Abstract
Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett-Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.
Highlights
Many processes occurring in molecular systems are dominated by rare transitions between long-lived states.[1,2] Examples include nucleation during rst-order phase transitions, chemical reactions in solution, and conformational changes of biological macromolecules
We obtain the correlation function hhA(0)hB(t)iS from a single long trajectory produced by a straightforward Brownian dynamics simulation of 5 Â 108 time steps
We have presented an algorithm to calculate reaction rate constants by combining dynamical information extracted from such brief trajectories with the results of free energy calculations
Summary
Many processes occurring in molecular systems are dominated by rare transitions between long-lived states.[1,2] Examples include nucleation during rst-order phase transitions, chemical reactions in solution, and conformational changes of biological macromolecules. In analyzing rare transitions in complex systems, the goal is to nd a reaction coordinate, i.e., a dynamically meaningful variable that captures the essential physics of the transition and is capable of quantifying its progress. Once a reaction coordinate is known it may be used to construct low-dimensional mechanistic models[3,4] and, enhance the sampling of transition pathways and the calculation of rate constants.[5,6,7,8]. The quality of a reaction coordinate can be assessed in terms of the committor, i.e., the probability of a given con guration to rst reach the product
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