2020-09-24 14:39:37 +02:00
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subroutine unrestricted_linear_response(ispin,dRPA,TDA,BSE,eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,nS_sc,lambda, &
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e,ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,OmRPA,rho_RPA,EcRPA,Omega,XpY,XmY)
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2020-09-22 15:32:26 +02:00
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! Compute linear response for unrestricted formalism
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implicit none
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include 'parameters.h'
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! Input variables
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integer,intent(in) :: ispin
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logical,intent(in) :: dRPA
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logical,intent(in) :: TDA
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logical,intent(in) :: BSE
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double precision,intent(in) :: eta
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integer,intent(in) :: nBas
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integer,intent(in) :: nC(nspin)
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integer,intent(in) :: nO(nspin)
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integer,intent(in) :: nV(nspin)
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integer,intent(in) :: nR(nspin)
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integer,intent(in) :: nSa
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integer,intent(in) :: nSb
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integer,intent(in) :: nSt
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2020-09-24 14:39:37 +02:00
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integer,intent(in) :: nS_sc
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2020-09-22 15:32:26 +02:00
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double precision,intent(in) :: lambda
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double precision,intent(in) :: e(nBas,nspin)
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2020-09-22 22:13:51 +02:00
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double precision,intent(in) :: ERI_aaaa(nBas,nBas,nBas,nBas)
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double precision,intent(in) :: ERI_aabb(nBas,nBas,nBas,nBas)
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double precision,intent(in) :: ERI_bbbb(nBas,nBas,nBas,nBas)
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2020-09-22 23:46:33 +02:00
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double precision,intent(in) :: ERI_abab(nBas,nBas,nBas,nBas)
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2020-09-23 22:48:54 +02:00
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2020-09-24 14:39:37 +02:00
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double precision,intent(in) :: OmRPA(nS_sc)
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double precision,intent(in) :: rho_RPA(nBas,nBas,nS_sc,nspin)
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2020-09-22 15:32:26 +02:00
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! Local variables
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integer :: ia
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double precision :: trace_matrix
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double precision,allocatable :: A(:,:)
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double precision,allocatable :: B(:,:)
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double precision,allocatable :: ApB(:,:)
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double precision,allocatable :: AmB(:,:)
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double precision,allocatable :: AmBSq(:,:)
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double precision,allocatable :: AmBIv(:,:)
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double precision,allocatable :: Z(:,:)
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! Output variables
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double precision,intent(out) :: EcRPA
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double precision,intent(out) :: Omega(nSt)
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double precision,intent(out) :: XpY(nSt,nSt)
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double precision,intent(out) :: XmY(nSt,nSt)
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! Memory allocation
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allocate(A(nSt,nSt),B(nSt,nSt),ApB(nSt,nSt),AmB(nSt,nSt),AmBSq(nSt,nSt),AmBIv(nSt,nSt),Z(nSt,nSt))
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! Build A and B matrices
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2020-09-22 23:46:33 +02:00
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call unrestricted_linear_response_A_matrix(ispin,dRPA,nBas,nC,nO,nV,nR,nSa,nSb,nSt,lambda,e, &
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ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,A)
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2020-09-22 15:32:26 +02:00
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2020-09-22 22:13:51 +02:00
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if(BSE) &
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2020-09-30 00:10:57 +02:00
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call unrestricted_Bethe_Salpeter_A_matrix(ispin,eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,nS_sc,lambda,e, &
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2020-09-24 14:39:37 +02:00
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ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,OmRPA,rho_RPA,A)
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2020-09-22 15:32:26 +02:00
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! Tamm-Dancoff approximation
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B = 0d0
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if(.not. TDA) then
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2020-09-22 23:46:33 +02:00
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call unrestricted_linear_response_B_matrix(ispin,dRPA,nBas,nC,nO,nV,nR,nSa,nSb,nSt,lambda, &
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ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,B)
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2020-09-22 15:32:26 +02:00
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2020-09-22 22:13:51 +02:00
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if(BSE) &
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2020-09-24 14:39:37 +02:00
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call unrestricted_Bethe_Salpeter_B_matrix(ispin,eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,nS_sc,lambda, &
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ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,OmRPA,rho_RPA,B)
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2020-09-22 15:32:26 +02:00
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end if
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! Build A + B and A - B matrices
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ApB = A + B
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AmB = A - B
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! Diagonalize linear response matrix
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call diagonalize_matrix(nSt,AmB,Omega)
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if(minval(Omega) < 0d0) &
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call print_warning('You may have instabilities in linear response: A-B is not positive definite!!')
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do ia=1,nSt
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if(Omega(ia) < 0d0) Omega(ia) = 0d0
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end do
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call ADAt(nSt,AmB,1d0*sqrt(Omega),AmBSq)
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call ADAt(nSt,AmB,1d0/sqrt(Omega),AmBIv)
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Z = matmul(AmBSq,matmul(ApB,AmBSq))
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call diagonalize_matrix(nSt,Z,Omega)
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if(minval(Omega) < 0d0) &
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call print_warning('You may have instabilities in linear response: negative excitations!!')
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do ia=1,nSt
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if(Omega(ia) < 0d0) Omega(ia) = 0d0
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end do
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Omega = sqrt(Omega)
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XpY = matmul(transpose(Z),AmBSq)
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call DA(nSt,1d0/sqrt(Omega),XpY)
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XmY = matmul(transpose(Z),AmBIv)
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call DA(nSt,1d0*sqrt(Omega),XmY)
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! Compute the RPA correlation energy
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EcRPA = 0.5d0*(sum(Omega) - trace_matrix(nSt,A))
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end subroutine unrestricted_linear_response
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