  Liquids displaying strong virial-potential energy correlations conform to an
approximate density scaling of their structural and dynamical observables. This
scaling property does not extend to the entire phase diagram, in general. The
validity of the scaling can be quantified by a correlation coefficient. In this
work a simple scheme to predict the correlation coefficient and the
density-scaling exponent is presented. Although this scheme is exact only in
the dilute gas regime or in high dimension d, a comparison with results from
molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the
behavior of generalized Lennard-Jones systems in a large portion of the fluid
phase.
