2022-11-29 12:11:09 +01:00
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subroutine SRG_qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,BSE2,TDA_W,TDA, &
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dBSE,dTDA,evDyn,singlet,triplet,eta,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,ERHF, &
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S,X,T,V,Hc,ERI_AO,ERI_MO,dipole_int_AO,dipole_int_MO,PHF,cHF,eHF)
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! Perform a quasiparticle self-consistent GW calculation
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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) :: maxSCF
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integer,intent(in) :: max_diis
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double precision,intent(in) :: thresh
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logical,intent(in) :: doACFDT
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logical,intent(in) :: exchange_kernel
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logical,intent(in) :: doXBS
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logical,intent(in) :: BSE
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logical,intent(in) :: BSE2
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logical,intent(in) :: TDA_W
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logical,intent(in) :: TDA
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logical,intent(in) :: dBSE
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logical,intent(in) :: dTDA
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logical,intent(in) :: evDyn
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logical,intent(in) :: singlet
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logical,intent(in) :: triplet
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double precision,intent(in) :: eta
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integer,intent(in) :: nNuc
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double precision,intent(in) :: ZNuc(nNuc)
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double precision,intent(in) :: rNuc(nNuc,ncart)
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double precision,intent(in) :: ENuc
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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) :: ERHF
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double precision,intent(in) :: eHF(nBas)
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double precision,intent(in) :: cHF(nBas,nBas)
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double precision,intent(in) :: PHF(nBas,nBas)
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double precision,intent(in) :: S(nBas,nBas)
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double precision,intent(in) :: T(nBas,nBas)
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double precision,intent(in) :: V(nBas,nBas)
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double precision,intent(in) :: Hc(nBas,nBas)
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double precision,intent(in) :: X(nBas,nBas)
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double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas)
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double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas)
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double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
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double precision,intent(in) :: dipole_int_MO(nBas,nBas,ncart)
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! Local variables
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integer :: nSCF
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integer :: nBasSq
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integer :: ispin
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integer :: n_diis
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double precision :: ET
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double precision :: EV
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double precision :: EJ
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double precision :: Ex
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double precision :: EqsGW
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double precision :: EcRPA
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double precision :: EcBSE(nspin)
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double precision :: EcAC(nspin)
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double precision :: EcGM
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double precision :: Conv
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double precision :: rcond
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double precision,external :: trace_matrix
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double precision :: dipole(ncart)
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logical :: print_W = .false.
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double precision,allocatable :: error_diis(:,:)
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double precision,allocatable :: F_diis(:,:)
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double precision,allocatable :: OmRPA(:)
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double precision,allocatable :: XpY_RPA(:,:)
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double precision,allocatable :: XmY_RPA(:,:)
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double precision,allocatable :: rho_RPA(:,:,:)
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double precision,allocatable :: c(:,:)
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double precision,allocatable :: cp(:,:)
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double precision,allocatable :: eGW(:)
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double precision,allocatable :: eOld(:)
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double precision,allocatable :: P(:,:)
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double precision,allocatable :: F(:,:)
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double precision,allocatable :: Fp(:,:)
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double precision,allocatable :: J(:,:)
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double precision,allocatable :: K(:,:)
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double precision,allocatable :: SigC(:,:)
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double precision,allocatable :: Z(:)
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double precision,allocatable :: error(:,:)
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! Hello world
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write(*,*)
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write(*,*)'************************************************'
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write(*,*)'| Self-consistent SRG-qsGW calculation |'
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write(*,*)'************************************************'
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write(*,*)
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! Warning
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write(*,*) '!! ERIs in MO basis will be overwritten in qsGW !!'
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write(*,*)
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! Stuff
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nBasSq = nBas*nBas
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! TDA for W
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if(TDA_W) then
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write(*,*) 'Tamm-Dancoff approximation for dynamic screening!'
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write(*,*)
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end if
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! TDA
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if(TDA) then
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write(*,*) 'Tamm-Dancoff approximation activated!'
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write(*,*)
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end if
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! Memory allocation
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allocate(eGW(nBas),eOld(nBas),c(nBas,nBas),cp(nBas,nBas),P(nBas,nBas),F(nBas,nBas),Fp(nBas,nBas), &
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J(nBas,nBas),K(nBas,nBas),SigC(nBas,nBas),Z(nBas),OmRPA(nS),XpY_RPA(nS,nS),XmY_RPA(nS,nS), &
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rho_RPA(nBas,nBas,nS),error(nBas,nBas),error_diis(nBasSq,max_diis),F_diis(nBasSq,max_diis))
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! Initialization
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nSCF = -1
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n_diis = 0
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ispin = 1
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Conv = 1d0
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P(:,:) = PHF(:,:)
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eGW(:) = eHF(:)
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eOld(:) = eHF(:)
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c(:,:) = cHF(:,:)
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F_diis(:,:) = 0d0
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error_diis(:,:) = 0d0
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rcond = 0d0
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2022-11-29 14:47:51 +01:00
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print*,max_diis
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2022-11-29 12:11:09 +01:00
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!------------------------------------------------------------------------
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! Main loop
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!------------------------------------------------------------------------
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do while(Conv > thresh .and. nSCF <= maxSCF)
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! Increment
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nSCF = nSCF + 1
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! Buid Coulomb matrix
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call Coulomb_matrix_AO_basis(nBas,P,ERI_AO,J)
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! Compute exchange part of the self-energy
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call exchange_matrix_AO_basis(nBas,P,ERI_AO,K)
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! AO to MO transformation of two-electron integrals
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call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO)
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! Compute linear response
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call linear_response(ispin,.true.,TDA_W,eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,ERI_MO, &
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EcRPA,OmRPA,XpY_RPA,XmY_RPA)
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if(print_W) call print_excitation('RPA@qsGW ',ispin,nS,OmRPA)
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! Compute correlation part of the self-energy
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call excitation_density(nBas,nC,nO,nR,nS,ERI_MO,XpY_RPA,rho_RPA)
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call self_energy_correlation_SRG(eta,nBas,nC,nO,nV,nR,nS,eGW,OmRPA,rho_RPA,EcGM,SigC)
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call renormalization_factor_SRG(eta,nBas,nC,nO,nV,nR,nS,eGW,OmRPA,rho_RPA,Z)
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! Make correlation self-energy Hermitian and transform it back to AO basis
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call MOtoAO_transform(nBas,S,c,SigC)
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! Solve the quasi-particle equation
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F(:,:) = Hc(:,:) + J(:,:) + 0.5d0*K(:,:) + SigC(:,:)
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! Compute commutator and convergence criteria
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error = matmul(F,matmul(P,S)) - matmul(matmul(S,P),F)
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! DIIS extrapolation
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2022-11-29 14:47:51 +01:00
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if(max_diis > 1) then
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n_diis = min(n_diis+1,max_diis)
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2022-11-29 12:11:09 +01:00
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call DIIS_extrapolation(rcond,nBasSq,nBasSq,n_diis,error_diis,F_diis,error,F)
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2022-11-29 14:47:51 +01:00
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2022-11-29 12:11:09 +01:00
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end if
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! Diagonalize Hamiltonian in AO basis
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Fp = matmul(transpose(X),matmul(F,X))
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cp(:,:) = Fp(:,:)
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call diagonalize_matrix(nBas,cp,eGW)
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c = matmul(X,cp)
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SigC = matmul(transpose(c),matmul(SigC,c))
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! Compute new density matrix in the AO basis
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P(:,:) = 2d0*matmul(c(:,1:nO),transpose(c(:,1:nO)))
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! Save quasiparticles energy for next cycle
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2022-11-29 14:47:51 +01:00
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Conv = maxval(abs(error))
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2022-11-29 12:11:09 +01:00
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eOld(:) = eGW(:)
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!------------------------------------------------------------------------
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! Compute total energy
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!------------------------------------------------------------------------
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! Kinetic energy
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ET = trace_matrix(nBas,matmul(P,T))
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! Potential energy
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EV = trace_matrix(nBas,matmul(P,V))
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! Coulomb energy
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EJ = 0.5d0*trace_matrix(nBas,matmul(P,J))
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! Exchange energy
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Ex = 0.25d0*trace_matrix(nBas,matmul(P,K))
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! Total energy
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EqsGW = ET + EV + EJ + Ex
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! Print results
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call dipole_moment(nBas,P,nNuc,ZNuc,rNuc,dipole_int_AO,dipole)
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call print_qsGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,SigC,Z,ENuc,ET,EV,EJ,Ex,EcGM,EcRPA,EqsGW,dipole)
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enddo
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!------------------------------------------------------------------------
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! End main 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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stop
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endif
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! Deallocate memory
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deallocate(c,cp,P,F,Fp,J,K,SigC,Z,OmRPA,XpY_RPA,XmY_RPA,rho_RPA,error,error_diis,F_diis)
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! Perform BSE calculation
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if(BSE) then
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call Bethe_Salpeter(BSE2,TDA_W,TDA,dBSE,dTDA,evDyn,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI_MO,dipole_int_MO, &
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eGW,eGW,EcBSE)
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if(exchange_kernel) then
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EcBSE(1) = 0.5d0*EcBSE(1)
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EcBSE(2) = 1.5d0*EcBSE(2)
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end if
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write(*,*)
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write(*,*)'-------------------------------------------------------------------------------'
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write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy (singlet) =',EcBSE(1)
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write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy (triplet) =',EcBSE(2)
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write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy =',EcBSE(1) + EcBSE(2)
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write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW total energy =',ENuc + EqsGW + EcBSE(1) + EcBSE(2)
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write(*,*)'-------------------------------------------------------------------------------'
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write(*,*)
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! Compute the BSE correlation energy via the adiabatic connection
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if(doACFDT) then
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write(*,*) '------------------------------------------------------'
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write(*,*) 'Adiabatic connection version of BSE correlation energy'
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write(*,*) '------------------------------------------------------'
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write(*,*)
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if(doXBS) then
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write(*,*) '*** scaled screening version (XBS) ***'
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write(*,*)
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end if
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call ACFDT(exchange_kernel,doXBS,.true.,TDA_W,TDA,BSE,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI_MO,eGW,eGW,EcAC)
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write(*,*)
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write(*,*)'-------------------------------------------------------------------------------'
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write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy (singlet) =',EcAC(1)
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write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy (triplet) =',EcAC(2)
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write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy =',EcAC(1) + EcAC(2)
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write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW total energy =',ENuc + EqsGW + EcAC(1) + EcAC(2)
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write(*,*)'-------------------------------------------------------------------------------'
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write(*,*)
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end if
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end if
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end subroutine SRG_qsGW
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