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quack/src/ADC/ADC2.f90

361 lines
7.9 KiB
Fortran
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subroutine ADC2(ispin,maxSCF,thresh,max_diis,nBas,nC,nO,nV,nR,e,ERI)
! Compute ADC(2) excitation energies: see Schirmer, Cederbaum & Walter, PRA, 28 (1983) 1237
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
integer,intent(in) :: maxSCF
double precision,intent(in) :: thresh
integer,intent(in) :: max_diis
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: nH,nP,nHH,nPP,nSCF,n_diis
double precision :: Conv
double precision,external :: Kronecker_delta
double precision,allocatable :: B_ADC(:,:),X_ADC(:,:),e_ADC(:),SigInf(:,:),G_ADC(:,:)
double precision,allocatable :: db_ERI(:,:,:,:),eOld(:),error_diis(:,:),e_diis(:,:)
integer :: i,j,k,l
integer :: a,b,c,d
integer :: p,q,r,s
integer :: nADC,iADC,jADC
! Hello world
write(*,*)
write(*,*)'***********************************'
write(*,*)'| 2nd-order ADC calculation |'
write(*,*)'***********************************'
write(*,*)
! Number of holes
nH = nO - nC
nHH = nH*(nH+1)/2
! Number of particles
nP = nV - nR
nPP = nP*(nP+1)/2
write(*,*) 'Total states: ',nH+nP
write(*,*) 'Hole states: ',nH
write(*,*) 'Particle states: ',nP
! Size of ADC(2) matrices
nADC = nH + nP + nH*nPP + nHH*nP
write(*,'(1X,A25,I3,A6,I6)') 'Size of ADC(2) matrices: ',nADC,' x ',nADC
! Memory allocation
allocate(db_ERI(nBas,nBas,nBas,nBas),error_diis(nADC,max_diis),e_diis(nADC,max_diis),eOld(nADC), &
B_ADC(nADC,nADC),X_ADC(nADC,nADC),e_ADC(nADC),G_ADC(nBas,nBas),SigInf(nBas,nBas))
! Create double-bar MO integrals
call antisymmetrize_ERI(ispin,nBas,ERI,db_ERI)
! Initialization
Conv = 1d0
nSCF = 0
n_diis = 0
e_diis(:,:) = 0d0
error_diis(:,:) = 0d0
SigInf(:,:) = 0d0
eOld(:) = 0d0
!------------------------------------------------------------------------
! Main SCF loop
!------------------------------------------------------------------------
!
! | e + SigInf (U^I)^t (U^II)^t |
! | |
! B = | U^I K^I + C^I 0 |
! | |
! | U^II 0 K^II + C^II |
!
!
do while(Conv > thresh .and. nSCF < maxSCF)
!
! Build ADC(2) B matrix -- Eq. (38b) --
!
write(*,'(1X,A7,1X,I4)') 'Cycle: ',nSCF
!
! Diagonal part: static self-energy and epsilon
!
B_ADC(:,:) = 0d0
B_ADC(nC+1:nBas-nR,nC+1:nBas-nR) = SigInf(nC+1:nBas-nR,nC+1:nBas-nR)
jADC = 0
do p=nC+1,nBas-nR
jADC = jADC + 1
B_ADC(jADC,jADC) = e(p)
enddo
!
! U matrices -- Eq. (40a) --
!
do p=nC+1,nBas-nR
iADC = p - nC
jADC = nH + nP
! U^I: 2p-1h -- Eqs. (40a) and (41a) --
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=a,nBas-nR
jADC = jADC + 1
B_ADC(iADC,jADC) = db_ERI(p,i,a,b)
enddo
enddo
enddo
! U^II: 2h-1p -- Eqs. (40a) and (41b) --
do i=nC+1,nO
do j=i,nO
do a=nO+1,nBas-nR
jADC = jADC + 1
B_ADC(iADC,jADC) = db_ERI(p,a,i,j)
enddo
enddo
enddo
enddo
!
! K matrices -- Eq. (40b) --
!
! K^I: 2p-1h -- Eqs. (40b) and (41a) --
jADC = nH + nP
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=a,nBas-nR
jADC = jADC + 1
B_ADC(jADC,jADC) = e(a) + e(b) - e(i)
enddo
enddo
enddo
! K^II: 2h-1p -- Eqs. (40b) and (41b) --
do i=nC+1,nO
do j=i,nO
do a=nO+1,nBas-nR
jADC = jADC + 1
B_ADC(jADC,jADC) = e(i) + e(j) - e(a)
enddo
enddo
enddo
!
! C matrices -- Eq. (42c)
!
! C^I: 2p-1h-TDA -- Eqs. (42a) and (42c) --
iADC = nH + nP
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=a,nBas-nR
iADC = iADC + 1
jADC = nH + nP
do j=nC+1,nO
do c=nO+1,nBas-nR
do d=c,nBas-nR
jADC = jADC + 1
B_ADC(iADC,jADC) = B_ADC(iADC,jADC) &
+ db_ERI(a,b,c,d)*Kronecker_delta(i,j) &
- db_ERI(j,b,i,d)*Kronecker_delta(a,c) &
- db_ERI(j,a,i,c)*Kronecker_delta(b,d) &
+ db_ERI(b,a,c,d)*Kronecker_delta(i,j) &
- db_ERI(j,a,i,d)*Kronecker_delta(b,c) &
- db_ERI(j,b,i,c)*Kronecker_delta(a,d)
enddo
enddo
enddo
enddo
enddo
enddo
! C^II: 2p-1h-TDA -- Eqs. (42b) and (42c) --
iADC = nH + nP + nH * nPP
do i=nC+1,nO
do j=i,nO
do a=nO+1,nBas-nR
iADC = iADC + 1
jADC = nH + nP + nH*nPP
do k=nC+1,nO
do l=k,nO
do b=nO+1,nBas-nR
jADC = jADC + 1
B_ADC(iADC,jADC) = B_ADC(iADC,jADC) &
- db_ERI(i,j,k,l)*Kronecker_delta(a,b) &
+ db_ERI(b,j,a,l)*Kronecker_delta(i,k) &
+ db_ERI(b,i,a,k)*Kronecker_delta(j,l) &
- db_ERI(j,i,k,l)*Kronecker_delta(a,b) &
+ db_ERI(b,i,a,l)*Kronecker_delta(j,k) &
+ db_ERI(b,j,a,k)*Kronecker_delta(i,l)
enddo
enddo
enddo
enddo
enddo
enddo
! Fold B onto itself
do iADC=1,nADC
do jADC=iADC+1,nADC
B_ADC(jADC,iADC) = B_ADC(iADC,jADC)
enddo
enddo
! Diagonalize B to obtain X and E -- Eq. (38a) --
X_ADC(:,:) = B_ADC(:,:)
call diagonalize_matrix(nADC,X_ADC,e_ADC)
! print results
write(*,*) '================================='
write(*,*) 'ADC(2) excitation energies (eV)'
do iADC=1,nADC
! if(NORM2(X_ADC(1:nH+nP,iADC)) > 0.1d0 ) &
write(*,'(2(2X,F12.6))') e_ADC(iADC)*HaToeV,NORM2(X_ADC(1:nH+nP,iADC))
enddo
write(*,*) '================================='
! Convergence criteria
Conv = maxval(abs(e_ADC - eOld))
! Store result for next iteration
eOld(:) = e_ADC(:)
! Compute W -- Eq (11) --
SigInf(:,:) = 0d0
do i=nC+1,nO
do p=nC+1,nBas-nR
do q=nC+1,nBas-nR
SigInf(p,q) = SigInf(p,q) - db_ERI(p,i,q,i)
enddo
enddo
enddo
! Compute the one-particle Greeen function -- Eq. (28) --
G_ADC(:,:) = 0d0
do iADC=1,nADC
if(e_ADC(iADC) > 0d0 ) cycle
do p=nC+1,nBas-nR
do q=nC+1,nBas-nR
G_ADC(p,q) = G_ADC(p,q) + X_ADC(p,iADC)*X_ADC(q,iADC)
enddo
enddo
enddo
! Compute static self-energy for next iteration -- Eq. (25) --
do r=nC+1,nBas-nR
do s=nC+1,nBas-nR
do p=nC+1,nBas-nR
do q=nC+1,nBas-nR
SigInf(p,q) = SigInf(p,q) + db_ERI(p,r,q,s)*G_ADC(r,s)
enddo
enddo
enddo
enddo
! Print results
! call print_ADC2(nBas,nO,nSCF,Conv,e,eADC)
! Increment
nSCF = nSCF + 1
enddo
!------------------------------------------------------------------------
! End main SCF loop
!------------------------------------------------------------------------
! Did it actually converge?
if(nSCF == maxSCF+1) then
write(*,*)
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)' Convergence failed '
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)
endif
end subroutine ADC2
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