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C..7 B88: Becke88 Exchange Functional

See reference [1] for more details.

\begin{dmath} K= \sum_s - \left( \rho_{s} \right) ^{4/3} \left( c+{\frac {\beta\... ...ta\,\chi_{s}{\,\text{arcsinh}} \left( \chi_{s} \right) }} \right) ,\end{dmath} where \begin{dmath} c=3/8\,\sqrt [3]{3}{4}^{2/3}\sqrt [3]{{\pi }^{-1}} \end{dmath} and \begin{dmath} \beta= 0.0042 .\end{dmath} To avoid singularities in the limit $\rho_{\bar{s}}\rightarrow 0$ \begin{dmath} G= - \left( \rho_{s} \right) ^{4/3} \left( c+{\frac {\beta\, \left... ...ta\,\chi_{s}{\,\text{arcsinh}} \left( \chi_{s} \right) }} \right) .\end{dmath}

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Oct 10, 2007