quack/src/QuAcK/UHF.f90

subroutine UHF(maxSCF,thresh,max_diis,guess_type,nBas,nO,S,T,V,Hc,ERI,X,ENuc,EUHF,e,c,P)

! Perform unrestricted Hartree-Fock calculation

  implicit none
  include 'parameters.h'

! Input variables

  integer,intent(in)            :: maxSCF
  integer,intent(in)            :: max_diis
  integer,intent(in)            :: guess_type
  double precision,intent(in)   :: thresh
  integer,intent(in)            :: nBas

  integer,intent(in)            :: nO(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(nBas,nBas,nBas,nBas)
  double precision,intent(in)   :: ENuc

! Local variables

  integer                       :: nSCF
  integer                       :: nBasSq
  integer                       :: n_diis
  double precision              :: conv
  double precision              :: rcond(nspin)
  double precision              :: ET(nspin)
  double precision              :: EV(nspin)
  double precision              :: EJ(nsp)
  double precision              :: Ex(nspin)

  double precision,allocatable  :: cp(:,:,:)
  double precision,allocatable  :: J(:,:,:)
  double precision,allocatable  :: F(:,:,:)
  double precision,allocatable  :: Fp(:,:,:)
  double precision,allocatable  :: K(:,:,:)
  double precision,allocatable  :: err(:,:,:)
  double precision,allocatable  :: err_diis(:,:,:)
  double precision,allocatable  :: F_diis(:,:,:)
  double precision,external     :: trace_matrix

  integer                       :: ispin

! Output variables

  double precision,intent(out)  :: EUHF
  double precision,intent(out)  :: e(nBas,nspin)
  double precision,intent(out)  :: c(nBas,nBas,nspin)
  double precision,intent(out)  :: P(nBas,nBas,nspin)

! Hello world

  write(*,*)
  write(*,*)'************************************************'
  write(*,*)'*    Unrestricted Hartree-Fock calculation     *'
  write(*,*)'************************************************'
  write(*,*)

! Useful stuff

  nBasSq = nBas*nBas

! Memory allocation

  allocate(J(nBas,nBas,nspin),F(nBas,nBas,nspin),Fp(nBas,nBas,nspin),   & 
           K(nBas,nBas,nspin),err(nBas,nBas,nspin),cp(nBas,nBas,nspin), &
           err_diis(nBasSq,max_diis,nspin),F_diis(nBasSq,max_diis,nspin))

! Guess coefficients and eigenvalues

  if(guess_type == 1) then

    do ispin=1,nspin
      F(:,:,ispin) = Hc(:,:)
    end do

  else if(guess_type == 2) then

    do ispin=1,nspin
      call random_number(F(:,:,ispin))
    end do

  end if

! Initialization

  nSCF = 0
  conv = 1d0

  n_diis          = 0
  F_diis(:,:,:)   = 0d0
  err_diis(:,:,:) = 0d0

!------------------------------------------------------------------------
! Main SCF loop
!------------------------------------------------------------------------

  write(*,*)
  write(*,*)'----------------------------------------------------------'
  write(*,'(1X,A1,1X,A3,1X,A1,1X,A16,1X,A1,1X,A16,1X,A1,1X,A10,1X,A1,1X)') & 
            '|','#','|','E(UHF)','|','Ex(UHF)','|','Conv','|'
  write(*,*)'----------------------------------------------------------'
  
  do while(conv > thresh .and. nSCF < maxSCF)

!   Increment 

    nSCF = nSCF + 1

!  Transform Fock matrix in orthogonal basis

    do ispin=1,nspin
      Fp(:,:,ispin) = matmul(transpose(X(:,:)),matmul(F(:,:,ispin),X(:,:)))
    end do

!  Diagonalize Fock matrix to get eigenvectors and eigenvalues

    cp(:,:,:) = Fp(:,:,:)
    do ispin=1,nspin
      call diagonalize_matrix(nBas,cp(:,:,ispin),e(:,ispin))
    end do
    
!   Back-transform eigenvectors in non-orthogonal basis

    do ispin=1,nspin
      c(:,:,ispin) = matmul(X(:,:),cp(:,:,ispin))
    end do

!   Compute density matrix 

    do ispin=1,nspin
      P(:,:,ispin) = matmul(c(:,1:nO(ispin),ispin),transpose(c(:,1:nO(ispin),ispin)))
    end do
 
!   Build Coulomb repulsion

    do ispin=1,nspin
      call Coulomb_matrix_AO_basis(nBas,P(:,:,ispin),ERI(:,:,:,:),J(:,:,ispin))
    end do

!   Compute exchange potential

    do ispin=1,nspin
      call exchange_matrix_AO_basis(nBas,P(:,:,ispin),ERI(:,:,:,:),K(:,:,ispin))
    end do

!   Build Fock operator
    do ispin=1,nspin
      F(:,:,ispin) = Hc(:,:) + J(:,:,ispin) + J(:,:,mod(ispin,2)+1) + K(:,:,ispin)
    end do

!   Check convergence 

    do ispin=1,nspin
      err(:,:,ispin) = matmul(F(:,:,ispin),matmul(P(:,:,ispin),S(:,:))) - matmul(matmul(S(:,:),P(:,:,ispin)),F(:,:,ispin))
    end do

    conv = maxval(abs(err(:,:,:)))
    
!   DIIS extrapolation

    n_diis = min(n_diis+1,max_diis)
    do ispin=1,nspin
      call DIIS_extrapolation(rcond(ispin),nBasSq,nBasSq,n_diis,err_diis(:,:,ispin),F_diis(:,:,ispin),err(:,:,ispin),F(:,:,ispin))
    end do

!   Reset DIIS if required

    if(minval(rcond(:)) < 1d-15) n_diis = 0

!------------------------------------------------------------------------
!   Compute UHF energy
!------------------------------------------------------------------------

!  Kinetic energy

    do ispin=1,nspin
      ET(ispin) = trace_matrix(nBas,matmul(P(:,:,ispin),T(:,:)))
    end do

!  Potential energy

    do ispin=1,nspin
      EV(ispin) = trace_matrix(nBas,matmul(P(:,:,ispin),V(:,:)))
    end do

!  Coulomb energy

    EJ(1) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,1),J(:,:,1)))
    EJ(2) = trace_matrix(nBas,matmul(P(:,:,1),J(:,:,2)))
    EJ(3) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,2),J(:,:,2)))

!   Exchange energy

    do ispin=1,nspin
      Ex(ispin) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,ispin),K(:,:,ispin)))
    end do

!   Total energy

    EUHF = sum(ET(:)) + sum(EV(:)) + sum(EJ(:)) + sum(Ex(:))

!   Dump results

    write(*,'(1X,A1,1X,I3,1X,A1,1X,F16.10,1X,A1,1X,F16.10,1X,A1,1X,F10.6,1X,A1,1X)') & 
      '|',nSCF,'|',EUHF + ENuc,'|',sum(Ex(:)),'|',conv,'|'
 
  end do
  write(*,*)'----------------------------------------------------------'
!------------------------------------------------------------------------
! End of SCF loop
!------------------------------------------------------------------------

! Did it actually converge?

  if(nSCF == maxSCF) then

    write(*,*)
    write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
    write(*,*)'                 Convergence failed                 '
    write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
    write(*,*)

    stop

  end if

! Compute final UHF energy

  call print_UHF(nBas,nO(:),e(:,:),c(:,:,:),ENuc,ET(:),EV(:),EJ(:),Ex(:),EUHF)

end subroutine UHF