(178p) Linear Basis Function Approaches to Efficient Free Energy Calculations

Computational calculations of free energies of transfer can provide important insights into thermodynamic behavior of molecules before they are synthesized. However, these calculations can be computationally expensive, have large statistical uncertainty, and only describe a few chemical species at a time. By modifying the potential energy pathway between chemical species, improvements can be made in all three aspects. We propose describing thermodynamic pathways for free energy calculations with linear combinations of potential energy basis functions in which the position component of the basis function is independent of the transformation (alchemical) variable. Linearizing the two variables speeds calculation by making the potential energy more computationally efficient. The alchemical variable usually only describes physical chemical species at its endstates, while all intermediates states serve as non-physical, but mathematically convenient pathways. This variable has been modified describe the change in the individual Lennard-Jones parameters, making available more pathways to access a large number of physical species by eliminating the need to scale to a reference potential energy. The infinite potentials, which cause a large source of statistical noise when removed, that arise from short-range interactions are eliminated by a capped potential with essentially zero Boltzmann weight. Statistical uncertainty is further reduced by fitting the basis functions to a known low-variance, soft-core potential energy pathway. We test the efficiency of the basis function approach on a range of alchemical transformations, and compare the speed to existing functionality in the GROMACS software package.