subroutine ufG0W0(dotest,TDA_W,nBas,nC,nO,nV,nR,nS,ENuc,ERHF,ERI,eHF) ! Unfold G0W0 equations implicit none include 'parameters.h' ! Input variables logical,intent(in) :: dotest logical,intent(in) :: TDA_W integer,intent(in) :: nBas integer,intent(in) :: nC integer,intent(in) :: nO integer,intent(in) :: nV integer,intent(in) :: nR integer,intent(in) :: nS double precision,intent(in) :: ENuc double precision,intent(in) :: ERHF double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas) double precision,intent(in) :: eHF(nBas) ! Local variables integer :: p integer :: s integer :: i,j,k,l integer :: a,b,c,d integer :: jb,kc,ia,ja integer :: klc,kcd,ija,ijb,iab,jab logical :: print_W = .false. logical :: dRPA integer :: ispin double precision :: EcRPA integer :: n2h1p,n2p1h,nH double precision,external :: Kronecker_delta double precision,allocatable :: H(:,:) double precision,allocatable :: eGW(:) double precision,allocatable :: Z(:) double precision,allocatable :: Aph(:,:) double precision,allocatable :: Bph(:,:) double precision,allocatable :: Om(:) double precision,allocatable :: XpY(:,:) double precision,allocatable :: XmY(:,:) double precision,allocatable :: rho(:,:,:) logical :: verbose = .true. double precision,parameter :: cutoff1 = 0.01d0 double precision,parameter :: cutoff2 = 0.01d0 double precision :: eF double precision,parameter :: window = 1.5d0 double precision :: start_timing,end_timing,timing ! Output variables ! Hello world write(*,*) write(*,*)'****************************************' write(*,*)'* Restricted Upfolded G0W0 Calculation *' write(*,*)'****************************************' write(*,*) ! Dimension of the supermatrix n2h1p = nO*nO*nV n2p1h = nV*nV*nO nH = 1 + n2h1p + n2p1h ! Memory allocation allocate(H(nH,nH),eGW(nH),Z(nH)) ! Initialization dRPA = .true. EcRPA = 0d0 eF = 0.5d0*(eHF(nO+1) + eHF(nO)) !-------------------! ! Compute screening ! !-------------------! if(.not. TDA_W) then ! Spin manifold ispin = 1 ! Memory allocation allocate(Om(nS),Aph(nS,nS),Bph(nS,nS),XpY(nS,nS),XmY(nS,nS),rho(nBas,nBas,nS)) call phLR_A(ispin,dRPA,nBas,nC,nO,nV,nR,nS,1d0,eHF,ERI,Aph) call phLR_B(ispin,dRPA,nBas,nC,nO,nV,nR,nS,1d0,ERI,Bph) call phLR(TDA_W,nS,Aph,Bph,EcRPA,Om,XpY,XmY) if(print_W) call print_excitation_energies('phRPA@RHF','singlet',nS,Om) !--------------------------! ! Compute spectral weights ! !--------------------------! call GW_excitation_density(nBas,nC,nO,nR,nS,ERI,XpY,rho) deallocate(Aph,Bph,XpY,XmY) end if !-------------------------! ! Main loop over orbitals ! !-------------------------! do p=nO-3,nO H(:,:) = 0d0 if(TDA_W) then ! TDA for W write(*,*) 'Tamm-Dancoff approximation actived!' write(*,*) !---------------------------! ! Compute GW supermatrix ! !---------------------------! ! ! ! | F V2h1p V2p1h | ! ! | | ! ! H = | V2h1p C2h1p 0 | ! ! | | ! ! | V2p1h 0 C2p1h | ! ! ! !---------------------------! call wall_time(start_timing) !---------! ! Block F ! !---------! H(1,1) = eHF(p) !-------------! ! Block V2h1p ! !-------------! ija = 0 do i=nC+1,nO do j=nC+1,nO do a=nO+1,nBas-nR ija = ija + 1 H(1 ,1+ija) = sqrt(2d0)*ERI(p,a,i,j) H(1+ija,1 ) = sqrt(2d0)*ERI(p,a,i,j) end do end do end do !-------------! ! Block V2p1h ! !-------------! iab = 0 do i=nC+1,nO do a=nO+1,nBas-nR do b=nO+1,nBas-nR iab = iab + 1 H(1 ,1+n2h1p+iab) = sqrt(2d0)*ERI(p,i,b,a) H(1+n2h1p+iab,1 ) = sqrt(2d0)*ERI(p,i,b,a) end do end do end do !-------------! ! Block C2h1p ! !-------------! ija = 0 do i=nC+1,nO do j=nC+1,nO do a=nO+1,nBas-nR ija = ija + 1 klc = 0 do k=nC+1,nO do l=nC+1,nO do c=nO+1,nBas-nR klc = klc + 1 H(1+ija,1+klc) & = ((eHF(i) + eHF(j) - eHF(a))*Kronecker_delta(j,l)*Kronecker_delta(a,c) & - 2d0*ERI(j,c,a,l))*Kronecker_delta(i,k) end do end do end do end do end do end do !-------------! ! Block C2p1h ! !-------------! iab = 0 do i=nC+1,nO do a=nO+1,nBas-nR do b=nO+1,nBas-nR iab = iab + 1 kcd = 0 do k=nC+1,nO do c=nO+1,nBas-nR do d=nO+1,nBas-nR kcd = kcd + 1 H(1+n2h1p+iab,1+n2h1p+kcd) & = ((eHF(a) + eHF(b) - eHF(i))*Kronecker_delta(i,k)*Kronecker_delta(a,c) & + 2d0*ERI(a,k,i,c))*Kronecker_delta(b,d) end do end do end do end do end do end do call wall_time(end_timing) timing = end_timing - start_timing write(*,*) write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for construction of supermatrix = ',timing,' seconds' write(*,*) else write(*,*) 'Tamm-Dancoff approximation deactivated!' write(*,*) !---------------------------! ! Compute GW supermatrix ! !---------------------------! ! ! ! | F W2h1p W2p1h | ! ! | | ! ! H = | W2h1p D2h1p 0 | ! ! | | ! ! | W2p1h 0 D2p1h | ! ! ! !---------------------------! call wall_time(start_timing) !---------! ! Block F ! !---------! H(1,1) = eHF(p) !-------------! ! Block D2h1p ! !-------------! ija = 0 do i=nC+1,nO do ja=1,nS ija = ija + 1 H(1+ija,1+ija) = eHF(i) - Om(ja) end do end do !-------------! ! Block W2h1p ! !-------------! ija = 0 do i=nC+1,nO do ja=1,nS ija = ija + 1 H(1 ,1+ija) = sqrt(2d0)*rho(p,i,ja) H(1+ija,1 ) = sqrt(2d0)*rho(p,i,ja) end do end do !-------------! ! Block D2p1h ! !-------------! iab = 0 do ia=1,nS do b=nO+1,nBas-nR iab = iab + 1 H(1+n2h1p+iab,1+n2h1p+iab) = eHF(b) + Om(ia) end do end do !-------------! ! Block W2p1h ! !-------------! iab = 0 do ia=1,nS do b=nO+1,nBas-nR iab = iab + 1 H(1 ,1+n2h1p+iab) = sqrt(2d0)*rho(p,b,ia) H(1+n2h1p+iab,1 ) = sqrt(2d0)*rho(p,b,ia) end do end do call wall_time(end_timing) timing = end_timing - start_timing write(*,*) write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for construction of supermatrix = ',timing,' seconds' write(*,*) end if !-------------------------! ! Diagonalize supermatrix ! !-------------------------! call wall_time(start_timing) call diagonalize_matrix(nH,H,eGW) call wall_time(end_timing) timing = end_timing - start_timing write(*,*) write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for diagonalization of supermatrix = ',timing,' seconds' write(*,*) !-----------------! ! Compute weights ! !-----------------! do s=1,nH Z(s) = H(1,s)**2 end do !--------------! ! Dump results ! !--------------! write(*,*)'-------------------------------------------' write(*,'(1X,A32,I3,A8)')'| G0W0 energies (eV) for orbital',p,' |' write(*,*)'-------------------------------------------' write(*,'(1X,A1,1X,A3,1X,A1,1X,A15,1X,A1,1X,A15,1X,A1,1X,A15,1X)') & '|','#','|','e_QP','|','Z','|' write(*,*)'-------------------------------------------' do s=1,nH if(eGW(s) < eF .and. eGW(s) > eF - window) then ! if(Z(s) > cutoff1) then write(*,'(1X,A1,1X,I3,1X,A1,1X,F15.6,1X,A1,1X,F15.6,1X,A1,1X)') & '|',s,'|',eGW(s)*HaToeV,'|',Z(s),'|' end if end do write(*,*)'-------------------------------------------' write(*,*) if(verbose) then if(TDA_W) then ! TDA printing format do s=1,nH if(eGW(s) < eF .and. eGW(s) > eF - window) then write(*,*)'-------------------------------------------------------------' write(*,'(1X,A7,1X,I3,A6,I3,A1,1X,A7,F12.6,A13,F6.4,1X)') & 'Orbital',p,' and #',s,':','e_QP = ',eGW(s)*HaToeV,' eV and Z = ',Z(s) write(*,*)'-------------------------------------------------------------' write(*,'(1X,A20,1X,A20,1X,A15,1X)') & ' Configuration ',' Coefficient ',' Weight ' write(*,*)'-------------------------------------------------------------' if(p <= nO) & write(*,'(1X,A7,I3,A16,1X,F15.6,1X,F15.6)') & ' (',p,') ',H(1,s),H(1,s)**2 if(p > nO) & write(*,'(1X,A16,I3,A7,1X,F15.6,1X,F15.6)') & ' (',p,') ',H(1,s),H(1,s)**2 ija = 0 do i=nC+1,nO do j=nC+1,nO do a=nO+1,nBas-nR ija = ija + 1 if(abs(H(1+ija,s)) > cutoff2) & write(*,'(1X,A3,I3,A1,I3,A6,I3,A7,1X,F15.6,1X,F15.6)') & ' (',i,',',j,') -> (',a,') ',H(1+ija,s),H(1+ija,s)**2 end do end do end do iab = 0 do i=nC+1,nO do a=nO+1,nBas-nR do b=nO+1,nBas-nR iab = iab + 1 if(abs(H(1+n2h1p+iab,s)) > cutoff2) & write(*,'(1X,A7,I3,A6,I3,A1,I3,A3,1X,F15.6,1X,F15.6)') & ' (',i,') -> (',a,',',b,') ',H(1+n2h1p+iab,s),H(1+n2h1p+iab,s)**2 end do end do end do write(*,*)'-------------------------------------------------------------' write(*,*) end if end do else ! non-TDA printing format do s=1,nH if(eGW(s) < eF .and. eGW(s) > eF - window) then write(*,*)'-------------------------------------------------------------' write(*,'(1X,A7,1X,I3,A6,I3,A1,1X,A7,F12.6,A13,F6.4,1X)') & 'Orbital',p,' and #',s,':','e_QP = ',eGW(s)*HaToeV,' eV and Z = ',Z(s) write(*,*)'-------------------------------------------------------------' write(*,'(1X,A20,1X,A20,1X,A15,1X)') & ' Conf. (p,ia) ',' Coefficient ',' Weight ' write(*,*)'-------------------------------------------------------------' if(p <= nO) & write(*,'(1X,A7,I3,A16,1X,F15.6,1X,F15.6)') & ' (',p,') ',H(1,s),H(1,s)**2 if(p > nO) & write(*,'(1X,A16,I3,A7,1X,F15.6,1X,F15.6)') & ' (',p,') ',H(1,s),H(1,s)**2 ija = 0 do i=nC+1,nO do ja=1,nS ija = ija + 1 if(abs(H(1+ija,s)) > cutoff2) & write(*,'(1X,A7,I3,A1,I3,A12,1X,F15.6,1X,F15.6)') & ' (',i,',',ja,') ',H(1+ija,s),H(1+ija,s)**2 end do end do iab = 0 do ia=1,nS do b=nO+1,nBas-nR iab = iab + 1 if(abs(H(1+n2h1p+iab,s)) > cutoff2) & write(*,'(1X,A7,I3,A1,I3,A12,1X,F15.6,1X,F15.6)') & ' (',ia,',',b,') ',H(1+n2h1p+iab,s),H(1+n2h1p+iab,s)**2 end do end do write(*,*)'-------------------------------------------------------------' write(*,*) end if ! If state s should be print end do ! Loop on s end if ! If TDA end if ! If verbose end do ! Loop on the orbital in the e block end subroutine