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Area of Science:

  • Chemical Kinetics
  • Theoretical Chemistry
  • Statistical Mechanics

Background:

  • Dynamical systems often exhibit complex kinetics governed by metastable states.
  • Understanding transition pathways and rates is crucial in various scientific domains.
  • Existing theoretical frameworks for analyzing activated dynamics have limitations.

Purpose of the Study:

  • To reconcile different theoretical formalisms for activated dynamics.
  • To identify the most effective reaction coordinate for describing transitions between metastable states.
  • To develop improved simulation algorithms for calculating transition rates.

Main Methods:

  • Activated-dynamics reactive flux formalism.
  • Markov state eigenvalue spectral decomposition.
  • Committor-based transition path theory.
  • Analysis of microscopic lag-times and correlation functions.

Main Results:

  • Theoretical formulations are consistent, highlighting the role of microscopic lag-times.
  • The committor gradient in the collective variable subspace is the optimal 1D reaction coordinate.
  • The reactive flux formalism is effective for sharp barriers but less so for broad, flat barriers.
  • A modified reactive flux weighted by the committor offers a more efficient simulation algorithm.

Conclusions:

  • The committor function provides a robust framework for analyzing complex reaction dynamics.
  • Improved simulation methods based on the committor can enhance the efficiency of rate calculations.
  • This work offers a unified perspective on activated dynamics and transition path theory.