19.1.24 PBEX: PBE Exchange Functional

J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

$$K=\frac{1}{2} \sum_s E(2\,\rho_{s}) ,$$ (119)

where

$$E(n)=-\frac{3}{4}\left(\frac {3}{\pi}\right)^{1/3}{n}^{4/3}F(S) ,$$ (120)

$$S={\frac {\chi_{s}}{2\left(6{{\pi }^{2}}\right)^{1/3}}} ,$$ (121)

$$F(S)=1+R-R\left (1+{\frac {\mu\,{S}^{2}}{R}}\right )^{-1} ,$$ (122)

$$R= 0.804 ,$$ (123)

$$\mu=\delta\,{\pi }^{2}/3$$ (124)

and

$$\delta= 0.066725 .$$ (125)