Theory and algorithms for mixed Monte Carlo-stochastic dynamics simulations

摘要

The recently introduced mixed MC-SD method is a fundamentally new procedure which essentially eliminates the distinction between Monte Carlo and dynamics. Unlike other methods which utilize forces, Brownian motion or dynamical steps to generate new trial configurations in a Monte Carlo search, mixed MC-SD does stochastic dynamics on the cartesian space of a molecule and Monte Carlo on the torsion space of the molecule simultaneously. After each dynamical step, a random deformation of a rotatable torsion is performed and accepted or rejected according to the Metropolis criteria. The next dynamical step is performed from the most recent configuration and the velocities from the previous dynamical step. The smooth merging of Monte Carlo and dynamics requires the use of the stochastic velocity Verlet integration scheme. Here, the velocity Verlet stochastic dynamics method is derived, and the reasons why it can be joined with Metropolis Monte Carlo in a continuous fashion are explored.