Electron Delocalization in the Theory of Intermolecular and Intergroup Interactions: Cause, Effect, Prevention

Abstract

It is common to think about complex electronic systems as if they were made up of distinct groups of electrons such as core and valence shells, or atoms and molecules. If one wishes, however, to base a computational method on such physical concepts, one must address certain basic questions. The classic question is, what keeps the electrons of a group from delocalizing to its neighbors and collapsing into their cores? A second question is, what is the effect of transfer and collapse in terms of wave functions and energies? The energies will be wrong, but can one recognize that they are wrong? And, finally, can transfer or collapse be prevented? The Pauli Exclusion Principle “explains” why physically there is no transfer and collapse, but that does not prevent the Schrodinger equation from having solutions corresponding to transfer and collapse. To prevent transfer and collapse, strong-orthogonality has often been imposed in variational theories which distinguish between groups of electrons. In the Hartree-Fock theory screening or localizing potentials have been introduced without making approximations. In contrast, the problem has been largely ignored in the perturbation theory of intermolecular interactions, which we believe to be a serious mistake. In this paper these questions are considered anew within the framework defined by the exact eigenfunctions of the nonrelativistic Hamiltonian for N-electron systems and within that defined by exact solutions of the Hartree-Fock equation. We focus on the question of how electron delocalization can be prevented without resorting to approximations.