Simulating structural transitions by direct transition current sampling: the example of LJ38

Abstract

Reaction paths and probabilities are inferred, in a usual Monte Carlo or Molecular Dynamic simulation, directly from the evolution of the positions of the particles. The process becomes time-consuming in many interesting cases in which the transition probabilities are small. A radically different approach consists of setting up a computation scheme where the object whose time evolution is simulated is the transition current itself. The relevant timescale for such a computation is the one needed for the transition probability rate to reach a stationary level, and this is usually substantially shorter than the passage time of an individual system. As an example, we show, in the context of the `benchmark' case of 38 particles interacting via the Lennard-Jones potential (`LJ38' cluster), how this method may be used to explore the reactions that take place between different phases, recovering efficiently known results and uncovering new ones with small computational effort.

19 pages, 9 figures

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• Kramers equation and supersymmetry
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• Modeling aggregation processes of Lennard-Jones particles via stochastic networks
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• Computing the Asymptotic Spectrum for Networks Representing Energy Landscapes using the Minimal Spanning Tree
• A Spin-1 Representation for Dual-Funnel Energy Landscapes
• Spectral analysis and clustering of large stochastic networks. Application to the Lennard-Jones-75 cluster