Anthony J. Stone

The theory of intermolecular forces

1. Introduction 2. Molecules in Electric Fields 3. Electrostatic Interactions between Molecules 4. Perturbation Theory of Intermolecular Forces at Long Range 5. Ab Initio Methods 6. Perturbation Theory of Intermolecular Forces at Short Range 7. Distributed Multipole Expansions 8. Short-Range Effects 9. Distributed Polarizabilities 10. Many-body Effects 11. Interactions Involving Excited States 12. Practical Models for Intermolecular Potentials 13. Theory and Experiment Appendix A Cartesian Tensors Appendix B Spherical Tensors Appendix C Introduction to Perturbation Theory Appendix D Conversion Factors Appendix E Cartesian-Spherical Conversion Tables Appendix F Interaction Functions

Distributed multipole analysis, or how to describe a molecular charge distribution

Abstract A method of analysing molecular wavefunctions is described. It can be regarded as an extension of Mulliken population analysis, and can be used both to give a qualitative or quantitative picture of the molecular charge distribution, and in the accurate evaluation of molecular multipole moments of arbitrary order with negligible computational effort.

Distributed multipole analysis

The conventional multipole expansion gives a description of electrostatic interactions which is only useful at long distances. Distributed multipole analysis gives a description which is accurate at all accessible distances, and also gives a much more detailed and instructive picture of the charge distribution. We report our recent investigations into the method and comment on its limitations.

An intermolecular perturbation theory for the region of moderate overlap

A perturbational method is described for calculating the interaction energy of two molecules in the region where the overlap between their wave-functions is significant. By working directly with a basis of determinants constructed from the SCF orbitals of the separated molecules, without orthogonalization, it is possible to avoid many of the disadvantages of other methods.

Towards an accurate intermolecular potential for water

A new ab initio potential for the water dimer is presented. It is obtained from monomer properties and perturbation theory calculations (IMPT) on the dimer. The long range electrostatic interaction is described by distributed multipoles: charge, dipole and quadrupole on oxygen and charge and dipole on hydrogen. The induction is modelled using polarizabilities on oxygen up to quadrupole. The short range repulsive energy is modelled by an exponential site-site function incorporating site anisotropy. Two models have been used for the dispersion energy: accurate dispersion coefficients for the water dimer with Tang-Toennies damping functions, and a site-site model. Neither is entirely satisfactory. The geometry of the global minimum on the potential surface is in very good agreement with the experimental result. The virial coefficient agrees moderately well with the experimental determination; the discrepancies suggest that the potential is not deep enough.

The electrostatic interactions in van der Waals complexes involving aromatic molecules

The minima in the electrostatic energy, for accessible orientations, have been located for the s‐tetrazine and benzene dimers and the 1:1 complexes of s‐tetrazine with hydrogen chloride, water, acetylene, and benzene, and of benzene with acetylene, anthracene, and perylene. The minima give reasonably successful predictions of the structures of these van der Waals molecules, demonstrating the importance of the electrostatic interactions in these systems. The electrostatic energy was calculated using sets of distributed multipoles obtained from ab initio wave functions of the monomers. This method is contrasted with empirical point charge and central multipole models for the electrostatic energy. It is shown that the simple models for the electrostatic interactions can give qualitatively misleading results for aromatic systems.

g factors of aromatic free radicals

A quantitative theory of the g factors of aromatic free radicals is presented, and is applied to hydrocarbon and semiquinone ions. The parameters required in the theory are obtained empirically, and the agreement with experiment is very satisfactory. The g factors of aromatic hydrocarbons are given by g=2·00257 - (19 × 10-5)λ, where α + λβ is the energy, in the Huckel approximation, of the molecular orbital occupied by the odd electron.

Explicit formulae for the electrostatic energy, forces and torques between a pair of molecules of arbitrary symmetry

The spherical multipole expansion has been used to derive explicit expressions for the terms up to and including R -5 in the R -1 expansion of the electrostatic energy of two molecules of arbitrary symmetry, in a simple form which is suitable for use in model potentials. We show also how the corresponding forces and torques can be readily derived from these energy expressions, and give explicitly the forces and torques which would be required for a molecular dynamics simulation of a fluid of linear molecules.

The description of bimolecular potentials, forces and torques: the S and V function expansions

Any scalar function of the orientation of a pair of molecules, of arbitrary shape, can be expanded in terms of a complete orthogonal set of functions called S functions. Any vector function can similarly be expanded in terms of V functions. Although the functions are expressed in terms of Wigner rotation matrices, they can be evaluated efficiently enough for use in molecular dynamics calculations. In particular, trigonometrical function evaluations are not required. The force and torque on a molecule can be derived, as V function expansions, from a potential given in S function form, and the necessary formulae are listed.

Are halogen bonded structures electrostatically driven

Halogen-bonded complexes B···XY, where B is a Lewis base and X a halogen atom, have been described as electrostatically driven, largely because of the close analogy between their structures and those of corresponding hydrogen-bonded complexes. Analysis of the components of the binding energy using symmetry-adapted perturbation theory suggests that while the main contribution to the binding is usually the electrostatic energy, the geometries are not always determined by electrostatics alone. In particular, the strong tendency to linearity of the B···XY bond is a consequence of exchange-repulsion, not electrostatics.