Calculation of Lennard-Jones energies of molecular fluids

In view of the ever increasing awareness of the importance of dispersion forces to chemical solvent effects, reliable liquid Lennard-Jones (LJ) energies are eagerly required in order to assess the dispersion component of nonionic solvation. For this purpose two major methods of calculating LJ energies - one based on nonpolar gases solubilities and the other on the generalized van der Waals (GvdW) equation of state - are critically reexamined and updated by applying modern liquid state theories. The former method is improved over previous evaluations by including the cavity formation term according to the Boublik-Mansoori-Carnahan-Starling-Leland equation and by a molecular-based calculation of the solute solvation energy due to both dispersion and induction forces. For the second approach, the attraction parameter of the GvdW equation of state is separated into the contributions of (i) dipole-dipole (permanent and induced) and (ii) dispersion interactions. The first part (i) is treated in the Wertheim theory of polar polarizable liquids. Liquid LJ energies are extracted from the second part (ii) by utilizing Weeks-Chandler-Andersen theory. The dispersion part of the compressibility factor is treated by two routes: (I) in the mean-field approximation and (II) by employing experimental liquid state data. Except for strongly polar liquids, route I appears to be presently the best method of calculating LJ energies as tested by two independent ways. The first is the principle of corresponding states. LJ energies of nonpolar liquids, calculated from route I, demonstrate a universal linear correlation with the logarithm of the vapor pressure at T = 298 K. The other way is calculation of the solvent-induced shift of the absorption line of a model chromophore through molecularly defined solute-solvent interactions. The dispersion component, assessed by using LJ energies from route I, adds up nicely with the induction component, calculated by an extended Wertheim theory, to produce the overall solvent effect showing a linear trend with the polarity function ψ = (∈_∞ - 1)/(∈_∞ + 2) of the liquid high-frequency dielectric constant ∈_∞ for both nonpolar and polar liquids, just as is typically found by experiment. The delicate compensatory influence of dispersion and induction forces stresses the importance of a rigorous parametrization of liquid properties in describing solvent effects.