A rigorous procedure for combining molecular dynamics and Monte Carlo simulation algorithms

Abstract

A combination of molecular dynamics (MD) and Monte Carlo (MC) simulation methods is proposed that may have advantages in some cases over either MD or MC alone. The method is simple: in each step of the algorithm, some of the particles are moved by MC rules and the rest by MD. We prove that the mixed method converges rigorously to the same equilibrium state as either MC or canonical MD alone; i.e., the sudden interruption of forces produced by the MC moves does not incorrectly bias the evolution of the MD particles. The method is tested on a simulation of a Lennard-Jones fluid. The results confirm that the mixed method (MDMC) achieves the correct statistics and that the overhead associated with the mixed methods is modest. MDMC may be more efficient than either MD or MC for simulating molecular systems in which some degrees of freedom are more effectively treated by MC (e.g., solvent motions) and others by MD (e.g., hydrocarbon chains).