Local Self-Consistent Ornstein-Zernike Integral Equation Theory and Application to a Generalized Lennard-Jones Potential

Local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) provides a rapid and easy route for obtaining independently thermodynamic and structural information for a single state point. Because of neglect of information of neighboring state points in determining a self-consistent adjustable parameter performance of the local self-consistent OZ IET is somewhat vulnerable and worthy of intensive investigation. For this reason, we have performed Monte Carlo simulations to obtain thermodynamic and structural properties of fluid with a generalized Lennard-Jones potential, and the present simulation results are employed to verify the quality of a local version of a recently developed global self-consistent OZ IET and a local expression for computation of excess chemical potential directly from the structural functions of the state point of interest. Comprehensive comparison and analysis demonstrate the following (i) the present local self-consistent OZ IET performs quite well for calculation of pressure and excess internal energy; (ii) using the same structural functions from the present local self-consistent OZ IET, the previously derived local expression by the present author has by and large the same accuracy in calculating the excess chemical potential as an exact virial formula for the pressure; (iii) although the excellent performance exhibited for the above thermodynamic quantities persists to very low temperature and very short-ranged potential and remains even in the liquid-solid coexistence region, the excess Helmholtz free energy calculated from the pressure and excess chemical potential shows evident inaccuracy for a density-temperature combination deep in the liquid-solid coexistence region, and this makes it necessary to derive a local formulation for the excess free energy.