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17.1.2 B: Becke (1988) gradient-corrected exchange energy

A. D. Becke, Phys. Rev. A 38 (1988) 3098.
$\displaystyle K$ $\textstyle =$ $\displaystyle k({\rho+\hat \rho\over 2})
+k({\rho-\hat \rho\over 2})$ (7)

where we define for each of the $\alpha$ and $\beta$ spin densities
$\displaystyle x(\rho)$ $\textstyle =$ $\displaystyle \rho^{-\frac43} \left\vert\nabla\rho\right\vert$ (8)
$\displaystyle k(\rho)$ $\textstyle =$ $\displaystyle - \rho^\frac43 \left[
{3\over 2} \left({3\over 4\pi}\right)^{1/3}
+\beta
{x(\rho)^2 \over 1+6\beta x(\rho) \sinh^{-1}x(\rho)}
\right]$ (9)

with $\beta = 0.0042$.

P.J. Knowles and H.-J. Werner
molpro-support@tc.bham.ac.uk
Mar 8, 2000