An efficient procedure for solving the reference hypernetted chain equation (RHNC) for simple fluids

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Abstract
A rapidly convergent method for solving the Orstein-Zernike equation is used in conjunction with a recently proposed iteration strategy. This combination yields a very efficient and stable procedure, which saves a considerable amount of computer time when an integral has to be repeatedly solved for related systems. The procedure is applied to solving the optimized Reference Hypernetted Chain equation for a system of particles interacting through a pairwise Lennard-Jones 12-6 potential. The reference bridge function is calculated through an empirical formula. Several isotherms and isochores are calculated to map the region where no solutions of the integral equation are found. Computations of the chemical potential and pressure are performed for several densities along a number of isotherms. Applying the conditions of phase equilibrium, the phase diagram is obtained and is found to be in good agreement with recent simulation results.

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