19.1.17 LTA: Local ${\tau }$ Approximation

J. P. Perdew and Y. Wang, J. Chem. Phys. 111, 911 (1999)

LSDA exchange functional with density represented as a function of ${\tau }$.

$$K=\frac{1}{2} \sum_s E(2\,\tau_{s}) ,$$ (80)

where

$$E(\alpha)=c\left(\frac{5\alpha}{3\left(3\pi^2\right)^{2/3}}\right)^{4/5}$$ (81)

and

$$c=-\frac{3}{4}\left(\frac{3}{\pi}\right)^{1/3} .$$ (82)