Computationally useful bridge diagram series for the structure and thermodynamics of Lennard-Jones fluids

The first two orders of bridge diagrams, those with two and three field points, have been calculated exactly for the Lennard-Jones fluid for several isotherms. The method of calculation was one of expansion in Legendre polynomials, and the dependence of the method on the number of polynomials needed for accurate results was investigated. Thermodynamic and structural properties of the Lennard-Jones fluid calculated from integral equation methods with the inclusion of bridge diagrams were found to be systematically improved. Two attempts at predicting the missing bridge diagrams of even higher order were discussed. The first, which uses the functional form of those diagrams that were calculated exactly, showed no significant improvement. The second, a series sum based on the first two orders of calculated diagrams and motivated by the success of a similar heuristic sum in the case of hard spheres, was extremely successful. When the series sum was employed, thermodynamic and structural quantities were improved to the point where the difference between simulation results and integral equation results was of the same order as the error in the simulations themselves.