The potential distribution-based closures to the integral equations for liquid structure: The Lennard-Jones fluid

The potential distribution theorems for the test particles provide a connection to the chemical potentials and the cavity distribution functions y(r) much used in molecular theory. These relations can be capitalized for establishing the closure relations for the Ornstein–Zernike equation. In this study, we formulate a class of closures with built-in flexibilities in order to satisfy the potential distribution theorems (or the related zero separation theorems) and thermodynamic consistency. The theory is self-contained within the integral equation framework. We test it on the Lennard-Jones fluid over ranges of temperatures (down to T*=0.81) and densities (up to ρ*=0.9). To achieve self-sufficiency, we exploit the connections offered by writing down n members of the mixture Ornstein–Zernike equations for the coincident oligomers up to n-mers. Then the potential distribution theorems generate new conditions for use in determining the bridge function parameters. Five consistency conditions have been identified (three thermodynamic and two based on zero-separation values). This self-consistency allows for bootstrapping and generation of highly accurate structural and thermodynamic information. The same procedure can potentially be extended to soft-sphere potentials other than the Lennard-Jones type.