Linear basis function approach to efficient alchemical free energy calculations. 2. Inserting and deleting particles with coulombic interactions.

We extend our previous linear basis function approach for alchemical free energy calculations to the insertion and deletion of charged particles in dense fluids. We compute a near optimal statistical path to introduce Coulombic interactions into various molecules in solution and find that this near optimal path is only marginally more efficient than simple linear coupling of electrostatics in all cases where a repulsive core is already present. We also explore the order in which nonbonded forces are coupled to the environment in alchemical transformations. We test two sets of Lennard-Jones basis functions, a Weeks-Chandler-Andersen (WCA) and a 12-6 decomposition of the repulsive and attractive forces turned on in sequence along with changes in charge, to determine a statistically optimized order in which forces should be coupled. The WCA decomposition has lower statistical uncertainty as coupling the attractive r(-6) basis function contributes non-negligible statistical error. In all cases, the charge should be coupled only after the repulsive core is fully coupled, and the WCA attractive portion can be coupled at any stage without significantly changing the efficiency. The statistical uncertainty of two of the basis function approaches with charged particles is nearly identical to the soft core approach for decoupling electrostatics, though the correlation times for sampling are often longer for a soft core electrostatics approach than the basis function approach. The basis function approach for introducing or removing molecules or functional groups thus represents a useful alternative to the soft core approach with a number of clear computational advantages.