A new biased Monte-Carlo method for computing coefficients of the bridge functions of liquids

We describe an efficient biased Monte-Carlo method for calculating the diagrams appearing in the coefficients of the so-called bridge function B = Sigma(n=2)(infinity) b(n)rho(n) of the integral equation theory of liquids. These diagrams represent multi-dimensional integrals of products of 'bond' functions of the intermolecular distances. The method rests on the generation of independent Markov chains and is well adapted to highly parallel computation. It can be used for systems with any pair potential. The feasibility and efficiency of the method are demonstrated for the second and third order coefficients of the bridge functions of fluids of hard and Lennard-Jones spheres. For these systems there are analytical expressions of the bridge function deduced from computer simulations to which we compare our bridge function approximations which include the second and third order coefficients with h as the bond function. Our new approximations of the bridge function are used in the closure of the Ornstein-Zernike relation. The obtained structural and thermodynamical properties are found in better agreement with the exact simulation data than the hypernetted chain results.