Structure of the Lennard-Jones liquid estimated from a single simulation

Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys.
152, 011102 (2020)] with isomorph theory, from a single simulation the structure of a single-component
Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the
temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van’t Hoff
assumption that energetic and entropic forces are temperature independent is valid to a good approximation.
A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures
at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden
scale-invariant system obeying the van’t Hoff assumption in the whole range of temperatures can be determined
in the whole liquid region of the phase diagram from a single simulation.