18.1.27 PW91C: Perdew-Wang 1991 GGA Correlation Functional

J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson and C. Fiolhais, Phys. Rev. B 46, 6671 (1992)

$$K= \rho \left (\epsilon(\rho_{\alpha},\rho_{\beta})+H(d,\rho_{\alpha}, \rho_{\beta})\right ) ,$$ (130)

where

$$d=\frac{\sqrt{\sigma}}{4u(\rho_{\alpha},\rho_{\beta})}\left(\frac{\pi}{3\rho^7}\right)^{1/6}$$ (131)

$$u(\alpha,\beta)=\left\{\left (1+\zeta(\alpha,\beta)\right )^{2/3}+ \left (1-\zeta(\alpha,\beta)\right )^{2/3}\right\}/2 ,$$ (132)

$$H(d,\alpha,\beta)=L(d,\alpha,\beta)+J(d,\alpha,\beta) ,$$ (133)

$$L(d,\alpha,\beta)=\frac{u^3(\rho_{\alpha},\rho_{\beta} {\lam... ...lpha,\beta){d}^{2}+A^2(\alpha, \beta){d}^{4}\right )}}\right) ,$$ (134)

$$J(d,\alpha,\beta)=\nu \left (\phi(r(\alpha,\beta))-\kappa-3... ...},\rho_{\beta}){d}^{2}}{\left (3\pi^5\right )^{1/3} \rho}}}}} ,$$ (135)

$$A(\alpha,\beta)=\frac{2 \iota}{\lambda}\left ({e^{-{\frac {... ...(\rho_{\alpha},\rho_{\beta}) {\lambda}^{2}}}}}-1\right )^{-1} ,$$ (136)

$$\iota= 0.09 ,$$ (137)

$$\lambda=\nu \kappa ,$$ (138)

$$\nu=16\left({\frac {3}{\pi }}\right)^{1/3} ,$$ (139)

$$\kappa= 0.004235 ,$$ (140)

$$Z=- 0.001667 ,$$ (141)

$$\phi(r)=\theta(r)-Z ,$$ (142)

$$\theta(r)={\frac {1}{1000}} {\frac { 2.568+\Xi r+\Phi {r}^{2}}{1+ \Lambda r+\Upsilon {r}^{2}+10 \Phi {r}^{3}}} ,$$ (143)

$$\Xi= 23.266 ,$$ (144)

$$\Phi= 0.007389 ,$$ (145)

$$\Lambda= 8.723 ,$$ (146)

$$\Upsilon= 0.472$$ (147)

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