Bridge function
The bridge functions are infinite series of irreducible diagrams :
![{\displaystyle B^{(2)}(r)=\rho ^{2}{\frac {1}{2}}D_{1}(r)+\rho ^{3}[D_{2}(r)+D_{3}(r)]+\rho ^{4}[...]+...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3a016aca53933b93dfb7fe63cc9d408238446bb)
and
![{\displaystyle 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}[...]+...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c9ce1bab48c7699f7cfc86d46a18dd90cc6259ff)
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} is the density of the fluid.
References
- 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)
- 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)