Vibronic reduction factors in E ⊗ (β1 + β2) and their Berry's phase manifestations

Robert Englman, Asher Yahalom

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In a linearly coupled dihedral E ⊗ (β1 + β2) Jahn-Teller system one finds two different q-factors (say, q1 and q2) and a p-factor. For stronger β1- than β2-coupling, one obtains q1 > q2 and in the strong linear vibronic coupling limit, q1 → 0.5, q2 → 0. At all strengths, the historical relation "p = 2q - 1" turns into p = q1 + q2 - 1. A slowly rotating external field induces in the electronic wave-functions, upon a full turn, a Berry's phase equal to the solid angle subtended by the field's vector at the origin. We have calculated (by employing a quasi-classical approximation to solve the dynamic problem for the ground vibronic state) the corresponding phase change, now diminished by the vibronic reduction factors.

Original languageEnglish
Pages (from-to)24-26
Number of pages3
JournalJournal of Molecular Structure
Issue number1-3
StatePublished - 16 Jul 2007


  • Berry's phase
  • Dihedral symmetry
  • Vibronic reduction


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