Progress in Physical Chemistry - Volume 1: Different Aspects of Intermolecular Interaction - Reviews from Zeitschrift für Physikalische Chemie 9783486843804, 9783486583137

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Progress in Physical Chemistry Different Aspects of Intermolecular Interaction Reviews from Zeitschrift für Physikalische Chemie Volume ι by Helmut Baumgärtel (Hrsg.)

Oldenbourg Verlag München Wien

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar.

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ISBN 978-3-486-58313-7

Preface

1

M. Havenith, G. W. Schwaab Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces

3

O. Dopfer IR Spectroscopy of Microsolvated Aromatic Cluster Ions: Ionization-Induced Switch in Aromatic Molecule-Solvent Recognition

39

C. F. Kaminski Fluorescence Imaging of Reactive Processes

83

T. Stangler, R. Hartmann, D. Willbold, Β. W. Koenig Modem High Resolution NMR for the Study of Structure, Dynamics and Interactions of Biological Macromolecules

Ill

M. Drescher Time-Resolved ESCA: a Novel Probe for Chemical Dynamics . . . .

159

C.Donner Kinetics of Electrochemical Phase Formation in Two-Dimensional Systems C. Czeslik Factors Ruling Protein Adsorption

221

T. Koop Homogeneous Ice Nucleation in Water and Aqueous Solutions

253

. . .

181

Die Bunsen-Gesellschaft Ihr NETZWERK der PHYSIKALISCHEN CHEMIE Die Bunsen-Gesellschaft verbindet seit mehr als 110 Jahren Hochschulund Industrieforscher aus der physikalischen Chemie in ihrem Netzwerk. Mit mehr als 1600 Mitgliedern fördert die BunsenGesellschaft den Nachwuchs, organisiert Veranstaltungen und engagiert sich in der Forschung.

Deutsche Bunsen-Gesellschaft www.bunsen.de

für Physikalische Chemie e. V.

Preface The number of scientific articles, which are published per year, continues to expand exponentially and there is no sign of a levelling off. Numerous journals dedicated to specific scientific fields are available, however, the synopsis of details becomes more and more difficult. Physical chemistry is strongly affected by this development due to its mutual connections to physics, chemistry, medicine, biology and engineering. Being aware of this situation, a few years ago the editorial board of "Zeitschrift für Physikalische Chemie" decided to publish reviews on specific modern developments in Physical Chemistry. Meanwhile it turned out that these reviews are a great success with the readers of the journal. With the intention to provide the interested scientific community a possibility of fast information on recent developments in Physical Chemistry publisher and editorial board decided to collect the best of these reviews in a series on "Progress in Physical Chemistry". Each of the volumes - the first one in your hand now contains several review articles written by competent scientists. This first volume of the series contains eight review articles (published in "Zeitschrift für Physikalische Chemie" between 2004 and 2006) in which the investigation and deeper understanding of the intermolecular interaction in different systems plays a dominant role. In the contribution of M. Havenith the aggregate Ar-CO, a prototype for studying intermolecular forces, is used to give an overview on the numerous theoretical concepts and experimental possibilities for studying intermolecular forces. O. Dopfer describes the interaction of aromatic molecules and ions with solvent molecules as studied by IR photodissociation spectroscopy (IRPD), a modern version of IR spectroscopy. The analysis of the spectra provides detailed information on the intermolecular interaction between aromatic ions and the ligand molecules and the cluster growth process including the formation of structural conformers. Laser induced fluorescence (LIF) is one of the most powerful spectroscopic tools to image reactive processes in a variety of systems. C.F. Kaminski shows in his article the most recent development of LIF. One aim of this article is to highlight common principles behind seemingly unconnected research applications. The evaluation of the structure and dynamics of biological macromolecules is a key problem in understanding biological systems. The paper of B.W. Koenig et al. reviews recent methodological and instrumental advances in the field of biologically focussed High Resolution NMR. The main emphasis of

2

Preface

the second part is on molecular interactions in biological systems, e.g. proteins in living systems. M. Drescher presents in his article time-resolved E S C A . The properties and capabilities of various X-ray pulse sources are discussed along with their prospects for dynamical studies. Examples are presented in the femtosecond to the attosecond (10~ 18 s) time regime, the latter marking the current ultimate limit for time-resolved pump-probe experiments. C. Donner describes the "Kinetics of Electrochemical Phase Formation in Two-dimensional Systems". She points out clearly the complex modelling of different pathways of the adsórbate formation at electrodes. Protein adsorption plays a central role in a wide variety of processes investigated in modern biochemistry and biotechnology - last not least - in daily life. In his article "Factors Ruling Protein Adsorption" C. Czeslik describes the principles of protein adsorption at interfaces and the experimental techniques to characterize protein adsorbates. The contribution "Homogeneous Ice Nucleation in water and aqueous solutions" by T. Koop is of broad interest, because it deals with the hitherto unsolved problem how the structure and dynamics of liquid water can be understood and connected properly with the unusual properties of liquid water. The liquid/solid phase transition of water plays an important role in modelling the atmosphere and consequently the evolution of the climate. The editorial board hopes that this volume will be widely accepted, not only by physical chemists but also by colleagues from other related disciplines. Finally we hope that some of the article will be used in teaching graduate students. Anyone who has proposals for the improvement or would like to contribute to the series is encouraged to contact the editors. The cooperation of the scientific community is indispensable and welcome. Helmut Baumgärtel, Berlin

Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces By Martina Havenith* and Gerhard W. Schwaab Department of Physical Chemistry II, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany

Intermolecular

Potentials / Infrared Spectroscopy / Ar-CO

The study of intermolecular forces has been of increasing interest in the past. New theoretical and experimental techniques have been developed which allow an improved understanding of these important interactions. We will give an introduction to the theoretical concepts of the description of intermolecular forces. We will tackle Ar-CO as prototype system of intermolecular forces which has been subject of intensive experimental and theoretical work in the past and has evolved to one of the most investigated intermolecular complexes. We will give here an overview over the numerous theoretical and experimental studies which have been published in the literature. A comparison between the most recent ab initio studies and the experimental work demonstrates a lack of sufficient agreement. We have carried out a semi-empirical fit of the potential energy surface to five of the seven known intermolecular modes. All modes could be reproduced within 0.4 cm using our new potential energy surface. The most significant deviation which was found in comparison to previous ab initio potentials was the appearance of a second local minimum in the potential energy surface. These results indicate a lack of a sufficient accurate theoretical description of intermolecular forces for this "little beast" which remains still a challenge for the future.

1. Introduction Intermolecular forces are the forces which cause attraction in the absence of chemical bonding. We are all aware of this attraction, since they appear in our everyday lives: intermolecular forces are, for example, responsible for the * Corresponding author. E-mail: [email protected] Z. Phys. Chem. 219 (2005) 1053-1088 © by Oldenbourg Wissenschaftsverlag, München

4

M. Havenith and G. W. Schwaab

sticking together of snowballs, the formation of water droplets, and the appearance of surface tension. These forces, which are about two orders of magnitude weaker than chemical bonds, are responsible for many phenomena in nature, such as • • • • •

the properties of real gases transport effects in gases such as viscosity, thermal conductivity and diffusion adsorption due to molecule-surface interaction molecular solids hydrogen bonding in biological systems.

Physical insight into the different contributions to intermolecular forces can be obtained e.g. by symmetry adapted perturbation theory (SAPT) [70] or a supermolecule approach [9]. To understand the structure and energetics of van der Waals complexes four fundamental intermolecular interactions have to be accounted for: • •

•

•

Electrostatic interaction is caused by the static charge distribution of the interacting systems. Induction describes the interaction of multipole moments of one monomer with the induced multipole moment of the second monomer. This interaction is always attractive. Overlap-exchange interaction is a mainly repulsive part of the intermolecular interaction and can be separated into two contributions. It contains terms describing the overlap of the wave functions (penetration effects) as well as the exchange energy that is due to the physical process of the (resonance) tunneling of electrons between the interacting systems. In many studies this part of the potential energy surface can be described very accurately by an exponentially decaying function, the so-called Born-Mayer potential Eexchov = A exp(—bR) with A and b being two adjustable parameters which depend on the relative angular orientation of the monomers [74]. The contributions of induction and electrostatic (multipole-multipole) interaction as discussed before involve non-overlapping wavefunctions. However, for R —> 0 overlap-exchange yields also an exponentially decaying attractive contribution to electrostatic and induction interaction (for Ar-CO this has been calculated by Kukawska-Tarnawska [39]). Dispersion: This contribution is a pure quantum mechanical quantity for which no classical analog can be found. It describes the attractive interaction which is also present between two monomers with no multipole moments. We can visualize this interaction as simultaneously induced multipole moments that interact with each other (see Fig. 1).

The relative size of the different contributions strongly depends on the charge distribution, multipole moments and polarizabilities of the interact-

Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces Ar

5

Ar

Fig. 1. The induced-dipole-induced-dipole interaction in (Ar)2.

Θ r R

Θ

Fig. 2. Example of an atom-diatom complex showing the coordinates R, r and θ of the intermolecular potential.

ing monomers. Even for polar molecules, however, the dispersion energy can be a significant contribution to the overall binding energy. Although HF-dimer, water dimer and ammonia dimer contain polar molecules with a significant contribution of the electrostatic binding energy, the contribution of the dispersion energy to the overall binding is quite high for each complex. More specifically, the portion of attractive components: electrostatics/induction/dispersion amounts to: 9.9/3.0/2.5 (HF-dimer); 11.2/2.7/2.9 (H 2 0 dimer); 9.2/3.6/6.2 (NH 3 dimer) [8]. Whereas theoretical models can very well predict electrostatic and induction interaction, the accurate description of dispersion and repulsion interaction remains still a challenge. Complexes consisting of a noble gas and a diatomic molecule are the simplest systems in which anisotropic intermolecular forces play an important role (see Fig. 2). For experimental reasons, many detailed studies of small complexes involve hydrogen-containing molecules. These molecules have large dipole and transition dipole moments and are therefore among the easiest to observe experimentally. For all these complexes induction is a considerable contribution to the overall binding energy. The equilibrium structures of the complexes Ar-HBr, Ar-HCl and Ar-HF show a linear structure, corresponding to the maximum in the induction energy. Nevertheless, dispersion plays an even more important role. One example where dispersion energy dominates the potential energy surface in spite of a strongly polar constituent is Ar-HF (see e.g. [33,42] and references therein) whose most recent and accurate potential surface is shown as a contour plot in two dimensions, namely R and Θ, in Fig. 3. A repulsive wall is seen at small R. Two minima are also evident in the potential surface at θ = 0° and θ — 180°. R gives the distance between the argon atom and the center of mass of HF

6

M. Havenith and G. W. Schwaab

θ/° Fig. 3. The potential of Ar-HF as obtained by Hutson.

Table 1. Contributions to the potential energy of Ar-HF.

θ

Repulsion

Induction

Dispersion

Rm

0° 90° 180°

257 cm- 1 90 cm" 1 105 cm" 1

- 7 2 cm" 1 - 8 cm" 1 —6 c m - 1

- 4 0 5 cm" 1 - 1 6 6 cm" 1 - 2 1 9 cm" 1

3.43 À 3.50 À 3.37 Â

which is very close to the fluorine atom. Both minima are caused by the detailed balance of the different contributions to the intermolecular potential. Table 1 shows the repulsive, inductive, and dispersion contributions of the intermolecular potential for θ = 0°, 90°, and 180° together with the minimum energy distance Rm of the Ar atom and the center of mass of the HF molecule. The minimum at θ = 0° corresponds to the hydrogen pointing towards the argon, giving a maximum in the induction energy. HF is a strongly polar molecule (dipole moment 1.8 D), so that the induction energy is expected to make a significant contribution.

Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces

7

Therefore, it is surprising that the dispersion energy is the main contribution to the potential energy. The increase in the repulsion from 105 to 257 cm - 1 when going from 180° to 0° can be explained in terms of the influence of the H atom. Since the H atom is pointing towards the argon atom at θ = 0°, the distance between the Η and the Ar atoms is only 2.56 A, whereas for θ = 180° the argon-fluorine distance is 3.32 À. The dispersion is approximately two times larger for θ = 180° than for θ = 0°. In comparison, the repulsion is only slightly increased for θ = 180° compared with θ = 90°, although the distance is considerably smaller. The latter is due to a lack of repulsion at θ = 180°, which corresponds to a decrease in charge density as a result of the electronwithdrawing effect of the HF bond. We can see here that for an understanding of the potential energy surface of complexes all contributions have to be well determined. In addition to the electrostatic part the induction energy is the part of the intermolecular interaction which can be most easily predicted theoretically. Reliable estimates can be obtained from the known polarizabilities and electrostatic moments (dipole moment μ and quadrupole moment Θ) of the monomers [31]. However, an accurate theoretical description of the parts involving correlation effects, such as the dispersion interaction, is much more challenging. Estimates are based on knowledge of the C° coefficients [77] and on the measured anisotropic polarizabilities of the molecules [16]. For Rg-CO complexes (Rg: rare gas) the contribution of induction energy is small. The potential and especially the anisotropic part of the potential surface are determined nearly exclusively by a balance of dispersion and repulsion. Therefore, they are especially suitable for testing recent theoretical developments since a direct comparison with ab initio studies is possible. Up to now Rg-CO complexes have been measured in several van der Waals states for all rare gases besides the radioactive radon. The He-CO [10,11] complex has been studied by McKellar et al. A pure ab initio prediction of the infrared spectrum of He-CO, which coincides very well with the experimental spectrum, is given in [50], However, for He-CO only a few bound states can be found in the flat potential (D c = —22.9 cm - 1 ; the lowest energy level is bound by only 6.6 cm - 1 )· As a prototype system, He-CO therefore lacks a sufficient number of possible experimental data values. Ne-CO has been studied by infrared and millimeter wave spectroscopy [46, 59]. Molecular parameters for the ground intermolecular vibrational state up to Κ = 3 and the first excited bending state up to Κ — 1 could be derived. Ab initio potential energy surfaces (PES) for Ne-CO were calculated using S APT [51] and supermolecule [44] techniques. The ab initio PES shows a single minimum at De ~ —50 to —53.5 cm - 1 with a ground state binding energy of ~ —31 cm - 1 . A comparison of the energy levels calculated from the ab initio PES and the experimentally determined values shows that the predictions agree well for the lower energy levels of Ne-CO, that the deviations for the highly excited levels, however, are small (< 0.5 cm - 1 ) but significant.

8

M. Havenith and G. W. Schwaab

For Kr-CO and Xe-CO so far no ab initio PES are available. Spectra of the two complexes have been measured by the McKellar group using IR and millimeter wave spectroscopy [5,76], For Ar-CO, binding energies of the order of 110 c m - 1 , and hence several hundred of bound states are predicted. Compared with the hydride complexes, which have even higher binding energies, the Ar-CO complex has an increased number of bound states owing to the small rotational constant bco of CO (as compared with bm for Ar-HF). This rotational constant b determines the energy separation of different rotor states for the CO complex within the Ar-CO complex and is therefore responsible for the density of van der Waals states in the potential. In addition, for Ar-CO we find as portion of attractive components: electrostatics/induction/dispersion a ratio of: (1.3/1.4/8.3) demonstrating the dominance of the theoretically challenging dispersion energy [39]. As an ideal test candidate for the study of dispersion effects, in recent years Ar-CO has become one of the most thoroughly studied small complexes. About 20 experimental and more than 10 theoretical papers have already dealt with this prototype, which makes it one of the best studied molecular complexes so far. In the following sections we will discuss our knowledge about what appears to be a "little beast".

2. Quantum-mechanical description of Ar-CO 2.1 The Ar-CO Hamiltonian In analogy to the Born-Oppenheimer approximation, the intramolecular motion can often be separated from the intermolecular motion. For Ar-CO this assumption implies that the intramolecular CO vibration should only be slightly influenced by the intermolecular vibration of the full complex which is indeed observed experimentally (see Sect. 4). Hence, a natural choice of van der Waals coordinates for Ar-CO is given by the distance R between the Ar-atom and the center of mass of the CO molecule and the Euler angles ζα) = (4>co, #co> Ψ co), that describe the orientation of the CO molecule relative to a space fixed (SF) frame or a body-fixed (BF) frame that is embedded in the dimer [2]. In the space fixed description the kinetic energy operator takes on an especially simple form: (1)

where Tco describes the internal kinetic energy of the CO monomer, /xArC0 is the dimer reduced mass and / SF describes the end-over-end rotation of the overall complex. However, although the expression for the kinetic-energy operator in the space-fixed axis system is very convenient, the potential is easier to describe in terms of the internal coordinates of the complex. For an atom-

Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces

9

diatom system, two coordinates R and θ are sufficient to describe the potential in the body-fixed (also called the embedded) axis system (see Fig. 2). In this paper 0 = 0 ° refers to the Ar-O-C orientation of the complex and θ = 180° to the Ar-C-O orientation. Within the body-fixed axis system, TCo is given by Tco = &coO BF ) 2 · The kinetic-energy operator can be written as [2] 1 Γ

9

, a

- h 2 i -dR» R 2 - LdR·

=

+

( / S F ) + l / c o r - 2C/CO/) (2)

where J is the total angular momentum of the dimer with respect to the embedded frame, J — jco

+1 ;

(3)

Jζ = je ο,ζ •

SF

J describes the total angular momentum in the space-fixed frame and jco is the angular momentum of the rotor CO in the space-fixed frame. An exact derivation is given in [4] and Appendix 4 of [2], It should be emphasized that Eq. (2) cannot be obtained directly by a change to body-fixed coordinates and the substitution l2 = ( J - j )

2

= J2 + j

2

- 2 ( j j ) ,

(4)

since j and J do not commute [2]. To be able to calculate matrix elements of the Hamiltonian, the last term in Eq. (2) can be written in terms of ladder operators (5)

j± = jx ± ijy

and pseudoladder operators J± = JxTiJy

(6)

as 2 ( 7 c o / ) = 2jzJz

+ j+J+

+ j_J_

.

(7)

Including the intermolecular potential energy V(R, Θ), the full Ar-CO Hamiltonian is given by H = b œco\jco) (jco)2 0

1

p2

—

2ßArCOR2 [(^SF)2

— R 2dR —+ dR

+ Uco)2

- 2jzJz

(8)w - j+J+

- j.jJi + V W R ,

θ).

It can be shown that the complex conjugates of the Wigner rotation functions D$K(R, 0 R , 0)* (App. Β in [2]) where R and θ κ describe the relative

10

M. Havenith and G. W. Schwaab

orientation of the space fixed and embedded frames of the Ar-CO molecule are simultaneous eigenfunctions of (7 SF ) 2 , (7 BF ) 2 , and 7®F with the eigen2 2 values h J(J + 1), h 7(7+1), hM, and hK, respectively. Furthermore, the relation J±D%K((PR, θκ, 0)* - hJj(J

+ l)-K(K±l)

ϋ^κ±ί(φκ,

eR, 0)*

(9)

holds. A complete set of parity adapted and normalized angular wave functions can be obtained from the spherical harmonics eigenfunctions YJK{9, φ) describing the rotation of the CO molecule in the embedded frame and the Wigner rotation functions after Wang transformation:

= χ

(io)

[y¿(0, Φ)ο%(φκ,

θ„, 0)*+Ρ(~\γΥίΩ(θ,

φ)θΐ__Ω(φΗ,

eR, o)*],

where ρ is the parity (ρ = ±1) and Ω = In the case of Ω = 0, both terms in the sum are equal and the factor 1 />/2 has to be replaced by 1 /2. As suitable basis for the solution of the Schrödinger equation in the embedded frame we chose product functions In, J, M, p, j, Ω) = \n)\J, M, p, j, Ω)

(11)

of the angular basis defined in Eq. (10) and radial wavefunctions I η) = Ψη{Κ) =

(12)

κ

where the x„(R) are numerical solutions of the one-dimensional Schrödinger equation /

92

2/z AiC0 3R2

+V(R, θ = 90°)ì

Xn(R)

= EnXn(R).

(13)

The \n, 7, M, p, j, Ω) are eigenfunctions of the total angular momentum (7 SF ) 2 and its projection J f f , with the eigenvalues 7(7 + 1) and M. The quantum number K a , which corresponds to the projection of 7 onto the intermolecular axis in the complex embedded frame, is nearly a conserved quantum number. This follows from (8), since Jz = jz commutes with the whole Hamiltonian, except for one term which is called the Coriolis term Hc: Hc

= "

2

+

(14)

11

Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces

From Eq. (9) and the equation j±YJK(ß, φ) = h J j { j + \)-K{K±\)YiK±l

(15)

it follows that this term will connect eigenfunctions with equal J and j values, but with Κ' — Κ ± 1. The connecting matrix elements are given generally by =