19.1.31 TH1:

D. J. Tozer and N. C. Handy, J. Chem. Phys. 108, 2545 (1998)

Density and gradient dependent first row exchange-correlation functional.

$$K= \sum _{i=1}^{n}\omega_{{i}}R_{{i}}S_{{i}}X_{{i}}Y_{{i}} ,$$ (168)

where

$$n=21 ,$$ (169)

$$R_{{i}}=\rho_{\alpha}^{t_{{i}}}+\rho_{\beta} ^{t_{{i}}} ,$$ (170)

$$S_{{i}}=\left ({\frac {\rho_{\alpha}-\rho_{\beta}}{\rho}}\right )^{2\,u _{{i}}} ,$$ (171)

$$X_{{i}}={\frac {\sigma_{\alpha \alpha}^{v_{ {i}/2}}+\sigma_{\beta \beta}^{v_{{i}/2}}}{2{\rho}^{4v_{{i}}/ 3\,}}} ,$$ (172)

$$Y_{{i}}=\left ({\frac {\sigma_{\alpha \alpha}+\sigma_{\beta ... ...qrt {\sigma_{\beta \beta}}}{{\rho}^{8/3 }}}\right )^{w_{{i}}} ,$$ (173)

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

$${\frac {11}{6}},2, 3/2,5/3,{\frac {11}{6}},2,7/6,4/3,3/2,5/3,1] ,$$ (174)

$$u = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0] ,$$ (175)

$$v = [0,0,0,0,1,1,1,1,2,2,2,2,0,0,0,0,0,0,0,0,0] ,$$ (176)

$$w = [0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]$$ (177)

and

$$\omega = [- 0.728255, 0.331699,- 1.02946, 0.235703,- 0.0876221, 0.140854,$$

$$0.0336982,- 0.0353615, 0.00497930,- 0.0645900, 0.0461795,$$

$$- 0.00757191, - 0.00242717, 0.0428140,- 0.0744891, 0.0386577,$$

$$- 0.352519, 2.19805,- 3.72927, 1.94441, 0.128877] .$$ (178)