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.

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 \frac{1}{k_BT} \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)