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Computing time scales from reaction coordinates by milestoning.

Anton K Faradjian1, Ron Elber

  • 1Department of Computer Science, Cornell University, Ithaca, New York 14853, USA.

The Journal of Chemical Physics
|July 23, 2004
PubMed
Summary
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This study introduces an algorithm to calculate complex process timescales using a non-Markovian hopping model. It provides analytical and numerical solutions applicable to various microscopic dynamics, including Brownian motion.

Area of Science:

  • Chemical kinetics
  • Theoretical chemistry
  • Computational physics

Background:

  • Calculating timescales for complex chemical processes is crucial for understanding reaction mechanisms.
  • Existing models often rely on Markovian assumptions, limiting their applicability to systems with memory effects.
  • Non-Markovian dynamics are essential for accurately describing processes influenced by past events.

Purpose of the Study:

  • To develop a general algorithm for computing timescales of complex processes along a reaction coordinate.
  • To model non-Markovian hopping mechanisms derived from underlying microscopic dynamics.
  • To provide a theoretical framework applicable to diverse microscopic dynamics.

Main Methods:

  • Developed a general analytical framework for non-Markovian dynamics.

Related Experiment Videos

  • Constructed a hopping mechanism based on microscopic dynamics.
  • Presented a pedagogical example and numerical solutions for the non-Markovian model.
  • Applied the method to Brownian dynamics with time-uncorrelated velocities.

    • Main Results:

    • The algorithm computes timescales for processes with memory effects.
    • Analytical and numerical solutions demonstrate the model's validity.
    • The approach is general and not limited to specific microscopic dynamics.
    • Demonstrated successful application to Brownian dynamics.

    Conclusions:

    • The presented algorithm effectively computes complex process timescales under non-Markovian conditions.
    • The theoretical framework accommodates various microscopic dynamics, enhancing its applicability.
    • This work provides a valuable tool for studying systems with memory in chemical and physical processes.