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C..6 B88C: Becke88 Correlation Functional

Correlation functional depending on B86MGC exchange functional with empirical atomic parameters, $t$ and $u$. The exchange functional that is used in conjunction with B88C should replace B88MGC here. See reference [11] for more details.

\begin{dmath} K= - 0.8 \rho_{\alpha}\rho_{\beta}{q}^{2} \left( 1-{\frac {\ln \l... ...{4} \left( 1-2 {\frac {\ln \left( 1+1/2 z \right) }{z}} \right) ,\end{dmath} where \begin{dmath} q=t \left( x+y \right) ,\end{dmath} \begin{dmath} x= 0.5 \left( c\sqrt [3]{\rho_{\alpha}}+{\frac {\beta \left( ... ..., \left( \chi_{\alpha} \right) ^{2} \right) ^{4/5}}} \right) ^{-1} ,\end{dmath} \begin{dmath} y= 0.5 \left( c\sqrt [3]{\rho_{\beta}}+{\frac {\beta \left( \... ... \left( \chi_{\beta} \right) ^{2} \right) ^{4/5}}} \right) ^{-1} ,\end{dmath} \begin{dmath} t= 0.63 ,\end{dmath} \begin{dmath} z=2 ur ,\end{dmath} \begin{dmath} r= 0.5 \rho_{s} \left( c \left( \rho_{s} \right) ^{4/3}+{\frac {\... ...mbda \left( \chi_{s} \right) ^{2} \right) ^{4/5}}} \right) ^{-1} ,\end{dmath} \begin{dmath} u= 0.96 ,\end{dmath} \begin{dmath} d=\tau_{s}-1/4 {\frac {\sigma_{ss}}{\rho_{s}}} ,\end{dmath} \begin{dmath} c=3/8 \sqrt [3]{3}{4}^{2/3}\sqrt [3]{{\pi }^{-1}} ,\end{dmath} \begin{dmath} \beta= 0.00375 \end{dmath} and \begin{dmath} \lambda= 0.007 .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= - 0.01 \rho_{s}d{z}^{4} \left( 1-2 {\frac {\ln \left( 1+1/2 z \right) }{z}} \right) .\end{dmath}

molpro@molpro.net
Aug 2, 2008