Direct correlation function

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

$h({\mathbf {r} })-c({\mathbf {r} })=\rho \int h({\mathbf {r} '})~c(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}$

and also in the compressibility equation, i.e.

${\frac {1}{k_{B}T}}\left.{\frac {\partial p}{\partial \rho }}\right\vert _{T}=1-\rho \int _{0}^{\infty }c(r)~4\pi r^{2}~{\rm {d}}r$

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)