The fluid structures for soft-sphere potentials via the zero-separation theorems on molecular distribution functions

We present a class of closures specifically designed to satisfy the zero-separation theorems for the correlation functions y(r) (the cavity function), gamma(r)=h(r)-C(r) (the indirect correlation), and B(r) (the bridge function) at coincidence r=0 for soft-sphere pair potentials. The rationale is to ensue the correct behavior of these correlation functions inside the core r<sigma. Since the coincidence theorems implicate the thermodynamic properties of the bulk fluid: the isothermal compressibility, the internal energy and the chemical potentials, we can hopefully enforce consistency between the structure and thermodynamic properties. We solve the Ornstein-Zernike equation for the Lennard-Jones molecules where plentiful Monte Carlo data are available for testing. It turns out that not only consistency is achieved, we also obtain accurate structures: the pair correlation function g(r), the cavity function, and the bridge function for wide ranges of fluid states (0.72 < T*< 1.5, rho*< 0.9). Comparison with MC data attests to the accuracy. The closure of the zero-separation type (ZSEP), is sufficiently robust and flexible to ensure not only fulfillment of the zero-separation theorems but also pressure consistency. Success with the Lennard-Jones potential implies its applicability to other similar soft-sphere potentials. (C) 1996 American Institute of Physics.