A New Class Of Accelerated Kinetic Monte Carlo Algorithms

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Download or read book Accelerated Molecular Dynamics Methods written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A long-standing limitation in the use of molecular dynamics (MD) simulation is that it can only be applied directly to processes that take place on very short timescales: nanoseconds if empirical potentials are employed, or picoseconds if we rely on electronic structure methods. Many processes of interest in chemistry, biochemistry, and materials science require study over microseconds and beyond, due either to the natural timescale for the evolution or to the duration of the experiment of interest. Ignoring the case of liquids xxx, the dynamics on these time scales is typically characterized by infrequent-event transitions, from state to state, usually involving an energy barrier. There is a long and venerable tradition in chemistry of using transition state theory (TST) [10, 19, 23] to directly compute rate constants for these kinds of activated processes. If needed dynamical corrections to the TST rate, and even quantum corrections, can be computed to achieve an accuracy suitable for the problem at hand. These rate constants then allow them to understand the system behavior on longer time scales than we can directly reach with MD. For complex systems with many reaction paths, the TST rates can be fed into a stochastic simulation procedure such as kinetic Monte Carlo xxx, and a direct simulation of the advance of the system through its possible states can be obtained in a probabilistically exact way. A problem that has become more evident in recent years, however, is that for many systems of interest there is a complexity that makes it difficult, if not impossible, to determine all the relevant reaction paths to which TST should be applied. This is a serious issue, as omitted transition pathways can have uncontrollable consequences on the simulated long-time kinetics. Over the last decade or so, we have been developing a new class of methods for treating the long-time dynamics in these complex, infrequent-event systems. Rather than trying to guess in advance what reaction pathways may be important, we return instead to a molecular dynamics treatment, in which the trajectory itself finds an appropriate way to escape from each state of the system. Since a direct integration of the trajectory would be limited to nanoseconds, while we are seeking to follow the system for much longer times, we modify the dynamics in some way to cause the first escape to happen much more quickly, thereby accelerating the dynamics. The key is to design the modified dynamics in a way that does as little damage as possible to the probability for escaping along a given pathway - i.e., we try to preserve the relative rate constants for the different possible escape paths out of the state. We can then use this modified dynamics to follow the system from state to state, reaching much longer times than we could reach with direct MD. The dynamics within any one state may no longer be meaningful, but the state-to-state dynamics, in the best case, as we discuss in the paper, can be exact. We have developed three methods in this accelerated molecular dynamics (AMD) class, in each case appealing to TST, either implicitly or explicitly, to design the modified dynamics. Each of these methods has its own advantages, and we and others have applied these methods to a wide range of problems. The purpose of this article is to give the reader a brief introduction to how these methods work, and discuss some of the recent developments that have been made to improve their power and applicability. Note that this brief review does not claim to be exhaustive: various other methods aiming at similar goals have been proposed in the literature. For the sake of brevity, our focus will exclusively be on the methods developed by the group.