subroutine qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS, & COHSEX,SOSEX,BSE,TDA_W,TDA,dBSE,dTDA,evDyn,G0W,GW0,singlet_manifold,triplet_manifold,eta, & nBas,nC,nO,nV,nR,nS,ENuc,ERHF,S,X,T,V,Hc,ERI_AO_basis,ERI_MO_basis,PHF,cHF,eHF) ! Perform a quasiparticle self-consistent GW calculation implicit none include 'parameters.h' ! Input variables integer,intent(in) :: maxSCF integer,intent(in) :: max_diis double precision,intent(in) :: thresh logical,intent(in) :: doACFDT logical,intent(in) :: exchange_kernel logical,intent(in) :: doXBS logical,intent(in) :: COHSEX logical,intent(in) :: SOSEX logical,intent(in) :: BSE logical,intent(in) :: TDA_W logical,intent(in) :: TDA logical,intent(in) :: dBSE logical,intent(in) :: dTDA logical,intent(in) :: evDyn logical,intent(in) :: G0W logical,intent(in) :: GW0 logical,intent(in) :: singlet_manifold logical,intent(in) :: triplet_manifold double precision,intent(in) :: eta integer,intent(in) :: nBas,nC,nO,nV,nR,nS double precision,intent(in) :: ENuc double precision,intent(in) :: ERHF double precision,intent(in) :: eHF(nBas) double precision,intent(in) :: cHF(nBas,nBas) double precision,intent(in) :: PHF(nBas,nBas) double precision,intent(in) :: S(nBas,nBas) double precision,intent(in) :: T(nBas,nBAs) double precision,intent(in) :: V(nBas,nBas) double precision,intent(in) :: Hc(nBas,nBas) double precision,intent(in) :: X(nBas,nBas) double precision,intent(in) :: ERI_AO_basis(nBas,nBas,nBas,nBas) double precision,intent(inout):: ERI_MO_basis(nBas,nBas,nBas,nBas) ! Local variables integer :: nSCF integer :: nBasSq integer :: ispin integer :: n_diis double precision :: EqsGW double precision :: EcRPA(nspin) double precision :: EcBSE(nspin) double precision :: EcAC(nspin) double precision :: EcGM double precision :: Conv double precision :: rcond double precision,external :: trace_matrix double precision,allocatable :: error_diis(:,:) double precision,allocatable :: F_diis(:,:) double precision,allocatable :: Omega(:,:) double precision,allocatable :: XpY(:,:,:) double precision,allocatable :: XmY(:,:,:) double precision,allocatable :: rho(:,:,:,:) double precision,allocatable :: rhox(:,:,:,:) double precision,allocatable :: c(:,:) double precision,allocatable :: cp(:,:) double precision,allocatable :: eGW(:) double precision,allocatable :: P(:,:) double precision,allocatable :: F(:,:) double precision,allocatable :: Fp(:,:) double precision,allocatable :: J(:,:) double precision,allocatable :: K(:,:) double precision,allocatable :: SigC(:,:) double precision,allocatable :: SigCp(:,:) double precision,allocatable :: SigCm(:,:) double precision,allocatable :: Z(:) double precision,allocatable :: error(:,:) ! Hello world write(*,*) write(*,*)'************************************************' write(*,*)'| Self-consistent qsGW calculation |' write(*,*)'************************************************' write(*,*) ! Warning write(*,*) '!! ERIs in MO basis will be overwritten in qsGW !!' write(*,*) ! Stuff nBasSq = nBas*nBas ! SOSEX correction if(SOSEX) write(*,*) 'SOSEX correction activated!' write(*,*) ! COHSEX approximation if(COHSEX) write(*,*) 'COHSEX approximation activated!' write(*,*) ! TDA for W if(TDA_W) write(*,*) 'Tamm-Dancoff approximation for dynamic screening!' write(*,*) ! TDA if(TDA) write(*,*) 'Tamm-Dancoff approximation activated!' write(*,*) ! Memory allocation allocate(eGW(nBas),c(nBas,nBas),cp(nBas,nBas),P(nBas,nBas),F(nBas,nBas),Fp(nBas,nBas), & J(nBas,nBas),K(nBas,nBas),SigC(nBas,nBas),SigCp(nBas,nBas),SigCm(nBas,nBas),Z(nBas), & Omega(nS,nspin),XpY(nS,nS,nspin),XmY(nS,nS,nspin),rho(nBas,nBas,nS,nspin),rhox(nBas,nBas,nS,nspin), & error(nBas,nBas),error_diis(nBasSq,max_diis),F_diis(nBasSq,max_diis)) ! Initialization nSCF = 0 n_diis = 0 ispin = 1 Conv = 1d0 P(:,:) = PHF(:,:) eGW(:) = eHF(:) c(:,:) = cHF(:,:) F_diis(:,:) = 0d0 error_diis(:,:) = 0d0 !------------------------------------------------------------------------ ! Main loop !------------------------------------------------------------------------ do while(Conv > thresh .and. nSCF <= maxSCF) ! Buid Coulomb matrix call Coulomb_matrix_AO_basis(nBas,P,ERI_AO_basis,J) ! Compute exchange part of the self-energy call exchange_matrix_AO_basis(nBas,P,ERI_AO_basis,K) ! AO to MO transformation of two-electron integrals call AOtoMO_integral_transform(nBas,c,ERI_AO_basis,ERI_MO_basis) ! Compute linear response if(.not. GW0 .or. nSCF == 0) then call linear_response(ispin,.true.,TDA_W,.false.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,ERI_MO_basis, & rho(:,:,:,ispin),EcRPA(ispin),Omega(:,ispin),XpY(:,:,ispin),XmY(:,:,ispin)) endif ! Compute correlation part of the self-energy call excitation_density(nBas,nC,nO,nR,nS,ERI_MO_basis,XpY(:,:,ispin),rho(:,:,:,ispin)) if(SOSEX) call excitation_density_SOSEX(nBas,nC,nO,nR,nS,ERI_MO_basis,XpY(:,:,ispin),rhox(:,:,:,ispin)) if(G0W) then call self_energy_correlation(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, & Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),EcGM,SigC) call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, & Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z) else call self_energy_correlation(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eGW, & Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),EcGM,SigC) call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eGW, & Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z) endif ! Make correlation self-energy Hermitian and transform it back to AO basis SigCp = 0.5d0*(SigC + transpose(SigC)) SigCm = 0.5d0*(SigC - transpose(SigC)) call MOtoAO_transform(nBas,S,c,SigCp) ! Solve the quasi-particle equation F(:,:) = Hc(:,:) + J(:,:) + 0.5d0*K(:,:) + SigCp(:,:) ! Compute commutator and convergence criteria error = matmul(F,matmul(P,S)) - matmul(matmul(S,P),F) Conv = maxval(abs(error)) ! DIIS extrapolation n_diis = min(n_diis+1,max_diis) call DIIS_extrapolation(rcond,nBasSq,nBasSq,n_diis,error_diis,F_diis,error,F) ! Reset DIIS if required if(abs(rcond) < 1d-15) n_diis = 0 ! Diagonalize Hamiltonian in AO basis Fp = matmul(transpose(X),matmul(F,X)) cp(:,:) = Fp(:,:) call diagonalize_matrix(nBas,cp,eGW) c = matmul(X,cp) ! Compute new density matrix in the AO basis P(:,:) = 2d0*matmul(c(:,1:nO),transpose(c(:,1:nO))) ! Print results ! call print_excitation('RPA ',ispin,nS,Omega(:,ispin)) call print_qsGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,ENuc,P,T,V,Hc,J,K,F,SigCp,Z,EcRPA(ispin),EcGM,EqsGW) ! Increment nSCF = nSCF + 1 enddo !------------------------------------------------------------------------ ! End main loop !------------------------------------------------------------------------ ! Compute second-order correction of the Hermitization error ! call qsGW_PT(nBas,nC,nO,nV,nR,nS,eGW,SigCm) ! Compute the overlap between HF and GW orbitals ! call overlap(nBas,cHF,c) ! Compute natural orbitals and occupancies ! call natural_orbital(nBas,nO,cHF,c) ! Did it actually converge? if(nSCF == maxSCF+1) then write(*,*) write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!' write(*,*)' Convergence failed ' write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!' write(*,*) stop endif ! Dump RPA correlation energy write(*,*) write(*,*)'-------------------------------------------------------------------------------' write(*,'(2X,A50,F20.10)') 'Tr@RPA@qsGW correlation energy (singlet) =',EcRPA(1) write(*,'(2X,A50,F20.10)') 'Tr@RPA@qsGW correlation energy (triplet) =',EcRPA(2) write(*,'(2X,A50,F20.10)') 'Tr@RPA@qsGW correlation energy =',EcRPA(1) + EcRPA(2) write(*,'(2X,A50,F20.10)') 'Tr@RPA@qsGW total energy =',ENuc + EqsGW + EcRPA(1) + EcRPA(2) write(*,*)'-------------------------------------------------------------------------------' write(*,*) ! Perform BSE calculation if(BSE) then call Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,singlet_manifold,triplet_manifold,eta, & nBas,nC,nO,nV,nR,nS,ERI_MO_basis,eGW,eGW,Omega,XpY,XmY,rho,EcRPA,EcBSE) write(*,*) write(*,*)'-------------------------------------------------------------------------------' write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy (singlet) =',EcBSE(1) write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy (triplet) =',EcBSE(2) write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW correlation energy =',EcBSE(1) + EcBSE(2) write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsGW total energy =',ENuc + EqsGW + EcBSE(1) + EcBSE(2) write(*,*)'-------------------------------------------------------------------------------' write(*,*) ! Compute the BSE correlation energy via the adiabatic connection if(doACFDT) then write(*,*) '------------------------------------------------------' write(*,*) 'Adiabatic connection version of BSE correlation energy' write(*,*) '------------------------------------------------------' write(*,*) if(doXBS) then write(*,*) '*** scaled screening version (XBS) ***' write(*,*) end if call ACFDT(exchange_kernel,doXBS,.true.,TDA_W,TDA,BSE,singlet_manifold,triplet_manifold,eta, & nBas,nC,nO,nV,nR,nS,ERI_MO_basis,eGW,eGW,Omega,XpY,XmY,rho,EcAC) write(*,*) write(*,*)'-------------------------------------------------------------------------------' write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy (singlet) =',EcAC(1) write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy (triplet) =',EcAC(2) write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW correlation energy =',EcAC(1) + EcAC(2) write(*,'(2X,A50,F20.10)') 'AC@BSE@qsGW total energy =',ENuc + EqsGW + EcAC(1) + EcAC(2) write(*,*)'-------------------------------------------------------------------------------' write(*,*) end if end if end subroutine qsGW