Self-consistent equations for the radial distribution function

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Abstract
A procedure for deriving integral equations for approximate radial distribution functions is described. It employs a functional expansion that guarantees that the pressure obtained from such an approximate radial distribution function by means of the virial theorem will be in agreement with the pressure obtained from the same function by means of fluctuation theory. A natural choice of a dependent functional is shown to yield an equation that has been discussed by Rowlinson and by Lado. A second equation that is self-consistent in the same sense as the first is also exhibited. When Verlet's approximation for the three-body term that is found in the equation is used, this equation stands with respect to the first self-consistent equation as Verlet's PY2 and HNC2 equations stand to the PY and HNC equations, respectively. Variants and extensions of the procedure leading to these self-consistent equations are also discussed.