Potential energy landscape-based extended van der Waals equation

TL;DR

This paper develops an extended van der Waals equation based on potential energy landscapes, capturing complex fluid behaviors like density anomalies and coexistence features by incorporating landscape contributions.

Contribution

It introduces a landscape-informed extension to the van der Waals equation that accounts for temperature-dependent landscape effects, improving predictions of fluid anomalies.

Findings

Extended vdW equation captures water-like anomalies

Landscape contribution affects pressure at lower temperatures

Model fits LJ fluid data across broad density range

Abstract

The inherent structures ({\it IS}) are the local minima of the potential energy surface or landscape, $U({\bf r})$, of an {\it N} atom system. Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$ coefficients, holds on the high-temperature plateau of the averaged {\it IS} energy. However, an additional ``landscape'' contribution to the pressure is found at lower $T$. The resulting extended {\it vdW} equation, unlike the original, is capable of yielding a water-like density anomaly, flat isotherms in the coexistence region {\it vs} {\it vdW} loops, and several other desirable features. The plateau energy, the width of the distribution of {\it IS}, and the ``top of the landscape'' temperature are simulated over a broad reduced density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be useful at high density; it nevertheless reproduces the known values of $a$ and $b$ at the critical point.