Charge overlap effects and the validity of the multipole results for first-order molecule-molecule interaction energies. Formalism and an application to H2-H2

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Abstract
For the interaction of two molecules, the first-order coulomb energy, E e (1), is expressed as a sum of non-expanded partial wave components which exhibit the orientation dependence of the energy explicitly. By comparing these non-expanded results with the analogous multipolar results for the first-order energy, the effects of charge overlap on the multipole representation of the energy can be investigated as a function of intermolecular separation and orientation, and the validity of the multipole results for E e (1) assessed. The interaction of two ground-state hydrogen molecules is considered as a specific example of this approach for studying the validity of the multipole expansion as a representation of molecular first-order Coulomb energies. All calculations are presented as a function of four molecular wave functions of varying degrees of sophistication in order to assess the sensitivity of (1) the representation of charge overlap effects and (2) the calculated quadrupole and hexadecapole moments of H2 with respect to the quality of the molecular wave function. The first-order partial wave energies, through partial wave indices la = lb = 2, are used to discuss the validity of severely truncated multipole expansions of the first-order interaction energy to represent the total and the orientation dependent part of the Coulomb energy for the H2-H2 interaction. The importance of first-order charge overlap effects for the interaction of more complicated molecules is also discussed briefly.