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

Abstract

Functions up to M-body (M>2) correlations can be determined by generalizing the hypernetted-chain theory (HNC) for two-body correlation. M-1 equations are obtained for the correlation functions based on the M-body density functional theory and a generalized Percus idea for M-1 particles held fixed in space. A closed set of equations is obtained with M-1 Ornstein-Zernike relations. The equations are presented for the case M = 3 due to the complexity of the coupled integral equations, and compared with the HNC2 equations.