Bonding through Code: Theoretical Models for Molecules and Materials 1498762212, 9781498762212

Table of contents :
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Acknowledgments
About the Author
Chapter 1 The Postulates of Quantum Mechanics
Chapter 2 Atoms and Atomic Orbitals
Introduction
The Radial Wavefunction
Visualizing Atomic Orbitals with MATLAB: The Angular Wavefunctions
Combining the Radial and Angular Functions
Focusing on the Valence Electrons: Slater-Type Orbitals
Chapter 3 Overlap between Atomic Orbitals
Introduction
Parameters for Slater-Type Orbitals
Combining the Radial and Angular Functions
Visualizing Isosurfaces of Slater-Type Orbitals
Programming Overlap Integrals in MATLAB
Exercises for Exploring Overlap Integrals
References
Chapter 4 Introduction to Molecular Orbital Theory
Introduction
Construction of the Hamiltonian Matrix
Solving for the Molecular Orbitals
Visualizing Isosurfaces of MOs in MATLAB
Extended Hückel vs. Simple Hückel
A Simplified Representation of MOs in MATLAB
References
Chapter 5 The Molecular Orbitals of N2
Introduction
Solving the General Problem of Building the Hamiltonian
The Brute Force Solution of the MOs of N2
Symmetrized Basis Functions
Chapter 6 Heteronuclear Diatomic Molecules
Introduction
Drawing Molecular Structures
HeH: Electronegativity Perturbation
HeH: Interatomic Interactions as a Perturbation
The MOs of CO and CN−
Chapter 7 Symmetry Operations
Introduction
Applying Symmetry Operations in MATLAB
The Identity Operation
Inversion through a Central Point
Reflections through a Plane
Rotations about an Axis
Improper Rotations
Creating More Complicated Operations
Chapter 8 Symmetry Groups
Introduction
Properties of Mathematical Groups
Demonstration of Mathematical Groups with MATLAB
Generating Operations
Applying Group Operations
Building the Molecular Symmetry Groups
Chapter 9 Group Theory and Basis Sets
Introduction
sp3 HYBRID ORBITALS OF H2O AS A BASIS FOR REPRESENTING POINT GROUP SYMMETRY
Basis Sets as Representations of Point Group Symmetry
Characters of a Matrix Representation
Reducible and Irreducible Representations
Reduction of Reducible Representations
Transformation of Basis Set to Irreducible Representations
Chapter 10 The MOs of H2O
Introduction
The MOs of H2O by Brute Force
The MOs of H2O from sp3 Hybrid SYMMETRY ADAPTED LINEAR COMBINATIONS (SALCs)
Perceiving Localized Bonding in H2O
Bonus Code: Better Ball-and-Stick Models
Chapter 11 MOs of the Trigonal Planar Geometry
Introduction
Construction of NH3 Geometries
MOs at Specific Geometries
SALCs for the Trigonal Planar Geometry
Building the MO Diagram from the SALCs
Chapter 12 Walsh Diagrams and Molecular Shapes
Introduction
Geometries of the AL3 Molecule
Constructing Walsh Diagrams
Chapter 13 Getting Started with Transition Metals
Introduction
Normalization of Double-Zeta Functions
Inclusion of d Orbitals into MATLAB Functions
The MOs of an Octahedral Complex with σ-Ligands; the 18-Electron Rule
Chapter 14 Translational Symmetry and Band Structures
Introduction
Translational Symmetry and Bloch’s Theorem
Constructing SALCs
Hamiltonian Matrices
A Simple Example: The Chain of H Atoms
Unique Values of k: The 1st Brillouin Zone
Building the Hamiltonian Matrices for Periodic Structures
Example: The Band Structure of Graphene
Determining the Fermi Energy for Graphene
Index