# Path integral computation of quantum free energy differences due to alchemical transformations involving mass and potential.

Journal Of Chemical Theory And Computation **7**, 2358 - 2369 (2011)

# Path integral computation of quantum free energy differences due to alchemical transformations involving mass and potential.

Thermodynamic integration, perturbation theory, and lambda-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to alchemical transformations. Several estimators were formulated to compute free energy dierences in solvable model systems undergoing changes in mass and/or potential. Linear and non-linear alchemical interpolations were simulated for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration and ab initio path integral molecular dynamics to compute the free energy dierence of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.