QuAcK/src/eDFT/UCC_lda_exchange_derivative_discontinuity.f90

subroutine UCC_lda_exchange_derivative_discontinuity(nEns,wEns,nCC,aCC,nGrid,weight,rhow,Cx_choice,doNcentered,kappa,ExDD)

! Compute the unrestricted version of the curvature-corrected exchange ensemble derivative

  implicit none
  include 'parameters.h'

! Input variables

  integer,intent(in)            :: nEns
  double precision,intent(in)   :: wEns(nEns)
  integer,intent(in)            :: nCC
  double precision,intent(in)   :: aCC(nCC,nEns-1)
  integer,intent(in)            :: nGrid
  double precision,intent(in)   :: weight(nGrid)
  double precision,intent(in)   :: rhow(nGrid)
  integer,intent(in)            :: Cx_choice
  logical,intent(in)            :: doNcentered
  double precision,intent(in)   :: kappa(nEns)

! Local variables

  integer                       :: iEns,jEns
  integer                       :: iG
  double precision              :: r
  double precision,allocatable  :: dExdw(:)
  double precision,external     :: Kronecker_delta

  double precision              :: a1,b1,c1,w1
  double precision              :: a2,b2,c2,w2
  double precision              :: dCxdw1,dCxdw2

! Output variables

  double precision,intent(out)  :: ExDD(nEns)

! External variable

  double precision,external     :: electron_number


! Memory allocation

  allocate(dExdw(nEns))


! Parameters for N -> N-1

  a1 = aCC(1,1)
  b1 = aCC(2,1)
  c1 = aCC(3,1)


! Parameters for N -> N+1

  a2 = aCC(1,2)
  b2 = aCC(2,2)
  c2 = aCC(3,2)
 
  w1 = wEns(2)
  w2 = wEns(3)


  if (doNcentered) then
  
    select case (Cx_choice)

      case(1)
        dCxdw1 = 2.d0*a1*(w1-1.d0)+(2.d0+3.d0*(w1-2.d0)*w1)*b1+2.d0*(w1-1.d0)*(1.d0+2.d0*(w1-2.d0)*w1)*c1
        dCxdw2 = 0.d0

      case(2)
        dCxdw1 = 0.d0
        dCxdw2 = 2.d0*a2*(w2-1.d0)+(2.d0+3.d0*(w2-2.d0)*w2)*b2+2.d0*(w2-1.d0)*(1.d0+2.d0*(w2-2.d0)*w2)*c2

      case(3)
        dCxdw1 = (2.d0*a1*(w1-1.d0)+(2.d0+3.d0*(w1-2.d0)*w1)*b1+2.d0*(w1-1.d0)*(1.d0+2.d0*(w1-2.d0)*w1)*c1) &
               * (1d0 - w2*(2d0 - w2)*(a2 + b2*(w2 - 1d0) + c2*(w2 - 1d0)**2))

        dCxdw2 = (1d0 - w1*(2d0 - w1)*(a1 + b1*(w1 - 1.d0) + c1*(w1 - 1.d0)**2))                            &
               * (2.d0*a2*(w2-1.d0)+(2.d0+3.d0*(w2-2.d0)*w2)*b2+2.d0*(w2-1.d0)*(1.d0+2.d0*(w2-2.d0)*w2)*c2)

      case default
        dCxdw1 = 0d0
        dCxdw2 = 0d0

    end select

  else


    select case (Cx_choice)

      case(1)
        dCxdw1 = (0.5d0*b1 + (2d0*a1 + 0.5d0*c1)*(w1 - 0.5d0) - (1d0 - w1)*w1*(3d0*b1 + 4d0*c1*(w1 - 0.5d0)))
        dCxdw2 = 0.d0

      case(2)
        dCxdw1 = 0.d0
        dCxdw2 =(0.5d0*b2 + (2d0*a2 + 0.5d0*c2)*(w2 - 0.5d0) - (1d0 - w2)*w2*(3d0*b2 + 4d0*c2*(w2 - 0.5d0)))

      case(3)
        dCxdw1 = (0.5d0*b1 + (2d0*a1 + 0.5d0*c1)*(w1 - 0.5d0) - (1d0 - w1)*w1*(3d0*b1 + 4d0*c1*(w1 - 0.5d0))) &
               * (1d0 - w2*(1d0 - w2)*(a2 + b2*(w2 - 0.5d0) + c2*(w2 - 0.5d0)**2))

        dCxdw2 = (1d0 - w1*(1d0 - w1)*(a1 + b1*(w1 - 0.5d0) + c1*(w1 - 0.5d0)**2))                            &
               * (0.5d0*b2 + (2d0*a2 + 0.5d0*c2)*(w2 - 0.5d0) - (1d0 - w2)*w2*(3d0*b2 + 4d0*c2*(w2 - 0.5d0)))  

      case default
        dCxdw1 = 0d0
        dCxdw2 = 0d0

    end select
  end if


  dCxdw1 = CxLSDA*dCxdw1
  dCxdw2 = CxLSDA*dCxdw2

  dExdw(:) = 0d0

  do iG=1,nGrid
    
    r = max(0d0,rhow(iG))
    
    if(r > threshold) then
 
      dExdw(1) = 0d0
      dExdw(2) = dExdw(2) + weight(iG)*dCxdw1*r**(4d0/3d0)
      dExdw(3) = dExdw(3) + weight(iG)*dCxdw2*r**(4d0/3d0)

    end if
     
  end do 

  ExDD(:) = 0d0
 
  do iEns=1,nEns
    do jEns=2,nEns

      ExDD(iEns) = ExDD(iEns) + (Kronecker_delta(iEns,jEns) - wEns(jEns))*dExdw(jEns)

    end do
  end do

  if(doNcentered) ExDD(:) = kappa(:)*ExDD(:)

end subroutine UCC_lda_exchange_derivative_discontinuity