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subroutine exchen(d,s,ex)
c gga91 exchange energy for a spin-unpolarized electronic system
c input d : density
c input s : abs(grad d)/(2*kf*d)
c output ex : exchange energy per electron
implicit double precision (a-h,o-z)
data a1,a2,a3,a4/0.19645d0,0.27430d0,0.15084d0,100.d0/
data ax,a,b1/-0.7385588d0,7.7956d0,0.004d0/
data thrd/0.333333333333d0/
fac = ax*d**thrd
s2 = s*s
s4 = s2*s2
p0 = 1.d0/dsqrt(1.d0+a*a*s2)
p1 = dlog(a*s+1.d0/p0)
p2 = dexp(-a4*s2)
p3 = 1.d0/(1.d0+a1*s*p1+b1*s4)
p4 = 1.d0+a1*s*p1+(a2-a3*p2)*s2
f = p3*p4
ex = fac*f
return
end
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