  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, 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 range where the van't Hoff's assumption that energetic and entropic
forces are temperature independent is valid. 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's assumption in the whole range of temperatures can be determined in the
whole liquid region of the phase diagram from only a single simulation.
