Calculation of intermolecular interaction energies by direct numerical integration over electron densities. I. Electrostatic and polarization energies in molecular crystals

A procedure for adapting electron densities obtained by molecular orbital calculations for isolated molecules to the evaluation of intermolecular energies is presented. It involves a reduction of the number of electron pixels in the original density by screening out insignificant points and condensing the others into super pixels and the duplication of the original density according to a given multimolecular arrangement or to crystal symmetry. Electrostatic energies are calculated by direct numerical integration. For the calculation of polarization energies, the total, many-body intermolecular electric field at points over molecular space is evaluated, and a semiempirical model for distributed polarizabilities is introduced. Calculations on well-studied crystalline systems lead to an assessment of the method as concerns the treatment of density overlap zones by a proper choice of the screening and condensation parameters: apart from these. and a few other atomic polarizability parameters, the method is totally ab initio. Results for Clusters of computer-generated polymorph crystal structures show that there is no relationship between the magnitudes of electrostatic and polarization energies, although some quantitative uncertainties remain for the latter because of its present semiempirical formulation. Electrostatic energies calculated with the present method are generally larger than, and not proportional to, the ones obtained by point-charge or distributed multipole methods. Partitioned analysis confirms the destabilizing and repulsive nature of some molecule-molecule interactions. hence the unreliability of localized qualitative models (e.g., parallel or antiparallel dipoles) of intermolecular interaction in crystals. The model presented here also opens the way to an evaluation of dispersion and exchange repulsion potentials.