**Analysis of the First Bridge Diagram of Liquid Bromine
**

**Sebastian Rast,**^{1,3,*}**
Pascal H. Fries**^{2} **and Hartmut
Krienke**^{1}

^{1} Institut für Physikalische und Theoretische Chemie der
Universität Regensburg, D–93049 Regensburg, Germany

^{2} CEA, INAC, SCIB (UMR_E 3, CEA, UJF), Laboratoire de Reconnaissance
Ionique et de Chimie de Coordination, F–38054 Grenoble, France

^{3} now at Max Planck Institute for Meteorology, Bundesstr. 53, D–20146
Hamburg, Germany

* Corresponding author: E-mail:
sebastian.rast@zmaw.de

**Abstract**

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.

**Keywords:** Bridge function, molecular Ornstein-Zernike
equation, liquid bromine