Accurate calculations of free-energy differences by the distribution method

We employ the strategy used in the successive umbrella sampling method [P. Virnau and M. Muller, J. Chem. Phys. 120, 10925 (2004)] to obtain the energy-difference distribution over its desired range. This is very helpful in calculating free-energy differences, where the source of the error is well recognized as the insufficient sampling over the relevant tail region in the energy-difference distribution. The distribution method proposed here employs the idea of restricting the sampling within an appropriate energy range, as was presented by Shing and Gubbins in their restricted umbrella sampling method [Mol. Phys. 46, 1109 (1982)]. We demonstrate the efficiency of the distribution method by calculating the free-energy difference of a model of harmonic oscillators where the systems exhibit nonoverlap features in their important phase spaces through the original Metropolis sampling. For this particular case, we show that the distribution method outperforms the free-energy perturbation method and even the Bennett's acceptance ratio method [J. Comput. Phys. 22, 245 (1976)] with the fastest convergence and the smallest relative errors. We further demonstrate the application of the distribution method with a simple point charge water model.