Thole's interacting polarizability model in computational chemistry practice

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Abstract

Thole's interacting polarizability model to calculate molecular polarizabilities from interacting atomic polarizabilities is reviewed and its major applications in computational chemistry are illustrated. The applications include prediction of molecular polarizabilities, use in classical expressions for intermolecular interactions for the computation of binding energies of molecular dimers, solvation (free) energies, and solvent effects in combined quantum-chemical-classical (QM-MM) calculations.

The examples demonstrate the wide applicability of the model, which is due to its firm foundation in the perturbation theory of intermolecular interactions, from which the polarizability emerges as one of the material properties determining the interaction between species. The true power of the model is its generality, rendering transferability to all sorts of chemical problems almost a non-issue.

Introduction

Computational approaches to probe nature's secrets have always looked for ways to escape brute-force methods. Two obvious reasons for this are the limitations computational resources put on the feasibility of brute-force methods and the fact that these methods do not provide us with anything we regard as `insight': a simple, appealing concept valid in a wider setting than the particular system under study.

Brute-force methods cannot be avoided, however, because one encounters the limitations of simpler material models in representing nature as it appears to us: there is a hierarchy of detail which is required to explain certain phenomena. More specifically, in physical chemistry virial coefficients may be calculated quite successfully by accounting for interactions between molecules, and infrared spectra may be simulated from an atomic interaction model, but, for example, bond-breaking/bond-making reactions and electronic spectra require a quantum-mechanical description at the level of interactions between nuclei and electrons, including the consequences of the Pauli principle. Also, the more detailed descriptions provide the underlying rationale for coarse-grained methods and may be used to obtain numerical input (the parameters) for them.

In chemistry, the entities of interest span a range of length-scales. There is a need to know about electronic motions for spectroscopy, atomic movement for reactions, and molecular behaviour for material properties. This diversity of interest explains the multitude of concepts current in chemistry. Initial approaches to explaining phenomena focus on a particular scale in isolation, as it were, but a second look obviates the need to consider other levels as well and the simple concepts need to be modified and expanded. A well-defined hierarchy is an asset to combine different levels sensibly, preserving the simple picture whilst accounting for subtle perturbative effects in a general, unforced way.

Thole's interacting polarizability model is one such sensible approach in computational chemistry, enabling the description of the effects of material directly surrounding a region of particular chemical interest (be it a reaction or a chromophore) which requires a quantum-chemical description (at the level of nuclei and electrons) without including the same level of detail of the surroundings. Rather it expresses the electronic response of the surroundings (the polarizability, which is a collective property) to an applied field in terms of the classical quantity. The power of the model lies in its simplicity and generality. In this short review, we will discuss the ideas underlying the model, and demonstrate its generality by recalling a selection of applications in computational chemical studies.

Section snippets

Concepts

Thole developed the interacting polarizability model as part of a scheme to perform meaningful calculations on processes of interest in biochemistry 1, 2. The idea was to model the region of interest by a quantum-chemical treatment, accounting for the attenuating effects of the surroundings via classical models. The parameterization of the classical models should be such that a maximum amount of physical content should be preserved.

Arguing from the perturbation theory of intermolecular

Molecular polarizabilities

The earliest application of Thole's interacting polarizability model was the prediction of molecular polarizabilities from interacting atomic polarizabilities as part of the fitting procedure to obtain parameters for the model [1]. Fig. 1 shows the correlation between the polarizabilities from experiment and Thole's model for both the learning set used by Thole, and for a number of molecules outside the learning set, using the so-called linear shape function. The agreement is remarkably good

Conclusion

It has been shown in this review that Thole's model of interacting polarizabilities for describing inter- as well as intramolecular interactions has a wide range of applicability with a minimum of effort. It can be used to predict molecular polarizabilities from a knowledge of structure. It can be used to provide induction and dispersion terms in a classical force field. In combined QM-MM methods, polarization of the surroundings at a microscopic level may be described for many types of

Acknowledgements

This paper is dedicated to the memory of Theo Thole, an unassuming, open-minded and helpful colleague and friend.

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