Atomic Multipole Expansions of Molecular Charge Densities. Electrostatic Potentials

Abstract

The molecular electrostatic potential has been shown to be a very useful tool for understanding the reactivities of molecules with ions or polar molecules¹ and the structure and energetics of intermolecular complexes, including hydrogen bonded complexes.² The electrostatic potential can be obtained as the by-product of a molecular orbital calculation in the form of a large table of numbers.³ A considerable computational advantage would be obtained if this information could be compressed into analytical form, and a large amount of effort has gone into the search for appropriate representations. For instance, Bonaccorsi, Scrocco and Tomasi⁴ have shown how one can resolve molecular electrostatic potentials into sums of contributions from fragments within the molecule; the fragment contributions are approximately transferable, allowing one to construct the potential for a large molecule without first performing a molecular orbital calculation on that molecule. Kollman⁵ has also addressed the problem of obtaining the potential without a wave function and has produced a family of point-charge models for which the necessary inputs are experimental bond lengths, bond angles, and dipole moments, atomic electronegativities, and van der Waals radii. These point-charge distributions produce electrostatic potentials at suitable reference points which are in reasonable accord with the potentials obtained from wave functions.