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Uniform Semiclassical Instanton Rate Theory.

Sameernandan Upadhyayula1, Eli Pollak1

  • 1Chemical and Biological Physics Department Weizmann Institute of Science, Rehovoth 76100, Israel.

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|October 31, 2023
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Summary
This summary is machine-generated.

This study presents a new instanton theory for thermal transmission probability, resolving divergence issues at crossover temperatures. The improved theory accurately models quantum tunneling and thermal activation across temperature ranges.

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Area of Science:

  • Quantum Mechanics
  • Statistical Mechanics
  • Chemical Physics

Background:

  • The standard instanton theory for thermal transmission probability exhibits divergences at crossover temperatures.
  • Existing models struggle to smoothly transition between quantum tunneling and thermal activation regimes.

Purpose of the Study:

  • To derive a uniform semiclassical instanton expression for thermal transmission probability.
  • To resolve the divergence issue at crossover temperatures and provide a smooth transition between tunneling and thermal activation.
  • To improve the high-energy behavior of the instanton theory.

Main Methods:

  • Utilized Kemble's uniform semiclassical energy-dependent transmission coefficient.
  • Developed a modified instanton theory incorporating a Boltzmann factor decay at high energies.
  • Applied the theory to Eckart barriers for comparison with numerical results.

Main Results:

  • The new theory avoids divergence at crossover temperatures, providing a smooth transition.
  • The instanton energy condition is modified (ℏβω‡ = π), differing from standard theory.
  • The improved theory reduces to classical behavior at high temperatures and accurately estimates results for Eckart barriers.

Conclusions:

  • The concept of a crossover temperature based on instanton rate divergence is obsolete.
  • The uniform instanton theory offers a more accurate and robust description of thermal transmission probability.
  • This work provides a better theoretical framework for understanding quantum effects in chemical reactions and condensed matter systems.