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C..21 LTA: Local $\tau$ Approximation

LSDA exchange functional with density represented as a function of $\tau$. See reference [18] for more details.

\begin{dmath} K= \sum_s 1/2 E \left( 2 \tau_{s} \right) ,\end{dmath} where \begin{dmath} E \left( \alpha \right) =1/9 c{5}^{4/5}\sqrt [5]{9} \left( {\frac... ...a \sqrt [3]{3}}{ \left( {\pi }^{2} \right) ^{2/3}}} \right) ^{4/5 } \end{dmath} and \begin{dmath} c=-3/4 \sqrt [3]{3}\sqrt [3]{{\pi }^{-1}} .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= 1/2 E \left( 2 \tau_{s} \right) .\end{dmath}

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Aug 2, 2008