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quack/src/MBPT/qsUGW.f90

434 lines
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Fortran
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subroutine qsUGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,COHSEX,SOSEX,BSE,TDA_W,TDA, &
G0W,GW0,dBSE,dTDA,evDyn,spin_conserved,spin_flip,eta,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO, &
nV,nR,nS,EUHF,S,X,T,V,Hc,ERI_AO,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_AO,dipole_int_aa, &
dipole_int_bb,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) :: spin_conserved
logical,intent(in) :: spin_flip
double precision,intent(in) :: eta
integer,intent(in) :: nNuc
double precision,intent(in) :: ZNuc(nNuc)
double precision,intent(in) :: rNuc(nNuc,ncart)
double precision,intent(in) :: ENuc
integer,intent(in) :: nBas
integer,intent(in) :: nC(nspin)
integer,intent(in) :: nO(nspin)
integer,intent(in) :: nV(nspin)
integer,intent(in) :: nR(nspin)
integer,intent(in) :: nS(nspin)
double precision,intent(in) :: EUHF
double precision,intent(in) :: eHF(nBas,nspin)
double precision,intent(in) :: cHF(nBas,nBas,nspin)
double precision,intent(in) :: PHF(nBas,nBas,nspin)
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(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_aaaa(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_aabb(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_bbbb(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_aa(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_bb(nBas,nBas,ncart)
! Local variables
logical :: doGWPT = .false.
integer :: nSCF
integer :: nBasSq
integer :: ispin
integer :: is
integer :: n_diis
integer :: nS_aa,nS_bb,nS_sc
double precision :: dipole(ncart)
double precision :: ET(nspin)
double precision :: EV(nspin)
double precision :: EJ(nsp)
double precision :: Ex(nspin)
double precision :: Ec(nsp)
double precision :: EcRPA
double precision :: EqsGW
double precision :: EcBSE(nspin)
double precision :: EcAC(nspin)
double precision :: Conv
double precision :: rcond(nspin)
double precision,external :: trace_matrix
double precision,allocatable :: error_diis(:,:,:)
double precision,allocatable :: F_diis(:,:,:)
double precision,allocatable :: OmRPA(:)
double precision,allocatable :: XpY_RPA(:,:)
double precision,allocatable :: XmY_RPA(:,:)
double precision,allocatable :: rho_RPA(:,:,:,:)
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 unrestricted qsGW calculation |'
write(*,*)'*************************************************'
write(*,*)
! Warning
write(*,*) '!! ERIs in MO basis will be overwritten in qsUGW !!'
write(*,*)
! Stuff
nBasSq = nBas*nBas
! SOSEX correction
if(SOSEX) then
write(*,*) 'SOSEX correction activated but BUG!'
stop
end if
! COHSEX approximation
if(COHSEX) then
write(*,*) 'COHSEX approximation activated!'
write(*,*)
end if
! TDA for W
if(TDA_W) then
write(*,*) 'Tamm-Dancoff approximation for dynamic screening!'
write(*,*)
end if
! TDA
if(TDA) then
write(*,*) 'Tamm-Dancoff approximation activated!'
write(*,*)
end if
! Memory allocation
nS_aa = nS(1)
nS_bb = nS(2)
nS_sc = nS_aa + nS_bb
allocate(eGW(nBas,nspin),c(nBas,nBas,nspin),cp(nBas,nBas,nspin),P(nBas,nBas,nspin),F(nBas,nBas,nspin),Fp(nBas,nBas,nspin), &
J(nBas,nBas,nspin),K(nBas,nBas,nspin),SigC(nBas,nBas,nspin),SigCp(nBas,nBas,nspin),SigCm(nBas,nBas,nspin), &
Z(nBas,nspin),OmRPA(nS_sc),XpY_RPA(nS_sc,nS_sc),XmY_RPA(nS_sc,nS_sc),rho_RPA(nBas,nBas,nS_sc,nspin), &
error(nBas,nBas,nspin),error_diis(nBasSq,max_diis,nspin),F_diis(nBasSq,max_diis,nspin))
! Initialization
nSCF = -1
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)
! Increment
nSCF = nSCF + 1
! Buid Coulomb matrix
do is=1,nspin
call Coulomb_matrix_AO_basis(nBas,P(:,:,is),ERI_AO(:,:,:,:),J(:,:,is))
end do
! Compute exchange part of the self-energy
do is=1,nspin
call exchange_matrix_AO_basis(nBas,P(:,:,is),ERI_AO(:,:,:,:),K(:,:,is))
end do
!--------------------------------------------------
! AO to MO transformation of two-electron integrals
!--------------------------------------------------
! 4-index transform for (aa|aa) block
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_aaaa)
! 4-index transform for (aa|bb) block
call AOtoMO_integral_transform(1,1,2,2,nBas,c,ERI_AO,ERI_aabb)
! 4-index transform for (bb|bb) block
call AOtoMO_integral_transform(2,2,2,2,nBas,c,ERI_AO,ERI_bbbb)
! Compute linear response
if(.not. GW0 .or. nSCF == 0) then
call unrestricted_linear_response(ispin,.true.,TDA_W,.false.,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,1d0, &
eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,OmRPA,rho_RPA,EcRPA,OmRPA,XpY_RPA,XmY_RPA)
endif
!----------------------!
! Excitation densities !
!----------------------!
call unrestricted_excitation_density(nBas,nC,nO,nR,nS_aa,nS_bb,nS_sc,ERI_aaaa,ERI_aabb,ERI_bbbb,XpY_RPA,rho_RPA)
!------------------------------------------------!
! Compute self-energy and renormalization factor !
!------------------------------------------------!
if(G0W) then
call unrestricted_self_energy_correlation(eta,nBas,nC,nO,nV,nR,nS_sc,eHF,OmRPA,rho_RPA,SigC)
call unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nS_sc,eHF,OmRPA,rho_RPA,Z)
else
call unrestricted_self_energy_correlation(eta,nBas,nC,nO,nV,nR,nS_sc,eGW,OmRPA,rho_RPA,SigC)
call unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nS_sc,eGW,OmRPA,rho_RPA,Z)
endif
! Make correlation self-energy Hermitian and transform it back to AO basis
do is=1,nspin
SigCp(:,:,is) = 0.5d0*(SigC(:,:,is) + transpose(SigC(:,:,is)))
SigCm(:,:,is) = 0.5d0*(SigC(:,:,is) - transpose(SigC(:,:,is)))
end do
do is=1,nspin
call MOtoAO_transform(nBas,S,c(:,:,is),SigCp(:,:,is))
end do
! Solve the quasi-particle equation
do is=1,nspin
F(:,:,is) = Hc(:,:) + J(:,:,is) + J(:,:,mod(is,2)+1) + K(:,:,is) + SigCp(:,:,is)
end do
! Check convergence
do is=1,nspin
error(:,:,is) = matmul(F(:,:,is),matmul(P(:,:,is),S(:,:))) - matmul(matmul(S(:,:),P(:,:,is)),F(:,:,is))
end do
if(nSCF > 1) conv = maxval(abs(error(:,:,:)))
! DIIS extrapolation
n_diis = min(n_diis+1,max_diis)
do is=1,nspin
if(nO(is) > 1) call DIIS_extrapolation(rcond(is),nBasSq,nBasSq,n_diis,error_diis(:,1:n_diis,is), &
F_diis(:,1:n_diis,is),error(:,:,is),F(:,:,is))
end do
! Reset DIIS if required
if(minval(rcond(:)) < 1d-15) n_diis = 0
! Transform Fock matrix in orthogonal basis
do is=1,nspin
Fp(:,:,is) = matmul(transpose(X(:,:)),matmul(F(:,:,is),X(:,:)))
end do
! Diagonalize Fock matrix to get eigenvectors and eigenvalues
cp(:,:,:) = Fp(:,:,:)
do is=1,nspin
call diagonalize_matrix(nBas,cp(:,:,is),eGW(:,is))
end do
! Back-transform eigenvectors in non-orthogonal basis
do is=1,nspin
c(:,:,is) = matmul(X(:,:),cp(:,:,is))
end do
! Compute density matrix
do is=1,nspin
P(:,:,is) = matmul(c(:,1:nO(is),is),transpose(c(:,1:nO(is),is)))
end do
!------------------------------------------------------------------------
! Compute total energy
!------------------------------------------------------------------------
! Kinetic energy
do is=1,nspin
ET(is) = trace_matrix(nBas,matmul(P(:,:,is),T(:,:)))
end do
! Potential energy
do is=1,nspin
EV(is) = trace_matrix(nBas,matmul(P(:,:,is),V(:,:)))
end do
! Coulomb energy
EJ(1) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,1),J(:,:,1)))
EJ(2) = 1.0d0*trace_matrix(nBas,matmul(P(:,:,1),J(:,:,2)))
EJ(3) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,2),J(:,:,2)))
! Exchange energy
do is=1,nspin
Ex(is) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,is),K(:,:,is)))
end do
! Correlation energy
Ec(1) = 0.25d0*trace_matrix(nBas,matmul(P(:,:,1),SigCp(:,:,1)))
Ec(2) = 0.25d0*trace_matrix(nBas,matmul(P(:,:,1),SigCp(:,:,2))) &
+ 0.25d0*trace_matrix(nBas,matmul(P(:,:,2),SigCp(:,:,1)))
Ec(3) = 0.25d0*trace_matrix(nBas,matmul(P(:,:,2),SigCp(:,:,2)))
! Total energy
EqsGW = sum(ET(:)) + sum(EV(:)) + sum(EJ(:)) + sum(Ex(:)) + sum(Ec(:))
!------------------------------------------------------------------------
! Print results
!------------------------------------------------------------------------
call dipole_moment(nBas,P(:,:,1)+P(:,:,2),nNuc,ZNuc,rNuc,dipole_int_AO,dipole)
call print_qsUGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,P,S,T,V,J,K,ENuc,ET,EV,EJ,Ex,Ec,EcRPA,EqsGW,SigCp,Z,dipole)
enddo
!------------------------------------------------------------------------
! End main loop
!------------------------------------------------------------------------
! Compute second-order correction of the Hermitization error
!if(doGWPT) call qsGW_PT(nBas,nC,nO,nV,nR,nS,eGW,SigCm)
! Did it actually converge?
if(nSCF == maxSCF) then
write(*,*)
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)' Convergence failed '
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)
stop
endif
! Deallocate memory
deallocate(c,cp,P,F,Fp,J,K,SigC,SigCp,SigCm,Z,OmRPA,XpY_RPA,XmY_RPA,rho_RPA,error,error_diis,F_diis)
! Perform BSE calculation
if(BSE) then
call unrestricted_Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,spin_conserved,spin_flip,eta,nBas,nC,nO,nV,nR,nS, &
S,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb,cHF,eGW,eGW,EcBSE)
if(exchange_kernel) then
EcBSE(1) = 0.5d0*EcBSE(1)
EcBSE(2) = 1.5d0*EcBSE(2)
end if
write(*,*)
write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsUGW correlation energy (spin-conserved) =',EcBSE(1)
write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsUGW correlation energy (spin-flip) =',EcBSE(2)
write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsUGW correlation energy =',EcBSE(1) + EcBSE(2)
write(*,'(2X,A50,F20.10)') 'Tr@BSE@qsUGW total energy =',ENuc + EUHF + 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@qsUGW correlation energy '
write(*,*) '--------------------------------------------------------------'
write(*,*)
if(doXBS) then
write(*,*) '*** scaled screening version (XBS) ***'
write(*,*)
end if
call unrestricted_ACFDT(exchange_kernel,doXBS,.true.,TDA_W,TDA,BSE,spin_conserved,spin_flip, &
eta,nBas,nC,nO,nV,nR,nS,ERI_aaaa,ERI_aabb,ERI_bbbb,eGW,eGW,EcAC)
write(*,*)
write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10)') 'AC@BSE@qsUGW correlation energy (spin-conserved) =',EcAC(1)
write(*,'(2X,A50,F20.10)') 'AC@BSE@qsUGW correlation energy (spin-flip) =',EcAC(2)
write(*,'(2X,A50,F20.10)') 'AC@BSE@qsUGW correlation energy =',EcAC(1) + EcAC(2)
write(*,'(2X,A50,F20.10)') 'AC@BSE@qsUGW total energy =',ENuc + EUHF + EcAC(1) + EcAC(2)
write(*,*)'-------------------------------------------------------------------------------'
write(*,*)
end if
end if
end subroutine qsUGW
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