C..9 BR: Becke-Roussel Exchange Functional

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C..9 `BR`: Becke-Roussel Exchange Functional

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

$\begin{displaymath} K=\frac{1}{2}\sum_s \rho_s U_s ,\end{displaymath}$

(68)

where

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

(69)

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

(70)

and

is defined by the nonlinear equation

$\begin{displaymath} \frac{xe^{-2x/3}}{x-2}=\frac{2\pi^{2/3}\rho_s^{5/3}}{3Q_s} ,\end{displaymath}$

(71)

where

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

(72)

$\begin{displaymath} D_s=\tau_s-\frac{\sigma_{ss}}{4\rho_s} \end{displaymath}$

(73)

and

$\begin{displaymath} \gamma=1. \end{displaymath}$

(74)

molpro@molpro.net 2012-02-09