MODULE m_xch91 c.....----------------------------------------------------------------- c gga91 exchange for a spin-unpolarized electronic system c.....----------------------------------------------------------------- c input d: density c s: abs(grad d)/(2*kf*d) c u: (grad d)*grad(abs(grad d))/(d**2 * (2*kf)**3) c v: (laplacian d)/(d*(2*kf)**2) c output: exchange energy (ex) and potential (vx) in ry. c kf=cbrt(3*pai**2*d). c.....----------------------------------------------------------------- CONTAINS SUBROUTINE xch91( > d,s,u,v, < exl,exg,vxl,vxg) IMPLICIT NONE REAL, INTENT (IN) :: d,s,u,v REAL, INTENT (OUT) :: exl,exg,vxl,vxg REAL a,a1,a2,a3,a4,ax,b1,ex,f,fac,fs,fss, + p0,p1,p10,p11,p2,p3,p4,p5,p6,p7,p8,p9,s2,s3,s4, + thrd,thrd4,vx,a4s2,expsm c.....----------------------------------------------------------------- c .. DATA a1,a2,a3,a4/0.19645,0.27430e0,0.15084e0,100.e0/ DATA ax,a,b1/-0.7385588e0,7.7956e0,0.004e0/ DATA thrd,thrd4/0.333333333333e0,1.33333333333e0/ c.....----------------------------------------------------------------- c expsm: argument of exponential-smallest. expsm=minexponent(expsm)/1.5 fac = ax*d**thrd s2 = s*s s3 = s2*s s4 = s2*s2 p0 = 1.e0/sqrt(1.e0+a*a*s2) p1 = log(a*s+1.e0/p0) a4s2=max(-a4*s2,expsm) p2 = exp(a4s2) p3 = 1.e0/ (1.e0+a1*s*p1+b1*s4) p4 = 1.e0 + a1*s*p1 + (a2-a3*p2)*s2 f = p3*p4 ex = fac*f c local exchange exl exl = fac exg = ex - exl c energy done. now the potential: p5 = b1*s2 - (a2-a3*p2) p6 = a1*s* (p1+a*s*p0) p7 = 2.e0* (a2-a3*p2) + 2.e0*a3*a4*s2*p2 - 4.e0*b1*s2*f fs = p3* (p3*p5*p6+p7) p8 = 2.e0*s* (b1-a3*a4*p2) p9 = a1*p1 + a*a1*s*p0* (3.e0-a*a*s2*p0*p0) p10 = 4.e0*a3*a4*s*p2* (2.e0-a4*s2) - 8.e0*b1*s*f - 4.e0*b1*s3*fs p11 = -p3*p3* (a1*p1+a*a1*s*p0+4.e0*b1*s3) fss = p3*p3* (p5*p9+p6*p8) + 2.e0*p3*p5*p6*p11 + p3*p10 + p7*p11 vx = fac* (thrd4*f- (u-thrd4*s3)*fss-v*fs) c local exchange vxl: vxl = fac*thrd4 vxg = vx - vxl c in ry and energy density. exl = exl*2.e0*d exg = exg*2.e0*d vxl = vxl*2. vxg = vxg*2. END SUBROUTINE xch91 END MODULE m_xch91