Bridge function

The bridge functions are infinite series of irreducible diagrams $D_{i}$:

$B^{(2)}(r)=\rho ^{2}{\frac {1}{2}}D_{1}(r)+\rho ^{3}[D_{2}(r)+D_{3}(r)]+\rho ^{4}[...]+...$

and

$B^{(1)}(r)={\frac {1}{3}}B^{(2)}(r)+\rho ^{3}\left[{\frac {1}{6}}D_{2}(r)-{\frac {1}{12}}D_{3}(r)\right]+\rho ^{4}[...]+...$

where $\rho$ is the density of the fluid.

Universality of the Bridge functional

For Rosenfeld's principle of the universality of the bridge functional see Ref. 2.

References

1. Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics 126 214504 (2007)
2. Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics 98 pp. 8126-8148 (1993)
3. Sang Kyu Kwak and David A. Kofke "Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation", Journal of Chemical Physics 122 104508 (2005)