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

Author(s)

Jon T. Hougen

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

Pub Type

Journals

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Keywords

Berry phase, Conical Intersections, Group Theory, Half-Integer Quantum Numbers, Jahn-Teller Effect, Phase Factors

Citation

Hougen, J. (2013), Remarks on the Phase Change of the Electronic Wave Function Upon Going Once Around a Jahn-Teller Conical Intersection in Vibrational Coordinate Space, Journal of Molecular Spectroscopy, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910751 (Accessed December 13, 2024)