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C..31 PW91X: Perdew-Wang 1991 GGA Exchange Functional

See reference [5] 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\,{\frac {\sqrt [3]{3}\sqrt [3]{{\pi }^{2}}{n}^ {4/3}F \left( S \right) }{\pi }} ,\end{dmath} \begin{dmath} S=1/12\,{\frac {\chi_{s}{6}^{2/3}}{\sqrt [3]{{\pi }^{2}}}} \end{dmath} and \begin{dmath} F \left( S \right) ={\frac {1+ 0.19645\,S{\,\text{arcsinh}} \left(... ...5\,S{\,\text{arcsinh}} \left( 7.7956\,S \right) + 0.004\,{S}^{4} }} .\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