M-body density functional theory and the generalized hypernetted-chain equation

The HNC (hypernetted-chain) theory for two-body correlation in fluids is ge neralized so that up to M-body (M > 2) correlation functions can be obtaine d self-consistently. Our approach is based on the M-body density functional theory and a generalized Percus idea where maximally M-1 particles are hel d fixed in space, leading to M-1 HNC equations for the correlation function s. These are supplemented with M-1 Ornstein-Zernike relations to give a clo sed set of equations. Due to the rather complicated structure of the couple d integral equations, we explicitly present the equations for the case M=3, which are compared with the HNC2 equations by Verlet. The M=3 theory is nu merically solved for the case of a one-dimensional liquid. (C) 2000 America n Institute of Physics. [S0021-9606(00)51934-5].