Collect. Czech. Chem. Commun. 2010, 75, 447-462
Published online 2010-04-15 09:30:49

The effect of truncation and shift on virial coefficients of Lennard–Jones potentials

Katherine R. S. Shaul, Andrew J. Schultz and David A. Kofke*

Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA


We present virial coefficients of up to fifth order computed by Mayer-sampling Monte Carlo for several truncated-and-shifted Lennard–Jones potentials. We employ these coefficients within the virial equation of state to compute vapor-branch spinodals and critical points for each potential considered. We find that truncation distances of 5.0σ and higher yield values in significantly better agreement with those of the unmodified potential than those resulting from the more commonly used truncation distances of 2.5 and 3.0σ. We also employ these virial coefficients to examine the perturbed virial expansion method of Nezbeda and Smith for estimating the critical point. We find that the first-order perturbation performs well in characterizing the effect of potential truncation on the critical point for the truncation distances considered, with errors in critical temperatures ranging from –3 to +2% and errors in critical densities about constant at –22%. Addition of higher-order terms to the perturbation treatment brings it closer to the behavior given by the virial equation of state, which at fifth order underestimates the critical temperatures by 2 to 4% and the critical densities by 20 to 30%.

Keywords: Equation of state; Virial coefficients; Truncated-and-shifted Lennard–Jones potential; Mayer sampling; Monte Carlo method; Molecular modeling; Thermodynamics.

References: 15 live references.