Communication: Long range corrections in liquid-vapor interface simulations.

Long range corrections (lrc) for the potential energy and for the force in planar liquid-vapor interface simulations are considered for spherically symmetric interactions. First, it is stated that for the Lennard-Jones (LJ) fluid the lrc for the energy Δu of Janeček [J. Phys. Chem. B , 6264 (2006)] is the same as that of Lotfi [Mol. Simul. , 233 (1990)]. Second, we present the lrc for the force Δ for any spherically symmetric interaction as a derivative of Δ plus a surface integral over the cut-off sphere by using the extended Leibniz rule of Flanders [Am. Math. Monthly , 615 (1973)]. This Δ corrects the incomplete lrc Δ of Lotfi and agrees with the result of Janeček obtained by direct averaging of the forces. Third, we show that the molecular dynamics (MD) results for the surface tension of the LJ fluid with size parameter obtained by Werth [Physica A , 2359 (2013)] with the lrc Δ of Janeček and a cut-off radius r = 3 agree with the results of Mecke [J. Chem. Phys. , 9264 (1997)] obtained with the lrc Δ of Lotfi and = 6.5 within -0.4% to +1.6%. Moreover, using only the MD results for γ of Werth , we obtain for the LJ fluid a new surface tension correlation which also represents the γ-values of Mecke within ±0.7%. The critical temperature resulting from the correlation is = 1.317 66 and is in very good agreement with = 1.32 of the reference equation of state for the LJ fluid given by Thol [J. Phys. Chem. Ref. Data , 023101 (2016)].