Mapped Averaging: Reformulation of Ensemble Averages for High-Precision, High-Efficiency Calculation of Properties By Molecular Simulation

We present a general approach that splits thermodynamic derivatives into a known but approximate contribution, plus ensemble averages that quantify deviation from the approximate behavior. Then, direct measurement of the deviations by molecular simulation can be performed without being degraded by noise generated by behavior that is already well characterized. The scheme is demonstrated in several applications, including calculation of anharmonic properties of crystalline solids for a variety of model systems, and calculation of the dielectric constant of dipolar molecules. The approach is easily implemented, and yields thermodynamic properties of a given precision with orders of magnitude reduction in computational effort and no loss of accuracy.