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Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism

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Summary

The quantum statistics of a symmetric hindered internal rotator in a molecule or molecular complex is developed within the Wigner function formalism. Different shapes of the rotational barrier are considered. The partition function and the thermodynamic functions are given as Wigner-Kirkwood series expansions in terms of powers of Planck's constant squared. One gets simple closed expressions containing the modified Bessel functionsJ 0 andJ 1 of the argumentiV 0/2kT whereV 0 is the barrier height. Some problems concerning the evaluation of equilibrium and rate constants of chemical reactions are discussed.

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Vojta, G., Zylka, C. Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism. Theoret. Chim. Acta 86, 439–449 (1993). https://doi.org/10.1007/BF01122434

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Key words

  • Hindered rotation
  • Wigner-Kirkwood series
  • Partition functions
  • Thermodynamic functions