Mapped Averaging for Highly Efficient Evaluation of Fluid-Phase Properties By Molecular Simulation

"Mapped averaging" is a recently published scheme for the reformulation of ensemble averages.^1,2 The framework uses approximate results from statistical mechanical theory to derive new ensemble averages (mapped averages) that represent exactly the error in the theory. Calculation of the mapped averages by molecular
simulation can proceed without contamination by noise produced by behavior that has already been captured exactly by the theory. Consequently,
accurate and precise values of properties can be obtained while using less
computational effort, in favorable cases, many orders of magnitude less. The mapped-averaging framework rests on two key elements: (a) the choice of the mapping; and (b) the formulas yielding the free-energy derivatives (properties) once the mapping is specified. For crystalline systems, a harmonic approximation provides a suitable starting point, allowing simulation to compute precisely the anharmonic contribution to the properties. For fluid systems, the formulation of a good mapping is not as obvious. In this work we examine ways to formulate a mapping and present new ensemble-average formulas for properties of interest to fluid-phase systems. We demonstrate the performance of these methods on several properties for a variety of molecular models.

(1) Schultz, A. J.; Moustafa, S. G.; Lin, W.; Weinstein, S. J.; and Kofke, D. A. Reformulation of Ensemble Averages via Coordinate Mapping, Journal of Chemical Theory and Computation 2016.

(2) Moustafa, S. G.; Schultz, A. J.; and Kofke, D. A. Very fast averaging of thermal properties of crystals by molecular simulation, Phys. Rev. E 2015, 92, 043303.