On Factorization of Molecular Wavefunctions

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$Φ$\} of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $Φ$ in the form $φχ$ where $χ$ is \textit{purely} a function of the nuclear coordinates, while $φ$ 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 $Φ$ can be achieved in this form with $φ$ and $χ$ 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.

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