19.1.4 B88C:

A. D. Becke, J. Chem. Phys. 88, 1053 (1988)

Correlation functional depending on the B86MGC exchange functional with empirical atomic parameters, $t$ and $u$. B86MGC should be used in conjunction with B88C.

$$K = - 0.8\,\rho_{\alpha}\rho_{\beta}{q}^{2}\left (1-{\frac {\ln (1+q)}{q}} \right )$$

$$-0.01 \sum_s \rho_{s}d{z}^{4}\left (1-2\,{\frac {\ln (1+1/2\,z)}{z}}\right ) ,$$ (15)

where

$$q=t\left (x_\alpha+x_\beta\right ) ,$$ (16)

$$x_{\alpha}= 0.5\,\left (c\rho_{\alpha}^{1/3}+{\frac {\beta\,... ...t (1+\lambda\, \chi_{\alpha}^{2}\right )^{4/5}}}\right )^{-1} ,$$ (17)

$$x_\beta= 0.5\,\left (c\rho_{\beta}^{1/3}+{\frac {\beta\, \ch... ...ft (1+\lambda\, \chi_{\beta}^{2}\right )^{4/5}}}\right )^{-1} ,$$ (18)

$$t= 0.63 ,$$ (19)

$$z=2\,ux_s ,$$ (20)

$$x_s= 0.5\,\rho_{s}\left (c\rho_{s}^{4/3}+{\frac {\beta\, \ch... ...{\left (1+ \lambda\,\chi_{s}^{2}\right )^{4/5}}}\right )^{-1} ,$$ (21)

$$u= 0.96 ,$$ (22)

$$d=\tau_{s}-\frac {\sigma_{ss}}{4\rho_{s}} ,$$ (23)

$$c=\frac{3}{2}\left (\frac{3}{4\pi}\right )^{1/3} ,$$ (24)

$$\beta= 0.00375$$ (25)

and

$$\lambda= 0.007 .$$ (26)