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Christophe L Vaillant1, Manish J Thapa2, Jiří Vaníček1

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The quantum and semiclassical instanton approximations for reaction rate constants differ for asymmetric barriers. A modified quantum instanton approach improves accuracy for asymmetric systems.

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Area of Science:

  • Quantum chemistry
  • Chemical kinetics
  • Computational physics

Background:

  • The reaction rate constant is crucial for understanding chemical reactions.
  • Instanton approximations are used to calculate reaction rates, particularly in quantum systems.
  • Discrepancies exist between quantum and semiclassical instanton methods.

Purpose of the Study:

  • To investigate the relationship between quantum and semiclassical instanton approximations for reaction rate constants.
  • To identify the source of errors in the quantum instanton approximation for asymmetric systems.
  • To propose a modification to the quantum instanton method for improved accuracy.

Main Methods:

  • Analysis of the quantum instanton expression for reaction rate constants.
  • Examination of minimum-action paths contributing to the rate.
  • Comparison of quantum and semiclassical instanton results for symmetric and asymmetric barriers.

Main Results:

  • Two dominant minimum-action paths contribute to the quantum instanton expression.
  • For symmetric barriers, these paths merge into the semiclassical instanton periodic orbit.
  • For asymmetric barriers, a spurious low-energy path leads to significant errors in the quantum instanton approximation.

Conclusions:

  • The semiclassical instanton approximation is directly derived from the quantum instanton only for symmetric systems.
  • A modified quantum instanton approach, avoiding the spurious path, provides accurate predictions for asymmetric systems.
  • The enhanced quantum instanton method offers a more reliable calculation of reaction rates in the low-temperature limit.