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C..25 LTA: Local $\tau$ Approximation

LSDA exchange functional with density represented as a function of $\tau$. \begin{dmath}
g=1/2\,E \left( 2\,\tau \left( s \right) \right)
,\end{dmath}

\begin{dmath}
E \left( \alpha \right) =1/9\,c{5}^{4/5}\sqrt [5]{9} \left( {\frac...
...\,\sqrt [3]{3}}{ \left( {\pi }^{2} \right) ^{2/3}}} \right) ^{4/5
}
,\end{dmath}

\begin{dmath}
c=-3/4\,\sqrt [3]{3}\sqrt [3]{{\pi }^{-1}}
,\end{dmath}

\begin{dmath}
G=1/2\,E \left( 2\,\tau \left( s \right) \right)
.\end{dmath}



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