Jonathan A. Yoffe

A point-charge representation of frost-model wave functions

A point-charge representation of Frost-model wave functions is derived from a symmetry-adapted perturbation theoretic expansion. The new point-charge model is simpler than those suggested previously yet gives good estimates of first-order molecular properties. The treatment can easily be extended to deal with second-order properties and, when this is done, formulae similar to those of the Drude theory are obtained. Using these formulae, theoretical expressions for the refractive indices of methane, ethane and water are computed and are in reasonable accord with experiment for the two hydrocarbons but less satisfactory for water.

Electric polarizabilities, magnetic susceptibilities and dispersion coefficients for hydrocarbons

Frost-model wavefunctions for CH4, C2H6, cyclo-C3H6, C2H4, C2H2, allene, transbutadiene and benzene are given using experimental rather than optimized geometries. Results for electric polarizabilities and magnetic susceptibilities are computed using several different optimizations, and results are in good agreement with experiment. Dispersion coefficientsC6,C8 andC10 are given for all pair interactions, as are values for γ3, the three-body interaction, andd4, a retardation correction term, for several interacting species. Results should be fairly reliable.

Long-Range Molecular Interaction Coefficients Computed from Frost-Model Wave Functions

The average long-range interaction energy between two molecules can be written as an inverse asymptotic series in the intermolecular separation distanceR. Using Frost-model wave functions, the dispersion coefficients of the first three (R−6,R−8,R−10 terms in the series are obtained. Coefficients of three- and four-body non-additive interaction energies are also calculated and the form of the dispersion interaction when retardation effects are included is examined.

Electric polarizabilities using point charge models

The formula for the electric polarizability of a molecule using a Frost model Lewis basis set, that is one orbital per electron pair, can be extended to include wavefunctions containing additional Gaussians using point charge models. Using these alternative formulae, results for hydrocarbon Lewis sets and molecular fragment wavefunctions are in good agreement with experiment and with the results obtained using the original formula. In addition results for atomically centred wavefunctions for molecules containing lone pairs are also good and show an improvement over the Lewis set results for these species.

Intermolecular interaction coefficients using point charge models

Values of the two-body interaction coefficientsC6 andd4 between like species, as well as the three-body term γ3, are obtained from point charge model formulae. Lewis set results may be compared with atomically centered wave-function values as well as results obtained using an experimental point charge model. Generally results are in good agreement with experiment and when theoretical values differ wildly from experiment they may be normalized using theoretical and experimental static polarizability values.

Hydrocarbon long-range interaction coefficients from point charge model formulae

Two-body interaction coefficientsC6 andd4 and the three-body coefficient γ3 are calculated for interactions between like species for a variety of hydrocarbons. Three different point charge models are employed and results are similar when Frost model Lewis set wavefunctions are used and in agreement with other literature values where available. We also consider simple Slater-Kirkwood type formulae for the coefficients and it turns out that very similar results to theab initio model values are found ford4. The formulae can also be used in conjunction with molecular fragment wavefunctions.