Exploiting Configurational Freezing in Nonequilibrium Monte Carlo Simulations

Abstract

To achieve acceptable accuracy in fast-switching free energy estimates by Jarzynski equality [ Phys. Rev. Lett. 1997 , 78 , 2690 ] or Crooks fluctuation theorem [ J. Stat. Phys. 1998 , 90 , 1481 ], it is often necessary to realize a large number of externally driven trajectories. This is basically due to inefficient calculation of path-ensemble averages arising from the work dissipated during the nonequilibrium paths. We propose a computational technique, addressed to Monte Carlo simulations, to improve free energy estimates by lowering the dissipated work. The method is inspired by the dynamical freezing approach, recently developed in the context of molecular dynamics simulations [ Phys. Rev. E 2009 , 80 , 041124 ]. The idea is to limit the configurational sampling to particles of a well-established region of the sample (namely, the region where dissipation is supposed to occur), while leaving fixed (frozen) the other particles. Therefore, the method, called configurational freezing, is based on the reasonable assumption that dissipation is a local phenomenon in single-molecule nonequilibrium processes, a statement which is satisfied by most processes, including folding of biopolymers, molecular docking, alchemical transformations, etc. At variance with standard simulations, in configurational freezing simulations the computational cost is not correlated with the size of the whole system, but rather with that of the reaction site. The method is illustrated in two examples, i.e., the calculation of the water to methane relative hydration free energy and the calculation of the potential of mean force of two methane molecules in water solution as a function of their distance.