A new method of solving the HNC equation for ionic liquids

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Abstract
We show that the Newton-Raphson method recently developed for solving the liquid-structure integral equations can be used to solve the hypernetted chain equation for two-component ionic systems. The characteristics of the new method are studied by applying it to a model ionic system for a range of thermodynamic states spanning the aqueous solution and molten salt régimes. We find that its stability and rate of convergence are much superior to those of the usual method. There is a region of thermodynamic states in which the method fails to produce solutions. However, our results indicate that this is the region bounded by the spinodal line, within which the hypernetted chain equation possesses no physical solutions.