C..9 BR: Becke-Roussel Exchange Functional

A. D. Becke and M. R. Roussel,Phys. Rev. A 39, 3761 (1989)


\begin{displaymath}
K=\frac{1}{2}\sum_s \rho_s U_s
,\end{displaymath} (64)

where
\begin{displaymath}
U_s=-(1-e^{-x}-xe^{-x}/2)/b
,\end{displaymath} (65)


\begin{displaymath}
b=\frac{x^3e^{-x}}{8\pi\rho_s}
\end{displaymath} (66)

and $x$ is defined by the nonlinear equation
\begin{displaymath}
\frac{xe^{-2x/3}}{x-2}=\frac{2\pi^{2/3}\rho_s^{5/3}}{3Q_s}
,\end{displaymath} (67)

where
\begin{displaymath}
Q_s=(\upsilon_s-2\gamma D_s)/6
,\end{displaymath} (68)


\begin{displaymath}
D_s=\tau_s-\frac{\sigma_{ss}}{4\rho_s}
\end{displaymath} (69)

and
\begin{displaymath}
\gamma=1.
\end{displaymath} (70)

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