  Many liquids have curves (isomorphs) in their phase diagrams along which
structure, dynamics, and some thermodynamic quantities are invariant in reduced
units. A substantial part of their phase diagrams is thus effectively one
dimensional. The shape of these isomorphs is described by a material-dependent
function of density $h(\rho)$, which for real liquids is well approximated by a
power law $\rho^\gamma$. However, in simulations, a power law is not adequate
when density changes are large; typical models such as the Lennard-Jones liquid
show that $\gamma(\rho) \equiv \mathrm{d} \ln h(\rho)/\mathrm{d} \ln \rho$ is a
decreasing function of density. This paper presents results from computer
simulations using a new pair potential that diverges at a nonzero distance and
can be tuned to give a more realistic shape of $\gamma(\rho)$. Our results
indicate that the finite size of molecules is an important factor to take into
account when modeling liquids over a large density range.
