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 γ 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 γ≅ 3 nR/ 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 γ versus R there is in all cases a transition around R≈ 0.9 , above which γ starts to decrease as R approaches unity. This is consistent with the fact that γ→ 2 n/ d for R→ 1 , a limit that is approached at high densities and/or high temperatures at which the repulsive r ^{- 2 n} term dominates the physics. Graphical Abstract: The paper presents numerical data for the density-scaling exponent γ 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 γ.[Figure not available: see fulltext.].