Linear Basis Function Approach to Efficient Alchemical Free Energy Calculations. 1. Removal of Uncharged Atomic Sites

We present a general approach to transform between molecular potential functions during free energy calculations using a variance minimized linear basis functional form. This approach splits the potential energy function into a sum of pairs of basis functions, which depend on coordinates, and 'alchemical' switches, which depend only on the coupling variable. The power of this approach is that, first, the calculation of the coupling parameter dependent terms is removed from inner loop force calculation routines, second, the flexibility in specifying basis functions and alchemical switches allows users to choose transformation pathways that maximize statistical efficiency, and third, it is possible to predict entirely in postprocessing, without any additional energy evaluations, the thermodynamic properties along any alchemical path with moderate overlap from an initial simulation that uses the same basis functions. This allows construction of optimized, minimum variance alchemical switches from a single simulation with fixed basis functions and trial alchemical switching functions. We describe how to construct these linear basis potentials for real molecular systems of different sizes and shapes, considering particularly the problems of eliminating singularities and minimizing variance of particle removal in dense fluids. The statistical error in free energy calculations using the optimized basis functions is lower than standard soft core models, and approach the minimum variance possible over all pair potentials. We recommend an optimized set of basis functions and alchemical switches for standard molecular free energy calculations.