Tuesday, July 24, 2007 - 11:00am - 12:00pm
Perhaps the greatest computational challenge of molecular dynamics is to generate molecular configurations at random from a prescribed probability distribution, for example, the Boltzmann-Gibbs distribution. Markov chain Monte Carlo methods provide a rigorous solution to this problem, but designing efficient trial moves is challenging. Two systematic approaches are presented: one based on Brownian dynamics, the other on molecular dynamics. The extra computational expense of rejected moves can be avoided by using dynamics instead, the drawback being the introduction of a bias due to the finite stepsize of the integrator. Either deterministic or stochastic dynamics may be used. To achieve reasonable performance, the basic sampling scheme must be combined with more advanced techniques, such as replica exchange and Wang-Landau Monte Carlo.