Direct correlation function

The direct correlation function, $c(1,2)$ is encountered in the Ornstein-Zernike relation, i.e.

$h(\mathbf{r})-c(\mathbf{r})=\rho \int h({\mathbf{r}}^{\prime })c(|\mathbf{r}-{\mathbf{r}}^{\prime }|)\mathrm{d}{\mathbf{r}}^{\prime }$

and also in the compressibility equation, i.e.

$\frac{1}{k_{B}T}{\frac{\partial p}{\partial \rho }|}_T=1-\rho \underset{0}{\overset{\mathrm{\infty }}{\int }}c(r)4\pi r^2\mathrm{d}r$

References

Related reading

• Shuangliang Zhao and Jianzhong Wu "An efficient method for accurate evaluation of the site–site direct correlation functions of molecular fluids", Molecular Physics 109 pp. 2553-2564 (2011)