Short-Range Intermolecular Forces. I

A method is given for accurately approximating most of the integrals which occur in calculations of intermolecular forces. Two types of integrals arise; those between orbital pairs which are separated by a considerable distance from each other, and those where the orbital pairs overlap. In the first case the orbital pairs are considered to be electrostatic charge distributions and their energy of interaction is given by a multipole expansion. From a practical standpoint it is necessary to consider only the first few terms (through quadrupoles) of such an expansion. When the orbital pairs overlap, the integral can be approximated by the Mulliken formula in terms of Coulombic type integrals which are then further approximated by the multipole expansion. The problem of calculating intermolecular forces is thereby reduced to the calculation of a number of classical electrostatic multipole interactions. The procedure can be applied to Coulombic as well as exchange forces. Examples are given for the interaction of two hydrogen atoms (in the triplet sigma state), first the repulsion energy alone, and then the combination of Coulombic and exchange energies showing the lack of additivity; the energy of repulsion between two helium atoms; and the energy of repulsion between a hydrogen and a helium atom.