(329f) A Linear Basis Function Approach to Efficient Molecular Transformation Free Energy Calculations

We present a formalism for inserting or removing atomic sites in free energy calculations based on splitting the potential energy function into a sum of pairs of basis functions, which depend only on coordinates, and alchemical switches, which depend only on the coupling variable. This formalism allows evaluation of nonbonded potentials at any intermediate state accessible to the potential outside of the simulation's force evaluation loop or entirely in post-processing, which may be particularly useful to minimize effort in coding for in complex architectures such as GPU's.

This method can design optimal minimal variance switches to reduce statistical uncertainty using a single simulation's worth of data for a given transformation. We show examples of this approach by minimizing the statistical uncertainty for the solvation free energy of a wide range of molecule types and sizes, from united atom spheres with sizes ranging from methane to buckmisterfullerenes, to large multi-ring aromatics and ions, as well as optimal transformations of one molecule type to another.

We find that the statistical error in free energy for the optimized basis function approach are lower than standard soft core models, and approach the minimum variance possible over all pair potentials. The basis function approach can easily be applied to essentially all systems, reduce code complexity, and reduce simulation times.