A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations

A method for sampling efficiently the free energy landscape of a complex system with respect to some given collective variables is proposed. Inspired by metadynamics [A. Laic, M. Parrinello, Proc. Nat. Acad. Sci. USA 99 (2002) 12562], we introduce an extended system where the collective variables are treated as dynamical ones and show that this allows to sample the free energy landscape of these variables directly. The sampling is accelerated by using an artificially high temperature for the collective variables. The validity of the method is established using general results for systems with multiple time-scales, and its numerical efficiency is also discussed via error analysis. We also show how the method can be modified in order to sample the reactive pathways in free energy space, and thereby analyze the mechanism of a reaction. Finally, we discuss how the method can be generalized and used as an alternative to the Kirkwood generalized thermodynamic integration approach for the calculation of free energy differences. (c) 2006 Elsevier B.V. All rights reserved.