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Publication Citation: Remarks on the Phase Change of the Electronic Wave Function Upon Going Once Around a Jahn-Teller Conical Intersection in Vibrational Coordinate Space

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Author(s): Jon T. Hougen;
Title: Remarks on the Phase Change of the Electronic Wave Function Upon Going Once Around a Jahn-Teller Conical Intersection in Vibrational Coordinate Space
Published: April 11, 2013
Abstract: In this paper we revisit, with pedagogical emphasis for high-resolution spectroscopists, some presently existing discussions of phase factors for fixed-nuclei electronic wavefunctions in the Jahn-Teller problem. We give explicit examples, for a symmetric pyramidal NH3-like molecular shape, of perfectly reasonable variants of such electronic wavefunctions that do not transform into their negatives upon going once around the conical intersection (i.e., that do not exhibit a Berry phase change of -1), as well as an example calculation for the pseudo-rotational energy levels and wavefunctions near the bottom of a deep Jahn-Teller moat that does not make use of half-integral quantum numbers and that does not require abandoning ordinary C3v group theory. Some cautionary remarks on drawing inappropriate conclusions from overly hasty Berry phase arguments are also presented.
Citation: Journal of Molecular Spectroscopy
Volume: 288
Pages: pp. 14 - 17
Keywords: Berry phase; Conical Intersections; Group Theory; Half-Integer Quantum Numbers; Jahn-Teller Effect; Phase Factors
Research Areas: Chemical Physics, Molecular Spectroscopy
PDF version: PDF Document Click here to retrieve PDF version of paper (269KB)