18.1.9 BR: Becke-Roussel Exchange Functional

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

$$K=\frac{1}{2}\sum_s \rho_s U_s ,$$ (47)

where

$$U_s=-(1-e^{-x}-xe^{-x}/2)/b ,$$ (48)

$$b=\frac{x^3e^{-x}}{8\pi\rho_s}$$ (49)

and $x$ is defined by the nonlinear equation

$$\frac{xe^{-2x/3}}{x-2}=\frac{2\pi^{2/3}\rho_s^{5/3}}{3Q_s} ,$$ (50)

where

$$Q_s=(\upsilon_s-2\gamma D_s)/6 ,$$ (51)

$$D_s=\tau_s-\frac{\sigma_{ss}}{4\rho_s}$$ (52)

and

$$\gamma=1.$$ (53)