Rapid Computation of Thermodynamic Properties over a Large Multidimensional Space of Nonbonded Parameters

We show how thermodynamic properties can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the computational cost to estimate thermodynamic properties for over 130,000 tested parameter combinations from over a thousand CPU years to less than one CPU minute. The speed increase is achieved primarily by computing the potential energy as a linear combination of basis functions, computed as the difference of energy between two reference states, which can be done without any simulation code modification. We estimate thermodynamic properties with the Multistate Bennett Acceptance Ratio (MBAR) over the high dimensional space without the need to define a priori thermodynamic paths connecting the states. Instead, we adaptively sample a set of points in parameter space to create mutual phase space overlap. Regions of poor phase space overlap are detected by analyzing the eigenvalues of the sample states' overlap matrix. The phase space overlap to sampled states is monitored alongside the mean and maximum uncertainty to determine convergence as neither the uncertainty nor the phase space alone is a sufficient metric of convergence. The adaptive sampling scheme is demonstrated by finding with high precision the solvation free energies, entropies, and enthalpies of all charged particles of Lennard-Jones plus Coulomb functional form with charges between -2 and +2 and any physical values of ε_ij and σ_ij in TIP3P water.