Optimizing the switching function for nonequilibrium free-energy calculations: an on-the-fly approach

Using nonequilibrium switching simulations to determine the free-energy difference between two thermodynamic states has gained tremendous popularity since Jarzynski's identity was proposed. The efficiency of a nonequilibrium switching simulation depends on the switching function. A well selected switching function can significantly minimize the associated dissipative work and reduce the computational cost of nonequilibrium free-energy simulations. In this paper, a method for estimating an efficient switching function during a nonequilibrium free-energy simulation is presented. The switching rate depends on the fluctuation of the fictitious force and a relaxation time. This method is similar to a prior method described by de Koning [J. Chem. Phys. 122, 104106 (2005)], except in our approach the switching rate is determined on-the-fly without the need for trial pulls. Our method can be easily incorporated into any existing implementation of the nonequilibrium switching method. The on-the-fly approach was used to determine the transformation free energy between two types of Einstein crystals and the isothermal free energy of expansion of a van der Waals gas. For both of the test cases, our on-the-fly method is found to provide a switching function much more superior than the standard one.