(384a) Efficient Property Prediction Using Expanded Ensemble Simulations Over Many Thermodynamic States

Expanded or generalized ensemble methods are a class of simulation methods that can be used to overcome sampling difficulties by adding transitions between thermodynamic ensembles. These additional thermodynamic ensembles can either be ensembles of interest (for example, the same system at different temperatures if temperature dependent effects are of interest) or auxiliary states added to either improve overlap between end states or to improve sampling by introducing states with faster kinetics.

One weakness of these methods is that in order to sample states at all ensembles with reasonable frequency, simulation weights for each of the subensembles must be introduced, which are equal to the free energies of each of the ensembles. These weights must be determined self-consistently, and the precise choice of algorithm to determine these self-consistent algorithms is an important choice in the implementation of these algorithms.

We show how approaches such as Wang-Landau and transition matrix methods can be generalized when dealing with expanded ensemble systems containing many thermodynamic states, and specifically as approximations to optimal multistate free energy estimators such as MBAR (the multistate Bennett's acceptance ratio method). This more general multistate approach allows more efficient determination of free energies and other observables over many states simultaneously, especially when the states are arranged in a multidimensional network, with multiple neighbors for each sate.

We additionally show how these multistate estimation methods can be combined with Gibbs sampling techniques, a generalization of Metropolis Monte Carlo methods which includes transitions to all possible states. This combination allows efficient sampling and property prediction over hundreds or thousands of thermodynamic states. We look at applications of these combined methods to searching the parameter space of spatially dependent Ising models as well as as well computing the binding free energy of small molecules to simple molecular containers.