corl91.f 2.93 KB
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      MODULE m_corl91
c.....-----------------------------------------------------------------
c     uniform-gas correlation of perdew and wang 1991
c.....-----------------------------------------------------------------
      CONTAINS
      SUBROUTINE corl91(
     >                  rs,zta,
     <                  ec,vcup,vcdn,ecrs,eczta,alfc)
c.....-----------------------------------------------------------------
c     input: seitz radius (rs), relative spin polarization (zta)
c     output: correlation energy per electron (ec),
c             up- and down-spin potentials (vcup,vcdn),
c             derivatives of ec wrt rs (ecrs) &zta (eczta).
c     output: correlation contribution (alfc) to the spin stiffness
c.....-----------------------------------------------------------------
      IMPLICIT NONE

      REAL, INTENT (IN)  :: rs,zta
      REAL, INTENT (OUT) :: alfc,ec,ecrs,eczta,vcdn,vcup

      REAL :: alfm,alfrsm,comm,ep,eprs,eu,eurs,f,fz,z4
      REAL :: fzz,gam,thrd,thrd4
c.....-----------------------------------------------------------------
c     ..
      DATA gam,fzz/0.5198421,1.709921/
      DATA thrd,thrd4/0.333333333333e0,1.333333333333e0/
c.....-----------------------------------------------------------------
      f = ((1.0+zta)**thrd4+ (1.0-zta)**thrd4-2.e0)/gam

      CALL gcor91(0.0310907,0.21370,7.5957,3.5876,1.6382,
     +          0.49294,1.00,rs,eu,eurs)

      CALL gcor91(0.01554535,0.20548,14.1189,6.1977,3.3662,
     +          0.62517,1.00,rs,ep,eprs)

      CALL gcor91(0.0168869,0.11125,10.357,3.6231,0.88026,
     +          0.49671,1.00,rs,alfm,alfrsm)

c  alfm is minus the spin stiffness alfc
      alfc = -alfm
      z4 = zta**4
      ec = eu* (1.0-f*z4) + ep*f*z4 - alfm*f* (1.0-z4)/fzz
c  energy done. now the potential:
      ecrs = eurs* (1.0-f*z4) + eprs*f*z4 - alfrsm*f* (1.0-z4)/fzz
      fz = thrd4* ((1.0+zta)**thrd- (1.0-zta)**thrd)/gam
      eczta = 4.e0* (zta**3)*f* (ep-eu+alfm/fzz) +
     +        fz* (z4*ep-z4*eu- (1.0-z4)*alfm/fzz)
      comm = ec - rs*ecrs/3.e0 - zta*eczta
      vcup = comm + eczta
      vcdn = comm - eczta

      END SUBROUTINE corl91
c.....-----------------------------------------------------------------
c     called by corl91
c.....-----------------------------------------------------------------
      SUBROUTINE gcor91(
     >                  a,a1,b1,b2,b3,b4,p,rs,
     <                  gg,ggrs)

      IMPLICIT NONE
      REAL, INTENT (IN)  :: a,a1,b1,b2,b3,b4,p,rs
      REAL, INTENT (OUT) :: gg,ggrs

      REAL :: p1,q0,q1,q2,q3,rs12,rs32,rsp
c.....-----------------------------------------------------------------
c     ..
      p1 = p + 1.0
      q0 = -2.e0*a* (1.0+a1*rs)
      rs12 = sqrt(rs)
      rs32 = rs12**3
      rsp = rs**p
      q1 = 2.e0*a* (b1*rs12+b2*rs+b3*rs32+b4*rs*rsp)
      q2 = log(1.0+1.0/q1)
      gg = q0*q2
      q3 = a* (b1/rs12+2.e0*b2+3.e0*b3*rs12+2.e0*b4*p1*rsp)
      ggrs = -2.e0*a*a1*q2 - q0*q3/ (q1**2+q1)
c
      END SUBROUTINE gcor91

      END MODULE m_corl91