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

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