Direct correlation function
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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.
\[\frac{1}{k_BT} \left.\frac{\partial p}{\partial \rho}\right\vert_{T} = 1 - \rho \int_0^{\infty} c(r) ~4 \pi r^2 ~{\rm d}r\]
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