CALCULATION OF FREE-ENERGY DIFFERENCES FROM COMPUTER-SIMULATIONS OF INITIAL AND FINAL-STATES

A class of simple expressions of increasing accuracy for the free-ener gy difference between two states is derived based on numerical thermod ynamic integration. The implementation of these formulas requires simu lations of the initial and fnal (and possibly a few intermediate) stat es. They involve higher free-energy derivatives at these states which are related to the moments of the probability distribution of the pert urbation. Given a specified number of such derivatives, these integrat ion formulas are optimal in the sense that they are exact to the highe st possible order of free-energy perturbation theory. The utility of t his approach is illustrated for the hydration free energy of water. Th is problem provides a quite stringent test because the free energy is a highly nonlinear function of the charge so that even fourth order pe rturbation theory gives a very poor estimate of the free-energy change . Our results should prove most useful for complex, computationally de manding problems where foe-energy differences arise primarily from cha nges in the electrostatic interactions (e.g., electron transfer, charg ing of ions, protonation of amino acids in proteins). (C) 1996 America n Institute of Physics.