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C..29 PW86:

GGA Exchange Functional. See reference [22] for more details.

\begin{dmath} K= \sum_s 1/2\,E \left( 2\,\rho_{s} \right) ,\end{dmath} where \begin{dmath} E \left( n \right) =-3/4\,\sqrt [3]{3}\sqrt [3]{{\pi }^{-1}}{n}^{4/3}F \left( S \right) ,\end{dmath} \begin{dmath} F \left( S \right) = \left( 1+ 1.296\,{S}^{2}+14\,{S}^{4}+ 0.2\,{S}^{6} \right) ^{1/15} \end{dmath} and \begin{dmath} S=1/12\,{\frac {\chi_{s}{6}^{2/3}}{\sqrt [3]{{\pi }^{2}}}} .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= 1/2\,E \left( 2\,\rho_{s} \right) .\end{dmath}

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Oct 10, 2007