2019-03-19 10:13:33 +01:00
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subroutine ADC2(ispin,maxSCF,thresh,max_diis,nBas,nC,nO,nV,nR,e,ERI)
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! Compute ADC(2) excitation energies: see Schirmer, Cederbaum & Walter, PRA, 28 (1983) 1237
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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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integer,intent(in) :: maxSCF
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double precision,intent(in) :: thresh
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integer,intent(in) :: max_diis
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integer,intent(in) :: nBas,nC,nO,nV,nR
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2019-05-04 17:13:50 +02:00
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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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2019-03-19 10:13:33 +01:00
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! Local variables
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integer :: nH,nP,nHH,nPP,nSCF,n_diis
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double precision :: Conv
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double precision,external :: Kronecker_delta
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double precision,allocatable :: B_ADC(:,:),X_ADC(:,:),e_ADC(:),SigInf(:,:),G_ADC(:,:)
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double precision,allocatable :: db_ERI(:,:,:,:),eOld(:),error_diis(:,:),e_diis(:,:)
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integer :: i,j,k,l
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integer :: a,b,c,d
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integer :: p,q,r,s
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integer :: nADC,iADC,jADC
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! Hello world
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write(*,*)
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write(*,*)'***********************************'
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write(*,*)'| 2nd-order ADC calculation |'
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write(*,*)'***********************************'
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write(*,*)
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! Number of holes
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nH = nO - nC
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nHH = nH*(nH+1)/2
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! Number of particles
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nP = nV - nR
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nPP = nP*(nP+1)/2
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write(*,*) 'Total states: ',nH+nP
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write(*,*) 'Hole states: ',nH
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write(*,*) 'Particle states: ',nP
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! Size of ADC(2) matrices
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nADC = nH + nP + nH*nPP + nHH*nP
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write(*,'(1X,A25,I3,A6,I6)') 'Size of ADC(2) matrices: ',nADC,' x ',nADC
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! Memory allocation
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2019-05-04 17:13:50 +02:00
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allocate(db_ERI(nBas,nBas,nBas,nBas),error_diis(nADC,max_diis),e_diis(nADC,max_diis),eOld(nADC), &
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B_ADC(nADC,nADC),X_ADC(nADC,nADC),e_ADC(nADC),G_ADC(nBas,nBas),SigInf(nBas,nBas))
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2019-03-19 10:13:33 +01:00
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! Create double-bar MO integrals
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call antisymmetrize_ERI(ispin,nBas,ERI,db_ERI)
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! Initialization
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Conv = 1d0
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nSCF = 0
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n_diis = 0
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e_diis(:,:) = 0d0
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error_diis(:,:) = 0d0
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SigInf(:,:) = 0d0
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eOld(:) = 0d0
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!------------------------------------------------------------------------
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! Main SCF loop
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!------------------------------------------------------------------------
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!
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! | e + SigInf (U^I)^t (U^II)^t |
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! | |
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! B = | U^I K^I + C^I 0 |
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! | |
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! | U^II 0 K^II + C^II |
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!
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!
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do while(Conv > thresh .and. nSCF < maxSCF)
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!
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! Build ADC(2) B matrix -- Eq. (38b) --
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!
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write(*,'(1X,A7,1X,I4)') 'Cycle: ',nSCF
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!
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! Diagonal part: static self-energy and epsilon
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!
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B_ADC(:,:) = 0d0
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2019-05-04 17:13:50 +02:00
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B_ADC(nC+1:nBas-nR,nC+1:nBas-nR) = SigInf(nC+1:nBas-nR,nC+1:nBas-nR)
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2019-03-19 10:13:33 +01:00
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jADC = 0
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2019-05-04 17:13:50 +02:00
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do p=nC+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(jADC,jADC) = e(p)
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enddo
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!
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! U matrices -- Eq. (40a) --
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!
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2019-05-04 17:13:50 +02:00
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do p=nC+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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iADC = p - nC
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jADC = nH + nP
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! U^I: 2p-1h -- Eqs. (40a) and (41a) --
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do i=nC+1,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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do b=a,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(iADC,jADC) = db_ERI(p,i,a,b)
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enddo
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enddo
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enddo
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! U^II: 2h-1p -- Eqs. (40a) and (41b) --
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do i=nC+1,nO
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do j=i,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(iADC,jADC) = db_ERI(p,a,i,j)
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enddo
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enddo
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enddo
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enddo
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!
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! K matrices -- Eq. (40b) --
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!
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! K^I: 2p-1h -- Eqs. (40b) and (41a) --
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jADC = nH + nP
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do i=nC+1,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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do b=a,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(jADC,jADC) = e(a) + e(b) - e(i)
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enddo
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enddo
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enddo
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! K^II: 2h-1p -- Eqs. (40b) and (41b) --
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do i=nC+1,nO
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do j=i,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(jADC,jADC) = e(i) + e(j) - e(a)
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enddo
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enddo
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enddo
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!
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! C matrices -- Eq. (42c)
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!
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! C^I: 2p-1h-TDA -- Eqs. (42a) and (42c) --
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iADC = nH + nP
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do i=nC+1,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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do b=a,nBas-nR
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2019-03-19 10:13:33 +01:00
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iADC = iADC + 1
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jADC = nH + nP
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do j=nC+1,nO
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2019-05-04 17:13:50 +02:00
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do c=nO+1,nBas-nR
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do d=c,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(iADC,jADC) = B_ADC(iADC,jADC) &
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+ db_ERI(a,b,c,d)*Kronecker_delta(i,j) &
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- db_ERI(j,b,i,d)*Kronecker_delta(a,c) &
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- db_ERI(j,a,i,c)*Kronecker_delta(b,d) &
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+ db_ERI(b,a,c,d)*Kronecker_delta(i,j) &
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- db_ERI(j,a,i,d)*Kronecker_delta(b,c) &
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- db_ERI(j,b,i,c)*Kronecker_delta(a,d)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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! C^II: 2p-1h-TDA -- Eqs. (42b) and (42c) --
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iADC = nH + nP + nH * nPP
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do i=nC+1,nO
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do j=i,nO
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2019-05-04 17:13:50 +02:00
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do a=nO+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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iADC = iADC + 1
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jADC = nH + nP + nH*nPP
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do k=nC+1,nO
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do l=k,nO
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2019-05-04 17:13:50 +02:00
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do b=nO+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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jADC = jADC + 1
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B_ADC(iADC,jADC) = B_ADC(iADC,jADC) &
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- db_ERI(i,j,k,l)*Kronecker_delta(a,b) &
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+ db_ERI(b,j,a,l)*Kronecker_delta(i,k) &
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+ db_ERI(b,i,a,k)*Kronecker_delta(j,l) &
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- db_ERI(j,i,k,l)*Kronecker_delta(a,b) &
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+ db_ERI(b,i,a,l)*Kronecker_delta(j,k) &
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+ db_ERI(b,j,a,k)*Kronecker_delta(i,l)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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! Fold B onto itself
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do iADC=1,nADC
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do jADC=iADC+1,nADC
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B_ADC(jADC,iADC) = B_ADC(iADC,jADC)
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enddo
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enddo
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! Diagonalize B to obtain X and E -- Eq. (38a) --
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X_ADC(:,:) = B_ADC(:,:)
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call diagonalize_matrix(nADC,X_ADC,e_ADC)
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! print results
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write(*,*) '================================='
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write(*,*) 'ADC(2) excitation energies (eV)'
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do iADC=1,nADC
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2019-05-04 17:13:50 +02:00
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! if(NORM2(X_ADC(1:nH+nP,iADC)) > 0.1d0 ) &
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2019-03-19 10:13:33 +01:00
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write(*,'(2(2X,F12.6))') e_ADC(iADC)*HaToeV,NORM2(X_ADC(1:nH+nP,iADC))
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enddo
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write(*,*) '================================='
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! Convergence criteria
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Conv = maxval(abs(e_ADC - eOld))
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! Store result for next iteration
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eOld(:) = e_ADC(:)
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! Compute W -- Eq (11) --
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SigInf(:,:) = 0d0
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do i=nC+1,nO
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2019-05-04 17:13:50 +02:00
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do p=nC+1,nBas-nR
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do q=nC+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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SigInf(p,q) = SigInf(p,q) - db_ERI(p,i,q,i)
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enddo
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enddo
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enddo
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! Compute the one-particle Greeen function -- Eq. (28) --
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G_ADC(:,:) = 0d0
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do iADC=1,nADC
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if(e_ADC(iADC) > 0d0 ) cycle
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2019-05-04 17:13:50 +02:00
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do p=nC+1,nBas-nR
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do q=nC+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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G_ADC(p,q) = G_ADC(p,q) + X_ADC(p,iADC)*X_ADC(q,iADC)
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enddo
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enddo
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enddo
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! Compute static self-energy for next iteration -- Eq. (25) --
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2019-05-04 17:13:50 +02:00
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do r=nC+1,nBas-nR
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do s=nC+1,nBas-nR
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do p=nC+1,nBas-nR
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do q=nC+1,nBas-nR
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2019-03-19 10:13:33 +01:00
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SigInf(p,q) = SigInf(p,q) + db_ERI(p,r,q,s)*G_ADC(r,s)
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enddo
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enddo
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enddo
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enddo
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! Print results
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! call print_ADC2(nBas,nO,nSCF,Conv,e,eADC)
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! Increment
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nSCF = nSCF + 1
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enddo
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!------------------------------------------------------------------------
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! End main SCF loop
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!------------------------------------------------------------------------
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! Did it actually converge?
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if(nSCF == maxSCF+1) then
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write(*,*)
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write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
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write(*,*)' Convergence failed '
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write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
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write(*,*)
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endif
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end subroutine ADC2
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