Estimating the density-scaling exponent of a monatomic liquid from its   pair potential
  This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for the density-scaling exponent directly in terms of the pair potential. The second conjecture is a refined version of this, which involves the most likely nearest-neighbor distance determined from the pair-correlation function. The two conjectures for the density-scaling exponent are tested by simulations of three systems, one of which is the standard Lennard-Jones liquid. While both expressions give qualitatively correct results, the second expression is more accurate. 
Lasse B{\o}hling, Nicholas P. Bailey, Thomas B. Schr{\o}der, and Jeppe   C. Dyre
cond-mat.soft cond-mat.stat-mech