A pair potential that reproduces the shape of isochrones in molecular liquids

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.