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https://github.com/pfloos/quack
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113 lines
3.1 KiB
Fortran
113 lines
3.1 KiB
Fortran
subroutine linear_response(ispin,dRPA,TDA,eta,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,Ec,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
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logical,intent(in) :: TDA
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double precision,intent(in) :: eta
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integer,intent(in) :: ispin
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integer,intent(in) :: nBas
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integer,intent(in) :: nC
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integer,intent(in) :: nO
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integer,intent(in) :: nV
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integer,intent(in) :: nR
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integer,intent(in) :: 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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integer :: i,j,k
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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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double precision,allocatable :: tmp(:,:)
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! Output variables
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double precision,intent(out) :: Ec
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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),tmp(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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! 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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! 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*dsqrt(Omega),AmBSq)
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call ADAt(nS,AmB,1d0/dsqrt(Omega),AmBIv)
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call dgemm('N','N',nS,nS,nS,1d0,ApB,size(ApB,1),AmBSq,size(AmBSq,1),0d0,tmp,size(tmp,1))
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call dgemm('N','N',nS,nS,nS,1d0,AmBSq,size(AmBSq,1),tmp,size(tmp,1),0d0,Z,size(Z,1))
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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 = dsqrt(Omega)
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call dgemm('T','N',nS,nS,nS,1d0,Z,size(Z,1),AmBSq,size(AmBSq,1),0d0,XpY,size(XpY,1))
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call DA(nS,1d0/dsqrt(Omega),XpY)
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call dgemm('T','N',nS,nS,nS,1d0,Z,size(Z,1),AmBIv,size(AmBIv,1),0d0,XmY,size(XmY,1))
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call DA(nS,1d0*dsqrt(Omega),XmY)
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end if
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! Compute the RPA correlation energy
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Ec = 0.5d0*(sum(Omega) - trace_matrix(nS,A))
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end subroutine linear_response
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