19.1.6 B95: Becke's 1995 Correlation Functional

A. D. Becke, J. Chem. Phys. 104, 1040 (1995)

${\tau }$-dependent dynamical correlation functional.

$$K= {\frac {E}{1+l\left (\chi_{\alpha}^{2}+ \chi_{\beta}^{2}\... ...silon(\rho_{s},0)}{H\left (1+\nu\,\chi_{s}^{ 2}\right )^{2}}} ,$$ (30)

where

$$E=\epsilon(\rho_{\alpha},\rho_{\beta})-\epsilon(\rho_{\alpha},0)- \epsilon(\rho_{\beta},0) ,$$ (31)

$$l= 0.0031 ,$$ (32)

$$F=\tau_{s}-\frac {\sigma_{ss}}{4\rho_{s}} ,$$ (33)

$$H=3\left ({6\pi }^{2}\right )^{2/3}\rho_{s}^ {5/3}/5 ,$$ (34)

$$\nu= 0.038$$ (35)

and ${\epsilon(\alpha,\beta)}$ is the correlation energy per particle of the Local Spin Density Approximation(PW92C).