Path-breaking schemes for nonequilibrium free energy calculations

We propose a path-breaking route to the enhancement of unidirectional nonequilibrium simulations for the calculation of free energy differences via Jarzynski's equality [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. One of the most important limitations of unidirectional nonequilibrium simulations is the amount of realizations necessary to reach suitable convergence of the work exponential average featuring the Jarzynski's relationship. In this respect, a significant improvement of the performances could be obtained by finding a way of stopping trajectories with negligible contribution to the work exponential average, before their normal end. This is achieved using path-breaking schemes which are essentially based on periodic checks of the work dissipated during the pulling trajectories. Such schemes can be based either on breaking trajectories whose dissipated work exceeds a given threshold or on breaking trajectories with a probability increasing with the dissipated work. In both cases, the computer time needed to carry out a series of nonequilibrium trajectories is reduced up to a factor ranging from 2 to more than 10, at least for the processes under consideration in the present study. The efficiency depends on several aspects, such as the type of process, the number of check-points along the pathway and the pulling rate as well. The method is illustrated through radically different processes, i.e., the helix-coil transition of deca-alanine and the pulling of the distance between two methane molecules in water solution.