Assessing the efficiency of free energy calculation methods

The efficiencies of two recently developed methods for calculating free energy changes along a generalized coordinate in a system are discussed in the context of other, related approaches. One method is based on Jarzynski's identity Phys. Rev. Lett. 78, 2690 (1997)]. The second method relies on thermodynamic integration of the average force and is called the adaptive biasing force method Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)]. Both methods are designed such that the system evolves along the chosen coordinate(s) without experiencing free energy barriers and they require calculating the instantaneous, unconstrained force acting on this coordinate using the formula derived by Darve and Pohorille. Efficiencies are analyzed by comparing analytical estimates of statistical errors and by considering two numerical examples-internal rotation of hydrated 1,2-dichloroethane and transfer of fluoromethane across a water-hexane interface. The efficiencies of both methods are approximately equal in the first but not in the second case. During transfer of fluoromethane the system is easily driven away from equilibrium and, therefore, the performance of the method based on Jarzynski's identity is poor.