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This paper investigates the relation between the density-scaling exponent$\gamma$ and the virial potential-energy correlation coefficient $R$ at severalthermodynamic 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 studiedinclude many low-density states at which the virial potential-energycorrelations are not strong. For these state points we find the roughly linearrelation $\gamma\cong 3nR/d$ in $d$ dimensions. This result is discussed inlight of the approximate "extended inverse power law" description ofgeneralized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508(2008)]. In the plot of $\gamma$ versus $R$ there is in all cases a transitionaround $R\approx 0.9$, above which $\gamma$ starts to decrease as $R$approaches unity. This is consistent with the fact that $\gamma\rightarrow2n/d$ for $R\rightarrow 1$, a limit that is approached at high densities and/ortemperatures at which the repulsive $r^{-2n}$ term dominates the physics.

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