There is a significant need for improved tools to validate thermophysical quantities computed via molecular simulation. In this paper we present the initial version of a benchmark set of testing methods for calculating free energies of molecular transformation in solution. This set is based on molecular changes common to many molecular design problems, such as insertion and deletion of atomic sites and changing atomic partial charges. We use this benchmark set to compare the statistical efficiency, reliability, and quality of uncertainty estimates for a number of published free energy methods, including thermodynamic integration, free energy perturbation, the Bennett acceptance ratio (BAR) and its multistate equivalent MBAR. We identify MBAR as the consistently best performing method, though other methods are frequently comparable in reliability and accuracy in many cases. We demonstrate that assumptions of Gaussian distributed errors in free energies are usually valid for most methods studied. We demonstrate that bootstrap error estimation is a robust and useful technique for estimating statistical variance for all free energy methods studied. This benchmark set is provided in a number of different file formats with the hope of becoming a useful and general tool for method comparisons.

We present an approach to calculate free energy and other thermodynamic property differences between molecules which have very little or no overlap in configuration space, but where a one-to-one mapping between the molecule geometries exists. The approach combines multistate reweighting with remapping of phase space between simulated states. We apply this method to calculate the free energy differences between non-overlapping, truncated harmonic oscillators, the free energy, enthalpy, and entropy differences between different parameterizations of rigid water, and differences in free energy of solvation between dipoles of different lengths. Previously difficult or impossible problems become either trivially easy or are improved in efficiency by two to five orders of magnitude.

Multistate reweighting methods such as the multistate Bennett acceptance ratio (MBAR) can predict free energies and expectation values of thermodynamic observables at poorly sampled or unsampled thermodynamic states using simulations performed at only a few sampled states combined with single point energy reevaluations of these samples at the unsampled states. In this study, we demonstrate the power of this general reweighting formalism by exploring the effect of simulation parameters controlling Coulomb and Lennard-Jones cutoffs on free energy calculations and other observables. Using multistate reweighting, we can quickly identify, with very high sensitivity, the computationally least expensive nonbonded parameters required to obtain a specified accuracy in observables compared to the answer obtained using an expensive "gold standard" set of parameters. We specifically examine free energy estimates of three molecular transformations in a benchmark molecular set as well as the enthalpy of vaporization of TIP3P. The results demonstrates the power of this multistate reweighting approach for measuring changes in free energy differences or other estimators with respect to simulation or model parameters with very high precision and/or very low computational effort. The results also help to identify which simulation parameters affect free energy calculations and provide guidance to determine which simulation parameters are both appropriate and computationally efficient in general.

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