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Exploration of effective potential landscapes using coarse reverse integration.

Thomas A Frewen1, Gerhard Hummer, Ioannis G Kevrekidis

  • 1Department of Chemical Engineering, Princeton University, Engineering Quadrangle, Olden Street, Princeton, New Jersey 08544, USA. tfrewen@princeton.edu

The Journal of Chemical Physics
|October 10, 2009
PubMed
Summary

This study introduces a novel reverse integration method for mapping complex potential energy landscapes. This approach efficiently navigates these landscapes to find key transition paths and escape local energy wells.

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Area of Science:

  • Computational chemistry
  • Physical chemistry
  • Chemical physics

Background:

  • Exploring low-dimensional effective potential landscapes is crucial for understanding chemical and physical processes.
  • Identifying transition paths and saddle points is computationally challenging, especially in complex systems.

Purpose of the Study:

  • To develop and demonstrate a reverse integration approach for efficient exploration of effective potential landscapes.
  • To enable navigation, escape from local wells, saddle point detection, and transition path identification.

Main Methods:

  • Coarse reverse integration initialized on a ring of coarse states.
  • Exploration of different ring evolution modes: backward time stepping, solution arc length, and effective potential.
  • Application to both deterministic and noisy systems, including stochastic simulators (Gillespie-type) and molecular dynamics.

Main Results:

  • Demonstrated efficient navigation on energy landscapes for deterministic problems.
  • Successfully applied reverse ring integration to noisy systems using an 'equation-free' approach.
  • Obtained approximations of effective landscapes by estimating local drift and diffusion coefficients from short simulation bursts.

Conclusions:

  • The reverse integration approach provides an effective strategy for exploring complex potential landscapes.
  • This method facilitates the identification of critical features like transition paths and saddle points.
  • The 'equation-free' implementation allows for the study of systems where closed-form solutions are unavailable.