An accurate integral equation for the pair and triplet distribution functions of a simple liquid

We present an accurate integral equation for the pair and triplet distribution functions of a simple classical liquid. The only approximation in the theory, the representation of the triplet distribution function, is improved systematically beyond the superposition approximation by a graphical resummation of the density expansion of the correction terms. In a sample calculation for liquid sodium near its triple point, the triplet distribution function calculated from our integral equation is compared with the results of a molecular dynamics simulation, and excellent agreement is obtained.