Some Formal Aspects of the Theory of Intermolecular Interactions and of the BSSE Problem

Abstract

Some results of mathematical character concerning the theory of intermolecular interactions and the BSSE problem are presented. It is shown that the concept of complete basis set may be introduced for intermolecular potential surfaces only by considering explicitly the limiting process in which the basis sets of both monomers approach completeness simultaneously. That does not lead to any overcompleteness problem if we do not postulate the existence of two complete basis sets from the outset. The intimate connection between the BSSE and the differences of some biorthogonal integrals and their "original" counterparts is also discussed. The operator of BSSE is given in terms of such differences. It is shown that in a special case, when only the overlap of the occupied orbitals is considered, the "bi-expectation" value of the energy coincides with the conventional expectation value for the single determinant wave function built up of the unperturbed orbitals of the individual monomers. It is discussed, by using a model of the biorthogonal perturbation theory, why the conceptually fully different a priori (CHA) and a posteriori (CP) schemes of BSSE correction usually give very close numerical results. (The necessary biorthogonal perturbation formalism is developed in the Appendices.) The results give justification for the additivity assumptions inherent in the CP method.