Smoother Alchemical Transformations via Enveloping Distribution Sampling for Free-Energy Estimation

The accuracy of the computational estimation of relative free energies (e.g., for solvation or protein-ligand binding) depends on the smoothness of the phase-space transformation between the two alchemical end-states. A smooth transformation ensures sufficient phase-space overlap between the neighboring intermediate states connecting the two end-states in equilibrium (EQ) simulations and generates less dissipative work in nonequilibrium (NEQ) simulations. The conventional energy interpolation (EI) coupling scheme constructs the intermediate states by linearly combining the end-state potentials. We show that the enveloping distribution sampling (EDS) coupling scheme, a generalization of EI where the corresponding Boltzmann factors are linearly combined, represents a much more flexible alternative. Through the use of a negative smoothing parameter, the EDS scheme increases the local curvature of the sampling phase space along the transformation axis, thereby avoiding phase transitions and creating a smoother transformation. We validate this behavior in increasingly complex settings, from harmonic oscillators and Ising model systems to absolute hydration free-energy (AHFE) calculations on the FreeSolv data set. EDS consistently yields more accurate and statistically robust free-energy estimates compared to the conventional EI scheme for the model system calculations, while a clear advantage is observed for AHFE in the NEQ regime, where less dissipative transitions lead to more reliable free-energy estimates.