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code done in BSE@GT
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src/LR/linear_response_Tmatrix.f90
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107
src/LR/linear_response_Tmatrix.f90
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@ -0,0 +1,107 @@
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subroutine linear_response_Tmatrix(ispin,dRPA,TDA,eta,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,A_BSE,B_BSE,EcRPA,Omega,XpY,XmY)
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! Compute linear response
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implicit none
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include 'parameters.h'
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! Input variables
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logical,intent(in) :: dRPA,TDA
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double precision,intent(in) :: eta
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integer,intent(in) :: ispin,nBas,nC,nO,nV,nR,nS
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double precision,intent(in) :: lambda
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double precision,intent(in) :: e(nBas)
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double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
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! Local variables
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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 :: A_BSE(:,:)
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double precision,allocatable :: B_BSE(:,:)
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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(nS)
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double precision,intent(out) :: XpY(nS,nS)
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double precision,intent(out) :: XmY(nS,nS)
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! Memory allocation
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allocate(A(nS,nS),B(nS,nS),ApB(nS,nS),AmB(nS,nS),AmBSq(nS,nS),AmBIv(nS,nS),Z(nS,nS))
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! Build A and B matrices
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call linear_response_A_matrix(ispin,dRPA,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,A)
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A(:,:) = A(:,:) + A_BSE(:,:)
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! Tamm-Dancoff approximation
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if(TDA) then
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B(:,:) = 0d0
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XpY(:,:) = A(:,:)
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call diagonalize_matrix(nS,XpY,Omega)
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XpY(:,:) = transpose(XpY(:,:))
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XmY(:,:) = XpY(:,:)
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else
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call linear_response_B_matrix(ispin,dRPA,nBas,nC,nO,nV,nR,nS,lambda,ERI,B)
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B(:,:) = B(:,:) + B_BSE(:,:)
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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(nS,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,nS
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! if(Omega(ia) < 0d0) Omega(ia) = 0d0
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! end do
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call ADAt(nS,AmB,1d0*sqrt(Omega),AmBSq)
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call ADAt(nS,AmB,1d0/sqrt(Omega),AmBIv)
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Z = matmul(AmBSq,matmul(ApB,AmBSq))
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call diagonalize_matrix(nS,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,nS
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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(nS,1d0/sqrt(Omega),XpY)
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XmY = matmul(transpose(Z),AmBIv)
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call DA(nS,1d0*sqrt(Omega),XmY)
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end if
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! Compute the RPA correlation energy
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EcRPA = 0.5d0*(sum(Omega) - trace_matrix(nS,A))
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end subroutine linear_response_Tmatrix
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@ -55,6 +55,14 @@ subroutine Bethe_Salpeter_Tmatrix(TDA_T,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR
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double precision,intent(out) :: EcBSE(nspin)
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! Dimensions of the pp-RPA linear reponse matrices
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nOOs = nO*nO
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nVVs = nV*nV
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nOOt = nO*(nO - 1)/2
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nVVt = nV*(nV - 1)/2
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! Memory allocation
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allocate(Omega1s(nVVs),X1s(nVVs,nVVs),Y1s(nOOs,nVVs), &
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@ -66,14 +74,6 @@ subroutine Bethe_Salpeter_Tmatrix(TDA_T,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR
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allocate(TA(nS,nS),TB(nS,nS),OmBSE(nS,nspin),XpY_BSE(nS,nS,nspin),XmY_BSE(nS,nS,nspin))
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! Dimensions of the pp-RPA linear reponse matrices
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nOOs = nO*nO
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nVVs = nV*nV
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nOOt = nO*(nO - 1)/2
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nVVt = nV*(nV - 1)/2
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! Initialize T matrix
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TA(:,:) = 0d0
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@ -126,8 +126,8 @@ subroutine Bethe_Salpeter_Tmatrix(TDA_T,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR
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! Compute BSE singlet excitation energies
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call linear_response(ispin,.true.,TDA,.true.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGT,ERI,OmRPA, &
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rho_RPA,EcBSE(ispin),OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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call linear_response_Tmatrix(ispin,.true.,TDA,.true.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGT,ERI,TA,TB, &
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EcBSE(ispin),OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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call print_excitation('BSE@GT ',ispin,nS,OmBSE(:,ispin))
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call print_transition_vectors(.true.,nBas,nC,nO,nV,nR,nS,dipole_int, &
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OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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@ -145,8 +145,8 @@ subroutine Bethe_Salpeter_Tmatrix(TDA_T,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR
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! Compute BSE triplet excitation energies
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call linear_response(ispin,.true.,TDA,.true.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGT,ERI,OmRPA, &
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rho_RPA,EcBSE(ispin),OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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call linear_response_Tmatrix(ispin,.true.,TDA,.true.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGT,ERI,TA,TB, &
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EcBSE(ispin),OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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call print_excitation('BSE@GT ',ispin,nS,OmBSE(:,ispin))
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call print_transition_vectors(.false.,nBas,nC,nO,nV,nR,nS,dipole_int, &
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OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
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