Controlling the Long-Range Corrections in Atomistic Monte Carlo Simulations of Two-Phase Systems

The long-range correction to the surface tension can amount to up to 55% of the calculated value of the surface tension for cutoffs in the range of 2.1-6.4 sigma. The calculation of the long-range corrections to the surface tension and to the configurational energy in two-phase systems remains an active area of research. In this work, we compare the long-range corrections methods proposed by Guo and Lu (J. Chem. Phys. 1997, 106, 3688-3695) and Janecek (J. Phys. Chem. B 2006, 110, 6264-6269) for the calculation of the surface tension and of the coexisting densities in Monte Carlo simulations of the truncated Lennard-Jones potential and the truncated and shifted Lennard-Jones potential models. These methods require an estimate of the long-range correction at each step in the Monte Carlo simulation. We apply the full version of the Guo and Lu method, which involves the calculation of a double integral that contains a series of density differences, and we compare these results with the simplified version of the method which is routinely used in two-phase simulations. We conclude that the cutoff dependencies of the surface tension and coexisting densities are identical for the full versions of Guo and Lu and Janecek methods. We show that it is possible to avoid applying the long-range correction at every step by using the truncated Lennard-Jones potential with a cutoff r(c) >= 5.5 sigma. The long-range correction can then be applied at the end of the simulation. The limiting factor in the accurate calculation of this final correction is an accurate estimate of the coexisting densities. Link-cell simulations performed using a cutoff r(c) = 5.5 sigma require twice as much computing time as those with a more typical cutoff of r(c) = 3.0 sigma. The application of the Janecek correction increases the running time of the simulation by less than 10%, and it can be profitably applied with the shorter cutoff.