Using a molecular benchmark set to compare free energy estimators and explore electrostatic potential parameter space

There is a significant need for improved tools to validate thermo-physical quantities computed via molecular simulation. In this work we present the initial version of a benchmark set for testing methods of 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 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. We also use MBAR to explore electrostatic potential parameters space in order to find the set of parameters resulting in shortest simulation time for a given accuracy in the free energy estimate of the transformations in benchmark set and enthalpy of vaporization of water. 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.

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