Density-scaling exponents and virial potential-energy correlation coefficients for the (2n, n) Lennard-Jones system

Abstract

This paper investigates the relation between the density-scaling exponent $$\gamma $$ and the virial potential-energy correlation coefficient R at several thermodynamic state points in three dimensions for the generalized (2n, n) Lennard-Jones (LJ) system for $$n=4, 9, 12, 18$$ , as well as for the standard $$n=6$$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $$\gamma \cong 3nR/d$$ in d dimensions. This result is discussed in light of the approximate “extended inverse power law” description of generalized LJ potentials (Bailey N P et al. 2008 J. Chem. Phys. 129 184508). In the plot of $$\gamma $$ versus R there is in all cases a transition around $$R\approx 0.9$$ , above which $$\gamma $$ starts to decrease as R approaches unity. This is consistent with the fact that $$\gamma \rightarrow 2n/d$$ for $$R\rightarrow 1$$ , a limit that is approached at high densities and/or high temperatures at which the repulsive $$r^{-2n}$$ term dominates the physics. The paper presents numerical data for the density-scaling exponent $$\gamma $$ and the virial potential-energy correlation coefficient R for generalized (2n, n) Lennard-Jones (LJ) systems. An unanticipated linear relation is observed between R and a properly scaled version of $$\gamma $$ .