Born-Green equation

$k_{B}T\frac{\partial \ln \mathrm{g}(r_{12})}{\partial {\mathbf{r}}_1}=\frac{-\partial \mathrm{\Phi }(r_{12})}{\partial {\mathbf{r}}_1}-\rho \int [\frac{\partial \mathrm{\Phi }(r_{13})}{\partial {\mathbf{r}}_1}]\mathrm{g}(r_{13})\mathrm{g}(r_{23})\mathrm{d}{\mathbf{r}}_3$

where $\mathrm{\Phi }(r_{nm})$ is the intermolecular pair potential, T is the temperature, and $k_B$ is the Boltzmann constant.

References

1. M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 188 pp. 10-18 (1946)