changes. For (b), the diagram refers to an electronic structure calculation. Cycle 2 and Methods Evaluations The second round of experimental work has students use the model fluoromethanes to examine how basis set and methods choices affect accuracy and computational time. The choices suggested in the experiment are shown in Table 1, where the C-F bond lengths calculated are compared to the experimentally determined value (23). Depending on an instructor’s time and number of students, this set of choices can be truncated or expanded. Table 1. Basis set and methods suggested for students to test in Cycle 2 with sample data for CH3F C-F bond length (Å)a Method Basis set

HF

B3LYP

MP2

6-31G*

1.36

1.38

1.39

6-311G*

1.36

1.39

1.39

cc-pVDZ

1.38

1.42

1.38

a Experimental value is 1.38 Å (23).

56

Using the electronic energy, C-F bond length, C-F and C-H stretching frequencies, and heat capacity, students create tables of results similar in layout to Table 1. These are compared to the experimental and computational results at the CCBDB3, and students determine the best method to reproduce accurate results. There are enough different options that teams will need to share data to complete the analysis. After choosing a method based upon accuracy, students are introduced to the concept of N4 scaling of computational methods and prompted to predict calculational times for fluoropropanes. Our testing suggests N4 is an overestimate, but it is a reasonable rule of thumb (see Figure 3). Students then revise their decision about the “best” method for calculation.

Figure 3. Scaling analysis for propane through perfluoropropane geometry optimization (employing symmetry and initial MM optimization). Optimization times are 10x faster for HF 6-31G* than B3LYP 6-31G*. HF optimization scales as N3.5; B3LYP scales as N2.4. All calculations were done on 1 core (Jetstream) using GAMESS version 20 Apr 2017 (R1). Finally, teams are asked to reevaluate their prediction of which fluoropropane would best replace HFC-227ea using the results from Cycles 1 and 2. The work in the experiment to this point is directed at providing students with sufficient experience and information to make a prediction about which fluoropropane would make a suitable replacement and to make a cost-benefit decision about which computational method would be preferred. The experiment will produce an analyzable result even if students make “wrong” choices here, but if students choose a calculational method which will not allow them time to do all the calculations, guidance may be necessary to push them toward a better option. Cycle 3 and Selecting a Final Candidate In order to determine the enthalpy of the HF elimination reaction, students must perform geometry optimizations and frequency calculations on the reactant fluoropropane as well as the product fluoropropene and HF using the same basis set and method. A particular fluoropropene is the product for two different fluoropropanes, so student teams are encouraged to consider two 57

fluoropropane reactions at a time. Students were also required to have at least one team perform calculations on HFC-227ea for comparison. After performing the calculations, students record Eelec (0 K) and Cv. Through guiding questions, students are led to obtain the zero point energy and the thermal correction to the enthalpy to correct their values for ΔEelec (0 K) for the reaction to (298 K). Postlab Questions and Experiment Extensions In POGIL-PCL labs, students work in their teams, with instructor guidance, to complete data analysis cooperatively. Hence, post-lab questions presume the students have already reached their conclusions. For this experiment, one question encourages the students to explore discrepancies between the standard bond enthalpy value and the electronic structure values for reaction enthalpy—as it turns out, fluorine compounds have wide discrepancies in bond enthalpies. Another has students evaluate the effect of the number of fluorines on the vibrational zero point energy and the vibrational thermal correction to the enthalpy. Increasing fluorines should decrease the zero point energy since the much larger mass results in lower frequency vibrations. The vibrational thermal energy correction is larger, however, since the lower frequency vibrations are populated and C-H stretches are too high to be populated at room temperature. A few other questions have students explore whether fluorinated butanes or cyclopropanes would make suitable fire suppressants. These questions can be answered relatively superficially, but some could be expanded to include another round of calculations or a separate experiment or project. Our expectation is that only a few would be assigned. This computational experiment could also lead to more sophisticated statistical mechanics calculations of heat capacities and enthalpies at various temperatures. We considered that as a fourth stage of the experiment, but rejected it as making this experiment too unwieldy. Lab Reports The subject material of this experiment would lend itself to alternative forms of lab reports. Teams could give oral presentations of the data in order to defend a particular replacement option. The lab can be framed as a request from a work superior for the analysis, and the report could be written as a response to such a request.

Implementation Details by the Authors The experiment was developed to be platform-independent. Platforms previously used by the authors include Gaussian03W (24), WebMO (25) (as a front end for Gaussian), NWChem (26) with ECCE (27) as a front end, and Chem Compute as a front end for GAMESS (28). All the authors are reasonably facile with both computational software and computing environments, however, and being platform-independent does little to help instructors lacking experience, hardware, and software. The work by Perri with Chem Compute (described further in Chapter 7 of this volume) has been done to address difficulties faced by professors with minimal experience. Local Environments Three of the authors have run this experiment with students. Two are at small schools and one at a medium-sized (on-campus enrollment of 18,000) regional university. All have small physical 58

chemistry enrollments. The computing environments at the schools differ, however, as shown in Table 2. While all utilized the bring your own device (BYOD) model, local software resources included NWChem, WebMO as a front end to Gaussian, or Gaussview (29) as a front end to Gaussian. Two of us used the Chem Compute server. Table 2. Local teaching and computing environments for the authors Author

Location

Times expt. used

Average no. of students

Chem Compute used

Environment

Berghout

Utah

3

7

Y(1)a

BYODc

Reeves

Alabama

3

3

Y(2)b

BYODc

Singleton

Iowa

2

1.5

N

BYODc

a Used

once with Chem Compute; other times with NWChem. time with Gaussian 03W. c Bring Your Own Device.

b Used

twice with Chem Compute; other

Computational Barriers and Errors Teaching a lab which utilizes computational chemistry has multiple barriers for the students. First, there is the lab content itself. Novices to the computational chemistry software will struggle with an array of menus and contextual click actions (especially when building complicated molecules). The computational environment itself leads to additional difficulties; for example, filename conventions, default “save” locations, unfamiliar operating systems (unix shells, terminal commands), and supercomputer queueing are not commonly encountered by chemistry majors. In the initial phases of developing this experiment with the Chem Compute server, students were building their molecules with downloads of shareware programs MacMolPlt (30) or Avogadro (31). In the “bring your own device” (BYOD) model, some students were using one graphical interface or the other depending on whether their laptop was Mac or PC. There were more problems with helping students navigate these programs than with completing the calculations and analyzing the results. The latest version of Chem Compute (chemcompute.org) includes a database search functionality. Typing in “1,1,1,2,3,3,3-heptafluoropropane” will load in the appropriate molecule. A molecule drawing javascript applet is also included so that students can draw molecules on the web page as well. A batch submission interface is provided as well, so that instructors can enter all the fluoropropanes into a csv file and Chem Compute will analyze all of them, returning information about the run time required and thermodynamics values / energies calculated. This gives instructors an easy way to evaluate parameters such as basis set choice before assigning to students. Facilitation Notes Guided inquiry methods require instructors to monitor student discussion or at least to have checkpoints to ensure that student teams don’t veer too far afield. In this experiment, there are several sticky points for students. First, having students develop a Hess’s Law diagram (as in Figure 2) specifically for a chosen reaction requires patience. In our initial naiveté, we thought assigning the question was sufficient. Students do not, as we learned, typically know what a Hess’s Law diagram is without prompting. In the end, we provided templates for them. While the templates helped, it did not make the question “easy.” 59

In three places, students have to make a choice and rationalize it. They must • Choose a basis set and method using scaling calculations and cpu data from CH3F and CF3H calculations • Choose a fluorocarbon to replace HFC-227ea and rationalize why it might be a reasonable choice based upon descriptions of the mechanism of HF elimination and the mechanism of fire suppression • Evaluate, using the electronic structure calculations, whether any of the chosen molecules will make suitable replacements for HFC-227ea. At all three of these points, it is vital to encourage appropriate decisions from the data; one method is to require the students to articulate their decision with the Toulmin model (32), making explicit use of claim (answer), evidence (data), and warrant (reasoning). As an example, consider the choice prompted at the end of cycle 2 where students balance accuracy of calculations against computational time from N4 scaling. The student handout reads “Review the information from the previous two questions in the context of the time available to perform further calculations. Does that change the class perspective on which method/basis set combinations should be used for further calculations?” There is no absolutely correct answer to this question. Students are asked to make a judgment call where accuracy must be balanced against available time. One class may choose to do a “quick and dirty” calculation because they are in a time crunch. Another class may choose to work outside class and do longer calculations with higher accuracy. The experimental objective is to have the students make a judgment call within the set of choices and to rationalize that judgment from the available data. Similarly, the teams may not pick the ideal candidates for testing as substitute fires suppressants. The individual instructor may choose to provide hints about heat capacity or permit other rationalizations as long as they are adequately justified. Related to the issue with the Hess’s Law diagram is guiding students to recognize the corrections which must be made to ΔEelec (0 K) to obtain (298 K). The correction terms are not obvious, and the places to find them in the output also require guidance. The last sticky point to mention is in data organization. Ensuring that all the necessary fluoropropanes and fluoropropenes (and HF) are calculated and the data are saved in recognizable files is not automatic for the students. Student Reception and Response The most gratifying aspect of this experiment is the student engagement with the “real-world” problem. Many of us found the students eager to test whether they could find an acceptable alternative to HFC-227ea. Classroom discussion about the article was lively. The structure of this experiment forces students to draw a conclusion. Without specific interventions, student lab reports have a tendency to present results and calculations without further interpretation. In this experiment, the “specific intervention” is the requirement that an alternative fire suppressant molecule be tested and either recommended or not. The report isn’t complete with a presentation of only the numerical values. We have worked with small numbers of students; hence, we can only offer an anecdotal result that students will make a choice and support it with the data in their notebooks and lab reports.

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Community of Teaching Before the launch of the POGIL-PCL project, none of the five authors knew each other. Before the 2015 workshop where the work on this experiment began, only two of the authors had previously collaborated (Reeves and Whitnell). The evolution of this experiment has involved three workshops, several Skype meetings, piloting at three institutions, and has resulted in two presentations (at the 2016 BCCE and the Fall 2017 ACS National Meeting). The collaboration for this experiment is an example of the success of the POGIL-PCL grant in fostering a community of physical chemistry professors.

Conclusions With this experiment, there are now three computationally-based POGIL-PCL experiments with differing learning objectives. While designed to be platform-independent, they are all capable of being run on the web-based Chem Compute server free of charge. This experiment, exploring the thermochemistry of HF elimination from fluoropropanes, has been found to engage students due to the real-world problem it addresses. With the spread in popularity of web-based servers using graphical interfaces such as WebMO and Chem Compute, computational chemistry is accessible to even the casually aquainted chemistry professor. It is no longer necessary to have either the institutional resources or personal abilities to purchase and maintain the software. With the set of POGIL-PCL computational experiments, we hope to make guided inquiry computational experiments accessible and available to anyone interested in using them. Finally, we recognize that without the POGIL-PCL project, this collaboration would not have occurred. The workshop model which brought together professors and lab coordinators was a driving force to create new experiments using the guided inquiry paradigm.

Acknowledgments The authors would like to thank their respective departments and all their students for support. Many thanks go to the other participating faculty in POGIL-PCL as well as PIs Sally Hunnicutt and Alex Grushow. (Four of us also thank PI Rob Whitnell.) The POGIL-PCL project was funded under NSF-DUE 1044624.

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22. Operationalized POGIL Process Skill Definitions. The POGIL Project November 17, 2015. 23. Demaison, J.; Breidung, J.; Thiel, W.; Papousek, D. The Equilibrium Structure of Methyl Fluoride. Struct. Chem. 1999, 10, 129–133. https://doi.org/10.1023/A:1022085314343. 24. Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Montgomery, J.; Vreven, T.; Kudin, K.; Burant, J.; Millam, J.; Iyengar, S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J.; Hratchian, H.; Cross, J.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R.; Yazyev, O.; Austin, A.; Cammi, R.; Pomelli, C.; Ochterski, J.; Ayala, P.; Morokuma, K.; Voth, G.; Salvador, P.; Dannenberg, J.; Zakrzewski, V.; Dapprich, S.; Daniels, A.; Strain, M.; Farkas, O.; Malick, D.; Rabuck, A.; Raghavachari, K.; Foresman, J.; Ortiz, J.; Cui, Q.; Baboul, A.; Clifford, S.; Cioslowski, J.; Stefanov, B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R.; Fox, D.; Keith, T.; Laham, A.; Peng, C.; Nanayakkara, A.; Challacombe, M.; Gill, P.; Johnson, B.; Chen, W.; Wong, M.; Gonzalez, C.; Pople, J. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford CT, 2003. 25. Schmidt, J. R.; Polik, W. F. WebMO; WebMO LLC: Holland, MI, 2018. 26. Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; de Jong, W. A. NWChem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477–1489. https://doi.org/10.1016/j.cpc.2010.04.018. 27. Black, G.; Schuchardt, K.; Gracio, D.; Palmer, B. The Extensible Computational Chemistry Environment: A Problem Solving Environment for High Performance Theoretical Chemistry. In Computational Science — ICCS 2003; Sloot, P. M. A., Abramson, D., Bogdanov, A. V., Gorbachev, Y. E., Dongarra, J. J., Zomaya, A. Y., Eds.; Lecture Notes in Computer Science; Springer: Berlin, Heidelberg, 2003; pp 122–131. 28. Gordon, M. S.; Schmidt, M. W. Advances in Electronic Structure Theory: GAMESS a Decade Later. In Theory and Applications of Computational Chemistry; Dykstra, C. E., Frenking, G., Kim, K. S., Scuseria, G. E., Eds.; Elsevier: Amsterdam, 2005; Chapter 41, pp 1167–1189. https://doi.org/10.1016/B978-044451719-7/50084-6. 29. Dennington, R.; Keith, T.; Millam, J. GaussView, Version 5; Semichem, Inc.: Shawnee Mission. KS, 2009. 30. Bode, B. M.; Gordon, M. S. Macmolplt: A Graphical User Interface for GAMESS. J. Mol. Graph. Model. 1998, 16, 133–138. https://doi.org/10.1016/S1093-3263(99)00002-9. 31. Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. J. Cheminformatics 2012, 4, 17. https://doi.org/10.1186/1758-2946-4-17. 32. Becker, N.; Rasmussen, C.; Sweeney, G.; Wawro, M.; Towns, M.; Cole, R. Reasoning Using Particulate Nature of Matter: An Example of a Sociochemical Norm in a University-Level Physical Chemistry Class. Chem. Educ. Res. Pract. 2013, 14, 81–94. https://doi.org/10.1039/ C2RP20085F.

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Chapter 6

Process Oriented Guided Inquiry Learning Computational Chemistry Experiments: Revisions and Extensions Based on Lessons Learned from Implementation Robert M. Whitnell*,1 and Melissa S. Reeves2 1Department of Chemistry, Guilford College, Greensboro, North Carolina 27410, United States 2Department of Chemistry, Tuskegee University, Tuskegee, Alabama 36088, United States *E-mail: [email protected].

The increasing prevalence of computational chemistry results in the chemical literature, either in standalone work or as a complement to experimental results, calls for more attention to these methods in undergraduate education. Our previous work has described POGIL (Process Oriented Guided Inquiry Learning) electronic structure and molecular dynamics experiments for the physical chemistry laboratory course. Further development of these experiments has included continuing review by physical chemistry lab instructors and testing in both faculty workshops and with students in their courses. The feedback from experiment review and student testing demonstrated that a significant barrier to adoption was the difficulty of both the instructor setting up and students running the calculations. A further complication was instructor unfamiliarity with the underlying theory, particularly for topics such as molecular dynamics simulations. Even motivated instructors may then choose not to adopt these experiments. This chapter describes approaches that make computational chemistry experiments more accessible to physical chemistry lab instructors and students. These approaches can parallel strategies for training students on high-end equipment in standard experiments for the physical chemistry lab course. Simpler interfaces for the programs and interactive background tutorials on the theory and methods can further develop the comfort level of instructors and students. Instructors can also tune each experiment to meet their desired degree of complexity while maintaining the fundamental learning objectives.

© 2019 American Chemical Society

Introduction The presence of published computational chemistry experiments and exercises for the chemistry curriculum has grown significantly over the past several years. In 2014, we published a description of two computational chemistry experiments in the POGIL-PCL (POGIL for Physical Chemistry Laboratory (1)) model (2). One experiment, “What makes an electron a valence electron?”, focused on electronic structure calculations of first and second row atoms and diatomic molecules to explore possible answers to the title question. A second experiment, “What factors govern the escapability of a molecule from a liquid?”, has students use molecular dynamics calculations to calculate the enthalpy of vaporization of pentane isomers, then analyze the detailed data to illustrate the significance (or lack thereof) of different intermolecular and intramolecular energy components in addressing the title question (3). Both experiments have seen increasing use among the POGIL-PCL community Our review of computational chemistry in the chemistry curriculum found a variety of electronic structure experiments available in the chemical education literature (including in textbooks), but fewer that explored theory and application of molecular mechanics and molecular dynamics calculations. Since then, there is an increasing recognition of the importance of building computational chemistry concepts and techniques into chemistry curricula, and not just for physical chemistry courses. Elmore, for example, notes the importance of molecular dynamics simulations in biochemistry as a motivation for bringing them into standard biochemistry courses (4). A review of recently published computational chemistry experiments shows a number of goals and learning objectives, some of which are described explicitly in the article or supplementary materials, others of which are implicit. Of particular note are the description of learning objectives in the experiment of Kholod, et al., for the docking of ligands to DNA (5) and the presence of clear research questions in the experiment of Kinnaman, Roller, and Miller that has students use molecular dynamics to explore the effectiveness of different classical force field models of water interactions (6). Computational chemistry experiments typically have one or more learning objectives or skill development goals, including • Following protocols to use the specified software in running the calculations; • Visualizing primary results—molecular orbitals, energy level diagrams, molecular dynamics trajectories; • Interpreting secondary results—vibrational frequencies, partial charges, dipole moments, classical energy decomposition; • Examining the effects parameters such as basis sets in electronic structure calculations or force fields and simulation time in molecular mechanics and molecular dynamics simulations; • Connecting and comparing the computational results to experimental data; • Developing theoretical foundations, such as the Schrödinger equation for atomic and molecular systems or Newton’s equations to simulate the dynamics of molecules; • Applying program acquisition, development and maintenance best practices including the use of source control tools such as GitHub (https://github.com); • Collecting data through mining of output files or through tools provided by the computational chemistry software or by the instructions;

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• Modifying or writing configuration files to explore different computation and/or simulation parameters; • Writing programs or modifying existing code to develop fundamental knowledge of implementing computational chemistry algorithms or to extend the functionality of the code; and • Evaluating the precision and accuracy of computational chemistry results. The wide range of possible learning objectives requires instructors to evaluate which objectives are most significant for their goals in using the experiment. Furthermore, the goals of the author who wrote the experiment may differ from the goals of the instructor who wishes to use it for a specific class with a specific set of students who have a specific background. To that end, instructors would typically ask the following questions: What can we assume students are ready to do? What do we want them to learn in the process of doing the experiment? These two questions are not significantly different from what a physical chemistry lab instructor would ask before adding any experiment to their curriculum. For example, an instructor may wish to add the experiment that studies the acidity of β-naphthol in ground and excited states through absorbance and fluorescence spectroscopy, an experiment for which there is a textbook version (7) and a POGIL-PCL version (8). The instructor might then ask what would we want students to know about fluorescence spectroscopy? What would we want them to know about a fluorimeter? In principle, what might be considered the primary learning objectives—mapping acidity values on to energy level diagrams and explaining the results through consideration of electron behavior in the neutral molecule and anion—do not necessarily require significant knowledge of the practice of fluorescence spectroscopy. We expect, however, that most physical chemistry instructors, even those trained in computational chemistry as the authors are, would have students explore at least the rudiments of obtaining a fluorescence spectrum and how that differs from an absorbance spectrum. Many instructors, depending on their comfort and background, may ask students to delve much further into the theory and practice of fluorescence spectroscopy. For each experiment, physical chemistry lab instructors make a judgment on this balance among theoretical foundations, knowledge of equipment functioning and procedures, data collection, summarizing and analyzing results, building connections to future work, and more. Computational chemistry experiments are no exception to this balance; at the most basic level, all that is needed in the previous sentence is replacing the word “equipment” with “software.” As we have seen in our development of computational chemistry experiments, any notion that a computational experiment is easier for students because it is on the computer or because of supposed student facility with technology quickly falls apart when an instructor attempts their use. A variety of issues can arise when an instructor takes a computational chemistry experiment from the literature and implements it in their course. Our experience and our examination of recently published experiments show several potential problems. • Supplemental materials or software referred to in the experiment may no longer be available (9). Not every journal archives supplemental material in the way that the Journal

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of Chemical Education does. Software may become unavailable, unsupported, or transition from open source to commercial. Experiments assume that faculty members can become proficient with what are now more esoteric software (using a command line, for example) and transmit that proficiency to students. One recent paper notes that “…we provide students an explicit set of instructions because the software is complex and oriented to the command line. Understanding student mistakes and being prepared to respond to them does require that instructors are quite familiar with the MD software (10).” The computational process is often invisible to the students (11, 12). The calculations may happen on a remote server or on a local computer, thereby enhancing a student’s cognitive load in considering what is actually happening, and the feedback may only come in the form of obscure text on a terminal screen or in a text file. When the calculations are done, the program output is often much more complex than what is required for analysis, with some authors (present ones included in earlier versions of their experiments) requiring students to do a deep dive into the output files in order to find the specific information needed (11). Given the relative dearth of computational chemistry experiments in the literature, those writing experiments are typically considerably more experienced in the theory, techniques, and tools. Even with detailed background in a published article and supplementary information, the instructions (and reasons for the instructions) that are obvious to the author may be opaque for the students and their instructors (13). Approaches such as detailed pre-lab videos that could also be used in lab can mitigate this problem but not always address the particular issues that arise in a specific setting (14, 15).

These issues certainly do not only apply to computational chemistry experiments, especially as the software required to run many pieces of lab equipment becomes more complex and requires more frequent updating. But the relative unfamiliarity of using computational chemistry experiments in the physical chemistry lab course creates an additional barrier to using the experiments, especially when one or more of the issues enumerated above arises. We describe here how we have approached several of these issues from the POGIL-PCL perspective. Our approach to computational chemistry experiments is to have students observe and experience how computational chemistry helps chemists understand behavior at the atomic and molecular level and, as appropriate, connect that sub-microscopic behavior to macroscopic behavior. This focus lowers the barrier to experiment implementation and student success. And it does not preclude instructors from having students build deeper knowledge of underlying theory, computational methods, and specific programs as desired. One example we’ll address here is how to have students develop a background in the underlying theory and models in a way that can be done as part of the experiment or as preparatory or postexperiment work. We use the concept of Explorable Explanations introduced by Victor (16) as a way of encouraging “active readers” who can explore both specific examples and general conclusions through manipulating quantities embedded in the text. The text, broadly defined to include figures, tables, and equations, updates in real-time in response to the reader’s manipulations. We describe an application of this concept in the context of molecular dynamics simulations, providing students with interactive guided explorations of force fields, system preparation, energy minimization, and molecular dynamics methods.

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Finally, we note that there are a number of interactive computational tools that are not in the realm of this discussion. Examples include the PhET interactive simulations (17) and the ODYSSEY® interactive molecular dynamics environment (18). Both have tremendous value both in their ability to introduce concepts and to have students explore parameters and build explanations. For the physical chemistry lab course, however, we wish to focus on students using software tools and developing skills that can transition to use in a research environment, even if many students in the physical chemistry lab course may not pursue a research career. Just as with most pieces of equipment used in experiments for the physical chemistry lab course, students will typically not explore everything that the software can do. But they will have the foundation to move on to the next level of complexity.

Testing and Refining POGIL-PCL Computational Chemistry Experiments The experiments presented in our earlier work (2) have seen increasing interest from physical chemistry lab instructors with 8-10 instructors now using one or both experiments regularly in their courses. However, getting to even this level of adoption was challenging because the original versions of these experiments exhibited several of the issues described in the previous section. For example, instructors who used early versions of the valence electron experiment typically had a high comfort level maintaining electronic structure calculation software on their own servers or computers and guiding students in it use. Depending on the tools the instructors used, students would be presented with the energy levels from the calculation or would have to comb through the output files to find them. Therefore, instructor comfort and facility with electronic structure correlations became directly correlated with a willingness to adopt the valence electron experiment. Early versions of the enthalpy of vaporization experiment required similar instructor facility. Those versions provided detailed instructions for installing software and running the calculations from the command line, followed by extracting energy information from the text output files. Later versions included self-contained packages for Mac OS X and Windows that included both the software and scripts that provided a simpler—but still text based—interface for running the calculations and extracting the desired energy information. Our observations with our own students and feedback from other instructors made clear how the complexity of implementing and running these experiments led to a focus on getting the results and not on how students could interpret those results and learn about atomic and molecular level behavior from them. Students are very technically savvy, but the technologies they are most comfortable with were not the ones needed to run these calculations. The primarily text-based interfaces, sometimes requiring significant work on an unfamiliar command line, meant that instructors were focused more on educating students about how to run the software rather than the science that could be obtained from it. We also frequently heard from instructors who had no specific training in computational chemistry about difficulties they had in running the experiment as we had intended. Many of the issues arose as instructors made the software work on the computers available to them in a way that their students would be able to use the tools effectively. When the software did not work as intended, or when there were problems with the calculations because a student did not enter a parameter correctly, for example, the experiment could grind to a halt while the problem was being solved, often through consultation with the authors. (And these issues were not always limited to instructors who had less familiarity with computational chemistry.) Both authors would occasionally

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run into similar problems in their own classes—the number of ways in which the instructions could be misinterpreted or followed incorrectly was substantial. As computational chemists who became those teaching physical chemistry lab at our institutions, with an understanding that we would implement a variety of experiments that were not always familiar to us, we sympathized greatly with our colleagues now trying to bring computational chemistry into their courses. Our approach to delivery of these experiments therefore continued to focus on how to provide a student experience similar to what students and instructors should be able to expect with any other instrument they use. Such an approach would include a clear, robust interface for students to set up and submit their calculations. At the most basic level, students would find running a calculation as straightforward as preparing a sample, filling a cuvette, and obtaining a spectrum. More functionality would be available for students to run more complex experiments, explore the theory and computational methods, or move into performing independent research. Fundamental data from the calculations is available to enter into other analysis tools or for graphing. And the system should typically work with minimal maintenance on the part of the instructor. For the valence electron experiment, a package such as WebMO (19) meets most of these criteria, provided there is sufficient institutional support for installing and maintaining the software (or the instructor has sufficient skills and time to maintain the software themselves). Students can readily set up and run a calculation, view energy levels and orbitals, and have access to the full output in order to perform more detailed analysis. Providing students instructions to run the valence electron experiment using WebMO is no more difficult than instructions to run a spectrometer. Physical chemistry faculty can rapidly develop enough WebMO knowledge to support students in their work. But the assumption that faculty can have access to a fully supported installation of WebMO is often not valid, particularly at smaller, underfunded institutions. And the use of classical force fields in WebMO is limited to molecular mechanics; no dynamics is available. We also encourage the use of Chem Compute (https://chemcompute.org), a web-based system that provides job setup for both electronic structure and molecular dynamics calculations (20), access to servers for running the calculation, and a visualization environment. The entire system is based on freely available (and often open-source) software. Our collaboration with Mark Perri, the developer and maintainer of Chem Compute, has resulted in an effective platform for both the molecular dynamics and valence electron experiments. Because Chem Compute was built to support student calculations, for both classes and independent student research, the focus is on simplicity of setup and clarity of running the calculations and delivering the results. Because Chem Compute provides access to servers for running the calculations, the level of instructor support and maintenance becomes small. For the purposes of the valence electron and enthalpy of vaporization experiments, the advantages of such a system becomes clear. Instructors and students can focus on the primary goals and learning objectives of the experiment without delving deeper into how to perform the calculations or extract results. Through systems such as WebMO and Chem Compute, faculty have much greater ability to introduce computational chemistry in their physical chemistry lab courses. As with any other instrumentation used in physical chemistry lab, instructors have more choice in matching their own expertise, experience and comfort level using these tools with how they wish students to use them. For all instructors, the valence electron and enthalpy of vaporization experiments are more accessible because of these tools, and increased implementation is a result.

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Faculty Development and Computational Chemistry Experiments A fundamental principle of the POGIL-PCL project is that development and adoption of guided inquiry experiments in physical chemistry is enhanced by a program of faculty development. The project’s faculty development program is centered around in-person and online workshops that serve to provide instructors with opportunities to experience existing experiments, work on the development of new experiments and ones in progress, and participate in a community of physical chemistry lab instructors. Using a survey of attendees, Stegall, et al. have evaluated and described the effectiveness of the POGIL-PCL in-person workshops, showing that instructor participation in the workshop correlated highly with implementation of POGIL experiments in their physical chemistry lab courses (21). The development and adoption of the valence electron and enthalpy of vaporization experiments have benefitted substantially from in-person development and implementation workshops in 2013, 2014, 2015, and 2018, and online workshops (one for each experiment) in 2017. We describe here what we have learned from faculty who have experienced these experiments at workshops and how that has affected continuing experiment development. We focus on detailed survey comments from the 2017 online molecular dynamics workshop, and those comments reflect what we have heard from participants in other workshops as well as those who have tested the experiment in their classes. Reports from the participants on the strengths of doing the experiment in a workshop environment focused on several common themes. The opportunity to try the experiment with the author present led to increased confidence in attempting implementation, particularly when the experiment is in an area with which they may not have much familiarity. That was further enhanced by the interaction with other colleagues and being able to share information and ideas about student approaches to these experiments, pacing and presentation of the material, and other practical matters. These comments are much in line with the observations of Stegall, et al. about the importance of personal influence in the decision to adopt new experiments (and new approaches) for the physical chemistry lab (21). Improvements suggested by participants included issues of both experiment design and implementation. As our students continually say, more time for completing the experiment would always be better, particularly in the ability to reflect on what is happening as they’re doing the experiment and after all the results are available. Specific design considerations included having students practice doing computational work before coming to lab in order to make lab time more efficient or even doing all the computational work and using a more flipped-classroom paradigm with a focus in class on analysis and discussion. And one suggestion was to “create a ‘mini-activity’ that introduces students to the basics of what is computed during a molecular dynamics simulation.” We will explore this idea in the next section. A common theme among participant insights was how important it was for instructors to have a student experience in the workshop. For example, one participant asked “Do students feel this rushed when I give them a certain time period for a particular portion of an experiment?” Others focused on what happens as students hit technical barriers or balancing building process skills (some as specific as using a spreadsheet) against gains in learning content. And it’s always gratifying to see a participant get at the primary goal of having students do guided-inquiry experiments: “This [how the group worked] reminded me of the fact that team-building and making collective decisions about how to collect and interpret data, as well as how to solicit input from all group members, is an important skill for our students to develop—especially in teaching environments that implement evidence-based pedagogy.” 71

From these comments and our observations at the workshops, we gather that instructors do obtain a better sense of student challenges and insights when the experiment they’re trying out is in an area unfamiliar to them. Computational chemistry is certainly such an area; we hear from instructors comments similar to students saying “computers don’t like me.” Placing instructors in an environment where they may be just as uncomfortable as students, but with scaffolding and facilitator support directed toward building comfort with implementation, is an effective way of encouraging instructors to adopt new and challenging—for them and for their students—experiments.

Building More Background with Explorable Explanations The preceding section addresses an implementation question: How can physical chemistry lab instructors effectively use computational chemistry in their courses when their expertise and comfort level is in other areas of physical chemistry? Even when the implementation of experiments such as we describe here is successful, that does not address everything an instructor might wish to accomplish. A continuing issue with computational chemistry experiments is balancing several desirable goals: building student knowledge about underlying theory and methods, approaches to setting up and running reliable calculations, and analyzing and interpreting results in a way that expands student knowledge about models of chemical systems and what they can tell us about molecular behavior. Achieving all three goals in the lab setting is problematic because of time constraints. The valence electron and enthalpy of vaporization experiments each typically require two three-hour lab periods (although instructors can reduce that by having students do some of the work outside of lab). They therefore emphasize the latter two goals to provide a clear and achievable focus in the available time. For the valence electron experiment, the fundamental background of the Schrödinger equation for atomic and molecular systems is typically covered in students’ previous or concurrent coursework, perhaps not including all necessary details, such as the Born-Oppenheimer approximation. On the other hand, students are unlikely to have worked with the background ideas for molecular dynamics calculations. Students may have seen specific elements such as the use of a harmonic oscillator potential energy function to approximate vibrational potential energy. But the idea of using such potential energy functions to create a classical force field is far less likely to have appeared. We therefore want to provide an approach for a student to develop this background knowledge that takes advantage of what we know about effective learning while acknowledging the constraint on student and instructor time, particularly time in the classroom. Explorable Explanations (EE) (16), a concept developed by Bret Victor that has many pedagogical antecedents, are applied here to allow students to develop that understanding. An EE encourages “active readers” who can explore both specific examples and general conclusions through manipulating quantities embedded in the text. The text, broadly defined to include figures, tables, and equations, updates in real-time in response to the reader’s manipulations, and should be accessible from any modern browser. We have developed an EE for the force fields, potential energy minimization, and solution of equations of motion that are required for molecular dynamics calculations. EE development and use is enhanced by taking advantage of data visualization tools that can run in any modern browser. For example, the work presented here uses the Observable interactive notebook platform (22) as the framework for text and equations with figures and molecular models incorporated using the d3.js data visualization (23) and the 3dmol.js molecular visualization (24) JavaScript libraries. This combination of frameworks provides several useful tools to create interactive, inquirydriven explorations of molecular dynamics calculations. 72

• Plots and equations both support inquiry through immediate feedback, scrubbable (25) numbers, and interactions with other dynamic elements, such as sliders. • Force-based diagrams can mimic particle interactions providing for highlight of specific concepts without carrying all the weight of a full simulation. • Support for KaTeX and Markdown give a rich, dynamic text environment that integrates with all other visual and user control elements. • All code is accessible and editable, but can also remain hidden. Users can therefore focus on the content without distraction, but they can also choose to modify the simulation at the code level. • Everything is written in JavaScript, giving access to many more visualization and other frameworks than what we have used here. The text includes questions that guide the student through specific manipulations of the interactive graphics, much in the style of a POGIL activity. Students can complete the exercises individually (in which case the activity may be seen as more of a worksheet) or they can be used with teams in a standard POGIL implementation. We describe two examples of EEs for molecular dynamics here. A full appreciation of this work requires interacting with the EE using a web browser. A sense of what an EE can accomplish can be gathered from this discussion and the accompanying figures. Several of the molecular dynamics EEs focus on potential energy functions for both intermolecular and intramolecular interactions. The EE for intermolecular interactions (26), shortrange dispersion or van der Waals and long-range Coulomb, has several features common to all the potential energy EEs. The EE, part of which is shown in Figure 1, allows for exploration of parameters that can affect the interaction potential energy. In this case, a Lennard-Jones (LJ) function is used to model the short-range interactions, and two relevant parameters are the well depth and the distance at which the potential energy is zero (a slightly smaller distance than the location of the minimum). The EE displays the full interaction, both attractive and repulsive components that contribute to the interaction, and gives the student control over both parameters of the LJ potential (and the exponents as well). Similar functionality is available for the Coulomb potential with charges being the primary adjustable parameter. Questions guide students to explore the balance between attractive and repulsive interactions and the effect of parameters on the overall shape of the potential. Students also explore the concept of long-range and short-range potentials and apply those concepts specifically to the pentane isomers used in the enthalpy of vaporization experiments. A different kind of EE has students develop concepts relevant to performing molecular dynamics simulations. For example, one approach to simulating bulk systems (as compared to gas phase clusters or systems confined to a box with walls) takes advantage of periodic boundary conditions, with duplication of the simulation box on all sides. Many discussions of periodic boundary conditions are accompanied by a single static figure that can require abstract thinking and mentally moving parts of the figure to develop a notion of how periodic boundary conditions model bulk behavior (27). The periodic boundary condition EE (28) shown in Figure 2 takes advantage of the force-based layout present in the d3.js environment. A two-dimensional model of atoms in a simulation box is shown both without periodic boundary conditions, to simulate the gas phase, and with, to simulate the bulk. A student can move an atom in the simulation box and see how each of the periodic replicas move in turn. As an atom is dragged out of the simulation box, its replica comes in on the opposite side. Releasing the atom relaxes the system to a local minimum. Questions guide the student to 73

compare the simulation systems for gas and bulk and explore why periodic boundary conditions give a better description of bulk behavior.

Figure 1. Explorable Explanation screenshot for Lennard-Jones potential (26). The values of σ and ε in the upper right are scrubbable. When those are changed, the values in the equation are updated. Moving the mouse updates both the markers on the plot and the values in the table. This interactive plot is embedded in a complete activity that provides guided exploration.

Figure 2. Explorable Explanation for periodic boundary conditions (28). The circles in the central box use a force-based layout. The user can drag one of those circles and each periodic replica will be highlighted. All circles will relax to a new stable configuration during the drag and when the mouse is released. 74

Through this combination of dynamic visualization and guided questions, our intent is to have students develop a better concept of how computational chemistry works and why we can generally expect that it will give good comparisons with experiment and reasonable descriptions of molecular behavior. Because each computational chemistry EE has a list of learning objectives, we will be able to evaluate student outcomes, first in our classes and then as other instructors adopt these tools.

Summary and Conclusion The development of the valence electron and enthalpy of vaporization experiments through a systematic testing, feedback, and revision process has proven successful in not only refining the experiments, but also encouraging and supporting instructor adoption in their courses. This development process has led to significant improvements in both experiment design and delivery. The experiments are now considerably more accessible to instructors who do not have substantial backgrounds in computational chemistry, particularly due to the use of the Chem Compute environment. However, just as with any physical chemistry experiment, instructors whose knowledge of the topic and goals for the course support their students doing deeper and more complex work, these experiments provide a foundation for more substantial work or student research projects. These experiments have already provided a foundation for other POGIL-PCL experiments, such as the computational thermochemistry experiment “How can we measure a reaction enthalpy without going into the laboratory?” described elsewhere in this volume (29). We have established a powerful combination of developing experiments within POGIL-PCL criteria (1), effective tools for faculty who do not have substantial computational chemistry experience to implement these experiments in their courses, and a framework for developing explanatory tools that can be used by individual students or student teams. This overall framework will support the development of future computational chemistry experiments.

Acknowledgments We thank Sally Hunnicutt (SSH) and Alex Grushow (AG) for their comments on and support for this work. We also thank Mark Perri for many useful discussions and adapting our experiments to the Chem Compute environment. This work would not be possible without the POGIL-PCL faculty community, whose review, testing, and feedback have resulted in improvements both in student instructions and instructor handbooks for the computational chemistry experiments. RMW especially thanks Elaine Marzluff for detailed testing and feedback on the enthalpy of vaporization experiment. This work was supported in part by NSF grant DUE-1044624 and DUE-1726066 awarded to SSH, AG, and RMW.

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Hunnicutt, S. S.; Grushow, A.; Whitnell, R. Guided-Inquiry Experiments for Physical Chemistry: The POGIL-PCL Model. J. Chem. Educ. 2015, 92, 262–268. Reeves, M. S.; Whitnell, R. M. New Computational Physical Chemistry Experiments: Using POGIL Techniques with ab Initio and Molecular Dynamics Calculations. In Addressing the Millennial Student in Undergraduate Chemistry; ACS Symposium Series 1180; American Chemical Society: Washington, DC, 2014; pp 71–90. 75

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22. Bostock, M. A Better Way to Code, 2017. https://medium.com/@mbostock/a-better-way-tocode-2b1d2876a3a0 (accessed June 22, 2018). 23. Bostock, M.; Ogievetsky, V.; Heer, J. D #x0B3; Data-Driven Documents. IEEE Trans. Vis. Comput. Graph. 2011, 17 (12), 2301–2309. 24. Rego, N.; Koes, D. 3Dmol.Js: Molecular Visualization with WebGL. Bioinformatics 2015, 31, 1322–1324. 25. “Scrubbing” is an interaction where a user can drag across an interface element to change its value and see an effect in real-time. A familiar example is dragging across a timeline navigating audio or video. A “scrubbable number” is a number that supports this kind of interaction: the user can drag across the number and see its value (and the value of anything that depends on its value) change. 26. Whitnell, R. M. How do we model the interactions between molecules (or between different parts of the same molecule)?. https://beta.observablehq.com/@rwhitnell/how-do-we-model-theinteractions-between-molecules-or-betwe (accessed July 14, 2018). 27. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids, 2nd ed.; Oxford University Press: Oxford, U.K., 2017. 28. Whitnell, R. M. What do we need to do before we can simulate molecular motion? Periodic boundary conditions. https://beta.observablehq.com/@rwhitnell/what-do-we-need-to-do-before-wecan-simulate-molecular-motion (accessed July 14, 2018). 29. Reeves, M. S.; Berghout, H. L.; Perri, M. J.; Singleton, S. M.; Whitnell, R. M. How Can You Measure a Reaction Enthalpy without Going into the Lab? Using Computational Chemistry Data to Draw a Conclusion. In Using Computational Methods To Teach Chemical Principles; Grushow, A., Reeves, M. S., Eds.; ACS Syposium Series 1312; American Chemical Society: Washington, DC, 2019; Chapter 5.

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Chapter 7

Chem Compute Science Gateway: An Online Computational Chemistry Tool Mark J. Perri,* Mary Akinmurele, and Matthew Haynie Department of Chemistry, Sonoma State University, 1801 E. Cotati Avenue, Rohnert Park, California 94928, United States *E-mail: [email protected].

The Chem Compute Science Gateway (chemcompute.org) is a free website where undergraduate chemistry students can easily setup a job, submit it to an XSEDE supercomputer, and visualize the output. Our website has several advantages over installing software packages locally. First, it is free to use and available anywhere on any device; it can be accessed by students off campus so that they can start a long job before class, leaving class time for data analysis. Second, jobs are run on XSEDE servers, enabling great computational power and long run times. Third, a web-interface is familiar to students, helping to put them more at ease with a difficult and feared subject. Fourth, several lab exercises are built into the website, eliminating the need for faculty to find or create computational labs. This free resource eliminates many barriers to computational chemistry such as cost of software, hardware, and faculty workload. This chapter describes the author’s early attempts and failures at using free computational packages in class, the web-based science gateway that was built to enable graphically-based access to these packages, and the successes encountered after using the gateway in classes at a primarily undergraduate institution.

Introduction History Years ago while teaching Physical Chemistry Lab for the first time I wanted our students to perform computational chemistry experiments. Our department had only one license for Spartan (Wavefunction, Inc.), a commercial package with an easy to use graphical interface (and no money to purchase more licenses). I tried having 12 students huddle around a single computer and perform some calculations. It went about as well as one would expect: one student did all the work and the rest worked on their social media accounts on their phones. I decided that I would find a way for all students to work on their own computers. Next year, (with much grumbling from IT) we © 2019 American Chemical Society

installed GAMESS (1), a free computational package, two other helper programs (Avogadro (2, 3) and MacMolPlt (4)), and some scripts that I wrote to help out with the process. Despite belonging to the “Digital Generation”, the students completely lacked command line skills and patience. Students complained and were mostly unable to correctly format an input file or spell file names (and extensions) correctly. After frantically running around the room fixing spaces, dollar signs, and DOS commands, I started working on a website to automate the process. The Chem Compute Science Gateway was first released locally in October, 2013 (5). Originally named GAMESS Web, the service was available only to Sonoma State University Undergraduates because of our University’s draconian firewall rules. This preliminary version of the website still required students to generate text input files and to download and view the output files themselves, but it handled job submission for them by assigning work to four desktops in my lab that I networked together using the Sun Grid Engine (SGE) Scheduler (6). I used the site in my Physical Chemistry class (second semester Quantum Mechanics lecture) with moderate success and found that even a primitive web interface was easier for undergraduate chemistry students to use than directly running GAMESS on the command line. I thought that other universities might benefit from this free tool. In January 2014 I convinced our IT department to allocate a small virtual machine (VM) to serve the website and it was then accessible to the outside world. The user base increased slowly, but eventually outgrew the computational capacity of the four desktops that I had networked together. In 2016, I turned to the NSF XSEDE Supercomputer Network (7) for a startup allocation on Comet, a supercomputer at the San Diego Supercomputing Center, and received 25,000 CPU-Hours (Service Units / SU) for calculations. The site had gotten so popular that large universities were using it and the small VM that Sonoma State provided to host the website was overloaded. The following year, I was allocated 25,000 CPU-Hours on Comet and another XSEDE supercomputer, Bridges (Pittsburgh Supercomputing Center), for computations. Importantly, I was also awarded 150,000 CPU-Hours on Jetstream (8) (Indiana University Pervasive Technology Institute) to host the website. Jetstream is an XSEDE cloud-based supercomputer, where users launch their own VMs for calculations or web hosting. Our current web hosting VMs on Jetstream are large enough to accommodate multiple institutions with hundreds of students simultaneously performing calculations. Barriers to Computational Chemistry While attempting to mount computational chemistry labs on a budget, I ran into three barriers. 1. Software: The cost of easy to use computational software can run thousands of dollars. Free software such as GAMESS (1) is available, but requires either command line knowledge to create an input file and run a job or installing third-party tools such as Avogadro (2, 3) and GamessQ (9). Viewing output files requires a third party program such as wxMacMolPlt (4). I have found that installing all these tools is just too burdensome and their use confuses the students. With Chem Compute, input files are created through a graphical user interface, run via batch scheduler (SLURM) (10), and output files are visualized using JSmol (11) integration. 2. Hardware: I originally tried running GAMESS locally in our University’s computer lab. Short jobs ran fine, but longer jobs are not possible with local resources; when one’s computer lab time is up, the next class comes in. At the end of my computational labs I require students to perform a calculation on a molecule of their choosing. Many of the 80

students choose to calculate IR or UV-Vis spectroscopy on a molecule for their research. These jobs typically take several hours to run and cannot be finished in a lab period. Any jobs beyond ~ 10 atoms require some dedicated server hardware. Our University and many like it do not have a University Cluster to use. Chem Compute makes use of the NSF XSEDE Supercomputer Network (7) (currently Comet, Bridges, and Jetstream) to run calculations using 1 core, 6 cores, or a full node (24 or 28 cores depending on the system). Jobs can run for as long as 48 hours, giving students plenty of time to do meaningful calculations. The web interface is accessible from anywhere, so students do not need to be in the computer lab to start a job or to view the output. 3. Experiments: Part of the barrier to computational chemistry is finding experiments / simulations to use in class. Many published experiments exist for General Chemistry (12–14), Organic Chemistry (15–20), and Physical Chemistry (21–26), but they usually require commercial software, and molecular dynamics experiments are not frequently published. If one has access to a different software package (or possibly even a different version) then the instructions require translation. I have spoken to many faculty who end up writing their own unpublished computational labs because the process is so daunting. This makes it difficult for departments without computational expertise to implement computational labs. Chem Compute contains several experiments that are ready to use. By clicking on an experiment a student is presented with background theory, a prelab (if applicable), and instructions overlaid on the web interface as they are doing the experiment.

Chem Compute Capabilities and Features In order to overcome the barriers encountered, I created the Chem Compute website. Chem Compute hosts two packages: GAMESS (1), an electronic structure software package, and TINKER (27), a molecular dynamics (MD) package. Anyone in the world can freely access the site and perform calculations on XSEDE (7) supercomputers. Guest users can run jobs for 1 hour on 1 core. Users can register an account on the site or login with their instutiton’s (or Google’s) single sign-on credentials through CILogon (28). Registered users get access to longer running / more powerful systems (up to 48 hours on 24 or 28 cores) and a dashboard which lists all their past jobs. To simplify registration for classes, faculty can register just one username / password to share with their students (though if no jobs run for more than one hour, registration is not necessary). Chem Compute provides all the services that students need to perform computational experiments: The experiment itself, creation of the input file, job submission, output visualization, and a log of past jobs. Experiments Chem Compute currently has nine ready to use quantum mechanics experiments using GAMESS, such as molecular orbitals and bonding and calculation of a potential energy surface. Collaborations introduced through writing this book chapter allowed us to add computational experiments exploring transition state theory applied to ammonia formation (K.M. Stocker) and an exploration of the ligand-free Suzuki-Miyaura coupling (17) (B. Esselman). Others have been added with permission from the original authors, and the rest were added by our group. In all, these computational exercises cover Introductory Chemistry for Non-Majors, General Chemistry (12–14), Organic Chemistry (17), and Physical Chemistry. Faculty are always encouraged to submit 81

their own experiments for inclusion on the website. These experiments include background theory, a prelab (where appropriate), and on-screen instructions and questions (Figure 1). These experiments remove the barrier of faculty having to develop their own labs or finding labs to run and adapting them to their particular software package. At present there is currently one experiment using molecular dynamics (TINKER), “What factors govern the escapability of a molecule from a liquid?” by Reeves and Whitnell (26). The MD community is actively encouraged to submit more experiments to further enhance our offering.

Figure 1. Instructions for investigating H2 (measuring the bond length).

Input File Generation Chem Compute employs an easy to use graphical interface for input file generation (Figure 2). GAMESS requires a molecule’s 3D coordinates be entered according to a strict format, and a working knowledge of numerous keywords to successfully setup a calculation. Chem Compute uses the interface from Angel Herráez’ DIY molecules site (29, 30) to setup calculations. Students draw their molecule in 2D using the Javascript Molecule Editor (JSME) (31) or can look up a molecule by name in a number of databases. JSmol (11), an all-purpose molecular structure viewer, will convert that 2D representation into 3D coordinates, add hydrogens as needed, and perform a quick molecular-mechanics optimization. SYVA (32), a program to analyze symmetry of molecules based on vector algebra, is used to determine the molecule’s point group, symmetrize the coordinates, and to determine how to align the molecule in the manner that GAMESS requires for its runs. The TINKER graphical interface is in a preliminary state. Students can choose from simulation boxes that are pre-setup for the molecular escapability lab (isopentane, neopentane, and n-pentane, either alone or in an ensemble). Students can vary temperature, timestep, and simulation length. In the future, the interface will allow students to create simulation boxes with molecules of their choosing. 82

Figure 2. Creating a molecule to investigate. Molecules can be loaded from a database, loaded from a previous run, copied from the clipboard, or drawn using JSME (31) (Javascript Molecule Editor). Job Submission Once the particulars of a simulation are setup, Chem Compute submits the job to the batch scheduler on an XSEDE cluster. Short jobs (less than 6 hours) are submitted using 1 core on Jetstream (located at Indiana University). Jetstream is an elastic cloud cluster. It consists of the web server for the site and one compute node for jobs. If the base compute node becomes fully allocated the Chem Compute site will launch additional nodes to meet demand and delete those nodes when the demand is over. This burst capability is used because the peak usage is much higher than the average usage. Most General and Physical Chemistry classes tend to use the website in November and April, coinciding with the topics of quantum mechanics and molecular orbitals. This elastic ability allows the site to handle peak loads efficiently. Longer jobs (up to 48 hours on 24 or 28 cores) are submitted to Bridges (Pittsburg Supercomputing Center) or Comet (San Diego Supercomputing Center). Instructors can quickly setup multiple runs by uploading a .csv file containing several molecules and settings. This batch job functionality can be used to explore the effect of different basis sets and settings on energy values (in order to find which more closely matches experiment) or to just quickly run several calculations on various molecules without having to submit calculations one at a time. Output Visualization Students can view the progress of their job on the status page. The output updates every ten seconds, displaying a summary of their job settings, the last few lines of the output file, and the current geometry of the molecule (Figure 3). I have found that students do not like to wait to see something happen, so it’s important to show them the intermediate output so that they can see the 83

job is running. Without intermediate output students have a tendency to resubmit jobs that they think are “stuck” or “not working”, leading to excessive job submissions. Students also have difficulty decoding and fixing error messages, which adds to their frustration. The Chem Compute site parses the output file for common error messages and attempts to translate them to a more readable form for the student.

Figure 3. Intermediate output displaying job status, the last few lines of the output file, and the current geometry visualized with JSmol. When a job is finished the output file is downloaded into JSmol (11) for visualization. JSmol can display molecular orbitals (Figure 4), vibrational modes, the dipole moment, the electrostatic potential, and can animate the molecule to show how its geometry changed during optimization (Figure 5). If IR or UV-Vis transitions are calculated, the site will graph them using a default line width and the calculated transition energies and oscillator strengths (Figure 6). Thermodynamic values (E, H, G, CV, CP, and S) are displayed along with the zero point energy, rotational constants, and partition function values. 84

Molecular Dynamics (TINKER) runs are visualized using ChemDoodle (33) and Google Charts (Figure 7) by displaying a movie of the simulation trajectory along with the energy of the system as a function of time. The output file is a zip archive with the trajectory file (for visualization in VMD (34)) and an energies.csv file that contains energies extracted as a function of time for further analysis by the student. The energies.csv file was created using scripts from R. Whitnell.

Figure 4. One of the π-molecular orbitals of benzene visualized with JSmol. Students refer to this orbital as “the hamburger orbital”.

Figure 5. Visualization Options available on Chem Compute.

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Figure 6. Calculated IR spectrum of benzene (cm-1) using a default linewidth. The y-axis is scaled from the oscillator strength. Screen Capture from Chem Compute.

Figure 7. TINKER output containing a movie of the simulation trajectory visualized with ChemDoodle and a plot of energy as a function of time using Google Charts. 86

Record of Past Jobs If a student is logged in they can view their dashboard, which shows a record of their past jobs and job settings. Often a student will forget to record some data, e.g. the units of energy, or otherwise need to look back at past jobs. If a student is running multiple jobs they can quickly see whether a job has finished. If the instructor shares one username / password with the class then the instructor can use the dashboard to monitor the class’ progress. When a student needs help with an error, the instructor can quickly locate their job on the dashboard and view the error. The dashboard also shows how many CPU-hours (service units, SU) the account has used and includes a link to request more CPU-hours and access to more cores / more powerful computing nodes.

Successes Using Chem Compute in Class Students Completed the Assignment When my class used GAMESS in command line mode with an input file setup through Avogadro, a significant number of students were not able to complete some of the calculations. Errors in positioning molecules (especially diatomics) and running command line scripts dominated class time, and I had to distribute output files for students to analyze. When I switched to using Chem Compute with a web-based interface, all students were able to correctly submit jobs and view their output. I feel that this is definitely a success because it reduced frustration, which is typically very high in a Physical Chemistry class. Student Evaluations Increased While using the Chem Compute website in class, students have made very positive comments, both informally, and through end-of-semester student evaluations. Informal comments include “I wish we used this in organic – it would have explained so much.”, “I liked the ability to see the orbitals and move the molecules around”, and “Can I use this in my research?” Importantly, student’s enthusiasm was recorded in their student evaluations, where scores increased on questions including: “In this course, my instructor enables me to participate actively in learning” and “My instructor stimulates interest in the course“ (Table 1). Table 1. Increase in student evaluation responses after using Chem Compute in class. Maximum score is 5.0 Evaluation Question

Before Chem Compute

After Chem Compute

In this course, my instructor enables me to participate actively in learning

4.6

4.6

5.0

5.0

My instructor stimulates interest in the course

4.2

4.4

4.9

4.9

Classes (left to right): 2012 Spring P-Chem (N=20), 2013 Spring P-Chem (N=29), 2015 Spring P-Chem (N=14), 2017 Summer Gen-Chem (N=7).

Identification and Corrections of Common Misconceptions and Knowledge Gaps Assigning computational chemistry exercises has introduced me to a number of misconceptions concerning Physical Chemistry. It is amazing what one takes for granted as common knowledge as a professor. “Basic” or “easy” exercises that look at fundamentals, like orbitals and bonding, are often surprisingly effective at exposing misconceptions that can be fatal to a student’s understanding. I have 87

found that for every student who voices a misconception, there are several students who are too afraid to speak up. Some General Chemistry students thought that the subshell d was the same as the D used for referring to the dimension of space. Students were comfortable with viewing a 3d atomic orbital, but questioned whether a 4d orbital should be viewable on a computer, because a 4-dimensional object is not possible to visualize. Now I make an extra effort to distinguish between a 3d orbital and a 3-D object. Nodes are a fundamental part of quantum mechanics, but many students don’t have the mathematical background to grasp this concept. When teaching Physical Chemistry, one can write the equation for a pz-orbital (35) on the board,

but getting students to recognize the angular node produced by the cos θ term is not easy. I have found that combining the mathematical equation with a visual exploration of the atomic orbitals (Figure 8, produced by calculating the single-point energy of neon) is useful to even Physical Chemistry students. I used to think that atomic orbitals, covered in General Chemistry, did not need much explanation in Physical Chemistry, because surely the students had a great deal of experience with them. I have since found that something as simple as comparing the equation with the visualization of an orbital helps fill in gaps in a student’s understanding.

Figure 8. Neon p-orbital visualized with JSmol. Students must understand spin to correctly setup computational chemistry jobs. I have repeatedly observed students running jobs on atoms such as fluorine as a singlet species (the default option). When students get an error they usually resubmit the job. After two or three tries at this they either ask for help or read the text on the screen, “You specified a singlet spin (all paired electrons), but you have an odd number of electrons”. Spin is such a fundamental concept, especially in optical transitions, that it is worthwhile to have students struggle a bit on this, even in General Chemistry. Students are surprised to learn that although a calculation may succeed, it may not give the desired answer. For example, when asked to calculate the ground state energy of B2, students will often accept the default option of singlet spin. However, this is not the ground state as the energy is 25.9 kcal / mol higher than the triplet state when using B3LYP/6-31G*. 88

Constructive and deconstructive interference is the basis for bond formation, which itself is the basis of chemistry. I have found that writing:

helps students correctly solve math problems, but does not offer much help in understanding bonding. However, when students visualize the bonding and anti-bonding orbitals in H2 (Figure 9), they internalize constructive and deconstructive interference. One takeaway from my experiences teaching Physical Chemistry is that students need both a qualitative and quantitative understanding of the subject. A thorough experience visualizing the output of computational jobs boosts a student’s qualitative understanding of chemistry.

Figure 9. Antibonding (left) and Bonding (right) orbitals of H2 used to teach destructive and constructive interference. The final misconception that I have come across is also the most important. I have had many students tell me “I’m not good at computers” and that they should not be required to use computers in chemistry lab. This lack of confidence is disastrous for a scientist in a STEM field. The confusion and frustration caused by having my students use GAMESS through the command line reinforced the students’ feelings and led to a negative lab experience. In subsequent years when I had the students use GAMESS through the Chem Compute web interface results were markedly different. Using preliminary survey data (Table 2) students reported slightly increased confidence and interest in using computers to solve chemical problems after using Chem Compute. The survey is voluntary, and low post-experiment cooperation limits the usefulness of this preliminary data. The students somewhat agree / agree that the computer assignments provided deeper insight into the class material. Table 2. Preliminary Survey Results PRE (N=117)

POST (N=27)

I feel confident using computers to solve chemical problems.

4.75

5.41

I am interested in using computers to solve chemical problems.

5.21

5.52

I feel that the computer assignments provided deeper insight into the class material. 1 Strongly Disagree … 4 Neither Agree nor Disagree … 7 Strongly Agree

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5.50

Connection Between Class Work and Research At the end of my computational labs I require students to perform a calculation on a molecule of their choice. Many students use their creativity to draw large, complex molecules with the molecule editor. One student even drew C60. Calculations on these large molecules invariably take too long to finish in class, and this is a good opportunity to reintroduce the concept of semi-empirical geometry optimization followed by higher level single-point energy calculation (facilitated by the “Do More Calculations” button on the output screen). Students also have chosen to run calculations on molecules they are using in their undergraduate research. Many students are involved in synthesizing novel compounds, and they use the Chem Compute site to calculate IR or UV-Vis spectra to compare with their experimental data. This connection between research and class work is invaluable. Computational chemistry has the advantage of being able to quickly create a complex molecule and perform calculations. This simply is not feasible in a typical wet chemistry lab, where students can only use compounds provided to them from the stock room. Students from around the world have used the site for research projects. One student from a liberal arts college used the site for his undergraduate honors thesis work (36). The computational power of the XSEDE network means that students have the tools to do some reasonably heavy computational work (for free) through the Chem Compute site. Engaging with Chemical Education Students Our department does not have a Chemical Educator, but a number of our students are interested in Chemical Education Research. This project has enabled me to serve as the research advisor for a number of students (two are co-authors on this chapter) who are interested in Chemical Education. These students analyze survey results, design experiments, test experiments, and provide feedback on how the experiments can be improved. It has been a great help for me to get input from a student’s perspective, and I am happy that I can bring another facet of chemistry research to my department with this project.

Conclusion The Chem Compute Science Gateway (chemcompute.org) is a free site where students can prepare, submit, and visualize computational chemistry jobs at no cost. Instructors don’t need to worry about purchasing, compiling, installing, or maintaining software and hardware. The site includes ready-to-use experiments. Chemcompute.org has provided resources for students to submit over 60,000 jobs in classes around the world. Preliminary survey results show that students who have used the site report an increased confidence and interest in using computers to solve chemical problems.

Acknowledgments This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562 under allocation TGCDA170003. It was supported by the Science Gateways Community Institute through their extended developer support (EDS). We would like to thank Sudhakar Pamidighantam, Paul Parsons, and Christopher Watkins for help with back-end job submissions and front-end redesign and Harry Price for helpful comments that improved this chapter.

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Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14 (11), 1347–1363. Avogadro: An Open-Source Molecular Builder and Visualization Tool. Version 1.1.1. Avogadro.Openmolecules.Net. Hanwell, M.; Curtis, D.; Lonie, D.; Vandermeersch, T.; Zurek, E.; Hutchison, G. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. J. Cheminf. 2012, 4 (1), 17. Bode, B. M.; Gordon, M. S. Macmolplt: A Graphical User Interface for Gamess. J. Mol. Graphics Modell. 1998, 16 (3), 133–138. Perri, M. J.; Weber, S. H. Web-Based Job Submission Interface for the Gamess Computational Chemistry Program. J. Chem. Educ. 2014, 91 (12), 2206–2208. Oracle Corporation. Sun Grid Engine, 6.2u4. Towns, J.; Cockerill, T.; Dahan, M.; Foster, I.; Gaither, K.; Grimshaw, A.; Hazlewood, V.; Lathrop, S.; Lifka, D.; Peterson, G. D. Xsede: Accelerating Scientific Discovery. Comput. Sci. Eng. 2014, 16 (5), 62–74. Stewart, C. A.; Cockerill, T. M.; Foster, I.; Hancock, D.; Merchant, N.; Skidmore, E.; Stanzione, D.; Taylor, J.; Tuecke, S.; Turner, G.; Vaughn, M.; Gaffney, N. I., Jetstream: A Self-Provisioned, Scalable Science and Engineering Cloud Environment. In Proceedings of the 2015 XSEDE Conference: Scientific Advancements Enabled by Enhanced Cyberinfrastructure; ACM: St. Louis, Missouri, 2015; pp 1−8. Bode, B. M. Gamessq, 1.2.1; 2015. Yoo, A. B.; Jette, M. A.; Grondona, M. In Slurm: Simple Linux Utility for Resource Management; Workshop on Job Scheduling Strategies for Parallel Processing. Springer: 2003; pp −60. Hanson, R. M.; Prilusky, J.; Renjian, Z.; Nakane, T.; Sussman, J. L. Jsmol and the Next-Generation Web-Based Representation of 3d Molecular Structure as Applied to Proteopedia. Isr. J. Chem. 2013, 53 (3-4), 207–216. Ruddick, K. R.; Parrill, A. L.; Petersen, R. L. Introductory Molecular Orbital Theory: An Honors General Chemistry Computational Lab as Implemented Using Three-Dimensional Modeling Software. J. Chem. Educ. 2012, 89 (11), 1358–1363. Feller, S. E.; Dallinger, R. F.; McKinney, P. C. A Program of Computational Chemistry Exercises for the First-Semester General Chemistry Course. J. Chem. Educ. 2004, 81 (2), 283. Linenberger, K. J.; Cole, R. S.; Sarkar, S. Looking Beyond Lewis Structures: A General Chemistry Molecular Modeling Experiment Focusing on Physical Properties and Geometry. J. Chem. Educ. 2011, 88 (7), 962–965. Esselman, B. J.; Hill, N. J. Integration of Computational Chemistry into the Undergraduate Organic Chemistry Laboratory Curriculum. J. Chem. Educ. 2016, 93 (5), 932–936. Esselman, B. J.; Hill, N. J. Proper Resonance Depiction of Acylium Cation: A High-Level and Student Computational Investigation. J. Chem. Educ. 2015, 92 (4), 660–663. Hill, N. J.; Bowman, M. D.; Esselman, B. J.; Byron, S. D.; Kreitinger, J.; Leadbeater, N. E. Ligand-Free Suzuki–Miyaura Coupling Reactions Using an Inexpensive Aqueous Palladium Source: A Synthetic and Computational Exercise for the Undergraduate Organic Chemistry Laboratory. J. Chem. Educ. 2014, 91 (7), 1054–1057. Helms, E.; Arpaia, N.; Widener, M. Assigning the Nmr Spectrum of Glycidol: An Advanced Organic Chemistry Exercise. J. Chem. Educ. 2007, 84 (8), 1328–1330. Habata, Y.; Akabori, S. Teaching H-1 Nmr Spectrometry Using Computer Modeling. J. Chem. Educ. 2001, 78 (1), 121–123.

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20. Palmer, D. R. J. Integration of Computational and Preparative Techniques to Demonstrate Physical Organic Concepts in Synthetic Organic Chemistry: An Example Using Diels-Alder Reactions. J. Chem. Educ. 2004, 81 (11), 1633–1635. 21. Mecozzi, S.; West, A. P.; Dougherty, D. A. Cation−Π Interactions in Simple Aromatics: Electrostatics Provide a Predictive Tool. J. Am. Chem. Soc. 1996, 118 (9), 2307–2308. 22. Shepherd, T. D.; Fortenberry, R. C.; Kennedy, M.; Sherrill, C. D. Can We Visually Predict Binding Energies? www.psicode.org/labs.php (accessed May 21). 23. Johnson, L. E.; Engel, T. Integrating Computational Chemistry into the Physical Chemistry Curriculum. J. Chem. Educ. 2011, 88 (5), 569–573. 24. Halpern, A. M.; Ramachandran, B. R.; Glendening, E. D. The Inversion Potential of Ammonia: An Intrinsic Reaction Coordinate Calculation for Student Investigation. J. Chem. Educ. 2007, 84 (6), 1067. 25. Parnis, J. M.; Thompson, M. G. K. Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator - an Undergraduate Vibrational Spectroscopy Laboratory Exercise. J. Chem. Educ. 2004, 81 (8), 1196–1198. 26. Reeves, M. R.; Whitnell, R. M., New Computational Physical Chemistry Experiments: Using Pogil Techniques with Ab Initio and Molecular Dynamics Calculations. In Addressing the Millennial Student in Undergraduate Chemistry; American Chemical Society: 2014; Vol. 1180, pp 71−90. 27. Ponder, J.; Richards, F. Tinker Molecular Modeling Package. J. Comput. Chem 1987, 8, 1016–1024. 28. Basney, J.; Fleury, T.; Gaynor, J. Cilogon: A Federated X. 509 Certification Authority for Cyberinfrastructure Logon. Concurrency and Computation: Practice and Experience 2014, 26 (13), 2225–2239. 29. Herráez, A. Do-It-Yourself Molecules: From 2d to 3d. http://biomodel.uah.es/en/DIY/ (accessed May 26, 2016). 30. Herráez, A. Diy Molecules a Web Application to Build Your Own 3d Chemical Structures; In 21st Biennial Conference on Chemical Education, Denton, TX, 2010. 31. Bienfait, B.; Ertl, P. Jsme: A Free Molecule Editor in Javascript. J. Cheminf. 2013, 5 (1), 1. 32. Gyevi-Nagy, L.; Tasi, G. Syva: A Program to Analyze Symmetry of Molecules Based on Vector Algebra. Comput. Phys. Commun. 2017, 215, 156–164. 33. Burger, M. C. Chemdoodle Web Components: Html5 Toolkit for Chemical Graphics, Interfaces, and Informatics. J. Cheminf. 2015, 7 (1), 35. 34. Humphrey, W.; Dalke, A.; Schulten, K. Vmd - Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33–38. 35. Karplus, M.; Porter, R. N. Atoms and Molecules; WA Benjamin, 1970. 36. Thiemann, N. Using Computational Tools to Design a Moleculary Imprinted Polymer with Selectivity and High Affinity for Acetylcholine; Trinity College: Hartford, Connecticut, 2017.

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Chapter 8

Using Computational Chemistry to Extend the Acetylene Rovibrational Spectrum to C2T2 William R. Martin and David W. Ball* Department of Chemistry, Cleveland State University, 2121 Euclid Avenue, Cleveland, Ohio 44115, United States *E-mail: [email protected]. Phone: 216-687-2456.

Although an analysis of the rovibrational spectrum of acetylene (C2H2) and deuterated acetylene (C2D2) are known physical chemistry laboratory experiments, an extension of the exercise to tritiated acetylene, C2T2, has never been proposed. While an experimental measurement of the rovibrational spectrum of C2T2 may be out of reach, computational methods do exist that allow us to predict the spectrum using data from the C2H2 and C2D2 spectra. Here, we detail the method of performing just such an exercise and show that the resulting spectrum agrees very well with an actual experimental spectrum available in the literature.

Introduction The spectroscopic measurement of the rovibrational spectra of acetylene (C2H2) and deuterated acetylene (C2D2) is an established physical chemistry laboratory experiment (1). Although similar experiments exist for HCl and HBr and their isotopomers (D for H, naturally-occurring 35Cl and 37Cl for chlorine, and 79Br and 81Br for bromine) (2), because the acetylene molecule is centrosymmetric, its spectrum shows intensity variations due to impact of nuclear spin on rotational degeneracies (3), making it one of the few direct observations of the influence of the nuclear wavefunction. Starting with calcium carbide, students can use H2O and D2O to generate acetylene isotopomers in situ and measure the spectra easily. Students can then fit the frequencies of the absorptions to mathematical equations to determine the rotational constants B′ and B″ as well as the centrifugal distortion constant De (1), much like they would do for the diatomic molecules HCl and DCl. One of the reasons this type of analysis works for acetylene, a polyatomic molecule, is because it is a linear molecule that has some vibrations whose oscillating dipole moments are parallel to the molecular axis. Such vibrations show rotational structures that follow the same spacing patterns as do © 2019 American Chemical Society

heteronuclear diatomic molecules; i.e. equally-spaced absorption lines separated by 2B but getting slightly farther apart (for the P branch) or slightly closer together (for the R branch) that can be modeled as centrifugal distortion. In the case of acetylene, the three parallel vibrations are labeled as ν1, ν2 and ν3 (Figure 1), which for C2H2 occur at 3374, 3289, and 1974 cm-1, respectively (4). Some combination bands also share these characteristics.

Figure 1. The three parallel normal vibrational modes of acetylene. The other two normal modes are the symmetric and asymmetric bending modes, both of which are doubly degenerate. This experiment is one of several instances where a (relatively rarer) isotope is prominent in an undergraduate lesson, in this case deuterium. Other examples include the mention of isotopes as tracers in reaction mechanisms, as radioactive signatures because of their specific decay properties, and in their use in atomic power. In organic chemistry, 13C becomes important in the discussion of NMR spectroscopy (as are deuterated solvents, if experimental NMR is available in the undergraduate curriculum) and in interpreting mass spectral patterns. Mössbauer spectroscopy is another isotope-specific experimental technique (most commonly, 57Fe) that is occasionally mentioned in upper-level inorganic curricula, and discussions of nuclear partition functions can arise in statistical thermodynamics, although experimental demonstration of its impact is rare – hence the value of the acetylene rovibrational spectrum experiment. Seldom, however, does tritium come up in the undergraduate curriculum, and even less frequently in an experimental way. There is the occasional mention of tritium as a radioactive tracer in water supplies, and possibly its application in nuclear sciences, especially ordnance and radioluminescence. Beyond this, however, tritium’s mention in the curriculum is negligible. We recently considered the reasons why students don’t do this experiment using C2T2 as well. There are several obvious reasons: • Tritium is exceedingly rare. Although it can be formed from 6Li in special breeder reactors, only kilogram quantities are produced each year, much of that going to nuclear ordnance. Tritium occurs naturally as cosmic rays produce fast neutrons that interact with 14N in the upper atmosphere, producing 12C and 3H; however, its natural occurrence is estimated at 1 in 1018 hydrogen atoms. • Tritium is radioactive, with a half-life of 12.32 y (5). As a low-energy beta emitter, it is not especially hazardous, but as a hydrogen isotope it has the chemical ability to replace 1H anywhere, and experimenters are appropriately cautious. Having pointed this out, it is also worth mentioning that the experimental rovibrational spectrum of C2T2 has been reported, by Jones et al. in 1967 (6). 94

But why not calculate the rovibrational spectrum of C2T2, and compare it to the available literature? Consider the data that the students have at their disposal from the C2H2/C2D2 lab. They calculate, by a fitting of the rovibrational frequencies: • • • •

ν0, the pure vibrational frequency assuming no rotation; B″, the rotational constant of the lower vibrational state; B′, the rotational constant of the upper vibrational state; and De, the centrifugal distortion constant.

Students also have access to modern computational chemistry software (in our case, the GAUSSIAN suite of programs (7)) that can be used to calculate data, data that can vary by isotope. The question then becomes: Can students who have determined the four molecular constants from C2H2 and C2D2, along with using computational chemistry software, reasonably calculate the rovibrational spectrum of C2T2 as an add-on to the existing experiment? Actually, the answer is “yes”. With a few reasonable assumptions or approximations, and thanks to some mathematical luck, it can be done rather easily. In fact, our analysis results in an absolute error less than 6 cm-1 from the experimental rovibrational spectral lines of C2T2.

Some Computational Background In addition to determining the appropriate molecular constants from the experimental data, students can use computational chemistry software to determine, either directly or indirectly, the appropriate molecular constants for C2T2 to predict its spectrum. In the course of determining the geometry of molecule, the program can (and in the case of GAUSSIAN, does) output a value of the rotational constant B. Because it is a linear molecule, acetylene has a single non-zero value for its rotational constant. This value depends on certain molecular parameters, namely the distances of the nuclei from the molecular center and the masses of those nuclei. In going from H to D to T, the relevant distances do not vary; the only things that vary are the masses of the two hydrogen atoms in the acetylene molecule. As such, these numbers are easy to calculate for the program and are part of the standard output file, in the case of GAUSSIAN having units of GHz. Students merely copy the value of B for the energy-minimized structure. The issue of using computational chemistry programs to predict vibrational frequencies is a bit trickier. This is because, unlike for a simple diatomic molecule (e.g. HCl or HBr), a threedimensional vibrational mode of a polyatomic molecule does not necessarily follow a simple mathematical rule that allows one to just re-substitute new isotopic masses and calculate a new vibrational frequency. However, the word “necessarily” is important here, because it turns out that in some case this is possible to make an accurate prediction. To understand why, it is useful to review how the computational chemistry program calculates vibrational frequencies. Here we follow the lead of a “white paper” discussion of vibrational modes available at the GAUSSIAN website (8), although our variables may be different. The program begins by numerically calculating what is known as the Hessian matrix, which is a 3N × 3N (N = number of atoms) matrix of force constants, evaluated at the minimum-energy geometry:

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where V is the potential energy of the molecule in 3N space, and qi and qj represent the 3N possible changes in Cartesian coordinates of the N atoms in the molecule. (The terms of this matrix are determined numerically, which is one reason vibrational calculations sometimes require a lot of computational time.) Then, the terms in this matrix are divided by the square roots of the masses of the atoms involved, generating a “mass-weighted coordinate” force constant matrix fMWC. As a matter of choice, the GAUSSIAN program then determines the principal axes of the moments of inertia of the molecule and transforms the coordinates to internal coordinates to remove translations and rotations. This matrix transformation (using a transformation matrix D; this will be used again later) generates a new version of the Hessian matrix labeled fint. This new matrix is diagonalized by determining a transformation matrix L such that

where L is the transformation matrix of eigenvectors and Λ is the diagonal matrix of mass-weighted frequency-equivalents. Each entry on the diagonal of Λ needs only one index, and so is designated λi. The program then calculates the frequency of the (now normal mode of) vibration as

These are the frequencies reported by the program. This is where the concept of “imaginary” frequencies arises, because if λi is negative (it is, after all, ultimately a second derivative of a potential energy curve) then the square root of a negative yields an imaginary number. What about the other characteristics of the vibration, like the reduced mass? The program now reverses to make a Cartesian coordinate-based version of L, labeled lcart:

where D is the original Cartesian-to-internal-coordinate matrix and M is a diagonal matrix of the square root of the masses of the atoms. The matrix lcart is important to understand how the mathematics of this analysis works, but it is important to clear up a misconception about reduced mass. What GAUSSIAN (and perhaps other programs) report as a “reduced mass” in vibrational calculations is more appropriately termed an “effective mass,” and this is what we get from lcart: the effective mass, still labeled μi, for each vibrational mode is the reciprocal of the sum of the squares of each column matrix entry, lcart,k,i in lcart:

The “effective” force constant for this normal mode, ki, is then calculated from the standard equation that relates the force constant of a vibration to the (effective) mass of the vibrator:

96

From this analysis, we have vibrational frequencies, effective (or “reduced”) masses, and force constants. In performing this analysis for the three isotopomers of acetylene, the only input data that changes is the masses (or more directly, the square root of the masses) of the atoms in the molecule. Now we have to ask a crucial question: How do the values of ki, as determined by the computational chemistry program, relate to the force constants of the actual motions – stretching and bending – of the molecule? From a physical point of view, the treatment of the acetylene molecule can be found in Herzberg (9). Figure 2 shows the acetylene molecule and how its stretches and bends, and the resulting force constants, are defined. Based on this, we can define three force constants, which are listed and described in Table 1. Analyzing the normal modes, the following equations can be defined (9):

Note that only for ν3 (equation 9), ν4 (equation 10), and ν5 (equation 11) do the vibrational frequencies depend directly on the force constants. On the other hand, for ν1 (equation 7) and ν2 (equation 8), the dependence on the force constants is more complicated. From this, we conclude that only for these three normal modes (ν3, ν4, and ν5) is there a simple and direct relationship between a force constant and the frequency.

Figure 2. The definition of the internal coordinates for the vibrational motions of acetylene. See equations 7–11. Table 1. Definitions of the three force constants based on the internal coordinates of acetylene (see Figure 2)

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We can verify this by looking at some of the characteristics that the program provides about the frequencies. Because of the way GAUSSIAN determines the vibrations, rather than comparing the force constants it calculates with the frequencies, we take advantage of the classical relationship

and look at the relationship between the frequencies and the reciprocal square of the effective mass as reported by the calculation. Figure 3 shows graphs of the frequencies of the normal modes (in cm-1) for each isotopomer versus the effective mass (in g/mol), along with the linear best fit and its correlation factor. For ν1, the trend is almost perfectly linear, which one might expect for the symmetric C-H stretching mode of acetylene. However, ν2, the C-C stretch, is obviously not even close to linear. The modes ν3, ν4, and ν5 show a perfect linear relationship between the reciprocal square of the reduced mass and the vibrational frequency. The normal mode ν3 is the only parallel stretching mode that demonstrates this correlation, as ν4 and ν5 are the C-C-H bending modes.

Figure 3. Graphs of the calculated frequency of the normal mode (in cm-1, y axis) versus the reciprocal of the square root of the effective mass of the mode (in g/mol, x axis). The axes have been left unlabeled for clarity. What this demonstrates is that we can use values of ν0 for the ν3 normal mode of C2H2 and C2D2 and linearly extrapolate a value of ν0 for C2T2. Then by using the rotational constants for C2T2 (extracted from the output file) and the B values for acetylene, we can calculate a predicted rovibrational spectrum for C2T2. 98

We make one additional approximation in graphing the positions of the rotational structure of C2T2. According to the published procedure (1), students measure the frequencies of the rotational structure and fit them according to the cubic equation

(Here, the index m equals -J for the P branch and J + 1 for the R branch.) In predicting the spectrum of C2T2, students are asked to use the rotational constant from the computational output, assume B′ = B″, and finally assume De = 0. This introduces negligible error in the predicted results (see below). The final step is to use the Boltzmann distribution and the degeneracies of the rotational states to predict the intensity alterations of each rotational line. The intensities are proportional to the populations of the initial states, which are populated thermally according to the expression

where gJ is the degeneracies of the Jth rotational energy level, h is Planck’s constant, c is the speed of light, B is the rotational constant, k is Boltzmann’s constant, and T is the absolute temperature (3). It is the degeneracies that concern us here, because for this particular system, the nuclear spin has an impact on the rotational degeneracies in order that the Pauli principle be satisfied, i.e. that the total wavefunction of the molecule be antisymmetric. Tritium has a nuclear spin quantum number I of ½, making it a fermion. As such, when the rotational quantum number J is odd, the rotational wavefunction is antisymmetric with a rotational degeneracy of 2J + 1 and the nuclear spin wavefunction must be symmetric with a degeneracy of (I + 1)(2I + 1):

However, when J is even, the rotational wavefunction is symmetric, requiring the nuclear wavefunction to be antisymmetric and having a degeneracy of 2I2 + I:

Thus, we should see a rough 3:1 ratio of adjacent absorptions in the rovibrational spectrum of C2T2. Students can either use the intensity values as calculated from equation 14, or alternately divide all intensity values by the lowest value, essentially normalizing it to 1 and scaling all other intensities relative to that one.

Procedure The following Procedure is available verbatim as a handout to the students performing this experiment. Note that different fonts are used to distinguish between the instructions and the input/ output text for the computational chemistry program.

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Addendum to Acetylene Rovibrational Spectrum Experiment There are many places in the chemistry curriculum that invoke deuterium, 2H (or D), as an example of an isotope. Generating C2D2 and measuring its rovibrational spectrum in this experiment is one of them. However, rarely does the undergraduate curriculum invoke tritium, 3H (or T), in discussions of isotopic substitution. Here is an additional exercise that uses tritium-substituted acetylene, C2T2. 1. Using the GAUSSIAN09 program, set up and perform an optimization and frequency analysis of C2H2. Use “B3LYP/6-31G**” as the method and basis set. For the Molecular Specification, use:

2. After the job is finished, perform two additional calculations by substituting D and T atoms for H in the optimized structure. The easiest way to do this is to open your original job file and add “(Iso=x)” next to each hydrogen atom:

Of course, Iso=2 is for deuterium, so use Iso=3 for tritium. 3. In the list of vibrational frequencies, the mode you are studying (labeled ν3 in the literature) is the final vibrational frequency, as GAUSSIAN09 lists vibrational frequencies in increasing order of wavenumber. As part of the vibrational frequency output, GAUSSIAN09 also prints the reduced mass of the normal mode. Record this reduced mass for this vibration for all three isotopomers of acetylene. For example, here is part of a GAUSSIAN output file for another molecule:

The frequencies (in units of cm-1, or wavenumbers) and force constants (in units of millidynes/ Angstrom) are highlighted in bold.

100

Also, record the rotational constant that GAUSSIAN09 calculates for the optimized geometry. Note that the units are gigahertz. Here is where you find the rotational constants – MAKE SURE YOU USE THE VALUES FROM THE OPTIMIZED GEOMETRIES:

Not far after this in the output file, there is a section showing the optimized molecular geometry (“Standard orientation:”), followed by the rotational constants:

Note that, unlike the molecule above, a linear molecule will have only two non-zero rotational constants, and they should be exactly the same (otherwise the molecule isn’t perfectly linear). 4. Perform your analysis of your C2H2 and C2D2 experimental data, following the original lab instructions from the text. Part of your results should be the ν0 values for the ν3 vibration of acetylene. Graph these values for C2H2 and C2D2 versus 1/√μ, where μ is the reduced mass of the vibration from the GAUSSIAN09 output. You should have two points in your graph. 5. Extrapolate the line you get to the value of 1/√μ for C2T2 from the appropriate GAUSSIAN output file, and read off the corresponding value of ν0 for C2T2. 6. Assuming that the two rotational constants are equal (that is, B′ = B″) and that the centrifugal distortion constant De = 0, determine the wavenumbers of the rovibrational spectra for ν3 of C2T2 using equation (11) in your handout – don’t forget that m is defined differently for the P and R branches! Using a spreadsheet and entering the equation would be easiest. Calculate the rovibrational values up to J = 30. 7. Now comes the fun part. The intensities of the C2T2 rovibrational lines are determined by two factors: thermal energy distributions and rotational degeneracies (see your lab handout). Because the molecule is centrosymmetric, the nuclear wavefunction impacts the degeneracies of the 101

rotational states. For 3H, the nuclear spin I = ½. This makes it a fermion (as opposed to a boson), and the degeneracies for fermions depend on whether J(lower) is odd or even. If J(lower) is odd, the degeneracies are

If J(lower) is even, the degeneracies are

Because I does not change, the “I” contribution to the degeneracies are the same for all odd J values and all even J values, so the two expressions above become

These degeneracies need to be combined with the thermal intensity contribution. The proper, complete form of equation (12) in your handout is then

where h is Planck’s constant (normal units), c is the speed of light (in cm/s!!!), B is the rotational constant (in cm-1!!), k is Boltzmann’s constant (normal units) and T is the absolute temperature. (Note that you will need to convert the B values from the GAUSSIAN output; that number has units of gigahertz, GHz). In two separate calculations, calculate the value of the intensity expression for the odd values of J and the even values of J (again, using Excel’s equation editor can be useful. Separating your J values into separate sections might be helpful as well.). For example, a sample calculation using the rotational constant of acetylene (B = 29.72524 MHz, converted to cm-1), the speed of light in the proper units (2.9979×1010 cm/s), J = 1, and the standard values and units of h and k, and at 298 K (approximate room temperature, maybe a bit warm), the first equation gives

(Verify this.) Perform a similar calculation for all 30 values of J, using a spreadsheet. (Question: Does the intensity pattern resemble C2H2 or C2D2 better? Can you explain your choice?) 8. Take all numbers and divide them by the value you get for Int (J = 1). This will make Int (J = 1) = 1.000…. exactly and will scale all other intensities to this one. 9. Graph your predicted rovibrational spectrum – both the P branch and the R branch – of the ν3 mode of C2T2; that is, graph lines with wavenumbers along the x axis with the height of the lines equaling Int (J = whatever). This should give you a stick spectrum that shows the proper wavenumbers and relative intensities for the rovibrational spectrum of C2T2. 102

To graph a stick spectrum in Excel: Sort your data by descending wavenumber. Select the column for wavenumber as well as your column for intensity, select Insert in Excel, then select Recommended Charts. On the All Charts tab, select the Column option on the left, and select Clustered Column at the top of the window. Ensure you have selected the chart with wavenumber as the x-axis (you should see a preview and it should look like a rovibrational spectrum), and click ok to add your chart. It is important that the data be sorted by descending wavenumber, or your chart will likely not graph correctly. For comparison, the experimental rovibrational spectrum can be found at: L.H. Jones, M. Goldblatt, R. S. McDowell, D.E. Armstrong. J. Mol. Spectrosc. 1967, 23, 9 – 14. 10. Turn in your calculations and your predicted spectrum as part of your report. (End of addendum.)

Results Figure 4 shows a representative summary of the experimental measurement of the rovibrational spectra of C2H2 and C2D2, along with the values of B′, B″ and De as determined by the best fit to a cubic equation. Figure 5 shows the linear fit of the calculated frequency parameters that can be used to predict ν0 for C2T2: ν̃0 = 2066.32 cm-1 (compared to an experimental value of 2072.4 cm1 (6)). Using the value of B from the computational output and using the simplified expression for ν̃

(simplified equation 13), and following the instructions for generating a stick spectrum, we can get the predicted spectrum shown in Figure 6. How does this compare to the experimental rovibrational spectrum of C2T2? Figure 7 shows the value of the absolute error versus J value, using the assignments from the previously published spectrum of C2T2 (6). The ~6 cm-1 error occurs at the band head and decreases as J deviates from 0. Sources of error include:

• error in the calculated values of the vibrational frequencies, including errors inherent in the computational model (including scale factors); • assumption that B′ = B″; • use of a calculated value for B for C2T2 rather than an extrapolated value; • neglect of De; and • possible inaccuracies in the experimentally-measured spectrum. That said, an error of ≤ 6 cm-1 should be considered extraordinarily low and an additional verification that this sort of exercise is justified. We requested feedback from the students who performed this experiment in two semesters of our physical chemistry lab. Specific comments on this lab were minimal, but one student did write “It’s kinda cool how a few quick calculations using Gaussian allows you to pretty accurately predict the IR spectrum for isotopes using the spectra for the other isotopes!” Other students gave oral feedback on the first draft of the Addendum, which allowed us to revise it to the form presented here.

103

Figure 4. A representative graph of the frequencies of the rovibrational lines versus the index m (see equation 13) and the molecular parameters derived from the coefficients of the cubic curve fitting.

Figure 5. Fitting used to extrapolate the value of ν0 of C2T2. Substitute the value of 1/sqrt(μ) from the C2T2 vibrational calculation to obtain the predicted value of ν0. 104

Figure 6. A graph of the predicted rovibrational spectrum of C2T2 without the impact of nuclear degeneracy (top) and with nuclear degeneracy (bottom). The relative intensities are in arbitrary units, but they have been scaled as described in the Addendum.

105

Figure 7. Error between the calculated frequencies for the rovibrational spectrum and the experimental frequencies for the rovibrational spectrum. See text for the definition of the variable m.

Conclusion We have demonstrated that it is possible to predict the rovibrational spectrum of C2T2, extending a known physical chemistry lab experiment to an isotope that is seldom considered in the undergraduate curriculum. This extension requires computation of the optimized geometry and vibrational frequencies of C2H2 and its isotopomers; for such a small molecule, even a reasonablysized basis set and basic computer resources allow for these calculations to be done on the order of minutes (if not faster). Most of the additional work is numerical work that can be done after analysis of the experimental data and using a spreadsheet. The accuracy of the prediction is excellent. If there is one lesson to be learned in this exercise, it is to understand as best as possible the mathematical manipulations being performed by a computational chemistry program. Without a better understanding of how the GAUSSIAN program performed its vibrational frequency analysis, we would never have understood the relationship between the effective masses and the vibrational frequencies; only a step-by-step analysis of the linear algebra involved gave us the clue to being able to confidently extrapolate to a spectrum of C2T2. The prevalence of inexpensive and easy-to-use computational chemistry programs, combined with the almost ubiquitous presence of computers in the modern workplace, have conspired to allow many users of these resources to treat them, effectively, as a black box. Put some numbers in, get some numbers out, and assume those numbers make sense. However, it should be better than that: someday we may be required to defend those numbers, and if we don’t know how they were generated as well as we should, we cannot defend them properly. Caveat utilitor. (If different computational chemistry packages are used—and there is no reason not to use them—users should understand how those packages calculate the normal modes of vibration.) Finally, the word “luck” was used in the Introduction, and although as scientists we don’t believe in luck per se, it is worth pointing out two facts, both of which had to be true for this procedure to work. First is the fact that the vibration involved (ν3, the asymmetric C-H stretching motion) is a parallel absorption. This allows the rovibrational spectrum to adopt a simple pattern similar to those found in heteronuclear diatomic molecules, i.e. the regular spacing of rovibrational absorptions that can be used to determine molecular parameters. Second is the fact that this is one of the five normal 106

modes, and the only parallel absorption, whose vibrational frequency is related to its effective mass in a straightforward way. It is probable that similar exercises can be performed on the other vibrations of acetylene, but likely the mathematics is much more complicated. Were either of these issues not satisfied, this exercise would not have been developed as easily as it was.

Acknowledgments The authors would like to thank the following students of our physical chemistry lab courses who performed the original experiment and the extension described here, pointing out issues and making valuable suggestions that improved the exercise: Hamoud Asi, Paul Benton, Nathan Canterbury, Stacey Cargill, Brian Davis, Teya Eshelman, Maranda Florjancic, Megan Frey, Rachel Grabowski, Kathryn Kiesel, Drew Kingery, William Knight, Marek Kowalik, Chris Lattanzio, Keith LeHotan, Carrie Lewis, James Maher, Connor Meek, Cody Orahoske, Abboud Sabbagh, Sydney Simpson, Daniel Terrano, Jocelyn Thompson, Ilona Tsuper, and Morgan Worthley.

References 1. 2. 3. 4. 5. 6. 7.

8. 9.

Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry, 8 ed. McGraw-Hill: Boston, MA, 2009; pp 424−436. Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry, 8 ed.; McGraw-Hill: Boston, MA, 2009; pp 416−424. Ball, D. W. Physical Chemistry, 2 ed.; Cengage Publishing: Stamford, CT, 2015; pp 644−648. Shimanouchi, T. Tables of Molecular Vibrational Frequencies; NBS Circular NSRDS-NBS 39, 1972. Tritium. https://en.wikipedia.org/wiki/Tritium (accessed 14 February 2018). Jones, L. H.; Goldblatt, M.; McDowell, R. S.; Armstrong, D. E.; Scott, J. F.; Williamson, J. G.; Rao, K. N. Vibration Rotation Bands of C2T2: Part I. ν3. J. Mol. Spectrosc. 1967, 23, 9–14. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian, Inc. Gaussian 09, Revision D.02; Wallingford, CT, 2009. Vibrational Analysis in Gaussian; White paper available at www.gaussian.com/vib/ (accessed 15 February 2018). Herzberg, G. Molecular Spectra and Molecular Structure: Infrared and Raman of Polyatomic Molecules; D. Van Nostrand Company, Inc.: Princeton, NJ, 1966.

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Chapter 9

Introducing Quantum Calculations into the Physical Chemistry Laboratory Thomas C. DeVore* Deparment of Chemistry and Biochemistry, James Madison University, Harrisonburg, Virginia 22807, United States *E-mail: [email protected].

This chapter contains computational chemistry exercises to explore topics often presented in upper level undergraduate courses. It is used to supplement the classic HCl/ DCl infrared spectroscopy experiment, to determine the IR spectra of the isoelectronic series BO2-, CO2, and NO2+ and to assign the IR and Raman spectra of benzene. Computational chemistry can be used to determine the ground state term symbols for atoms and compare them to the predictions made using the aufbau principle and Hund’s rules. The final project investigates possible reaction pathways to form the ions found in the mass spectrum of methane.

Introduction Computational chemistry was largely left to the experts until the 1990’s when more powerful computer systems started becoming common on campuses and ways to integrate the computational chemistry into the curriculum began to appear in the chemical education literature (1–7). Rapid advances in computer technology since then have led to the development of high level computational software that can be run on personal computers (8, 9). This has led to many publications devoted to incorporating computational chemistry into lecture and laboratory courses throughout the chemistry undergraduate curriculum as indicated by a small sampling of suggested exercises published since 1995 given in the references (1–7, 10–30). Much of the software needed to do these exercises can now be operated using the personal computers found on most campuses. By acquiring a site license, this software can be used by multiple users making it easy to add this tool to an undergraduate laboratory courses. Computational chemistry has the advantage of requiring no chemicals, requiring no instrumentation other than the computer/software needed to do the exercise, and always producing results. The exercises presented in this chapter are focused on investigating the concepts rather than of presenting computational methods that will produce the best answers possible. While these exercises were designed for the physical chemistry laboratory or similar upper level undergraduate laboratory, some, such as the atomic investigations presented, © 2019 American Chemical Society

explore topics presented in lower level courses and could be modified for use in these laboratories if desired. A convenient way to introduce computational chemistry into the laboratory is to compare the results calculated using different methods and/ or basis sets to those measured experimentally. This lets students investigate the calculations and discover the advantages and limitations of the various computational methods available while they are learning to use the software. This approach is illustrated using the calculations done for HCl and CO2 given below. Computational chemistry can also be used to produce quantities that cannot be obtained because of lack of instrumentation, expense, or safety concerns. This enables students to gain experience with topics that normally would not be covered in the lab. Examples of this are using the investigation of the dissociation energy with and without zero point corrections done as part of the HCl/DCl project and the exercise comparing the IR spectra of CO2 to the spectra of the isoelectronic BO2- and NO2+ ions. Computational chemistry can be used to support the measurements as shown for the project presented where students assign the IR and Raman spectra of benzene. The exercises investigating the aufbau principle and Hund’s rule and investigating the ions formed in the mass spectrum of methane are computational only exercises. These exercises could also be done as a homework assignment as part of a lecture course.

Computational Methods Most of the calculations presented were originally obtained using Gaussian 03 on Dell personal computers (8, 9). While Gaussian 09 on newer Dell PC’s is now being used, the original system would still be adequate for the exercises presented in this chapter. Calculations are generally done by first building the molecule in GaussView and sending it to Gaussian where the energy is minimized. The bond lengths, bond angles, rotational constants, the molecular energy, and Mulliken populations are determined by this program during this calculation. The vibrational frequencies are calculated to confirm that the minimized structure is at least a local minimum on the energy surface by checking for imaginary frequencies (these are given as negative frequencies in the Gaussian output file). One imaginary frequency often indicates that the structure is a transition state while two or more imaginary frequencies indicates the program is trying to determine an unrealistic structure. While multiple imaginary frequencies are seldom found for the small molecules presented here, they can occur when trying to compute the structures of larger molecules. The zero point energy, temperature corrections for the enthalpy, heat capacity, and the entropy are also determined by this program as part of the vibrational calculation. I. Integrating Calculations with IR Spectroscopy Infrared spectroscopy is typically introduced in organic chemistry, where student are taught about characteristic vibrations of functional groups for use in qualitative analysis (10, 24). The visualization software in GaussView lets students examine the normal modes of vibration and discover that the characteristic frequencies presented in the frequency tables are usually coupled with other modes in the molecule (8, 9). This shows why a range rather than isolated frequencies are given in the frequency tables.

110

A. Ro-vibrational IR spectra of HCl/DCl Learning objectives: The objectives for the experimental part of this project are to use the IR spectrum of a mixture of gaseous HCl and DCl to determine the vibrational frequencies, the rotational constants, and the bond lengths of these molecules (4, 7, 31–35). The objectives for the computational part are to learn to use the software and to evaluate the calculations by comparing the results calculated for 1H35Cl using Hartree-Fock (HF), MP2, and DFT-B3LYP with one small and one larger basis set to the measured values. One of the oldest and still most commonly used physical chemistry laboratory exercises is the analysis of the ro-vibrational IR spectra of the four isotopes of HCl (See Figure 1) (4, 7, 31–35). Students discover that while some properties like the rotational constants and the vibrational frequencies depend on the reduced mass, others like the bond length and the force constant do not. In the computational part of this exercise, students learn to use the software to compute the quantities that are measured in the lab and to determine some quantities that were not measured to gain experience using the software. Since the bond length, the vibrational frequency and the rotational constant were determined from the IR spectra, these values can be compared to the calculated values. By changing the method (we use HF, MP2 and DFT-B3LYP) and the basis set (we use 6-31+G (d) and 6-311+G (2p,d)) the accuracy of the results obtained from each method can be evaluated. One discovery is that the HF method consistently gives values that are ~ 10 % too large and must be scaled to give values in reasonable agreement with the experimental values. As shown in the Tables below, the DFT calculations are generally in better agreement with the measured values and the errors tend to be more random. As a result, we do not have the students scale their DFT results. Typical results obtained for 1H35Cl using the DFT-B3LYP method with the 6-31+G (d) and the 6-311+G (2d,p) basis sets are compared to the measured and the literature values in Table 1 (36). Students quickly discover that the calculations using the larger basis set take longer to finish but often produce results in better, but still not exact, agreement with experiment. They also discover that for some applications, the smaller basis set works as well as the larger one. Most applications will involve a trade-off between speed and accuracy. The animated vibrations also provide useful insights about the atomic displacements occurring during the vibration. This is especially useful for larger molecules where the modes are more coupled. The main discovery for HCl is that most of the vibration comes from the movement of the hydrogen. Students also learn to calculate the dissociation energies (De and Do), the enthalpy of formation (ΔfH), the entropy (S) and the heat capacity at constant volume (Cv) during this exercise (37, 38). The accuracy of these calculations is established by comparing the results to the values given in the literature (36). We usually have the students determine the dissociation energy relative to the bottom of the well (De) by subtracting the energy calculated for each atom from the energy calculated for the molecule using the same method and basis set. While this approach does not produce research quality results because it ignores a detailed analysis of electronic states of the molecule dissociation pathway, it reinforces the description of De given in physical chemistry textbooks (37). As shown in Table 1, the values produced are acceptable for this laboratory exercise. Attempting to calculate the Morse potential by doing single point calculations at several bond lengths clearly shows the effect of using a limited basis set since HCl dissociates into the ions rather than the atoms. The dissociation energy from the first vibrational level (Do) is determined by subtracting the zero point energy from De. The enthalpy of formation (ΔfH) is determined from the energies calculated for 111

H2, Cl2, and HCl. The value at absolute zero is given by E(HCl) – ½ E(H2) – ½ (Cl2) (38). ΔfH at 298 K can be found using the temperature corrections calculated by the program. The entropy and heat capacities are determined from statistical thermodynamics by the program. The translational, rotational, vibrational, and electronic contributions of each are also determined, so students studying statistical thermodynamics can investigate this in detail if desired. Since most of the contribution is from translation and rotation which are determined by the high temperature approximation of the partition functions, the entropy and heat capacity are largely independent of the method used (9, 38).

Figure 1. The ro-vibronic IR spectrum of HCl (A) and DCl (B) obtained using 128 scans at 0.125 cm-1 resolution Based on the Morse potential, the anharmonicity constant (xe) can be determined from the vibrational frequency and the Morse dissociation energy (De) using the equation given in Table 1 (4, 37). Our students use these calculated values to estimate ωexe as shown in Table 1. Once the value for ωexe is established, ωe can be determined from the measured ωo since ω0 = ωe - 2ωexe. This exercise helps the students understand the difference between harmonic and anharmonic frequencies and between De and Do.

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Table 1. Comparison of the measured molecular constants for 1H35Cl to the values calculated using the DFT- B3LYP method with the 6-31+G (d) and the 6-311+G (2d,p) basis sets Constant

Measured

6-31G+ (d)

6-311G+ (2d,p)

Literaturea

ω0 (cm-1)

2885.2

2802.9

2812.4

2885.309

Be (cm-1)

10.59

10.33

10.45

10.59342

re (pm)

127.5

129.0

128.25

127.455

αe (cm-1)

0.303

-------

-------

0.3071

ωexe (cm-1)

-------

61.16b

58.88b

52.8186

De (ev)

-------

4.34c

4.52c

4.574

Do (eV)

-------

4.16d

4.34d

4.432

ΔfH (kJ/ mol)

------

-62.75e

-95.39e

-92.31

S (J/K/mol)

------

186.7

186.6

186.9

Cv (J/K/mol)

------

20.786

20.786

20.788

a from

ref. (36).

b Calculated

using ωexe = ωe2 / 4 De.

c Calculated

from E(HCl) – E(H) - E(Cl) without

d Calculated from E(HCl) – E(H) - E(Cl) with zero point corrections.

zero point corrections. from E(HCl) – ½ E(H2) - ½ E(Cl2) with thermal corrections.

e Calculated

B. IR of Isoelectronic XO2 Molecules Learning objectives: The experimental objectives are to use the ro-vibronic spectrum to determine the vibrational frequencies, the rotational constant and the bond length of CO2. The computational objective is to compute these quantities for BO2-, CO2 and NO2+ to investigate similarities and differences in this isoelectronic series. As shown in Figure 2, the ro-vibrational spectrum of the ν3 band of CO2 is sufficiently resolved at modest resolution to permit rotational analysis and resolved well enough to also determine these quantities for 13CO2 at 0.125 cm-1 resolution. The procedure for determining the vibrational frequencies and the rotational constants from the IR spectrum of CO2 and a method for using the IR spectrum of this molecule to determine, the rotational temperature, Plank’s constant, the Boltzmann constant, or the speed of light from the measured intensities have been published previously (39–41). Including computational chemistry permits investigating concepts similar to those done for HCl. Typical results for 12C16O2 using DFT-B3LYP/6-311+G (2p,d) are compared to those measured and from Herzberg in Table 2 (42, 43).

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Figure 2. The IR spectrum of the ω3 band of CO2 at 1 cm-1(A), 0.5 cm-1(B), 0.25 cm-1(C) and 0.125 cm1 (D) resolution.

Table 2. Comparison of the molecular constants determined for 12C16O2 using DFT-B 3LYP/ 6-311+G (2p, d) to the experimental values Constant

Measured

Calculated

Literaturea

Bo (cm-1)

0.3903b

0.39114

0.39021

B1 (cm-1)

0.3872 b

-----------

0.3871

ro (pm)

116.22

116.03

116.21

ω2 (cm-1)

667.39b

675.64

667.40

ω1 (cm-1)

--------

1364.47

1388.17c

ω3 (cm-1)

2349.2b

2400.49

2349.16

α2 (cm-1)

-0.00041b

----------

-0.00072

α3 (cm-1)

0.0031b

----------

0.00309

(42, 43). b Determined using ωi = ωio + (B1 + B0) m + (B1 - B0) m2 (39–41). Resonance with 2w2 (42, 43). a From

c Shifted

by Fermi

BO2-, CO2, and NO2+ form an isoelectronic series and the Walsh diagram predicts that each of these 16 electron species should be linear (43). Relying on the familiar Lewis dot structures often done in general chemistry, students confidently predict that each bond will be a double bond (44, 45). Hence, similar IR spectra are expected for each species. Although the IR spectra of the gaseous ions cannot be investigated at most institutions, computational chemistry can be used to compare the IR spectra of BO2- CO2 and NO2+ obtained at the same level of theory. B3LYP-6-311+G(2d, p) calculations confirm that each molecule is linear. The molecular constants produced are given in Table 3. 114

Table 3. Molecular constants determined for 11B16O2-, 12C16O2 and 14N16O2+ using DFTB3LYP- 6-311+G (2p, d) Constant

11B16O -

12C16O

14N16O +

re (pm)

126.16

116.03

111.83

θ (degrees)

180.0

180.0

180.0

Be (cm-1)

0.3316

0.3911

0.4211

Πu (cm-1)

598.70

675.64

653.78

Σg (cm-1)

1101.53

1364.47

1434.91

Σu (cm-1)

1963.24

2400.50

2405.95

fr (N/m)

1036

1617

1800

frr (N/m)

107

136.7

194.0

2

2

2

The trend in the bond lengths, the vibrational frequencies and the stretching force constants indicate that the bonds are strongest in NO2+ and weakest in BO2-. Most students hypothesize that the charge of the ion is a possible reason for this. Since Lewis dot theory indicates that the formal charges expected for B in BO2-, C in CO2 and N in NO2+ are -1, 0, and + 1 respectively, they conclude that the interaction of this charge with the slightly negative charges expected for the more electronegative oxygen are responsible for the observed trends (44, 45). However, the Mulliken populations produce a different picture for the bonding in these species (9, 46). The calculated charge on the boron in BO2- is +0.3418 with the charge on each oxygen being -0.6709 showing that the negative charge is not on the boron. The charges on NO2+ are +0.5458 on N and +0.2271 on each O indicating that the positive charge is spread over the molecule and not isolated on the N. Even CO2 is calculated to have a charge separation with the charge on C being 0.4318 and the charge on O is -0.2159. The stronger bonds in NO2+ are from increased covalent bond strengths rather than ionic charge stabilization. While there are other, more sophisticated ways to investigate the charge separations in these species, we use Mulliken populations because they are included in the out-put file for the program. Students can examine them without having to do additional calculations reducing the time needed for this exercise. C. IR and Raman of Benzene Learning objectives: This project investigates the relationship between the IR and Raman frequencies for a molecule that has an inversion center to confirm the exclusion rule. Students discover that degeneracies lead to fewer unique frequencies than the 30 frequencies predicted using the 3N-6 rule (37, 42, 43). The role computation plays in this exercise depends upon the available instrumentation. If IR and Raman are available, then the calculations are used to assist in making the spectral assignments. The calculations can also provide the data for any part of this exercise that can’t be measured because a needed instrument is not available. Although benzene is a known carcinogen and must be handled with care, measuring the IR and Raman spectra of this molecule reinforces several concepts about vibrational spectroscopy. While it 115

is easy to obtain the IR spectrum of benzene vapor by placing a few drops of the liquid in a gas cell and/or of benzene liquid by placing a drop of the liquid between two salt plates and to obtain the Raman spectrum of benzene liquid if a Raman spectrometer is available, this exercise can be done totally computationally if avoiding using benzene in the lab is desirable. Computational chemistry can also be used to provide data if one of the instruments needed to collect the data is not available. Results obtained from the calculations for the vibrational frequencies sorted by symmetry are presented in Tables 4 and 5. Fifteen (15) of the 30 normal modes of vibration are symmetric with respect to inversion (given as gerade (g) in the output) and 15 change sign on inversion (given as ungerade (u)). All of the normal modes with calculated Raman intensities greater than zero have gerade symmetry, while those with calculated IR intensities greater than zero have ungerade symmetry confirming the exclusion rule. Some normal modes are calculated to have zero intensity in both the IR and Raman spectra establishing that not every normal mode is spectroscopically active. Students often ask whether it is possible for a normal mode not to be observed. This exercise clearly shows that it is. Table 4. Calculated symmetries, frequencies, IR and Raman intensities for the normal modes of benzene with gerade symmetry. Frequencies and intensities were calculated using DFTB3LYP/ 6-311+G (2d, p). Symmetry

cm-1

IIR

IRaman

A1g

3190.2351

0.0000

362.3573

A1g

1010.4558

0.0000

54.7730

A2g

1389.4582

0.0000

0.0000

B2g

1002.0778

0.0000

0.0000

B2g

713.2584

0.0000

0.0000

E1g

857.5413

0.0000

3.2437

E2g

3165.4700

0.0000

130.5507

E2g

1632.1368

0.0000

12.8463

E2g

1198.8029

0.0000

7.1596

E2g

624.5751

0.0000

3.8623

Table 5. Calculated symmetries, frequencies, IR and Raman intensities for the normal modes of benzene with ungerade symmetry. Frequencies and intensities were calculated using DFTB3LYP/ 6-311+G (2d, p). Symmetry

cm-1

IIR

IRaman

A2u

681.8153

107.2564

0.0000

B1u

3156.1551

0.0000

0.0000

B1u

1030.4782

0.0000

0.0000

B2u

1329.0925

0.0000

0.0000

B2u

1175.4644

0.0000

0.0000

116

Table 5. (Continued). Calculated symmetries, frequencies, IR and Raman intensities for the normal modes of benzene with ungerade symmetry. Frequencies and intensities were calculated using DFT-B3LYP/ 6-311+G (2d, p). Symmetry

cm-1

IIR

IRaman

E1u

3180.4998

62.6327

0.0000

E1u

1517.0657

11. 6090

0.0000

E1u

1058.2068

2.8933

0.0000

E2u

975.6244

0.0000

0.0000

E2u

411.1954

0.0000

0.0000

II. Investigating the Properties of Atoms While the electronic structure of atoms is a common topic in physical and general chemistry, there are few laboratory exercises designed to investigate this topic (37, 44, 45). This section presents a way to use computational chemistry to investigate the electronic structures of atoms. Aufbau Principle and Hund’s Rules Learning objectives: This computational exercise is used to confirm that the aufbau principle and Hund’s rules predict the most stable ground state term symbols for atoms and for many ions. The aufbau principle and Hund’s rules are usually introduced as part of the discussion of electron configurations in general chemistry texts (44, 45). These configurations are used to determine term symbols in more advanced courses (37, 42, 43). With some knowledge about wave functions and electron configurations coupled with the realization that larger negative energies indicate the more stable state, students can use computational chemistry to investigate these concepts. For example, knowing that an s orbital can hold two electrons, it is easy to show that a pair of electrons in an s orbital with opposite spins produces a 1S state while a pair of electrons with the same spin would produce a 3S. Since this would violate the Pauli Exclusion Principle, the lowest energy triplet state corresponds to the promotion of an electron into the next available orbital. Hence the lowest 3S state for He corresponds to the 1s12s1 configuration, the lowest 3P for Be corresponds to the 2s12p1 configuration, and the lowest 3D state for Ca corresponds to the 4s13d1 configuration. By calculating the triplet – singlet energy differences for helium and the group 2 metals, the more stable state can be identified. As shown in Table 6, this value is positive in all cases confirming that the singlet states are more stable than the triplet states confirming that the electrons are paired in the s orbital as predicted by the aufbau principle. Computing the quartet – doublet energy difference for the group 13 elements for the term symbols determined for the ns2np1 (2P) and the ns1np2 (4P) configurations confirms that two electrons remain paired in the s orbitals after an electron is added to the p orbital. A similar result is obtained for Sc after an electron is added to the 3d orbital. As shown by the relative energies in in Table 7, the configurations where the low spin state where the s electrons remain paired are more stable in all cases, again confirming the predictions made using the aufbau principle.

117

Table 6. The calculated triplet – singlet energy differences using DFT-B3LYP/ 6-311+G (2d, p). All values are in atomic units. Atom

Esinglet

Etriplet

Etriplet – Esinglet

He

- 2.9135 a

- 2.1525 b

0.7611

Be

-14. 6713 a

-14.5811 c

0.0902

Mg

-200.093 a

-199.991c

0.1021

Ca

-677.576 a

-577.505d

0.0706

a ns2.

b 1s1 2s1.

c ns1 np1.

d ns1 (n-1)d1.

Table 7. Calculated quartet – doublet energy differences using DFT-B3LYP/ 6-311+G (2d, p). All values are in atomic units. Atom

Edoublet

Equartet

Equartet − Edoublet

B

- 24.6626 a

- 24.5300 b

0.1326

Al

-242.3867 a

-242.2472 b

0.1394

Ga

-1924.821 a

-1924.640 b

0.1915

Sc

-760.6207 c

-760.5866 d

0.0341

a ns2 np1.

b ns1 np2.

c 4s2 3d1.

d 4s13d2.

Adding additional p electrons increases the number of possible states. Using carbon as an example, there are possible states corresponding to the 2s12p3(5S), 2s22p2 with the p electrons unpaired (3P), and 2s22p2 with the p electrons paired (1D). Similar configurations, albeit with different term symbols, can be determined for any atom expected to have half-filled or less orbital (p1-3 or d1-5). Some examples of the calculated energies for several second period elements and ions and a few first row transition metals are presented in Table 8. Since the multiplicities depend on the number of unpaired electrons, the states are listed as high (2s12pn or 4s13dn), middle (2s22pn or 4s23dn with the p, d spins unpaired) and low (2s22pn or 4s23dn with the p, d spins paired). In all cases but chromium, the middle spin state has the lowest energy confirming the s electrons are paired and that the p or d electrons are unpaired as predicted by the aufbau principle and Hund’s rules. The results for Cr are consistent with the discussion of the stability of the half-filled d orbitals often presented in general chemistry textbooks (44, 45). Atoms with half-filled shells or higher can also be investigated, but the highest spin states will no longer automatically correspond to the promotion of an s electrons. To avoid confusion, these atoms are not investigated at JMU. One topic related to the aufbau principal that gives our students trouble is electron configurations for the 3d transition metal ions. Removing a paired 4s electron will produce a higher multiplicity while removal of an unpaired 3d electron will produce a lower multiplicity for the Sc, Ti, V, and Mn ions. As shown in Table 9, DFT calculations indicate the high spin state is more stable for these ions showing that removal of the s orbital is energetically more favorable. Once the d electrons are paired or for Cr, removal of either a d or an s electron produces the same multiplicities so term symbols must be determined to extend the analysis to these atoms. 118

Table 8. Calculated high, middle, and low spin energies for atoms and ions using MP2/ 6311+G (2d, p). All values are in atomic units. Element

ELow spin

EMiddle spin

EHigh spin

C

-37.67709 a

-37.75083 b

-37.62003c

C-

-37.71500 a

-37.79369 b

-37.53259 d

N+

-53.84417 a

-53.95151 b

-53.76551c

N

-54.36075 a

-54.48405 b

-53.89342d

N-

-54.38674 a

-54.45746 b

-53.85890e

O+

-74.28278 a

-74.45263 b

-73.36128d

O

-74.82509 a

-75.93517 b

-73.50158e

O-

-74.97782 a

-74.76729d

--------------

Ti

-849.2908 f

-849.3455 g

-849.3443h

V

-942.8066 f

-942.9014g

-942.8943h

Cr

-1043.167 f

-1043.341g

-1044.388h

Mn

-1149.638 f

-1149.831 g

-1149.842 i

Fe

-1262.374f

-1262.539 g

-1262.462 i

a 2s2 2pn p

spins paired. b 2s2 2pn p spins unpaired. c 2s1 2pn p spins unpaired. unpaired. e 2s2 2pn-13s1 p spins unpaired. f 4s2 3dn d spins paired. h 1 n i 1 n 1 unpaired. 4s 3d d spins unpaired. 4s 3d 4p d spins unpaired.

d 2s1 2pn-13s1 p g 4s2 3dn d

spins spins

Table 9. The calculated high and low spin energies for selected first row transition metal 1+ ions Using DFT-B3LYP/ 6-311+G (2d, p). All values are in atomic units. Element

ELow spina

EHigh spinb

ELow spint − EHigh spin

Sc

-760.3227

-760.3796

0.0569

Ti

-849.0873

-849.1099

0.0206

V

-943.6142

-943.6521

0.0379

Mn

-1149.586

-1149.657

0.0710

a 4s23dn.

b 4s13dn.

III. Mass Spectrometry Illustrated with Methane Gas chromatography-mass spectrometers (GC-MS) have become more common in organic and instrumental laboratories (47, 48). While students usually know or soon discover that a molecule will fragment into several different ions in the ion source, they have little understanding of the pathways that produce these ions. Computational chemistry can be used to investigate the energy needed to produce ions in the ionization source of the mass spectrometer. These exercises provide insight into one method of determining the ionization potential for an atom or a molecule. 119

Learning objectives: This exercise is used to investigate the chemical reactions that produce ions in the ionization source of a mass spectrometer. The minimum energy needed to produce each ion is determined and compared the values measured (appearance potentials) from the literature. A gas chromatography-mass spectrometers (GC-MS) are used in the JMU Applied Physical Chemistry Laboratory to measure the isotopic abundance of the chlorine using chloroform as the source molecule. As part of this exercise students use computational chemistry to investigate the ions observed in the mass spectrum. Since methane is the simplest hydrocarbon and can be used as a model hydrocarbon, it is used to investigate some possible ionization pathways that could produce the ions observed in the mass spectrum of this molecule. In an EI-MS, the ions are formed from a collision between an accelerated electron and the molecule in the ion source. This collision removes an electron and may also fragment the molecule to create positive ions that are detected by the mass spectrometer. Most EI-MS are done with a fixed voltage of 70 eV (47–50). Historically, variable electron energies were often used to produce the ions (49, 50). The ionization energy for the molecule could be determined by measuring the minimum energy needed to observe the ion (the appearance potential). Bond energies could also be determined from the difference in the appearance potentials for various ions produced as the electron energy was increased. It is assumed that all ions are produced from one collision between methane and the electron in this exercise. Students estimate the appearance potentials by calculating the energy needed to form an ion for several possible reaction pathways. The mass spectrum of methane taken with a 70 eV ionization voltage has mass/ charge signals at 16, 15, 14, 13, and 12 amu (36, 50). Assuming only species containing 12C and 1H are observed, these signals are readily assigned as CH4+, CH3+, CH2+, CH+ and C+ respectively. The appearance potentials and possible chemical reactions that could produce these ions have been reported by Stano et al. (50) The literature values reported below are all from this source. The simplist reaction for forming CH4+ is from the collision of methane with the energetic electron (50).

The minimum energy needed to observe the CH4+ is the ionization energy for CH4 and can be approximated from equation (2) (9).

The value determined using DFT-B3LYP/ 6-311+G (2d,p) is 12.70 eV (Lit. = 12.65 eV) when calculated using the energy minimized ground states of methane and the methane +1 ion. As shown in Figure 3, CH4+ has D2d symmetry rather than the Td structure most students predict. While this is expected from the Jahn – Teller effect, this topic is generally not discussed in most undergraduate physical chemistry textbooks. Fragmentation occurs at higher excitation energies. Two pathways that produce CH3+ from the interaction with one electron are possible (50).

120

Figure 3. Energy minimized structures for methane and the methane+1 ion Computational chemistry can be used to explore each of these pathways and to investigate the CH3+ ion. The appearance potential for reaction (3) determined using equation (5) is 14.52 eV (lit. = 13.58 eV).

A similar calculation for equation (4) gives14.72 eV (lit = 14.34 eV). Better agreement with the literature can be obtained by adding zero point energies and temperature corrections for the enthalpy to reaction (5). The lowest energy pathway to form CH2+, CH+ and C+ involve forming hydrogen during the electron collision (50).

The appearance potentials calculated with zero point corrections are 15.05 eV (lit 15.1 eV), 19.78 eV (lit. 19.8 eV) and 19.45 eV (lit. 20.5eV) for reactions 6-8 respectively.

Conclusions Most physical chemistry laboratories do not have access to every instrument needed to let students to investigate all of the topics introduced in a typical physical chemistry lecture course. Adding calculations compliments the experiments that can be done by allowing students to visualize concepts like molecular structures, molecular vibrations, dissociation pathways, etc. This manuscript presented some of the computational exercises that have been done at JMU, but it certainly is not a complete list of things that could be done. Since the goal of this chapter was to present applications that investigate topics normally discussed in the physical chemistry curriculum that could be done using modest systems, the systems presented use small molecules that can be calculated quickly at 121

a high enough level of theory to produce reasonable (though not exact) agreement between the calculated and the experimentally measured values. The focus is on exploring the chemical concepts rather than obtaining the highest precision possible using the best theory available. Our experience shows that these exercises often clear up misconceptions that students have about the topic and produce a better understanding of it.

Acknowledgments The author is grateful to the NSF- REU- 1062629, the NSF- REU – 1461175, and the Research Corporation Departmental Development Grant #7957 for providing the software and the summer support to develop these exercises.

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Chapter 10

Learning by Computing: A First Year Honors Chemistry Curriculum Arun K. Sharma* and Lukshmi Asirwatham Department of Chemistry and Physics, Wagner College, 1 Campus Road, New York, New York 10301, United States *E-mail: [email protected].

This chapter describes a second semester Honors General Chemistry course at Wagner College. Free computer software and online resources were embedded in the course to develop greater understanding of concepts presented in the lecture, engage students with computational interfaces, and to encourage greater ownership of the student learning experience. Every week one lecture period was dedicated to guided-inquiry style computational activities to supplement and supplant the conventional lecture presentations. The activities were focused on modeling and simulations to further understanding of topics covered during the conventional lecture times. All of these computational activities can be implemented on consumer grade computing devices like laptops or smartphones. Student Assessment of Learning Goals (SALG) survey results were highly encouraging and highlight an increase in student appreciation of the content and an increased interest in learning Chemistry.

Introduction Computational methods are now ubiquitous in all aspects of natural sciences. In particular, computational tools and methods have transformed chemistry. For example, modern drug development rests firmly on the foundations and developments in computational chemistry. Chemists have recognized this development and attempted to integrate computational chemistry into the chemistry undergraduate curriculum. A simple search for the word “computational” in Journal of Chemical Education titles gives more than 100 results. A search for the word “computational” anywhere in the article or publication across all American Chemical Society journals results in thousands of publications per year. These journals represent the breadth of chemistry research across the world and the number of papers with computational elements is only going to increase in the future. However, many undergraduate students have extremely limited exposure to these modern methods, even though the hardware and software costs for computational infrastructure have been dropping rapidly. © 2019 American Chemical Society

The chemistry community has invested significant effort to introduce undergraduate students to computational methods (1–6). Integration of molecular modeling and computational chemistry into organic chemistry (1) has also been reported and similar efforts have been successful for the physical chemistry laboratory (7). A strong trend in chemistry education has been the design and implementation of laboratory activities with computational chemistry for upper level courses. Instructors have a plethora of activities to choose in publications such as Journal of Chemical Education, The Chemical Educator, and American Journal of Physics. Students typically experience one or more computational chemistry exercises in their organic chemistry laboratory or during their physical chemistry coursework. However, the majority of students do not experience, or are not alerted to, the pervasiveness of computing and computational chemistry in modern chemistry research and the workplace. We think that introducing first-year students to computational methods has the potential to attract more students to the chemistry major. Adding computational tools to the first year courses also provides student centered learning opportunities for our students. The decreasing financial barrier to computer hardware and the increasing user-friendliness of researchgrade software packages that can be adapted to teaching now presents opportunities to introduce computation and computational tools as skills that can be practiced by students at all levels including first year students. The importance of visualization in disciplines like chemistry and biology cannot be overstated (8, 9), and the power of computational thinking to assist students in physics and other disciplines has been well documented (5, 6, 10–12). Computational tools provide an especially attractive mechanism to engage students with visualizations and animations. The Science, Technology, Engineering, and Mathematics (STEM) education community has also focused its attention on introducing students to computational thinking and computation as distinct from routine computer usage (13–15). The physics education community has been instrumental in adopting computer aided instruction and full-fledged curricula and majors in Computational Physics exist at many institutions (11, 16–20). Similar attempts to introduce computing in the chemistry curriculum have also been reported in the literature (5, 6, 21–23). These curricular level transformations are important milestones in modernizing and improving educational outcomes and skills of future graduates. However, an institution without the resources to engage in curricular overhaul may not be able to take advantage of such approaches. It is particularly challenging for smaller liberal arts colleges with limited faculty size and infrastructure to embed computing holistically in an entire discipline or program. The use of computational programs as instructional tools for first year laboratory experiments has become increasingly popular over the past two decades (4, 24–26). Recently, specialized courses that introduce students to scientific computing have also been developed for Chemistry students (27, 28). These efforts to incorporate computing in chemistry education as stand-alone courses or additional modules will particularly impact sophomore and higher-level courses in a few years, and students will appreciate and even anticipate computational approaches in those courses. An added advantage of computational tools is the integration of guided inquiry approaches in the learning experience. There are multiple approaches to teaching guided-inquiry and discoveryoriented learning. Process Oriented Guided Inquiry Learning (29) (POGIL) has been a very successful methodology for guided inquiry and has been adopted by a large community of educators (30–34). Our approach of guided-inquiry to lead students to discover physical or chemical phenomena has been previously used to create activities for the General Chemistry curriculum (35, 36) as well as a computational laboratory activity for organic chemistry students (37). 128

The overarching goal of the addition of computational modules to the curriculum was to introduce first year students to a variety of computational aids to understand chemical principles. In general chemistry, integrating technology throughout the curriculum presents the opportunity to encourage great strides in learning. The pedagogical goals of this course were for students to develop greater conceptual understanding of the material presented in lecture, make connections to real life situations, engage in scientific thinking and to take ownership of their learning. Our course provides students with a toolbox of molecular visualization and editing tools and computational tools that can be advantageously applied to a variety of courses offered in the STEM disciplines. The easy availability and widespread acceptance of these tools by students has the potential to increase the richness and depth of coursework in many disciplines.

Course Design The layout of a traditional college course was modified for an honors second semester general chemistry course. This course was designed to introduce students to using computers as a tool for both learning and solving problems in chemistry. Students met for hour-long classroom lectures twice a week. During lectures, students were introduced to the topic, engaged in class discussions, and solved numerical problems. The third lecture period in most weeks was dedicated to computational activities. During this period, students had the opportunity to explore and expand on the learning accomplished in the lecture. The computational activities included construction of small molecules, engaging in simple simulations to predict and explore impact of variables, and performing quantum chemistry calculations. These activities were designed to provide students with opportunities for visualization and to provide hands-on interaction with chemical concepts. The replacement of traditional lecture period with the hands-on computing activities necessitated that students stay current with reading assignments and take greater ownership of their learning. These students also participated in the standard second semester chemistry laboratory curriculum. However, the laboratory curriculum was not modified because there is no mechanism in place for a dedicated laboratory course for the Honors cohort. We think that the addition of a dedicated laboratory component would certainly allow a more in-depth exploration of some of the computational activities. However, we think that adding computational activities to the lecture provides opportunities for active learning and engagement and can be scaled to work with large classes. A key feature of all the applications chosen for this course is that they are all available at no cost to the student or the institution. Additionally, these applications are light-weight, portable, and can be installed on all three major operating systems: Windows, Mac, and mainstream Linux distributions. A number of platforms were used including Avogadro (38), Coggle (39), Kinetiscope (40), MolCalc (41), Molecular Workbench (42), NetLogo (5), and PhET simulations (43). Student work was assigned and submitted through Google Forms throughout the course. Each computational activity was completed with a supplementary worksheet created using Google Forms. These worksheets provided students with instructions to carry out the activities as well as with questions to guide their thinking about the simulations. Table 1 presents the activities and associated software packages/ online portals used for the computational element of the course. A brief description of each activity follows the table to highlight their applicability to the curriculum. We encourage interested readers to contact the corresponding author for access to these resources.

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Table 1. Computational activities implemented in the course Number

Activity Title

Key Idea

Software

Computing Device

1

Construction of small Connect molecular molecules composition to a macroscopic property

Avogadro

Laptop, desktop

2

Bond lengths and Explore bonding and vibrational motions of geometry of small small molecules molecules and examine their vibrational modes

MolCalc

Smartphone and all other devices

3

Optimization of water Intermolecular forces and Avogadro, Molecular network hydrogen bonding Workbench

Smartphone and all other devices

4

Analysis of reversible reaction

NetLogo

Laptop, desktop

5

Competing reactions Stochastic simulation of competing pathways in chemical reactions

Kinetiscope

Laptop, desktop

6

Acids and Bases

Dissociation, weak electrolyte, strong electrolyte, ocean acidification

PhET

Smartphone and all other devices

7

Le Châtelier’s Principle

Analysis of Haber’s process of ammonia production

NetLogo

Laptop, desktop

8

Vibrational contribution to entropy

Quantum mechanical calculation of thermodynamic properties for straightchain alkanes

MolCalc

Smartphone and all other devices

9

Mind maps / Concept Review and create study maps material for all chapters

Coggle / MindMeister

Smartphone and all other devices

Concentration profiles of reactants and products

The activities have been selected and adapted from published literature and designed to progress from construction of small molecules to identification and connection of molecular details to macroscopic properties. This is in line with the typical sequence of concepts covered in a standard second semester chemistry curriculum. Each activity is described briefly here: 1. Using Avogadro, students practiced constructing molecules. They identified bond lengths, bond angles, and molecular shape. The activity involved identifying nitro-functional groups prevalent in explosives and relating their heats of formation to their applicability as explosives (44). 130

2. Students used the Molecule Calculator (41) web application to perform geometry optimization of small molecules (45) (less than 10 Carbon atoms) using the Merck Molecular Force Field (MMFF) (46). This optimized structure is then used to perform low-level calculations using the GAMESS (47) computational chemistry engine through the web interface. The program computes the molecular orbitals and orbital energies at the RHF/STO-3G level of theory. (RHF = restricted Hartree-Fock and STO-3G is the basis set of atomic orbitals). The program also computes thermodynamic properties, vibrational frequencies and vibrational modes using the semi-empirical method PM3 (48). The defaults are chosen in the engine to ensure a fast turn-around time for calculations. The students optimize geometries of simple molecules like O2, N2, HCl, HF, HBr, H2O, CO2, NH3 and CH4, increasing in complexity from homonuclear diatomic molecules to heteronuclear penta-atomic molecules. The calculation presents students with the vibrational modes of each molecule and the electrostatic potential. This exercise is used to connect basic chemical bonding principles and dipole moment concepts. The students particularly enjoy visualizing the vibrational modes and the electrostatic potential for these molecules. 3. Intermolecular forces were explored through the application of simple molecular mechanics optimization in Avogadro (38). The students construct a small cluster of water molecules and perform energy minimization and observe in real-time, the impact of hydrogen bonding on the final arrangement. For a sufficiently advanced cohort, this activity also allows a brief exploration of force field effects. In particular, the MMFF94 (46) variant has an explicit hydrogen bonding term, while the Universal Force Field (49) (UFF) does not include hydrogen bonding. The application of these differing force fields gives rise to different overall arrangements of the water cluster. Students also explored the effect of temperature on intermolecular bonding through a simulation in the Molecular Workbench (42) application. The unoptimized and optimized collection of water molecules is shown in Figure 1. 4. Students analyzed the kinetics of a reversible reaction and simulated the impact of different reaction conditions: differing rates of forward and reverse reactions in the NetLogo (5, 21) agent-based modeling language. This exercise is adapted from a pre-built model in the NetLogo distribution. The students predicted concentration profiles for the specific reaction conditions and then simulated the specified conditions to record the output and compared it with their prediction. 5. The next exercise involved students implementing and analyzing a stochastic simulation (50, 51). Numerous publications in chemical education literature (52–55) have argued in favor of introducing students to stochastic aspects of chemical behavior and this activity attempts to provide a general introduction through the application of Kinetiscope (40) program. Kinetiscope is a general purpose, stand-alone stochastic chemical kinetics simulator. It has a user-friendly graphical interface and is well suited for modeling both, simple and complex chemical kinetics in gas, solution, and solid phases. The students simulate and analyze a set of competing reactions under different conditions of reaction rates. This activity allows students to explore complicated reactions which are not typically accessible to first year students in a General chemistry course. The students predict the expected concentration profiles and then run the simulation to check their understanding. An important aspect of the output is the fluctuations that are inherent to a stochastic 131

6.

7.

8.

9.

simulation. This exercise provides a segue to introduce students to the difference between stochastic simulations and numerical solutions of differential equations. Figure 2 presents a simulation result of a set of competing reactions. Le Châtelier’s Principle was explored in the NetLogo (21) modeling environment to study the impact of various system parameters. This chemical principle states that if a system that is at equilibrium is perturbed, the system will readjust to establish a new equilibrium. The students simulated a reaction that is bimolecular in the forward direction and unimolecular in the reverse direction. The corresponding canonical example is the dimerization of nitrogen dioxide, 2 NO2(g) ⇌ N2O4(g). Students discover the role of each variable, rate constants, temperature, concentration of reactants and products, and the impact of volume on the equilibrium. Students utilized the PhET (43) website to engage with the Acid Base solutions activity. This activity connects degree of dissociation to conduction of electric current and provides a very strong visual reinforcement of these concepts to students. Students solve questions associated with acid-base concepts and then engage in a class discussion on ocean acidification and climate change. This connection helps students to understand that even simple concepts like acids and bases can be useful to understand large scale phenomena like climate change. PhET simulations were also used in many of the in-class activities during the course. The penultimate activity in the course corresponds to the Thermodynamics unit in the curriculum. Students use the MolCalc (41) web application to study a series of straightchain alkane molecules and compute their thermodynamic properties. The activity engages students to notice the connection between number of atoms in a molecule, the number of vibrational modes, and the subsequent increase in vibrational contribution to entropy. This activity, like most other activities in the course, presents opportunities to pool data across the class, and present visualizations of the data to engage in class discussion. The connection between increased number of atoms in the molecule and a subsequent increase in vibrational contribution to the entropy is made clear by this exercise. Figure 3 shows aggregated data from this activity, where the vibrational entropy of a series of straight chain alkanes is plotted against the number of atoms. This activity highlights the increasing contribution of vibrational entropy as the number of atoms in the molecule increased. The students also study the variety of molecular vibrations displayed by these molecules. The final activity engaged students to create mind-maps or concept-maps to aid in their studies of Chemistry as well as other subjects. We have utilized Coggle (39) and MindMeister (56) apps for this purpose. These apps work on all platforms and have free versions which can be used by students. We split the class into groups and assigned each group to create mind-maps for a specified number of topics. The students pooled all the mind-maps together and peer reviewed each other’s contribution to prepare a set of resources to aid in their preparation for the final exam. This exercise also provided a student driven review of all units covered during the semester.

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Figure 1. Water molecules arranged randomly in Avogadro. On the right, the water molecules reorient themselves during energy minimization. The hydrogen bonds are displayed as dashed lines.

Figure 2. A concentration profile of a competing reaction analyzed in Kinetiscope. The rate constants for the reactions are represented on the arrows.

Figure 3. The computed vibrational entropy as a function of the number of atoms in a molecule.

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Course Assessment A Student Assessment of Learning Goals (SALG) (57, 58) survey was completed at the end of each iteration of the course. The questions and student responses are shown in Table 2. This Honors General Chemistry course has been taught twice at Wagner College, with 9 students in the first iteration in Spring 2017 and with 5 students in the second iteration in Spring 2018. Over the two years, students reported on the quality and impact of the computational activities embedded in the course on the SALG. The class sizes are small, however, they are typical of enrollment for the Chemistry Honors section at this institution. The overall impact of the computational activities on the learning goals of the course appears to be positive. The students seem to indicate that computational activities helped them visualize chemical and physical properties. The proportion of students reporting “Great gain” has increased in the second attempt of the course. Some of the factors that could be responsible are a refinement of the activities resulting from feedback of the first cohort and a smaller enrollment in the Spring 2018 semester. Student feedback from the first iteration of the course provided the authors with tips to improve the learning experience. We integrated Google Forms to streamline the process of implementing the activities in the course. We also added a discussion of results at the end of the class. This allowed students to present their interpretation of each activity and achieve a global view of the results. The students informally reported satisfaction with the variety of interfaces and programs that were used in the course. The integration of specialized software packages such as NETLOGO and Kinetiscope provided an opportunity to highlight their applications beyond introductory chemistry. We think that introducing students to different interfaces was one of the unique experiences and we were glad that students responded positively to this element of the experience. We plan to integrate some of these activities in a regular General Chemistry section with larger student enrolment in the next academic year. Table 2. SALG assessment data for the two iterations of the course. How did the weekly computer activities enhance your learning in Year the course?

No gains

A little gain

Moderate gain

Good gain

Great gain

10%

10%

50%

10%

10%

0%

20%

0%

20%

60%

2017

0%

20%

30%

30%

10%

2018

0%

20%

20%

40%

20%

The computer activities increased 2017 my interest in learning about the subject 2018

0%

10%

60%

10%

10%

20%

0%

20%

20%

40%

2017 Visualizing chemical and physical processes 2018 Using the computer activities helped my learning of chemistry

Conclusion We have provided a model for the inclusion of computational activities in a general chemistry curriculum. This model explores various graphical user interfaces as well as specialized applications. The applications used are all freely available and include cross platform support. Students displayed remarkable enthusiasm for these activities. Their responses in the SALG survey and informal communication reinforce their support and excitement for such pedagogical endeavors. One of the 134

key advantages of the applications and activities chosen is that some of the activities could be used as part of homework exercises or exploration exercises that motivated students could pursue in their own time. These exercises could also be expanded to provide laboratory experiences. We believe that the model can also be expanded and scaled up to provide an interactive learning experience for large classes. The positive student comments, both formal and informal, indicate that such an exposure at an early stage has the potential to boost and sustain student interest in Chemistry.

Acknowledgments We are grateful to the students in the Chemistry 112 Honors section for participation in this course and suggesting multiple improvements. We also acknowledge the support provided by the Department of Chemistry & Physics at Wagner College.

References 1. 2. 3.

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Chapter 11

Integrating Computational Chemistry into an Organic Chemistry Laboratory Curriculum Using WebMO Brian J. Esselman* and Nicholas J. Hill* Department of Chemistry, University of Wisconisn, 1101 University Avenue, Madison, Wisconsin 53706, United States *E-mail: [email protected] (B.J.E.). *E-mail: [email protected] (N.J.H.).

Given the fundamental importance of computational analysis in organic chemistry, it is incumbent upon instructors to incorporate computational chemistry into any contemporary laboratory course. As a result, educators must decide how best to implement computational chemistry tools and concepts in their courses. We report a suite of introductory exercises has been developed for use in the introductory organic chemistry laboratory at the University of Wisconsin-Madison to train students in the use of computational chemistry to support experimental work throughout the term. By completing these exercises, students become familiar with WebMO as an interface for Gaussian and learn to perform simple geometry optimization, vibrational frequency calculation, NMR chemical shift prediction, molecular orbital (MO), coordinate scan, intrinsic reaction coordinate (IRC), and natural bond orbital (NBO) calculations. These introductory calculations are performed in the context of studying the conformational isomerism of 1,3-butadiene, the impact of electron-withdrawing and electron-donating groups on aromatic π systems, the prediction of IR and NMR spectra, orbital overlap and geometry changes of a nucleophilic acyl addition reaction, and the fragmentation of radical cations. Most importantly, students learn how to use their computational chemistry results to rationalize experimentally observable chemical phenomena. Thus, the guided exercises provide the foundation upon which students analyze their own computational and experimental data throughout the course.

© 2019 American Chemical Society

Introduction Computational chemistry is a thriving field of modern chemical and biological research and is becoming increasingly prominent in the contemporary undergraduate chemistry curriculum. The pedagogical value of the technique to the organic chemistry instructor lies in its ability to reasonably predict and rationalize electronic and molecular structures, reactivity profiles, and chemical and physical properties of molecules. Although traditionally more common within the domain of physical chemistry or computational chemistry courses (1–4), an initial implementation of computational modeling in an organic chemistry course was described over 20 years ago (5). The majority of subsequently reported implementations have been either stand-alone exercises or calculations associated with an individual laboratory experiment (6–19), however there have been a few reports of course-wide or curriculum-wide integrations of computational chemistry (20–23). The recent increase in computational chemistry exercises utilized in the undergraduate curriculum has been spurred by the wider availability of computing resources (24–26) and software designed for the novice (24, 27–30). The goal of this chapter is to provide a guide for the complete and authentic incorporation of computational chemistry into an organic chemistry curriculum. Our implementation is described in the context of a single-semester laboratory course at an R1 institution, however the ideas and resources are equally applicable to a lecture course. Along the way, we highlight the advantages (identification of student misconceptions, ability to augment interpretation of experimental and spectroscopic data) and challenges (infrastructure requirements and instructor expertise) inherent to the operation. The Introductory Organic Chemistry Laboratory course (CHEM 344) at UW-Madison is a two-credit course in which ~ 1200 students enroll per calendar year. Students routinely collect NMR, GC-MS, and IR data on state-of-the-art instruments. As described in a previous publication (22), we believe that a key analytical tool such as computational chemistry should be employed wherever it can provide insight to students. Thus, we have effectively integrated computational chemistry into our organic chemistry laboratory curriculum to the same extent as NMR, IR or GC-MS data analysis. Our curricular implementation is more than just a stand-alone experiment; computational chemistry is utilized throughout the course. The integrated nature of our approach increases student understanding of the role of computational chemistry, allows them to feel that their learning investment has been worthwhile, and removes the perceived novelty of the tool. Indeed, our students and teaching assistants experience and use computational chemistry as simply another tool for understanding structure and reactivity. The timeline for our implementation of computational chemistry can be separated into three phases: 1) introduction to the use of computational chemistry while learning spectroscopy, 2) the computational chemistry experiment during the skill-building portion of the semester, and 3) the post-experiment utilization to support each experiment throughout the semester. Foundational experimental and computational techniques are presented early in the course, and thus students are encouraged to view computational chemistry as a routine tool to use in support of their experimental work providing a deeper conceptual understanding of the material. The current chapter focuses on the latest version of our computational chemistry experiment, building upon the exercises described previously, and highlights its position in the laboratory curriculum with respect to other experiments and computational exercises (22).

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Curriculum Implementation The organic chemistry laboratory course (CHEM 344 – Introductory Organic Chemistry Laboratory) is designed and coordinated by two full-time laboratory directors (the authors) and taught by 25-35 graduate student teaching assistants (TAs). The content of the course corresponds to the typical two-semester organic chemistry lecture sequence, and students enroll in the lab course subsequent to or concurrent with the second semester lecture. The laboratory curriculum features topics from both the first- and second-semester lecture courses, but nevertheless is an independent course with its own curricular goals and assessments. Throughout the entire semester, students complete computational exercises using research-level hardware and software infrastructure to support their spectroscopic analyses and to rationalize their experimental outcomes. Students use the UW-Madison chemistry department shared computer cluster designated for use in all of the undergraduate and graduate courses (Sunbird), upon which Gaussian 09 (27) and WebMO (24) are installed for general use. All of the exercises and examples described herein have been implemented within the framework of CHEM 344. The WebMO software serves as a user interface to a variety of computational programs, such as Gaussian 09 (27) (commercially available), to PSI 4 (26) (free), or GAMESS (free) (28). Thus, WebMO is a convenient option for computational chemistry regardless of institutional computational resources and infrastructure. In the context of CHEM 344, WebMO is installed as a front-end for Gaussian 09 on the departmental computer cluster (approximately one processor available for every five students), which has been adequate. Each student is assigned an individual WebMO account in which to perform all of the required calculations. The account can be accessed via any computer connected to the internet, thus it is not necessary for the students to be physically present on campus to log into their account. All student calculations described in this work are performed with in Gaussian 09 using density functional theory (B3LYP) with a 6-31G(d) basis set without a solvation model. The results of these gas-phase calculations are sufficiently accurate and obtained within an appropriate time frame (800 students) project is the Freshman Research Initiative (FRI) at the University of Texas at Austin (9). In this program undergraduates gain their core chemistry competencies participating in one of several “streams” that focused on genuine research projects in one of four areas of chemistry: organic, analytical, inorganic, or biochemistry. Examples of streams are: Supramolecular Sensors, Nanomaterials for Chemical Catalysis, Functional Materials Based on Metal Complexes, Synthesis and Biological Recognition, and Virtual Drug Screening (9). In each stream students gain skills in synthesizing molecules, measuring and analyzing UV-vis spectra, and characterizing chemical molecules, complexes, etc. In the context of computational chemistry, notably, computer modeling has been an integral part of a larger FRI stream, such as the Virtual Drug Screening. In that stream, students perform protein synthesis and purification, and then characterize target proteins with UVVis spectroscopy. As a part of FRI activities students explore 3D structures of proteins, run docking simulations, and analyze obtained results (9). As emphasized by the authors of the FRI model, faculty buy-in and participation of postdoctoral-level research educators play a critical role in the success of larger (30-35 students) FRI streams (9). Another example is a smaller-scale (33 students) one-semester CURE in Physical Chemistry laboratory at Emory University as reported by Williams et al. (10). It has been shown that the project helped to standardize undergraduate research training, and increased student sense of ownership of their projects. Chemistry majors worked on investigating of intermolecular interactions of ligands (uremic toxins) with human serum albumin (10). The ultimate goal of that research project was to improve dialysis methods. During their CURE activities, students used stopped-flow kinetics, isothermal titration calorimetry, and molecular dynamics simulations to study ligand binding (10). Molecular modeling can be integrated into organic chemistry laboratory. For example, in the project on investigation of the dimerization of isobutylene students performed synthesis, isolation, and characterization of obtained trimethylpentene isomers by Schuster et al. (11). The characterization employed NMR, IR, CG-MS, and molecular modeling techniques. Students performed geometry optimization of possible isomers with the B3LYP/6-31G(d) method, studied the Lowest Unoccupied Molecular Orbital (LUMO) of the intermediate structure in order to understand the mechanism of the reaction. In this example, addition of molecular modeling helped to gain a better understanding of the mechanism of the isobutylene dimerization reaction. A research-related laboratory course focused on modeling organic photovoltaics has been also proposed by Schellhammer et al. (12). In that course, students modeled dipyrromethene molecules that can be potentially used as donor materials in organic photovoltaics. Students used densityfunctional theory-based tight-binding (DFTB) method implemented in DFTB+ package to run the simulations (13). Classical molecular dynamics (MD) simulation package (e.g. Amber) (14), can be used to cover concepts of diffusion and radial distribution functions (RDFs) in physical chemistry laboratory as reported by Kinnaman et al. (15). These MD simulations help to interpret the physical meaning of RDFs and diffusion coefficients and compare various water models (e.g. TIP3P, OPC, etc.), (15). There are also a few recent projects beyond traditional computational chemistry where molecules are constituted and optimized with standard molecular modeling and/or electronic structure packages. A special molecular dynamics software has been created in the Foley lab (16) to 230

interactively model real gases using the Lennard-Jones potential approximation. The package enables quantitative measurement of deviations in properties (e.g. macroscopic compressibility) of real gases from ideal behavior. Recently developed software (17, 18), which integrates YAeHMOP and Avogadro Molecular Editor and Visualizer packages enables calculation of electronic band structure and other properties of bulk materials traditionally covered in physical chemistry or materials science. The calculations are based on the extended Hückel theory and accounts for the periodicity of materials in 1, 2, or 3 dimensions. The software enables calculation of band structure (crystal orbitals), density of states (DOS), crystal orbital overlaps, etc. It has been shown by Avery et al. (19) that the software is capable to model electronic band structure and DOS of such important materials as silicon and graphite. One of the main advantages of the software is that students can start modeling electronic band structure of materials with the software even before they completely mastered underlying quantum mechanics. Chemical kinetics of oscillating chemical systems (e.g. Belousov-Zhabotinsky reaction) can be simulated with the Brusselator model (20). This model has been implemented by Lozano-Parada et al. (20) with Comsol Multiphysics, Matlab, and Microsoft Excel packages. This approach provides undergraduate students to quantitatively model complex kinetics of autocatalytic chemical reactions. There is an interesting idea of a classroom lecture demonstration/student laboratory exercise proposed by Brom (21), which integrates theoretical and experimental components to cover the wave–particle duality as one of fundamental concepts of quantum physics. First, the photon wavelength is derived through the calculation of the interference of quantum probability amplitudes. Then, this theoretical result is confirmed by the light scattering experiment to determine the wavelength of the photon. This activity provides an opportunity for students to directly experience and explore the wave–particle duality in the experiment and describe it in the precise mathematical form.

Laboratory Units Implemented at Monmouth University In order to improve students’ critical thinking and avoid “cookbook” labs we have developed a series of project-based laboratory units that integrate elements of scientific research into undergraduate courses at Monmouth University. Each project is constructed to balance instructional and research objectives. While literature examples show that CUREs can be implemented in larger classes of 30-35 students (8, 9) the described units implemented at Monmouth University have primarily been used in Physical Chemistry Laboratory (2 semesters) and Computational Chemistry courses that typically enroll 8-10 students per section. The experiments have been performed in our Physical Chemistry Laboratory equipped with typical instrumentation (e.g. FTIR, UV-Vis spectrometers, pH probes, etc.) to carry out traditional physical chemistry experiments. Some additional equipment (e.g. microcontrollers) and supplies needed for the implementation of laboratory units were purchased with departmental lab-fee funds and from external grants. The full list of equipment and supplies needed to carry out the experiments is given in the corresponding references. Development of Laboratory Instrumentation: A Titration Experiment The project is focused on development and integration of chemistry laboratory instrumentation (e.g., automatic titrator) into the industrial internet. The industrial internet incorporates physical hardware and software, which is able to receive data from sensors, analyze it, and carry out necessary laboratory procedures automatically. Students participation in this project build and calibrate an 231

automatic titrator (22). The titrator is based on an open-source microcontroller Arduino platform (23) and novel methodology of data integration developed in our lab (Figure 1), (22). The titrator is programmed by students to perform automatic acid/base titration. Skills learned in this lab by students can be also used to construct the hardware and software necessary to automate, remotely control, and integrate a variety of sensors commonly used in chemistry and environmental science (e.g. salinity, temperature, pressure, etc.) into the Internet. The main goal of the first part of the unit is to give students a basic knowledge and understanding of the microcontroller board and electronic circuit components. Upon completion of the unit, students will also be able to create a simple circuit by connecting the microcontroller board and a pH sensor. Then students build the titrant dispenser circuit and volumetric assembly. The instrument is calibrated with the desired titrant (e.g., NaOH solution).

Figure 1. Automatic titrator: an electronic circuit and Arduino software perform automatic measurements of pH. Control valve is used to dispense titration solution. The software performs recording and analysis of the obtained pH values. Adapted with modifications with permission from Ref. (22). Copyright 2016 American Chemical Society. The unit integrates topics in chemical kinetics, equilibrium, electric circuits and building instrumentation for research purposes. Students involved in this laboratory unit develop a sense of ownership of the project. Critical thinking is encouraged when they work on assembling and calibrating the instrument, debugging the software, and troubleshooting hardware problems. In our experience, a team of two students working on the project is best, as they can exchange ideas, collaborate, and stay motivated. The titration experiment includes the following CURE elements: Practicing Science – students build an experimental setup by themselves (2); Iterative Approach – the experiment has been revised a few time to improve performance (e.g., increasing signal to noise ratio) (4); Collaboration and Teamwork – students work in teams to build the titrator. This laboratory unit covers the following ACCM concepts: chemical measurements: electrochemical methods (IX.D.3.a), appropriate experimental design is required to obtain 232

trustworthy data (IX.F.1-3), proper safety precautions must be taken to minimize risks associated with chemical experiments (IX.G.1.a). Modeling Ligand Binding to DNA Binding of small organic ligands to DNA minor groove (24) as well as stabilization of human telomeric DNA high-order structures (e.g. G-quadruplexes) has become a promising approach to introduce novel anticancer drugs (25). In the proposed unit students investigate binding of naphthalene diimide (26) and diminazene (Figure 2) ligands (27) in order to evaluate the principal factors determining contributions to DNA-ligand binding. A molecular docking technique and ab initio based fragment molecular orbital method are used to estimate binding affinities of ligands. Students select ligands based on primary literature search and based on recommendations by the instructor. Then, students find the optimal ligand based on results of binding energies and docking modes (positions of the ligands with respect to the DNA) using the computational protocol developed in our lab (27). The unit integrates topics in molecular modeling, thermodynamics, kinetics, and quantum theory. The modeling ligand binding to DNA laboratory unit embeds the following CURE elements: Practicing Science – students formulate a hypothesis about potential abilities of organic molecules to bind to DNA; Discovery and Inquiry – students verified their hypotheses performing molecular docking simulations; Science Relevance and Novelty – students are offered structures of newly synthesized ligands to check their affinity to DNA.

Figure 2. Organic ligand diminazene (DMZ) docked to the minor grove of DNA. Adapted with modifications with permission from Ref. (27). Copyright 2018 American Chemical Society. Main ACCM concepts covered in this unit include: finding minimal energy structures with quantum chemistry methods (III.C.1.a,c), intermolecular forces (IV.A.1.a-d, IV.A.2.a-b) in general and hydrogen bonding specifically (IV.C.7.a-c) determines conformations of large biological molecules (IV.B.1.a-c). Solvatochromism of Organic Dyes Organic solvatochromic molecules, such as Reichardt’s betaine Et30 (2,6-diphenyl-4-(2,4,6triphenyl-1-pyridinio) phenolate) and Brooker’s merocyanine (4-[(1-methyl-4(1H)233

pyridinylidene) ethylidene]-2,5-cyclohexadien-1-one) dyes change their color depending on polarity of the surrounding solvent (28). Thus, they are used to investigate the intermolecular interactions between solute and solvent molecules and find their applications as sensors for identification of organic solvents. In this unit students study solvatochromic effects in organic molecules. This solvatochromic behavior is largely due to intermolecular charge transfer under electronic excitation. Students participating in this project have investigated the solvatochromic behavior of Reichardt’s and Brooker’s dyes by UV-Vis spectroscopy in solvents of varying polarity (Figure 3).

Figure 3. UV-Vis absorption spectra of the Reichardt’s betaine Et30 dye (shown in inset) in solvent of various polarities demonstrate a strong solvatoshimic shift of absorption maxima (marked with arrows). The unit can be enhanced by adding a computational component – quantum chemical modeling of solvatochromic shifts using our fragmentation-based approach (29). In the course of the experiment, students choose a solvatochromic dye and determine appropriate solvents to dissolve the molecule. Comparing measured and simulated UV-Vis spectra, students determine which electronic excited states contribute to the solvatochromic behavior and which solvents can be discriminated using their molecule chosen as a sensor. The unit integrates topics in electronic spectroscopy, computer simulations, and quantum theory. This experiment includes three CURE elements: Practicing Science – students read primary literature on solvatochromic properties of organic compounds; Taking an Iterative Approach – students refine experimental procedure finding the best conditions (e.g. solvents, concentrations of solutions) to observe solvatochromic properties of organic dyes; Discovery and Inquiry – running spectroscopic experiments students observe solvatochromic shifts of given samples and can compare obtained results with their expectations based on literature data. The ACCM concepts covered here include molecular spectroscopy (IX.D.1.a,e), various intermolecular interactions (IV.A.1.a-d, IV.A.2.a-b, IV.C.7.a-c), effects of solvents (IV.E.1.b) and their polarity (IX.C.2.a-b) on molecular properties. Transient UV-Vis Spectroscopy of cis-trans Conformational Transitions in Diazo Dyes. Molecular diazo dyes (Figure 4) undergo a light-induced trans-cis isomerization and transform back to the trans conformation in the dark. These compounds recently received widespread attention because of their applications in neuroscience (30). In their extended trans conformations they are able to block engineered ion channels in neurons, which opens a possibility of controlling neurons 234

with pulses of laser light. The time scale of the cis-trans transition in diazo dyes is long enough (10-4-10-2s) to make it possible to determine rates of photoinduced reactions using a KRONOS flash photolysis instrument (31), available in our laboratory. The unique feature of this experimental setup is a custom-made temperature control unit assembled by students (Figure 4), (32). Using this setup students study the kinetics of cis-trans transition at various temperatures, which allows them to determine the activation energy of the cis-trans isomerization in diazo dyes experimentally using the Arrhenius plot.

Figure 4. “Transient UV-Vis spectroscopy of cis-trans conformational transitions in N,N-dimethyl-4,4′azodianiline” Kinetics of isomerization is studied at various temperatures in order to estimate the activation energy of cis-trans transition. Adapted with modifications with permission from Ref. (32). Copyright 2016 American Chemical Society. Students can also compare experimental results with computational (DFT) study, and analyze molecular structures and relative Gibbs free energies between the model isomers in the gas-phase and in solution in order to characterize potential photoswitches. The transient UV-Vis spectroscopy of cis-trans conformational transitions in diazo dyes experiment involves three CURE elements, similarly to the titration experiment: Practicing Science – an experimental setup is built by students; Iterative Approach – the experiment has been revised and the procedure has been fine-tuned by the participating students; Collaboration and Teamwork – students work in teams to build the temperature-controlled sample holder. The experiment above covers the following ACCM concepts: experimental molecular UV/ Vis spectroscopy (IX.D.1.a,e), temperature control and measurement of temperature effects (IX.D.2a,b), spectroscopic observation of reaction intermediates (IX.F.2.a) and Arrhenius equation (V.C.1.b) . Computational Laboratory Units The two laboratory units described below purely computational and require only a computer laboratory and R software. They are offered as a part of our physical chemistry laboratory course, but can be implemented in a computational chemistry course as well. 235

In the two computational laboratory units described below (“Michaelis–Menten Kinetics”, “Hückel Molecular Orbital Method”), the most important CURE component is Discovery and Inquiry – students check proposed hypotheses about changes in results of simulations (concentrations of products of enzymatic reactions or energies and shapes of molecular orbitals) as a result of changes in initial parameters of simulations (e.g., an initial concertation of the substrate or energies of atomic orbitals). ACCM concepts covered by those laboratory units include chemical kinetics topics (VII.B.1.a-f) including the reaction mechanism (VII.C.1.a-b), the Michaelis–Menten model of enzymatic kinetics (VII.E.3.a), Visualization and estimation of energies of π-orbitals with the Hückel method (X.A.4.b). Michaelis–Menten Kinetics This computational laboratory unit is dedicated to modeling of chemical reactions catalyzed by enzymes in accordance with the Michaelis–Menten kinetics model (Eq. 1), (33):

where E is the enzyme, S is the substrate, ES is the enzyme-substrate complex, and P is the product. It is emphasized that the reaction scheme is rather general. However, the approach can be used to model aminoacylase catalyzed hydrolysis reaction (34). A brief and excellent introduction to basics of Michaelis-Menten and Briggs-Haldane Kinetics is available at the Prof. W.M. Atkins website (35). Students model concentrations of reactants and produce of functions of rate constants and initial concentrations of substrate and enzyme. Students also investigate the steady-state, free ligand, rapid equilibrium approximations (35). In our implementation of the laboratory unit, students use Rlanguage (36) to explore the kinetic model (Scheme 2):

Scheme 2. Excerpt of the R-script used by students to model enzymatic kinetics. Hückel Molecular Orbital Method One of the few basic approximations in computational quantum chemistry is the molecular orbital theory which commonly employs a linear combination of atomic orbitals molecular orbitals (MOs) (37). In the Hückel approximation the diagonal matrix of MO energies (ε) and matrix of coefficients (c) of molecular orbitals are obtained by solving the eigenvalue problem (Eq. 2) diagonalizing the Hamiltonian matrix (H): 236

In this laboratory unit, the matrix formulation of the Hückel method is employed to compute and interpret energies and coefficients that show contributions of separate atomic p-orbitals to molecular orbitals of simple conjugated systems. Students define and diagonalize the Hamiltonian matrix using R-language in order to obtain energies and coefficients of molecular orbitals (Scheme 3).

Scheme 3. Excerpt of the R-script used by students to obtain energies and coefficients of molecular orbitals of cyclobutadiene with the Hückel Molecular Orbital Method. Skill-Building Laboratory Units There are several skill-building laboratory units where students learn specific experimental techniques (e.g. FTIR, UV-Vis spectroscopy, etc.), apply theoretical models learned in the lecture courses (harmonic oscillator, particle in a box model, etc.), and gain skills in standard computational quantum chemistry tools and methods (e.g., geometry optimization with Gaussian (38) or Spartan (39) packages, etc.) A brief overview of those laboratory units is given below. Skill-building laboratory units are, indeed, more traditional labs. They may not contain substantial research or inquiry components at this moment. However, those labs help students to master basic skills that are critical for further labs (e.g. research-based lab on UV-Vis spectroscopy of cis-trans conformational transitions in diazo dyes). Skill-building labs cover ACCM topics on molecular IR spectroscopy (IX.D.1.a-f), isotopic effects on IR spectra (1.A.3.a) simple quantum mechanical models (e.g. particle in a box) – (X.A.1.e), transition state theory (VII.D.4.d), modeling of transition states (X.D.2.b, III.C.3.c) with quantum chemistry methods. Vibrational Spectroscopy: Isotopic Shift Another laboratory unit integrating experimental and computational components is dedicated to principles of vibrational spectroscopy and the harmonic oscillator model. Students record FTIR spectra of water (H2O) and deuterium oxide (D2O) (40), and then interpret observed isotopic shift applying the harmonic oscillator model. Harmonic frequency of the O–H stretching vibrational modes (Eq. 3):

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where k is force constant, and μ is reduced mass μx (x = H2O or D2O). The reduced mass μx = momx/(mo + mx) for water or deuterium oxide are computed from masses of oxygen atom (mo) and either hydrogen (mH) or deuterium (mD) respectively. Then students estimate the effect of the reduced mass on the vibrational frequency, which can be presented as the ratio (Eq. 4):

Then, students assign experimental vibrational modes and learn selection rules of FTIR spectroscopy performing obtained results with normal mode analysis with traditional DFT methods (e.g., B3LYP/6-31G*), (41–44). UV-Vis Spectroscopy of Conjugated Dyes Students record UV-Vis spectra of a series of conjugated dyes (e.g. 3,3′-diethylthiacarbocyanine iodide, 3,3′-diethylthiadicarbocyanine iodide, and 3,3′-diethylthiatricarbocyanine iodide) with increasing length of the conjugated chain and determine maxima of their absorption due to electronic π- π* transitions. Then, the particle in a box model is used to predict the relationship between the lengths of the molecules and maxima of their UV-Vis spectra (longer molecules have lower wavelength of absorption) as proposed earlier (45). Additionally, students learn basics of molecular modeling building 3D models of the dyes and computing molecular orbitals with DFT methods (41). Dissociation of Formaldehyde The laboratory unit is focused on investigation of the dissociation of formaldehyde with formation of carbon monoxide and hydrogen (46). Students optimize formaldehyde, carbon monoxide, and hydrogen molecules. Then they optimize the transition state in the dissociation reaction with B3LYP/6-31G* method. Students learn basics of the Transition State Theory (TST) exploring the mechanism and estimating the activation energy of the reaction. Then, students calculate the rate constants of the forward and reverse reactions with the simplified version of the Eyring equation (Eq. 5), (47):

where Δ‡E°, is the activation energy of the reaction, calculated as energy difference between the transition state and reactant, kB is the Boltzmann constant and h is the Planck constant, and T is the temperature. All quantum chemical calculations in this lab are performed with Gaussian package (38). Another skill-building lab where students use Spartan package (39) is focused on a concept of intermolecular interactions and specifically hydrogen bonding. Students build various dimers of formic acid to determine which dimers are stabilized by hydrogen bonds, analyze the effect of hydrogen bonding on vibrational frequencies of O-H stretching vibrations and estimate energies of hydrogen bonds. 238

Assessment Approach The goals of our revisions to the courses is to give students hands-on experience in modern chemistry using research-based projects. The proposed units aim to introduce students to electronic and vibrational spectroscopy, thermodynamics, chemical kinetics, and computer simulations with state-of-the-art computational quantum chemistry software. We broadly define objectives of our courses as follows: students should be able to devise and perform experiments, to analyze the data obtained, to assess the significance of the results and to write about their work in a professional manner. They should be able to: i) explain the fundamental concepts underlying the major computational and experimental techniques used in the lab and, as a consequence, be able to critically evaluate evidence in the chemical literature; ii) apply modern laboratory techniques and use the interpretations of chemical concepts therein as a part of the practice of science in their future careers; iii) use the connection between the hands-on practice and the mathematical formalism of quantum mechanics to create appropriate interpretations of observed phenomena; iv) demonstrate collegial interaction as an integral part of the learning process. Evaluation of Laboratory Units The key learning goals and objectives given above are communicated to students at the beginning of the course. In order to assess the learning outcomes the following tools are used: direct pre/posttests, lab reports, comprehension checks, and reflective assessments to track students’ performance for each unit. The pre/post-test questions are designed in the way to test each learning outcome at three levels of knowledge: understanding (ability to explain or identify basic concepts), analysis (ability to critically examine relationships between provided data or observations), and generalization (ability to gain new knowledge or broaden the context from provided or obtained information). Based on their projects, students write reports following standards of chemical research papers that are used to assess analysis and generalization skills. We have received direct feedback from students during and after the laboratory units. Additionally, a comprehensive evidence-based portfolio approach is used to put assessment into a broader context (48). Specific results of evaluation of laboratory units has been recently presented in our publications (22, 27, 32). Students actively participating in the described projects co-authored 5 papers (22, 26, 27, 32, 49), and gave 26 presentations at undergraduate and professional conferences, including ACS Regional and National Meetings. Over four consecutive years (2013-2016), they received Dean’s awards for their research presentations at MU. Five students were recognized with external grants, scholarships, and awards by ACS, NSF, and The Independent College Fund of New Jersey (ICFNJ). Students also received awards for their research presentations at the Undergraduate Research Symposium at William Paterson University (2016), the New Jersey Water Environment Association (NJWEA) Meeting (2016), ACS-North Jersey Meeting at Fairleigh Dickinson University (2015), Independent College Fund of New Jersey (ICFNJ) Undergraduate Research Symposium (2015), the Conference on Current Trends in Computational Chemistry (2013), the Southern School on Computational Chemistry and Material Science (2013) at Jackson State University.

Conclusions Based on our experience it is evident that regular involvement of students in research activities and gradual increasing of complexity of assignments is a key for student success in undergraduate research. As it follows from the developed laboratory units it is possible to implement CUREs with a 239

subset of its elements. It is evident that involvement of undergraduate students in research activities and gradual increasing of complexity of assignments is a key for students’ success. Student participation in conferences and meetings to present results obtained from the labs, external fellowships, participation in summer research, co-authorship in publications, and ability to enter to desired graduate and professional programs indicates the success of the proposed approach. The feedback obtained from students is continuously used to adjust the course to achieve the stated learning outcomes. This helps us to gradually integrate research-based projects into the courses. A full-size research based laboratory course may seem a distant goal for someone who just starts. Creating a fully CURE-based course with all CURE elements included is a great challenge. However, that should not prevent one, out of discouragement, from gradually implementing research and inquiry-based activities in their courses. Our experience suggests that a combination of more traditional, skill-building laboratory units, followed by one or several research and inquiry-based units provide a balance necessary for an instructor to comfortably handle a laboratory course, at least during the transition period. Skill building labs help to achieve learning objectives with traditional methods and provide practice necessary for building students confidence in their ability to perform basic lab procedures.

Acknowledgments Financial support was partially provided by the Research Corporation for Science Advancement through a Cottrell Scholar Award, the Independent College Fund of New Jersey, National Science Foundation MRI #1662030, Donors of the American Chemical Society Petroleum Research Fund though grant #58019-UR6, and Monmouth University though the School of Science SRP program and Creativity Grants.

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Chapter 17

Using the Hydrogen Bond as a Platform for the Enhancement of Integrative Learning Harry L. Price* Department of Chemistry and Biochemistry, Stetson University, DeLand, Florida 32723, United States *E-mail: [email protected].

The primary aim of this work is to illustrate how hydrogen bonding may be used to promote integrative learning in core and other related courses, thereby reinforcing the central role interdisciplinary learning has in the natural and physical sciences. Using a simplified computational approach, hydrogen bonding between a homologous series of carboxylic acids and formaldehyde is characterized in terms of acidity, hydrogen bond distance, interaction energies, vibrational frequencies, and bond critical point descriptors. Statistical analysis is used to reveal correlations between descriptor pairs with the goal of relating carboxylic acid structure to the stability of a hydrogen bond. It is the belief of the author that this work can serve as a resource for the development of lecture topics, in-class problems, out-of-class assignments, and lab activities not only in chemistry courses, but in mathematics, physics, and statistics courses as well.

Introduction Background As a faculty member in a chemistry department at a liberal arts college, I teach a two-semester course in general biochemistry and an advanced course on nucleic acid biochemistry, first and second-semester general chemistry lab, and mentor student research. I have also taught organic chemistry on several occasions over the years. Like many chemistry faculty, or faculty in general, I have noticed a decline in students’ retention of prerequisite knowledge. Deficiencies are most often observed when students are given diagnostic tests, in-class problems, or group work that require the application of prior learning. Students tend to compartmentalize their learning with little regard to the importance that core and other required coursework have in future courses. After all, what possible application can related rates, as taught in calculus, have in medicine? What if students learning about related rates were introduced to this fundamental concept not only via the classic example of water filling a cone, but by way of problems relevant to the kinetics of drug release from © 2019 American Chemical Society

swelling nanospheres for instance? Similarly, what if students learning about Pearson’s correlation coefficient in a statistics course were provided with examples of its application as relates to rational drug design, quantitative structure-activity relationships, catalyst development, chemical reactivity, or even toxicology? As educators, we often create problems, lab exercises, and lecture topics in our courses that reflect the multidisciplinary nature of our field of study and curriculum. Students unfortunately, are less likely to enthusiastically embrace our efforts to imbue them with functional knowledge because their learning has become increasingly compartmentalized. This mindset that what is learned in one course has no relevance to future coursework does not favor retention of knowledge and only diminishes a student’s ability to apply prior knowledge to solve complex problems. While not a novel concept, integrated learning is an essential pedagogical element that needs to be more deeply embedded into curricula. Encouraging the development of more integrative learning will help to mitigate the negative effects of compartmentalized learning, increase deeper comprehension, and strengthen cognitive skills via cross-curricular application of principles (1–5). Compartmentalization is not just reserved for students. Faculty are guilty of compartmentalizing their course work too. Intra-and inter-departmental barriers abound that favor curricular compartmentalization. Course limits for example are especially problematic, making it more difficult for students to take important collateral coursework. Continuity between required collateral and core courses is another issue. How often do faculty in biology, chemistry, physics, and math departments have the opportunity to engage in meaningful discussions focused on learning objectives in foundational courses, or on ways to better link courses between disciplines? Recalling the old African proverb, “It takes a village to raise a child,” I have come to think of our institutions as the village and the students as our children, which makes it that much more important that we do everything possible to prepare them for what comes after their college experience. Intra- and interdepartmental barriers do not have to be insurmountable. What if we as educators do a better job reaching out to our colleagues and through collaboration, whether formal or informal, develop problems and activities designed to emphasize the integrative nature of learning? What if students taking calculus, chemistry, biochemistry, physics, statistics, or even biology learn through problems, lab exercises, and in-class activities, how fundamental concepts specific to those courses are applied to solve chemical or biochemical problems? Providing students with more concrete examples that reinforce the importance of prior learning, and highlight the application of concepts across curricula, will not only improve retention of prior knowledge, but enhance their ability to analyze, understand, and solve complex problems. With this in mind, the author has endeavored to demonstrate how the hydrogen bond can serve as a pedagogical platform to create integrative learning activities useful in core and required collateral courses across curricula. In the next section, I outline the motivation for and strategy for achieving these integrative activities. The Hydrogen Bond as an Instructive Tool My interest in using hydrogen bonding to reinforce the importance of integrative learning came about as a result of mentoring an undergraduate research project several years ago. The project was computational and focused on the relationship between dielectric constant of the medium and Hbond formation in model nucleotide dimers (6). During the investigation, the student learned not only basic aspects of computational chemistry, but also came to understand H-bonding in more descriptive terms. It is this latter outcome that I found interesting. Using Natural Bond Order analysis (NBO) (7, 8), and the Atoms-In-Molecules (AIM) theory to calculate bond critical point descriptors (9, 10), the student came to learn that an H-bond is more than a dashed line between a hydrogen and 246

a more electronegative element. He learned that it is a bonding interaction that can be characterized in terms of orbital-orbital interactions, and topological descriptions of electron density. While visualization of molecular surfaces and contour plots of electron density and electrostatic potential proved informative for accessing the effect H-bond formation has on charge distribution, it was the information obtained from the NBO and AIM analyses that proved far more impactful for him. An essential element of this student’s new found understanding and interest, relied on a series of scheduled meetings that allowed me the opportunity to offer thoughtful explanations and demonstrations via chalk-talks and guided interpretation of key literature. During these sessions, my top priority was not only to help my student understand the meaning of the NBO and AIM descriptors as they related to H-bonding, but to reinforce the important role that coursework in general, organic, and physical chemistry, as well as calculus and physics had in allowing a deeper understanding of the computational results. While reviewing this project nearly five years later, it occurred to me that from a teaching perspective, the hydrogen bond can be used as an integrative learning platform to reinforce the application of concepts rooted in chemistry, calculus, physics, and even statistics. And so, it is with this insight that I set out to develop a series of integrative learning activities suitable for use in foundational and advanced courses within a chemistry/biochemistry curriculum. These activities may also foster collaboration with colleagues who teach important collateral courses (e.g., calculus, physics and statistics) to create new learning opportunities.

Methods The model system used in this work is shown in Figure 1. Structures were built and optimized using GaussView and Gaussian 09 (11), respectively. Calculations were performed from terminals students would use in the department that are linked to the university server. This was done to ascertain problems students would encounter if doing these calculations as part of a lab exercise or class assignment. The most significant issue involved computation time. Since these calculations could be included as part of a real-time lab exercise or activity, it is important that a round of calculations be completed in 20-30 minutes, which allows ample time for teacher-student interaction and discussion. In the case of this work, the time to complete a cycle of optimization and single-point calculation varied considerably depending on how heavily the server was being used. Computation time was, as expected, dependent on the size of the basis set, and was exacerbated primarily as a result of institutional computational resources. The computational approach used in this work, therefore, represents a compromise between sophistication and efficiency. More sophisticated basis sets and computational methods can be applied depending on available resources. Geometry optimizations and single-point calculations to obtain descriptors of hydrogen bonding were performed using the ωB97X-D functional (12), the 3-21+G* basis set, and a simulated dielectric constant (scrf=iefpcm, ethanol 24.852 D) (13).

Figure 1. Carboxylic acid-formaldehyde model dimers. 247

Frequency analysis of optimized monomers and complexes did not produce any imaginary frequencies, confirming an energy minimum and not a transition state had been reached. Vibrational frequencies specific to the hydroxyl group in the monomer, νo, and hydrogen bonded dimer, νHB, were identified using GaussView. Parameters describing the electron density (ρ(r)) and the Laplacian of the electron density (∇2ρ(r)) at the bond critical point (9, 10) were determined using the Gaussian AIM=bondorder keyword. Atomic charges (q), molecular orbital related parameters, the Fock matrix overlap (Fi,j), and the second-order perturbation energy (E(2)), which estimates donoracceptor (bond-antibond) interactions, were obtained using NBO analysis (7, 8) via the POP=(nbo, savenbo) keyword. Statistical analysis using Microsoft Excel Analysis ToolPak© was done to obtain correlation coefficients for descriptor pairs.

Results and Discussion The activities described in this section can serve as guides for the development of a variety of learning activities in foundational and advanced courses in chemistry, math, and physics. It is important to note that although the computations in these activities have been validated, they have not been used with students at the time of this publication. Moreover, it is important to keep in mind that these learning activities have been designed to help students apply prior knowledge to enhance their learning, problem-solving skills, and use of interdisciplinary knowledge to understand new ideas and complex concepts. Integrative Learning Activity #1: The Inductive Effect and Hydrogen Bonding Students typically learn about the inductive effect in organic chemistry and the important role it plays in influencing chemical reactivity. They learn that electron donating or withdrawing groups alter electron distribution and bond polarity which in turn affects positional reactivity (regioselectivity) and reaction rate. Their understanding of aromatic electrophilic substitution reactions is linked to resonance and substituent-dependent inductive effects. Students are taught that acid-base behavior is dependent on structure, environment, temperature and other factors. A classic example is the effect electron-donating and -withdrawing groups have on a compound’s acidity or basicity. Of all the concepts covered in a one or two semester course in organic chemistry, or even a biochemistry course, do students have an opportunity to gain a deeper understanding of how the inductive effect influences an interaction as fundamental as hydrogen bonding? This is an ideal question for students to explore. The results and concepts related to pKa, H-bond length, and energy of interaction described in this section are ideal for inclusion in a foundational organic chemistry course. Advanced chemistry-based concepts derived from NBO and AIM theories are aptly suited for advanced courses in organic, physical, or computational chemistry. The data presented in Table 1 links the inductive effect to changes in H-bonding via acidity and changes in the lengths of the carboxyl OH bond and H-bond. The pKa values can be determined experimentally as part of a lab exercise suitable for a biochemistry or organic chemistry course, or literature values can also be used. Moreover, depending on the availability of computational resources, students can either be given pre-calculated data or perform computations to obtain the data provided in Table 1. A variety of lessons, questions and discussions based on the trends in the data can be created. Students will have an opportunity to improve their analytical skills by studying multivariate data and relating trends in the data to changes in H-bonding brought on by the inductive effect. In terms 248

of Lewis acid-base interactions, changes in pKa resulting from the inductive effect can be related to changes in bond length for both the carboxyl OH (rOH) and the H-bond (rHB). Thoughtful examination of the relationship of pKa to the type of substituent (R) on the carboxylic acid will provide students with an enhanced appreciation of the role acidity and molecular structure play in H-bond formation, as well as, allow students to make the connection that rHB is representative of the distance of maximum interaction and hence minimum energy. The data in Table 1 can also serve as a starting point for additional calculations and discussions. For instance, students could carry out additional calculations to determine if similar trends are observed for the other halogens. Students can also consider why rOH increases as pKa decreases, and how this change is related to the stability of an H-bond. Table 1. Effect of Substituent on Acidity and Bond Lengths in H-Bonded Complexes Dimer RCOOH---O=CH2

pKaa

rOH (Å)

rHB (Å)

Formic Acid (R = -H)

3.75

1.0155

1.5993

Acetic acid (R = -CH3)

4.76

1.0259

1.6168

Fluoroacetic acid (R = -CH2F)

2.59

1.0351

1.5696

Difluoroacetic acid (R = -CHF2)

1.34

1.0448

1.5295

Trifluoroacetic acid (R = -CF3)

0.52

1.0561

1.4859

a The

pKa value of difluoroacetic acid was obtained from Chemical Book https://www.chemicalbook.com/ ProductMSDSDetailCB2700577_EN.htm Entry: Difluoroaceticacid (381-73-7). The remaining pKa values were obtained from the CRC Handbook of Chemistry and Physics 91st edition.

The descriptors listed in Table 2 are related to the degree of interaction between the carboxyl group H-donor and the formaldehyde carbonyl oxygen lone pair H-acceptor. Stereo-electronic interactions specific to a hydrogen bond as described by the AIM model are linked to the electron density ρ(r), the Laplacian of the electron density ∇2ρ(r), and the third curvature of the density directed along the path of interaction λ3, via the bond critical point (9, 10, 14–16). These descriptors are dependent on the localization and transfer of electron density between interacting atoms. Indicators of H-bond stability are given by the coulombic interaction energy (EHB) (17), and the NBO second-order perturbation energy E(2) (7, 8, 16, 18, 19). Table 2. Effect of Substituent on Calculated H-bond Specific Descriptors Substituent

ρ(r) (au)

∇2ρ(r) (au)

λ3

EHB (kJ/mol)

E(2) (kJ/mol) n → σ*

Acid (R = -H)

0.04109

0.2440

0.3940

-10.67

194.0

(R = -CH3)

0.03941

0.2317

0.3744

-10.84

183.3

(R = -CH2F)

0.04249

0.2553

0.4132

-11.21

219.6

(R = -CHF2)

0.04510

0.2787

0.4509

-11.55

255.3

(R = -CF3)

0.04784

0.3062

0.4947

-11.88

296.5

249

The significance of descriptors describing H-bonding in terms of the AIM model will not be immediately appreciated or understood by the majority of students, which provides a wonderful opportunity to enhance their understanding. From an integrative learning perspective, the theory and application of the AIM model is best suited for students who are taking, or have taken, multivariate or vector calculus, advanced physical chemistry, or a course in applied physics such as electromagnetism, and thus have a general working knowledge of concepts such as line integrals, applications of the gradient and divergence theorems, vector fields, and matrix manipulations (9, 10). The general, more conceptual aspects of the AIM model however, as related to bonding, can still be made tangible to students who have not taken advanced mathematics courses. As shown in Figure 2, a chemical bond is characterized as a line or path between two atomic centers A and B. The electron density ρ(r) is greatest at the atomic centers and decreases exponentially, approaching zero rapidly as the distance from an atomic center increases. In the bonding region between centers A and B, ρ(r) is maximal along this path. Any lateral displacement from the ridge results in a decrease in ρ(r). A bond critical point (BCP) is a saddle point, and represents the location in space between atomic centers where the gradient of electron density ∇2ρ(r) = 0.

Figure 2. Contour representation of the bond path between atomic centers A and B. Maximum electron density occurs at the atomic centers. The bond critical point (white circle) is that position in space between atomic centers A and B where the gradient of the electron density is zero and represents a saddle point. The eigenvectors u1, u2, and u3 define the directionality of ρ(r) with respect to the bond path. The topology of the BCP is described by three orthogonal eigenvectors, u1, u2, and u3, which define the directionality of ρ(r) with respect to the bond path (Figure 2). At the BCP, the second derivative of ρ(r) with respect to x, y, and z directions yield a 3x3 Hessian matrix

Diagonalization of the matrix eliminates off-diagonal elements. The remaining diagonal elements (eigenvalues) represent the three principle curvatures λ1, λ2, andλ3 of the surface at the 250

BCP with respect to the principal x, y, and z axes, respectfully (9, 10). Curvatures λ1 andλ2 are negative and perpendicular to the bond path described by curvature λ3 which is positive. The negative curvatures measure the degree to which the electron density is concentrated along the bond path, and the positive curvature measures the degree to which it is depleted in the interatomic region and concentrated at the individual atomic centers. The sum of the curvatures is the Laplacian of the electron density ∇2ρ(r) = λ1u1 + λ2u2 + λ3u3. The characteristics of a BCP as based on the topology of electron density, thus provides information about the interaction between two atomic centers (9, 10). More descriptively, at the BCP, the magnitudes of the curvatures are related to the type of bonding interaction. When λ3 is < |λ1 + λ2|, ∇2ρ(r) < 0, charge is accumulated in the region between atomic centers (e.g., covalent bond). When λ3 is > |λ1 + λ2|, ∇2ρ(r) > 0, charge is depleted in the region between atomic centers (e.g., closed-shell interactions such as ionic, electrostatic, hydrogen bonding and Van der Waals interactions). For the series of complexes listed in Table 2, the values of ρ(r), ∇2ρ(r) and λ3 reflect the effect that the substituent has on H-bonding. As students learn about the mechanism of H-bonding by application of AIM theory, an opportunity arises to reinforce the concept of intensive properties specifically as relates to electron density. Students generally appreciate the concept of electron density, but chances are they have not considered its significance as an intensive property. Similarly, will students grasp the significance of the units of ∇2ρ(r) being equivalent to charge density per unit area (e/bohr3/bohr2)? Will they recognize this unit is equivalent to a flux of charge density passing through a specific unit of area? In terms of bonding, these two terms can be viewed as describing the flux, localization, and concentration of electron charge between two interacting atomic centers. Including a discussion of units affords yet another opportunity to enhance learning. Together, the AIM descriptors provide students with a novel way to understand bonding interactions; a way that is more comprehensive than the traditional dashed line. From an integrated learning perspective, the concept of a bond critical point is compatible with topics covered in multivariate and vector calculus, physical chemistry, or a course in advanced physics, and provides a wonderful opportunity to highlight the relevance of mathematics as applied to the characterization of one of nature’s most important molecular interactions. The descriptor linked to the electrostatic nature of the H-bond, the interaction energy (EHB) is derived from Coulomb’s Law (17)

where, q1 and q2 are the charges on the hydrogen and carbonyl oxygen that form the H-bond, D is the dielectric constant, and rHB is the distance between the hydrogen bonded pair. The constant 1/4πε° has been converted to a constant having units of (kcal-Å)/mol. Students, especially those majoring in life sciences, chemistry and biochemistry, learning about electrostatic forces in chemistry or physics would benefit from a discussion of hydrogen bonding as an example of an attractive electrostatic interaction described in part using Coulomb’s Law. The conversion to kcal/mol should pique the curiosity of students as it is not immediately apparent how Coulomb’s Law can be expressed in thermochemical units. In fact, having students convert Coulomb’s Law from units of N m2 C−2 to kcal/mol or kJ/mol offers an opportunity for them to apply their understanding of units, which is a 251

crucial level of competency. Coulomb’s Law is versatile and can be used to illustrate H-bonding in terms of the concepts related to Coulombic force (20), electric field (20), and electrostatic potential (20, 21–23). Using molecular modeling software, students can create electrostatic maps to visualize charge distribution and bond polarity of H-bonded complexes, and relate differences to the inductive effect and its influence on H-bonding. Visualization of the molecular electrostatic potential (MEP) mapped onto the electron density surface provides meaningful information about bond polarity and charge distribution (Figure 3). The dimers shown in Figure 3 provide a visual comparison of hydrogen bonding when an electron donating methyl group (top) or electron withdrawing trifluorogroup (bottom) is present. Careful examination of each MEP reveals changes in charge distribution (polarity) as well as differences in the volume and polarity of the H-bond.

Figure 3. Changes in the molecular electrostatic potential as a function of carboxyl functional group. Electron donating group (top), electron withdrawing group (bottom). Dark color represents regions of more positive electrostatic potential. Light color represents regions of more negative electrostatic potential. Arrows point to the approximate location of the H-bond critical point. Note the difference in the volumes and the polarity enclosing the H-bond. Based on data in Tables 1 and 2, the acetic acid-formaldehyde H-bond (top) is approximately 9% longer and exhibits a BCP ρ(r) that is 20% less than the H-bond formed between trifluoroacetic acid and formaldehyde (bottom). These differences are linked to the inductive effect and provide further support that changes in bond polarity brought on by the inductive effect exert an influence on Hbond formation. Like AIM, NBO analysis provides useful information specific to H-bonding interactions (7, 8, 16, 18, 19). In the case of the model system described in this work, H-bonding is characterized as the transfer of electron density from a lone pair (no) on the oxygen of formaldehyde into the unfilled σ* antibonding orbital of the carboxyl OH group. The strength of this no→σ* interaction between Hbonded atoms is related to E(2), the second-order perturbation energy according to

252

where E(2) describes the relationship between the degree of occupancy of the donor orbital qi, the Fock matrix off-diagonal elements Fi,j, which represent the degree of orbital overlap, and the energies of the interacting orbitals εi and εj. Figure 4 provides an illustration of the NBO orbital interaction contour plots of hydrogen bonded dimers. Maps were created by selecting the orbitals from the NBO output associated with the corresponding Fi,j and E(2) values. The wavefunction contours are provided to emphasize the importance of orbital-orbital interaction. It is worth noting that NBO output reveals the stereoelectronic preference of the donor lone pair interaction with the acceptor H. This stereo-electronic selection is significant. Using the acetic acid formaldehyde dimer as an example, the oxygen lone pairs n1 and n2 donated by formaldehyde, contribute 34.85 and 183.3 kJ/mol of stabilization energy, to the H-bond interaction with the σ* orbital of the OH group of acetic acid. This preferential interaction reflects the spatial position of the oxygen lone pair orbitals. Stereo-electronic preference is also reflected in the value of Fi,j as well. In this instance, the n2 interaction is associated with a twofold greater Fi,j, compared to n1.

Figure 4. Representative NBO ψ2 contour maps showing orbital-orbital overlap of the hydrogen bond. The formaldehyde oxygen is the Lewis base lone pair donor, designated by (i)no. The Lewis acid acceptor is the hydroxyl group of the substituted carboxylic acid, designated by (j)σ*OH. The values of Fi,j and E(2) represent the n→σ* delocalization that provides the greatest stabilization energy, respectively. Linking the quantum theory of the NBO approach to hydrogen bonding is ideally suited for students learning about bonding in a biophysical or physical chemistry course. Students enrolled in advanced courses in physical chemistry, physics or a computational chemistry course will certainly benefit from a more formal discussion of the application of NBO analysis as it applies to bonding interactions; while students enrolled in biochemistry or organic chemistry for example can benefit from a more conceptual approach based on the maps and data shown in Figure 4. 253

Integrated Learning Activity #2: Hydrogen Bonding and Hooke’s Law In foundational chemistry courses chemical bonds are classically modeled as balls attached by a spring that behave as harmonic oscillators obeying Hooke’s Law (24). This practical description serves as the basis of understanding foundational elements of infrared (IR) spectroscopy. Students first learn about IR spectroscopy when taking organic chemistry, where it is used to characterize functional groups (e.g., OH, NH2, carbonyl, carboxylic, etc.), bond hybridization (e.g., sp, sp2, sp3), substitution (e.g., -CH3, RCH2‑, R2CH‑, and R3C-), and the presence of weak interactions such as hydrogen bonds. This last attribute of IR spectroscopy is quite useful since H-bonding broadens and shifts the characteristic frequencies associated with the -OH, -C=O, or H-N- vibrations. Derived from Hooke’s Law, the frequency of vibration of the -OH bond, ν, is given by

where mA and mB are the masses of the hydroxyl oxygen and hydrogen atoms, respectively, c is the speed of light in cm/s, and the stiffness of the spring connecting these atoms is given by the force constant, k. Note the units of k have been converted from dyn/cm to dyn/Å as listed in Table 3. Vibrational analysis of the carboxylic acids shown in Figure 1 alone or H-bonded to formaldehyde was carried out to generate the data in Table 3. Table 3. Effect of Substituent on the Calculated -OH Stretching Freqency

νHB − νo

Substituent

rOH (Å)

k (dyn/Å)

νo (cm-1)

νHB (cm-1)

R = -H

1.0155

4.95x10-3

3114

2654

-460

R = -CH3

1.0259

5.30x10-3

2999

2750

-249

R = -CH2F

1.0351

4.69x10-3

3394

2580

-814

R = -CHF2

1.0448

4.30x10-3

3384

2470

-914

R = -CF3

1.0561

3.70x10-3

3386

2276

-1110

Δν (cm-1)

The data in Table 3 reveal the influence a substituent has on the vibrational behavior of the OH group in the absence (νo) and presence of an H-bond with formaldehyde (νHB). Specifically, the electron withdrawing substituents -CH2F, -CHF2, and -CF3 progressively weaken the OH bond as evidenced by decreases in k and νHB. Compared to the fluorinated carboxylic acids and formic acid (R = -H), the electron donating methyl group stiffens the OH bond which results in a larger force constant and a corresponding increase in νHB. The calculated spectral shifts denoted by negative values of Δν are consistent with the observation that H-bonding is associated with a red-shift of the OH stretching frequency (16, 19). From an integrative learning perspective, this vibrational analysis activity provides students with data that tie together fundamental concepts of molecular structure, substituent effects, and bonding. One can also envision students in an introductory physics course, who are learning about springs and harmonic oscillations, being introduced to the hydrogen bond as another example of a real-world application of Hooke’s Law (24). 254

Integrated Learning Activity #3: Correlation Analysis We live in a world flooded with data. Students, more now than ever, need to gain experience using statistical methods to analyze data (25). Computational chemistry programs are powerful tools for characterizing molecular properties and interactions. Accordingly, computations produce large amounts of data. Analysis of data can be done graphically to obtain useful parameters using the single variable linear regression equation Y = b0 + b1X. In more complex cases, a multivariable linear regression equation taking the form Y = b0 + b1X + b2X + ··· bnX is used to create a model. The goodness of fit is generally given by the Pearson correlation coefficient (r-value), although other descriptive statistics such as the F-value, p-value, and t-test are important for testing the significance of extra variables on the fitness of a regression model (25). Calculating molecular descriptors for a series of homologous molecules, as was done in this work, provide students with the opportunity to apply statistical analysis to reveal for instance, how the NBO stabilization energy E(2) varies with Hbond distance rHB or how E(2) varies when plotted against λ3, the curvature eigenvalue that follows the bond path. A large number of graphs can be created using the descriptors in Tables 1-3, and although graphic representation of data is useful when visualizing correlations, an alternative way to analyze large sets of data to identify correlations is to create a correlation matrix (26). Correlations are useful because they can be used to develop predictive models of chemico-physical properties, reactivity, and biological activity (e.g., binding affinity, toxicity, etc.) (26, 27). In the case of this learning activity there are several options: (1) students can create a correlation matrix using data given to them, (2) they can perform computations to obtain the descriptors shown in Tables 1-3, and then create a correlation matrix, or (3) they can perform calculations to create a different set of descriptors to analyze. Once data is available, analysis can be performed using any number of software packages depending on availability. Since Microsoft Excel is accessible on virtually every computer, students can use the add-in Analysis ToolPak© to create a correlation matrix. The data listed in Table 4 represent a pair-wise correlation matrix of r-values calculated using

where xi and yi represent the ith value of a descriptor pair, and the average value of a pair is given by x and y. The parameters n, sx and sy represent the number of examples and the respective standard deviations of each group of data. The value of r can range from a minimum of -1 when data pairs are negatively correlated, to a maximum of +1 when data pairs are positively correlated. Data pairs that exhibit no correlation yield r = 0. So, what does the data in Table 4 reveal about H-bonding? Consider for instance, the strong negative correlation between the curvature eigenvalue λ3, and the vibrational force constant k (r = -0.997). This correlation is negative because as one descriptor increases the other decreases, which is consistent with the weakening of the OH bond as H-bonding interaction increases. Increased Hbonding would be associated with an increase in charge transfer between the interacting atoms. Data in Table 2 indicate that increases in λ3 are associated with greater H-bond interaction. Likewise, the strong positive correlation between λ3 and E(2) (r = 0.998), is consistent with increasing orbitalorbital interaction as more electron density from the lone pair of the H-acceptor is delocalized into the unfilled σ* orbital of the H-donor via the bond path. The strong correlations between pKa and 255

the other descriptors reveal the important role acidity has in H-bonding. The positive correlation between EHB and k could surprise students, because they may think that EHB should increase as Hbonding interaction increases. In fact, the data in Table 2 shows EHB becoming more negative as Hbonding interaction increases, which is associated with a decrease in k. Table 4. Correlation Matrix of Representative H-bond Descriptors pKa

rHB

λ3

ρ(r)

EHB

E(2)

pKa

1.000

rHB

0.986

1.000

ρ(r)

-0.985

-0.998

1.000

λ3

-0.975

-0.997

0.999

1.000

EHB

0.946

0.968

-0.949

-0.953

1.000

E(2)

-0.974

-0.998

0.995

0.998

-0.972

1.000

k

0.978

0.993

-0.998

-0.997

0.939

-0.992

k

1.000

Construction of a correlation matrix not only allows for comparison of multiple variables at once, it allows for identification of weaker correlations. Integrating this activity into an appropriate chemistry or statistics course will provide students with the opportunity to use an important method of statistical analysis to further enhance their understanding of H-bonding.

Conclusions My motivation for contributing this chapter is rooted in the realization that a former student’s undergraduate research project was a treasure trove of learning activities. These activities can foster integrative learning not only in chemistry courses, they can be adapted for use as learning activities in multivariate calculus, statistics and physics courses too. Additional motivation to translate an undergraduate research project into a pedagogical tool was derived from conversations with colleagues who teach courses in chemistry, math, and physics In closing, using a modest computational strategy, a homologous series of carboxylic acids Hbonded to formaldehyde have been characterized. The results presented here agree with previous computations of hydrogen bonding done at higher levels of theory (14–16, 18, 19), as well as satisfy the relevant IUPAC criterion for what constitutes a hydrogen bond (28). Taken together, these two outcomes validate the use of this method to characterize this particular model system. It is the author’s hope that some or all of the learning activities described in this work prove useful to those interested in developing novel integrated learning activities. This is an exciting possibility, because the cost is minimal while the potential gain is significant.

Acknowledgments The author would like to thank the editors, Drs. Alexander Grushow and Melissa Reeves for the opportunity to share the results of my work.

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Editors’ Biographies

Alexander Grushow Alexander Grushow received a B.A. in chemistry from Franklin & Marshall College and a Ph.D. from University of Minnesota. He is currently a Professor of Chemistry at Rider University and Chair of the Department of Chemistry, Biochemistry and Physics. Since his days as an undergraduate he has been fascinated by intermolecular forces and has published papers on molecules held together by hydrogen bonding, van der Waals forces, dative bonding and ion-molecule interactions. He has worked as a Program Director for the National Science Foundation and has worked in chemistry examination development for both ETS and the ACS Examinations Institute. He has also been heavily involved in innovating the teaching of physical chemistry; starting as a member of the Physical Chemistry Online Consortium (PCOL) and most recently as a coPI on two NSF grants to develop POGIL experiments in Physical Chemistry (POGIL-PCL).

Melissa S. Reeves Melissa S. Reeves received her B.S. in chemistry at University of Florida and her Ph.D. in chemistry at Indiana University at Bloomington. She is an associate professor of chemistry at Tuskegee University where she specializes in physical chemistry and computational chemistry. Her research interests have ranged from calculating transition states of small molecule reactions in solution to molecular dynamics of polymers. She was part of the Physical Chemistry Online (PCOL) group in the early 2000s, has worked on two American Chemical Society Physical Chemistry Exam Committees, and works as part of the Process Oriented Guided Inquiry Learning Physical Chemistry Laboratory (POGIL-PCL) community.

© 2019 American Chemical Society

Indexes

Author Index Akinmurele, M., 79 Asirwatham, L., 127 Ball, D., 93 Berghout, H., 51 Bruce, C., 11 DeVore, T., 109 Esselman, B., 139 Grushow, A., 1, 211 Hagen, J., 195 Haynie, M., 79 Hill, N., 139 Kholod, Y., 227 Kosenkov, D., 227

Martin, W., 93 McDonald, A., 195 Perri, M., 51, 79 Phillips, J., 33 Price, H., 245 Reeves, M., 1, 51, 65 Sharma, A., 127 Singleton, S., 51 Singleton, S., 163 Stocker, K., 21 Tribe, L., 183 Whitnell, R., 51, 65

263

Subject Index A Acetylene rovibrational spectrum, using computational chemistry conclusion, 106 acetylene, vibrations, 106 introduction, 93 acetylene, three parallel normal vibrational modes, 94f procedure, 99 results, 103 calculated frequencies for the rovibrational spectrum, error between, 106f C2T2, graph of the predicted rovibrational spectrum, 105f fitting used to extrapolate the value, 104f rovibrational lines, representative graph of the frequencies, 104f some computational background, 95 acetylene, internal coordinates, 97t internal coordinates for the vibrational motions of acetylene, definition, 97f normal mode, graphs of the calculated frequency, 98f

C Chem compute science gateway Chem compute capabilities and features, 81 benzene, calculated IR spectrum, 86f Chem compute, visualization options available, 85f creating a molecule to investigate, 83f intermediate output displaying job status, 84f investigating H2, instructions, 82f π-molecular orbitals, 85f simulation trajectory, TINKER output, 86f class, successes using Chem Compute, 87 Chem Compute in class, student evaluation responses, 87t H2, antibonding and bonding orbitals, 89f neon p-orbital visualized with JSmol, 88f preliminary survey results, 89t

conclusion, 90 introduction, 79 Computational chemistry as a course conclusion, 192 course structure and content, 184 atomistic calculations, computational package, 189 HOMO, LUMO, energy, 190t Lennard-Jones potential energy vs. distance graphed in Excel, 186f molecules, Spartan models, 187f program spring and graph of distance, 191f two diol models and the beginning of the output file, 188f introduction, 183 Computational narrative activities classroom, observations after using CNAs, 176 computational notebooks versus computational narratives, 164 conclusions, 179 designing computational activities, strategies, 165 black body radiation, introducing the Planck model, 172f CNA exploring black body radiation, title, introduction, and learning objectives, 170f computational narrative activities, examples, 168 ELIPSS Project process skills definitions, 166t exercise with a prompt for narrative, 173f form of a worked example, model presented, 172f markdown cells and code cells with title, 169f model introducing a stellar classification system, 171f python background skills, 170f several computational narrative activities, 168t writing tasks, conceptual hierarchy, 174t introduction, 163

265

physical chemistry courses, using computational narrative activities, 175

conclusion, 134 student interest in Chemistry, 134 course assessment, 134 SALG assessment data, 134t course design, 129 atoms in a molecule, computed vibrational entropy, 133f Avogadro, water molecules arranged, 133f competing reaction analyzed in Kinetiscope, concentration profile, 133f computational activities implemented in the course, 130t kinetics of a reversible reaction, students, 131 introduction, 21

D Discovery-based computational activities conclusions, 239 introduction, 227 density functional theory-based tightbinding (DFTB) method, 230 four hierarchical ACCM levels, example, 229t physical chemistry courses, top-level anchoring concepts traditionally covered, 229 Monmouth University, laboratory units implemented, 231 automatic titrator, 232f cis-trans conformational transitions, transient UV-Vis spectroscopy, 235f formaldehyde, dissociation, 238 model enzymatic kinetics, excerpt of the Rscript used, 236 molecular orbitals, obtain energies and coefficients, 237 organic ligand diminazene (DMZ), 233f Reichardt’s betaine Et30 dye, UV-Vis absorption spectra, 234f

F First-semester general chemistry, molecular dynamics simulations conclusions, 15 clicker question summary, 17t computational chemistry, 18 representative statements from students, 16 introduction, 11 aid student learning, using molecular dynamics software, 12 argon, student-submitted plot for virtual substance simulation, 15f 128 argon atoms, screenshot of virtual substance initial set up, 13f virtual substance, screenshot, 14f virtual substance simulation, studentsubmitted plot, 15f visualization activities, 12 First year honors chemistry curriculum

I Introducing quantum calculations computational methods, 110 atoms, investigating the properties, 117 atoms and ions, calculated high, middle, and low spin energies, 119t benzene, calculated symmetries, frequencies, IR and Raman intensities, 116t benzene with ungerade symmetry, calculated symmetries, frequencies, IR and Raman intensities, 116t 11B16O , molecular constants determined, 2 115t 12C16O , comparison of the molecular 2 constants determined, 114t DFT-B3LYP, calculated triplet, 118t DFT-B3LYP doublet energy differences, calculated triplet, 118t HCl and DCl, ro-vibronic IR spectrum, 112f mass spectrometer, ionization source, 120 measured molecular constants, comparison, 113t methane, energy minimized structures, 121f ω3, IR spectrum, 114f selected first row transition metal, calculated high and low spin energies, 119t conclusions, 121 introduction, 109

266

K

M

Kinetics of gas-phase ammonia synthesis, investigate using electronic structure calculations conclusions, 30 data analysis and results, 27 calculated rate constants, 29t calculated thermodynamic quantities relative, 27t forward reactions, transition state theory values, 28t internal energy, reaction coordinate diagram, 28f reverse reactions, transition state theory values, 28t experimental procedure, 23 angstrom, transition state structures with interatomic distances, 26f calculations, simplified workflow, 23f transition state 1 XYZ coordinates, 24t transition state 2 XYZ coordinates, 24t transition state 3 XYZ coordinates, 25t transition state 4 XYZ coordinates, 25t introduction, 21 why ammonia synthesis?, 22

Modeling reaction energies and exploring noble gas chemistry methods Ar, HF, HArF, and reaction 1a, energy data, 39t argon hydrofluoride (HArF), modeling the formation, 35 ΔrE (kJ/mol), model chemistry comparison, 40t energetic benchmarks, 42 exploring new noble gas compounds, part 2, 42 HArF, Lewis structure and B3LYP/6-31G* geometry parameters, 41f Lewis structure, geometry parameters, atomic charges (NPA), 46f modeling and extending calorimetry results, 47 organizing student thermochemical calculations, sample spreadsheet, 38f part 1, discussion questions, 42t structure parameters, atomic charges (NPA), 44f van der Waals radii, summing covalent, 45f overview and context, 33 summary, 49

L Lab course in computational chemistry early explorations with Gaussian, 214 fluoropropene, transition state, 216f formaldehyde, HOMO-2 orbital, 215f final project and presentations, 220 final project introduced, 217 guiding principles to course structure, 212 initial exercises, 213 introduction, 211 learning goals and activities, summary activities in the lab course, summary, 222t 13-week semester, timeline for general activities, 223f other chemistry questions, 218 charge densities, calculation, 219 simple isodesmic reaction, 218f responses and reflections, 223 two-credit lab course, 224

O Organic chemistry laboratory curriculum using WebMO, 139 curriculum implementation, 141 benzene, optimized structures, 146f benzyl halide radical cations, comparison of EI-MS fragmentation reaction energetics, 151f 1,3-butadiene, conformational scan, 145f chemical shift values, chloroacetophenone and authentic HSQC NMR spectrum, 142f chloroacetophenone, experimental and computational, 142t cis and trans 4-tert-butylcyclohexanol, oxidation, 155f computational chemistry laboratory exercises, 143t

267

computational chemistry throughout the laboratory curriculum, 153t conjugated systems, conformational isomers, 144 fluorobenzene, nitration, 156f 1H- and 13C-NMR chemical shifts, 147 imidazole, five isomeric conjugate acids, 149f inter-ring dihedral angles, 157f intrinsic reaction coordinate, 150f introductory computational chemistry laboratory exercises, 152t 4-methoxyphenylboronic acid, SuzukiMiyaura coupling, 157f SN1 synthesis, analysis of the intermediate and product, 155f solid phase, experimental IR spectrum, 148f introduction, 140 supporting note, 158

P Physical chemistry, using mathematical software to enhance understanding barriers to adoption and how to overcome them, 207 conclusion, 209 design principles of our ramped strategy, 197 introduction, 195 physical chemistry learning objectives and MATLAB skills, 197t our ramped strategy, description, 198 example MATLAB tutorial worksheet, 201f homework assignment, example, 202f MATLAB activities, 199t numerical methods test given in kinetics course, example, 203f quantum mechanics course, example of numerical methods test given, 203f surface tension lab handout, last page, 204f outcomes, 208 ramped approach, improvements in learning allowed, 204 error propagation handout, example, 206f symbolic mathematics, 205 Platform for the enhancement of integrative learning, using the hydrogen bond conclusions, 256

introduction, 245 methods, 247 carboxylic acid-formaldehyde model dimers, 247f results and discussion, 248 bond path between atomic centers A and B, contour representation, 250f calculated -OH stretching freqency, effect of substituent, 254t Coulomb's law, descriptor linked to the electrostatic nature, 251 H-bonded complexes, effect of substituent on acidity and bond lengths, 249t H-bonding, 255 hydrogen bond, orbital-orbital overlap, 253f molecular electrostatic potential, changes, 252f representative H-bond descriptors, correlation matrix, 256t substituent on calculated h-bond specific descriptor, effect, 249t Process oriented guided inquiry learning computational chemistry experiments, 65 explorable explanations, building more background, 72 Lennard-Jones potential (26), explorable explanation, 74f periodic boundary conditions, explorable explanation, 74f faculty development and computational chemistry experiments, 71 introduction, 66 summary and conclusion, 75 testing and refining POGIL-PCL computational chemistry experiments, 69

R Reaction enthalpy, how can you measure, 51 conclusions, 61 experiment, the, 54 CH3F, basis set and method, 56t cycle 1 and properties calculations, 55 Hess’s law diagrams, 56f perfluoropropane geometry optimization, scaling analysis for propane, 57f implementation details by the authors, 58

268

authors, local teaching and computing environments, 59t student reception and response, 60 introduction, 52 HFC-227ea, elimination of HF, 54f

undergraduate teaching, 6f chapters, overview, 6 MATLAB assignments, 7 computational chemistry education, selected landmarks, 3 computational chemistry education, timeline of landmark events, 4f computational in chemistry in our classes, history, 2 conclusion, 8 introduction, 1

U Using computational methods to teach chemical principles balancing theory and application, 5

269