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Topological phase transitions in the vibration–rotation dynamics of an isolated molecule

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Abstract

One of the characteristic features of rotation–vibration dynamics is the existence of a variety of energy bands which result from organization of energy levels into bands depending on control parameters. Symmetry and topology aspects of the organization of energy bands and generic modifications of this structure for molecular systems with symmetry are discussed in a way parallel to the description of topological quantum transitions extensively studied in condensed matter physics. A special class of axially symmetric molecular systems is analyzed. It is shown that only a finite number of different band structures are possible for rotation–vibration problem with a finite number of vibrational states in the case of continuous axial symmetry, whereas for problems with finite group symmetry an arbitrary large number of different band structures are formally allowed.

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Notes

  1. The number of one-dimensional representations of a group is equal to the order of Abelianization, i.e., the order of the Abelian group \(G/[G,G],\) the quotient of \(G\) by the commutator \([G,G].\)

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Authors and Affiliations

  1. Kyoto University, Kyoto, Japan

    T. Iwai

  2. Université du Littoral, 59140, Dunkerque, France

    B. Zhilinskii

Authors
  1. T. Iwai
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  2. B. Zhilinskii
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Correspondence to B. Zhilinskii.

Additional information

Dedicated to Professor Greg Ezra and published as part of the special collection of articles celebrating his 60th birthday.

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Iwai, T., Zhilinskii, B. Topological phase transitions in the vibration–rotation dynamics of an isolated molecule. Theor Chem Acc 133, 1501 (2014). https://doi.org/10.1007/s00214-014-1501-x

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  • DOI: https://doi.org/10.1007/s00214-014-1501-x

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