excpbex Subroutine

public subroutine excpbex(rho, s, u, v, ex, vx, llda, um)

PBE exchange for a spin-unpolarized electronic system. This is calculated using the fact that the exchange in LDA is given by $$\begin{equation} e_x[unif]=a_x\rho^{\frac{4}{3}} \end{equation}$$ with $$\begin{equation} a_x = -\frac{3}{4}\left(\frac{3}{\pi}\right)^{\frac{1}{3}} \end{equation}$$ where the $e_x[PBE]$ is given by $$\begin{equation} e_x[PBE] =e_x[unif]*F_x^{PBE}(s) \end{equation}$$ where $$\begin{equation} F_x^{PBE}(s)=1+u_k-\frac{u_k}{1+u_l s^2} \end{equation}$$ with $u_k$ and $u_l$ being defined in Eq.13 of [a]

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	rho	density
real(kind=dp),	intent(in)			::	s	$\frac{\| \nabla \rho\|}{2K_F \rho}$ with $\K_F=\left(3 \pi^2 \rho\right)^\frac{1}{3}$
real(kind=dp),	intent(in)			::	u	$\frac{\nabla^2 \rho}{\rho\left(2K_F\right)^2}$
real(kind=dp),	intent(in)			::	v
real(kind=dp),	intent(out)			::	ex	exchange energy per electron
real(kind=dp),	intent(out)			::	vx	exchange potential
integer,	intent(in)			::	llda
real(kind=dp),	intent(in)			::	um