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C..36 TH3:

Density and gradient dependent first and second row exchange-correlation functional. See reference [25] for more details.

\begin{dmath} K= \sum _{i=1}^{n}\omega_{{i}}R_{{i}}S_{{i}}X_{{i}}Y_{{i}} ,\end{dmath} where \begin{dmath} n=19 ,\end{dmath} \begin{dmath} R_{{i}}= \left( \rho_{\alpha} \right) ^{t_{{i}}}+ \left( \rho_{\beta} \right) ^{t_{{i}}} ,\end{dmath} \begin{dmath} S_{{i}}= \left( {\frac {\rho_{\alpha}-\rho_{\beta}}{\rho}} \right) ^{2 \,u_{{i}}} ,\end{dmath} \begin{dmath} X_{{i}}=1/2\,{\frac { \left( \sqrt {\sigma_{\alpha \alpha}} \right... ...{\sigma_{\beta \beta}} \right) ^{v_{{i}}}}{{\rho} ^{4/3\,v_{{i}}}}} ,\end{dmath} \begin{dmath} Y_{{i}}= \left( {\frac {\sigma_{\alpha \alpha}+\sigma_{\beta \beta... ...a}}\sqrt {\sigma_{\beta \beta}}}{{\rho}^{8/3 }}} \right) ^{w_{{i}}} ,\end{dmath} \begin{dmath} t = [7/6,4/3,3/2,5/3,{\frac {17}{12}},3/2,5/3,{\frac {11}{6}},5/3,... ...{ 11}{6}},2,5/3,{\frac {11}{6}},2,7/6,4/3,3/2,5/3,{\frac {13}{12}}] ,\end{dmath} \begin{dmath} u = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0] ,\end{dmath} \begin{dmath} v = [0,0,0,0,1,1,1,1,2,2,2,0,0,0,0,0,0,0,0] ,\end{dmath} \begin{dmath} w = [0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0] \end{dmath} and \begin{dmath} \omega = [- 0.142542,- 0.783603,- 0.188875, 0.0426830,- 0.304953, ... ...1157, 0.0121316, 0.441190,- 2.27167, 4.03051,- 2.28074, 0.0360204 ] .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= \sum _{i=1}^{n}1/2\,\omega_{{i}} \left( \rho_{s} \right) ^{t_{{... ...{i}}} \left( \left( \rho_{s} \right) ^{4/3\,v_{{i}}} \right) ^{-1} .\end{dmath}

molpro@molpro.net
Oct 10, 2007