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Kinetic Analysis of Discrete Path Sampling Stationary Point Databases.pdf

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Kinetic Analysis of Discrete Path Sampling Stationary Point Databases

a r X i v : c o n d - m a t / 0 6 0 4 1 6 5 v 1 [ c o n d - m a t .s o f t ] 6 A p r 2 0 0 6 Kinetic Analysis of Discrete Path Sampling Stationary Point Databases Semen A. Trygubenko? and David J. Wales? University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK February 6, 2008 Abstract Analysing stationary point databases to extract phenomenological rate con- stants can become time-consuming for systems with large potential energy bar- riers. In the present contribution we analyse several different approaches to this problem. First, we show how the original rate constant prescription within the discrete path sampling approach can be rewritten in terms of committor proba- bilities. Two alternative formulations are then derived in which the steady-state assumption for intervening minima is removed, providing both a more accurate kinetic analysis, and a measure of whether a two-state description is appropri- ate. The first approach involves running additional short kinetic Monte Carlo (KMC) trajectories, which are used to calculate waiting times. Here we in- troduce ‘leapfrog’ moves to second-neighbour minima, which prevent the KMC trajectory oscillating between structures separated by low barriers. In the second approach we successively remove minima from the intervening set, renormalising ?E-mail: sat39@cam.ac.uk ?E-mail: dw34@cam.ac.uk 1 the branching probabilities and waiting times to preserve the mean first-passage times of interest. Regrouping the local minima appropriately is also shown to speed up the kinetic analysis dramatically at low temperatures. Applications are described where rates are extracted for databases containing tens of thousands of stationary points, with effective barriers that are several hundred times kBT . 1 Introduction A great deal of effort is currently focused on the development of new methods to treat ‘rare events’. A number of these methods employ a coarse-graining approximation of some kind to the phase space.1