Analysis of the first bridge diagram of liquid bromine

The first bridge diagrams of the classical theory of liquids are discussed for two fluids of Lennard-Jones spheres and for a fluid of a two-centre Lennard-Jones model of liquid bromine. The bridge diagram of liquid bromine is calculated using a biased Monte-Carlo method. We investigate the first bridge diagrams, the bonds of which are either Mayer functions f or total correlation functions h. The Mayer f-bond representation leads to very high values of the first bridge diagram, which can not be used alone in a truncated expansion of the diagrammatic series of the bridge function. We analyse the origin of these high values. In the case of the h-function representation, the bridge function series truncated to the sole first bridge diagram is introduced into the closure of the Ornstein-Zernike equation and leads to some improvement of the pair distribution function upon the HNC result, as compared to the exact simulated values.