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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 {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 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. An erratum is available here and published in J. Phys. A: Math. Theor. 51, 2018, 149501.
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Submitted on : Wednesday, May 5, 2021 - 10:45:07 AM
Last modification on : Saturday, October 1, 2022 - 3:52:45 PM
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Thierry Jecko, Brian T Sutcliffe, R Guy Woolley. On Factorization of Molecular Wavefunctions. Journal of Physics A: Mathematical and Theoretical, 2015, ⟨10.1088/1751-8113/48/44/445201⟩. ⟨hal-03217883⟩



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