Potential-energy-landscape-based extended van der Waals equation

The inherent structures (IS) are the local minima of the 3N-dimensional potential energy surface, or landscape, of an N-atom system. Stillinger has given an exact IS formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals (vdW) equation, with density-dependent a and b coefficients, holds if the averaged IS energy is close to its high-temperature plateau value. The density-dependence alone significantly enriches the equation of state. Furthermore, an additional “landscape” contribution to the pressure is found at lower T. The resulting extended vdW equation is capable of yielding a waterlike density anomaly, flat isotherms in the coexistence region vs vdW loops, and several other desirable features. The plateau IS energy, the width of the distribution of IS, and $T_{\mathrm{TOL}},$ the “top of the landscape” temperature at which the plateau is reached, are simulated over a broad reduced density range, $2.0>~\rho >~0.20,$ in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be plausible at high density. Nevertheless, $a\left({\rho }_c\right)$ and $b\left({\rho }_c\right),$ where ${\rho }_c$ is the critical density, are in excellent agreement with the standard values obtained by fitting the vdW equation at the critical point.