A finite-time variational method for determining optimal paths and obtaining bounds on free energy changes from computer simulations

Abstract

This paper elaborates on the method introduced by Reinhardt and Hunter [J. Chem. Phys. 97, 1599 (1992)] for determining upper and lower bounds on free energy changes and systematically improving these bounds by variational optimization of the Hamiltonian switching path connecting the two states of interest. The advantages, conditions of applicability, and potential pitfalls of this finite‐time variational method are illustrated in detail in a Monte Carlo calculation of the free energy change accompanying the reversal of magnetic field in a two‐dimensional Ising model. The power of its flexibility in an inhomogeneous system is demonstrated by computing the boundary tension between domains of positive and negative magnetization in the Ising model. Its success in a problem involving molecular dynamics and continuous potentials is illustrated by computing the free energy difference between a Lennard‐Jones fluid and a soft‐sphere fluid. Finally, its connection with the method of dynamically modified slow growth is discussed.