19.1.37 THGFCFO:

D. J. Tozer, N. C. Handy and W. H. Green, Chem. Phys. Lett. 273, 183 (1997)

Density and gradient dependent first row exchange-correlation functional. The closed- and open-shell parts are fitted to training sets of closed- and open-shell systems independently.

$$K= \sum _{i=1}^{n}\omega_{{i}}R_{{i}}S_{{i}}X_{{i}}Y_{{i}} ,$$ (207)

where

$$n=20 ,$$ (208)

$$R_{{i}}=\rho_{\alpha}^{t_{{i}}}+\rho_{\beta} ^{t_{{i}}} ,$$ (209)

$$S_{{i}}=\left ({\frac {\rho_{\alpha}-\rho_{\beta}}{\rho}}\right )^{2\,u _{{i}}} ,$$ (210)

$$X_{{i}}={\frac {\sigma_{\alpha \alpha}^{v_{ {i}/2}}+\sigma_{\beta \beta}^{v_{{i}/2}}}{{2\rho}^{4v_{{i}}/ 3\,}}} ,$$ (211)

$$Y_{{i}}=\left ({\frac {\sigma_{\alpha \alpha}+\sigma_{\beta ... ...qrt {\sigma_{\beta \beta}}}{{\rho}^{8/3 }}}\right )^{w_{{i}}} ,$$ (212)

$$t = [7/6,4/3,3/2,5/3,4/3,3/2,5/3,{\frac {11}{6}},3/2,5/3,$$

$${\frac {11}{6}},2, 3/2,5/3,{\frac {11}{6}},2,7/6,4/3,3/2,5/3] ,$$ (213)

$$u = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1] ,$$ (214)

$$v = [0,0,0,0,1,1,1,1,2,2,2,2,0,0,0,0,0,0,0,0] ,$$ (215)

$$w = [0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]$$ (216)

and

$$\omega = [- 0.864448, 0.565130,- 1.27306, 0.309681, - 0.287658,$$

$$0.588767,- 0.252700, 0.0223563, 0.0140131,- 0.0826608,$$

$$0.0556080,- 0.00936227,- 0.00677146, 0.0515199,- 0.0874213,$$

$$0.0423827, 0.431940, - 0.691153,- 0.637866, 1.07565] .$$ (217)