A Comparision of Methods for Computing Transition Rates from Molecular Dynamics Simulation

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Abstract
Correlation function and direct counting methods for the evaluation of the isomerization rates in equilibrium molecular dynamics (MD) simulations are studied for a system of 64 independent particles, each undergoing transitions between two stable states according to a Poisson process. Three different numerical implementations of the number correlation function and two different counting formulas based on different ordering of averages over trajectory and particles are tested. All methods yield correct results for sufficiently long simulations. However, for simulations where a given particle undergoes a small (< 5-10) number of transitions, accurate rates are obtained only when the correlation function is normalized after averaging over particles; this correlation function is shown to be equivalent to the relaxation function of Brown and Clarke (J. Chem. Phys. 92, 3062, 1990). Similarily, accurate rates are obtained with a counting formula where the average first passage time is first calculated over all particles and inverted, as opposed to calculating rates for each particle and then averaging. These distinctions are shown to be significant when calculating isomerization rates from 500 ps MD simulations of n-butane. Correction of overcounts is also illustrated for the butane system, where “glassy” or low friction dynamics is evident.