On Factorization of Molecular Wavefunctions

Abstract

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$\Phi$\} of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $\Phi$ in the form $\phi \chi$ where $\chi$ is \textit{purely} a function of the nuclear coordinates, while $\phi$ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be achieved in this form with $\phi$ and $\chi$ interpretable as `electronic' and `nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.

Manuscript submitted to Journal of Physics A: Mathematical and Theoretical, May 2015. Accepted for Publication August 24 2015

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