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 110, 6264 (2006)] is the same as that of Lotfi et al. [Mol. Simul. 5, 233 (1990)]. Second, we present the lrc for the force ΔF for any spherically symmetric interaction as a derivative of Δu plus a surface integral over the cut-off sphere by using the extended Leibniz rule of Flanders [Am. Math. Monthly 80, 615 (1973)]. This ΔF corrects the incomplete lrc Δ1F of Lotfi et al. 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 γ of the LJ fluid with size parameter σ obtained by Werth et al. [Physica A 392, 2359 (2013)] with the lrc ΔF of Janeček and a cut-off radius rc = 3σ agree with the results of Mecke et al. [J. Chem. Phys. 107, 9264 (1997)] obtained with the lrc Δ1F of Lotfi et al. and rc = 6.5σ within −0.4% to +1.6%. Moreover, using only the MD results for γ of Werth et al., we obtain for the LJ fluid a new surface tension correlation which also represents the γ-values of Mecke et al. within ±0.7%. The critical temperature resulting from the correlation is Tc = 1.317 66 and is in very good agreement with Tc,ref = 1.32 of the reference equation of state for the LJ fluid given by Thol et al. [J. Phys. Chem. Ref. Data 45, 023101 (2016)].