Enhancement of canonical sampling by virtual-state transitions

A novel method was developed to enhance canonical sampling. A system is divided into virtually introduced sub-states, called "virtual states," which does not exist in reality. The configuration sampling is achieved by a standard canonical sampling method, the Metropolis Monte Carlo method, and confined in a virtual state for a while. In contrast, inter-virtual state motions are controlled by transition probabilities, which can be set arbitrarily. A simple recursive equation was introduced to determine the inter-virtual state transition probabilities, by which the sampling is enhanced considerably. We named this method "virtual-system coupled canonical Monte Carlo (VcMC) sampling." A simple method was proposed to reconstruct a canonical distribution function at a certain temperature from the resultant VcMC sampling data. Two systems, a one-dimensional double-well potential and a three-dimensional ligand-receptor binding/unbinding model, were examined. VcMC produced an accurate canonical distribution much more quickly than a conventional canonical Monte Carlo simulation does.