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Diffusive barrier crossing rates from variationally determined eigenvalues.

Alexander M Berezhkovskii1, Irina V Gopich2, Attila Szabo2

  • 1Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.

The Journal of Chemical Physics
|July 23, 2021
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Summary
This summary is machine-generated.

This study links Kramers' procedure to eigenvalue methods for calculating activated process rates. It shows how the flux-over-population rate constant emerges from a variational eigenvalue in high-barrier systems.

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Area of Science:

  • Chemical Kinetics
  • Statistical Mechanics
  • Theoretical Chemistry

Background:

  • Kramers' procedure calculates activated process rates using dividing surfaces and steady-state flux.
  • An alternative method estimates the rate constant from the first non-zero eigenvalue of the dynamics operator.

Purpose of the Study:

  • Establish the relationship between Kramers' procedure and eigenvalue-based methods for diffusive dynamics.
  • Derive Kramers' flux-over-population expression from a variational eigenvalue approach.

Main Methods:

  • Utilized a variational principle for the eigenvalue of interest.
  • Employed a trial function with two adjustable dividing surfaces.
  • Leveraged the modern theory of activated rate processes, incorporating the committor probability.

Main Results:

  • Demonstrated that Kramers' flux-over-population rate constant can be obtained from the variationally determined eigenvalue for high barriers.
  • Showcased that the upper bound for the eigenvalue can be expressed using mean first-passage times and mean transition-path times.

Conclusions:

  • The study provides a theoretical link between two prominent methods for calculating activated process rates.
  • Highlights the utility of variational principles and the committor probability in understanding rate processes.