subroutine exchpt(d,s,u,v,vx)
c  gga91 exchange potential for a spin-unpolarized electronic system
c  input d   : density
c  input s   :  abs(grad d)/(2*kf*d)
c  input u   : (grad d)*grad(abs(grad d))/(d**2 * (2*kf)**3)
c  input v   : (laplacian d)/(d*(2*kf)**2)
c  output vx :  exchange potential 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,thrd4/0.333333333333d0,1.33333333333d0/
      fac = ax*d**thrd
      s2 = s*s
      s3 = s2*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
      p5 = b1*s2-(a2-a3*p2)
      p6 = a1*s*(p1+a*s*p0)
      p7 = 2.d0*(a2-a3*p2)+2.d0*a3*a4*s2*p2-4.d0*b1*s2*f
      fs = p3*(p3*p5*p6+p7)
      p8 = 2.d0*s*(b1-a3*a4*p2)
      p9 = a1*p1+a*a1*s*p0*(3.d0-a*a*s2*p0*p0)
      p10 = 4.d0*a3*a4*s*p2*(2.d0-a4*s2)-8.d0*b1*s*f-4.d0*b1*s3*fs
      p11 = -p3*p3*(a1*p1+a*a1*s*p0+4.d0*b1*s3)
      fss = p3*p3*(p5*p9+p6*p8)+2.d0*p3*p5*p6*p11+p3*p10+p7*p11
      vx = fac*(thrd4*f-(u-thrd4*s3)*fss-v*fs)
      return
      end