(119f) Accelerating Replica Exchange and Generalized Ensemble Simulations Through Gibbs Sampling In State Space

The widespread popularity of replica exchange and generalized ensembles algorithms for simulating complex molecular systems in chemistry and chemical engineering has generated great interest in improving the efficiency of these protocols in ways that enhance phase space mixing and therefore increase sampling efficiency.  We demonstrate how both classes of algorithms can be considered as special cases of a statistical technique called Gibbs sampling (not to be confused with Gibbs ensemble sampling) within a Markov chain Monte Carlo (MCMC) framework.  Seen in this framework, new ways of updating of the thermodynamic states associated with these configurations can be easily identified and substantially increase mixing in a way that still sample from the desired distributions.  We present some simple alternatives to standard protocols that improve mixing of the overall Markov chain, thus reducing simulation times required to converge. These improved schemes are demonstrated in several common applications, including expanded ensembles among Hamiltonians for estimation of free energies, parallel tempering, and multidimensional replica exchange umbrella sampling.  In some standard cases, these simulation techniques can increase the rate of configurational sampling by four to ten times.