subroutine eDFT_UKS(x_rung,x_DFA,c_rung,c_DFA,nEns,wEns,aCC_w1,aCC_w2,nGrid,weight,maxSCF,thresh,max_diis,guess_type, & nBas,AO,dAO,nO,nV,S,T,V,Hc,ERI,X,ENuc,Ew) ! Perform unrestricted Kohn-Sham calculation for ensembles implicit none include 'parameters.h' ! Input variables integer,intent(in) :: x_rung,c_rung character(len=12),intent(in) :: x_DFA,c_DFA integer,intent(in) :: nEns double precision,intent(in) :: wEns(nEns) double precision,intent(in) :: aCC_w1(3) double precision,intent(in) :: aCC_w2(3) integer,intent(in) :: nGrid double precision,intent(in) :: weight(nGrid) integer,intent(in) :: maxSCF,max_diis,guess_type double precision,intent(in) :: thresh integer,intent(in) :: nBas double precision,intent(in) :: AO(nBas,nGrid) double precision,intent(in) :: dAO(ncart,nBas,nGrid) integer,intent(in) :: nO(nspin),nV(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 :: xc_rung logical :: LDA_centered = .false. integer :: nSCF,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 :: Ec(nsp) double precision :: Ew double precision,allocatable :: eps(:,:) double precision,allocatable :: c(:,:,:) double precision,allocatable :: cp(:,:,:) double precision,allocatable :: J(:,:,:) double precision,allocatable :: F(:,:,:) double precision,allocatable :: Fp(:,:,:) double precision,allocatable :: Fx(:,:,:) double precision,allocatable :: FxHF(:,:,:) double precision,allocatable :: Fc(:,:,:) double precision,allocatable :: err(:,:,:) double precision,allocatable :: err_diis(:,:,:) double precision,allocatable :: F_diis(:,:,:) double precision,external :: trace_matrix double precision,external :: electron_number double precision,allocatable :: Pw(:,:,:) double precision,allocatable :: rhow(:,:) double precision,allocatable :: drhow(:,:,:) double precision :: nEl(nspin) double precision,allocatable :: P(:,:,:,:) double precision,allocatable :: rho(:,:,:) double precision,allocatable :: drho(:,:,:,:) double precision :: E(nEns) double precision :: Om(nEns) integer :: ispin,iEns ! Hello world write(*,*) write(*,*)'************************************************' write(*,*)'* Unrestricted Kohn-Sham calculation *' write(*,*)'* *** for ensembles *** *' write(*,*)'************************************************' write(*,*) ! Useful stuff nBasSq = nBas*nBas !------------------------------------------------------------------------ ! Rung of Jacob's ladder !------------------------------------------------------------------------ ! Select rung for exchange write(*,*) write(*,*) '*******************************************************************' write(*,*) '* Exchange rung *' write(*,*) '*******************************************************************' call select_rung(x_rung,x_DFA) ! Select rung for correlation write(*,*) write(*,*) '*******************************************************************' write(*,*) '* Correlation rung *' write(*,*) '*******************************************************************' call select_rung(c_rung,c_DFA) ! Overall rung xc_rung = max(x_rung,c_rung) ! Memory allocation allocate(eps(nBas,nspin),c(nBas,nBas,nspin),cp(nBas,nBas,nspin), & J(nBas,nBas,nspin),F(nBas,nBas,nspin),Fp(nBas,nBas,nspin), & Fx(nBas,nBas,nspin),FxHF(nBas,nBas,nspin),Fc(nBas,nBas,nspin),err(nBas,nBas,nspin), & Pw(nBas,nBas,nspin),rhow(nGrid,nspin),drhow(ncart,nGrid,nspin), & err_diis(nBasSq,max_diis,nspin),F_diis(nBasSq,max_diis,nspin), & P(nBas,nBas,nspin,nEns),rho(nGrid,nspin,nEns),drho(ncart,nGrid,nspin,nEns)) ! Guess coefficients and eigenvalues if(guess_type == 1) then do ispin=1,nspin cp(:,:,ispin) = matmul(transpose(X(:,:)),matmul(Hc(:,:),X(:,:))) call diagonalize_matrix(nBas,cp(:,:,ispin),eps(:,ispin)) c(:,:,ispin) = matmul(X(:,:),cp(:,:,ispin)) end do else if(guess_type == 2) then do ispin=1,nspin call random_number(F(:,:,ispin)) end do else print*,'Wrong guess option' stop end if ! Initialization nSCF = 0 conv = 1d0 nEl(:) = 0d0 Ex(:) = 0d0 Ec(:) = 0d0 Fx(:,:,:) = 0d0 FxHF(:,:,:) = 0d0 Fc(:,:,:) = 0d0 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,A16,1X,A1,1X,A10,1X,A1,1X,A10,1X,A1,1X)') & '|','#','|','E(KS)','|','Ex(KS)','|','Ec(KS)','|','Conv','|','nEl','|' write(*,*)'------------------------------------------------------------------------------------------' do while(conv > thresh .and. nSCF < maxSCF) ! Increment nSCF = nSCF + 1 !------------------------------------------------------------------------ ! Compute density matrix !------------------------------------------------------------------------ call unrestricted_density_matrix(nBas,nEns,nO(:),c(:,:,:),P(:,:,:,:)) ! Weight-dependent density matrix Pw(:,:,:) = 0d0 do iEns=1,nEns Pw(:,:,:) = Pw(:,:,:) + wEns(iEns)*P(:,:,:,iEns) end do !------------------------------------------------------------------------ ! Compute one-electron density and its gradient if necessary !------------------------------------------------------------------------ do ispin=1,nspin do iEns=1,nEns call density(nGrid,nBas,P(:,:,ispin,iEns),AO(:,:),rho(:,ispin,iEns)) end do end do ! Weight-dependent one-electron density rhow(:,:) = 0d0 do iEns=1,nEns rhow(:,:) = rhow(:,:) + wEns(iEns)*rho(:,:,iEns) end do if(xc_rung > 1 .and. xc_rung /= 666) then ! Ground state density do ispin=1,nspin do iEns=1,nEns call gradient_density(nGrid,nBas,P(:,:,ispin,iEns),AO(:,:),dAO(:,:,:),drho(:,:,ispin,iEns)) end do end do ! Weight-dependent one-electron density drhow(:,:,:) = 0d0 do iEns=1,nEns drhow(:,:,:) = drhow(:,:,:) + wEns(iEns)*drho(:,:,:,iEns) end do end if ! Build Coulomb repulsion do ispin=1,nspin call hartree_coulomb(nBas,Pw(:,:,ispin),ERI(:,:,:,:),J(:,:,ispin)) end do ! Compute exchange potential do ispin=1,nspin call exchange_potential(x_rung,x_DFA,LDA_centered,nEns,wEns(:),aCC_w1,aCC_w2,nGrid,weight(:),nBas, & Pw(:,:,ispin),ERI(:,:,:,:),AO(:,:),dAO(:,:,:),rhow(:,ispin),drhow(:,:,ispin), & Fx(:,:,ispin),FxHF(:,:,ispin)) end do ! Compute correlation potential call unrestricted_correlation_potential(c_rung,c_DFA,nEns,wEns,nGrid,weight,nBas,AO,dAO,rhow,drhow,Fc) ! Build Fock operator do ispin=1,nspin F(:,:,ispin) = Hc(:,:) + J(:,:,ispin) + J(:,:,mod(ispin,2)+1) + Fx(:,:,ispin) + Fc(:,:,ispin) end do ! Check convergence do ispin=1,nspin err(:,:,ispin) = matmul(F(:,:,ispin),matmul(Pw(:,:,ispin),S(:,:))) - matmul(matmul(S(:,:),Pw(:,:,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 ! 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),eps(:,ispin)) end do ! Back-transform eigenvectors in non-orthogonal basis do ispin=1,nspin c(:,:,ispin) = matmul(X(:,:),cp(:,:,ispin)) end do !------------------------------------------------------------------------ ! Compute KS energy !------------------------------------------------------------------------ ! Kinetic energy do ispin=1,nspin ET(ispin) = trace_matrix(nBas,matmul(Pw(:,:,ispin),T(:,:))) end do ! Potential energy do ispin=1,nspin EV(ispin) = trace_matrix(nBas,matmul(Pw(:,:,ispin),V(:,:))) end do ! Coulomb energy EJ(1) = 0.5d0*trace_matrix(nBas,matmul(Pw(:,:,1),J(:,:,1))) EJ(2) = trace_matrix(nBas,matmul(Pw(:,:,1),J(:,:,2))) EJ(3) = 0.5d0*trace_matrix(nBas,matmul(Pw(:,:,2),J(:,:,2))) ! Exchange energy do ispin=1,nspin call exchange_energy(x_rung,x_DFA,LDA_centered,nEns,wEns,aCC_w1,aCC_w2,nGrid,weight,nBas, & Pw(:,:,ispin),FxHF(:,:,ispin),rhow(:,ispin),drhow(:,:,ispin),Ex(ispin)) end do ! Correlation energy call unrestricted_correlation_energy(c_rung,c_DFA,nEns,wEns,nGrid,weight,rhow,drhow,Ec) ! Total energy Ew = sum(ET(:)) + sum(EV(:)) + sum(EJ(:)) + sum(Ex(:)) + sum(Ec(:)) ! Check the grid accuracy by computing the number of electrons do ispin=1,nspin nEl(ispin) = electron_number(nGrid,weight,rhow(:,ispin)) end do ! Dump results write(*,'(1X,A1,1X,I3,1X,A1,1X,F16.10,1X,A1,1X,F16.10,1X,A1,1X,F16.10,1X,A1,1X,F10.6,1X,A1,1X,F10.6,1X,A1,1X)') & '|',nSCF,'|',Ew + ENuc,'|',sum(Ex(:)),'|',sum(Ec(:)),'|',conv,'|',sum(nEl(:)),'|' 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 KS energy call print_UKS(nBas,nO,eps,c,ENuc,ET,EV,EJ,Ex,Ec,Ew) !------------------------------------------------------------------------ ! Compute individual energies from ensemble energy !------------------------------------------------------------------------ call unrestricted_individual_energy(x_rung,x_DFA,c_rung,c_DFA,LDA_centered,nEns,wEns,aCC_w1,aCC_w2,nGrid,weight,nBas, & AO,dAO,nO,nV,T,V,ERI,ENuc,eps,Pw,rhow,drhow,J,Fx,FxHF,Fc,P,rho,drho,Ew,E,Om) end subroutine eDFT_UKS