Excluded volume and molecular field in the Lennard-Jones fluid: a modified first-order perturbation theory
The equation of state and, more generally, the thermodynamics of the Lennard-Jones fluid have long served as a benchmark problem in the statistical theory of fluids. Among available theoretical approaches, first-order perturbation theory occupies a special position: only at this level does the correction to the Helmholtz free energy admit an exact statistical-mechanical expression. In this work, we present a systematic, simulation-based assessment of a non-classical first-order perturbation theory in which the reference system incorporates the entire short-range part of the interaction, while the perturbation is confined to the remaining long-range tail. We show that this range-based decomposition transforms the perturbation contribution into a small, smoothly varying, near-mean-field quantity over a broad supercritical thermodynamic domain. When its density and temperature derivatives are consistently retained, the resulting equation of state reproduces high-accuracy reference data with excellent fidelity. The results demonstrate that the success of first-order perturbation theory is governed primarily by the physical content of the reference system and by the consistent treatment of its state dependence, rather than by the formal truncation order of the expansion.