subroutine get_s2(key_i,key_j,s2,Nint) implicit none use bitmasks BEGIN_DOC ! Returns END_DOC integer, intent(in) :: Nint integer(bit_kind), intent(in) :: key_i(Nint,2) integer(bit_kind), intent(in) :: key_j(Nint,2) double precision, intent(out) :: s2 integer :: exc(0:2,2,2) integer :: degree double precision :: phase_spsm integer :: nup, i s2 = 0.d0 !$FORCEINLINE call get_excitation_degree(key_i,key_j,degree,Nint) select case (degree) case(2) call get_double_excitation(key_j,key_i,exc,phase_spsm,Nint) if (exc(0,1,1) == 1) then ! Mono alpha + mono-beta if ( (exc(1,1,1) == exc(1,2,2)).and.(exc(1,1,2) == exc(1,2,1)) ) then s2 = -phase_spsm endif endif case(0) nup = 0 do i=1,Nint nup += popcnt(iand(xor(key_i(i,1),key_i(i,2)),key_i(i,1))) enddo s2 = dble(nup) end select end BEGIN_PROVIDER [ double precision, S_z ] &BEGIN_PROVIDER [ double precision, S_z2_Sz ] implicit none BEGIN_DOC ! z component of the Spin END_DOC S_z = 0.5d0*dble(elec_alpha_num-elec_beta_num) S_z2_Sz = S_z*(S_z-1.d0) END_PROVIDER BEGIN_PROVIDER [ double precision, expected_s2] implicit none BEGIN_DOC ! Expected value of S2 : S*(S+1) END_DOC logical :: has_expected_s2 call ezfio_has_determinants_expected_s2(has_expected_s2) if (has_expected_s2) then call ezfio_get_determinants_expected_s2(expected_s2) else double precision :: S S = (elec_alpha_num-elec_beta_num)*0.5d0 expected_s2 = S * (S+1.d0) endif END_PROVIDER BEGIN_PROVIDER [ double precision, s2_values, (N_states) ] implicit none BEGIN_DOC ! array of the averaged values of the S^2 operator on the various states END_DOC integer :: i call u_0_S2_u_0(s2_values,psi_coef,n_det,psi_det,N_int,N_states,psi_det_size) END_PROVIDER subroutine u_0_S2_u_0(e_0,u_0,n,keys_tmp,Nint,N_st,sze_8) use bitmasks implicit none BEGIN_DOC ! Computes e_0 = / ! ! n : number of determinants ! END_DOC integer, intent(in) :: n,Nint, N_st, sze_8 double precision, intent(out) :: e_0(N_st) double precision, intent(in) :: u_0(sze_8,N_st) integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n) double precision, allocatable :: v_0(:,:) double precision :: u_dot_u,u_dot_v integer :: i,j allocate (v_0(sze_8,N_st)) call S2_u_0_nstates(v_0,u_0,n,keys_tmp,Nint,N_st,sze_8) do i=1,N_st e_0(i) = u_dot_v(v_0(1,i),u_0(1,i),n)/u_dot_u(u_0(1,i),n) + S_z2_Sz enddo end subroutine S2_u_0(v_0,u_0,n,keys_tmp,Nint) use bitmasks implicit none BEGIN_DOC ! Computes v_0 = S^2|u_0> ! ! n : number of determinants ! END_DOC integer, intent(in) :: n,Nint double precision, intent(out) :: v_0(n) double precision, intent(in) :: u_0(n) integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n) call S2_u_0_nstates(v_0,u_0,n,keys_tmp,Nint,1,n) end subroutine S2_u_0_nstates(v_0,u_0,n,keys_tmp,Nint,N_st,sze_8) use bitmasks implicit none BEGIN_DOC ! Computes v_0 = S^2|u_0> ! ! n : number of determinants ! END_DOC integer, intent(in) :: N_st,n,Nint, sze_8 double precision, intent(out) :: v_0(sze_8,N_st) double precision, intent(in) :: u_0(sze_8,N_st) integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n) double precision :: s2_tmp double precision, allocatable :: vt(:,:) integer :: i,j,k,l, jj,ii integer :: i0, j0 integer, allocatable :: shortcut(:,:), sort_idx(:,:) integer(bit_kind), allocatable :: sorted(:,:,:), version(:,:,:) integer(bit_kind) :: sorted_i(Nint) integer :: sh, sh2, ni, exa, ext, org_i, org_j, endi, istate ASSERT (Nint > 0) ASSERT (Nint == N_int) ASSERT (n>0) PROVIDE ref_bitmask_energy allocate (shortcut(0:n+1,2), sort_idx(n,2), sorted(Nint,n,2), version(Nint,n,2)) v_0 = 0.d0 call sort_dets_ab_v(keys_tmp, sorted(1,1,1), sort_idx(1,1), shortcut(0,1), version(1,1,1), n, Nint) call sort_dets_ba_v(keys_tmp, sorted(1,1,2), sort_idx(1,2), shortcut(0,2), version(1,1,2), n, Nint) !$OMP PARALLEL DEFAULT(NONE) & !$OMP PRIVATE(i,s2_tmp,j,k,jj,vt,ii,sh,sh2,ni,exa,ext,org_i,org_j,endi,sorted_i,istate)& !$OMP SHARED(n,u_0,keys_tmp,Nint,v_0,sorted,shortcut,sort_idx,version,N_st,sze_8) allocate(vt(sze_8,N_st)) vt = 0.d0 !$OMP DO SCHEDULE(dynamic) do sh=1,shortcut(0,1) do sh2=sh,shortcut(0,1) exa = 0 do ni=1,Nint exa = exa + popcnt(xor(version(ni,sh,1), version(ni,sh2,1))) end do if(exa > 2) then cycle end if do i=shortcut(sh,1),shortcut(sh+1,1)-1 org_i = sort_idx(i,1) if(sh==sh2) then endi = i-1 else endi = shortcut(sh2+1,1)-1 end if do ni=1,Nint sorted_i(ni) = sorted(ni,i,1) enddo do j=shortcut(sh2,1),endi org_j = sort_idx(j,1) ext = exa do ni=1,Nint ext = ext + popcnt(xor(sorted_i(ni), sorted(ni,j,1))) end do if(ext <= 4) then call get_s2(keys_tmp(1,1,org_i),keys_tmp(1,1,org_j),s2_tmp,Nint) do istate=1,N_st vt (org_i,istate) = vt (org_i,istate) + s2_tmp*u_0(org_j,istate) vt (org_j,istate) = vt (org_j,istate) + s2_tmp*u_0(org_i,istate) enddo endif enddo enddo enddo enddo !$OMP END DO NOWAIT !$OMP DO SCHEDULE(dynamic) do sh=1,shortcut(0,2) do i=shortcut(sh,2),shortcut(sh+1,2)-1 org_i = sort_idx(i,2) do j=shortcut(sh,2),i-1 org_j = sort_idx(j,2) ext = 0 do ni=1,Nint ext = ext + popcnt(xor(sorted(ni,i,2), sorted(ni,j,2))) end do if(ext == 4) then call get_s2(keys_tmp(1,1,org_i),keys_tmp(1,1,org_j),s2_tmp,Nint) do istate=1,N_st vt (org_i,istate) = vt (org_i,istate) + s2_tmp*u_0(org_j,istate) vt (org_j,istate) = vt (org_j,istate) + s2_tmp*u_0(org_i,istate) enddo end if end do end do enddo !$OMP END DO NOWAIT !$OMP CRITICAL do istate=1,N_st do i=n,1,-1 v_0(i,istate) = v_0(i,istate) + vt(i,istate) enddo enddo !$OMP END CRITICAL deallocate(vt) !$OMP END PARALLEL do i=1,n call get_s2(keys_tmp(1,1,i),keys_tmp(1,1,i),s2_tmp,Nint) do istate=1,N_st v_0(i,istate) += s2_tmp * u_0(i,istate) enddo enddo deallocate (shortcut, sort_idx, sorted, version) end subroutine get_uJ_s2_uI(psi_keys_tmp,psi_coefs_tmp,n,nmax_coefs,nmax_keys,s2,nstates) implicit none use bitmasks integer(bit_kind), intent(in) :: psi_keys_tmp(N_int,2,nmax_keys) integer, intent(in) :: n,nmax_coefs,nmax_keys,nstates double precision, intent(in) :: psi_coefs_tmp(nmax_coefs,nstates) double precision, intent(out) :: s2(nstates,nstates) double precision :: s2_tmp,accu integer :: i,j,l,jj,ll,kk integer, allocatable :: idx(:) BEGIN_DOC ! returns the matrix elements of S^2 "s2(i,j)" between the "nstates" states ! psi_coefs_tmp(:,i) and psi_coefs_tmp(:,j) END_DOC s2 = 0.d0 do ll = 1, nstates do jj = 1, nstates accu = 0.d0 !$OMP PARALLEL DEFAULT(NONE) & !$OMP PRIVATE (i,j,kk,idx,s2_tmp) & !$OMP SHARED (ll,jj,psi_keys_tmp,psi_coefs_tmp,N_int,n,nstates)& !$OMP REDUCTION(+:accu) allocate(idx(0:n)) !$OMP DO SCHEDULE(dynamic) do i = n,1,-1 ! Better OMP scheduling call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,i),s2_tmp,N_int) accu += psi_coefs_tmp(i,ll) * s2_tmp * psi_coefs_tmp(i,jj) call filter_connected(psi_keys_tmp,psi_keys_tmp(1,1,i),N_int,i-1,idx) do kk=1,idx(0) j = idx(kk) call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,j),s2_tmp,N_int) accu += psi_coefs_tmp(i,ll) * s2_tmp * psi_coefs_tmp(j,jj) + psi_coefs_tmp(i,jj) * s2_tmp * psi_coefs_tmp(j,ll) enddo enddo !$OMP END DO deallocate(idx) !$OMP END PARALLEL s2(ll,jj) += accu enddo enddo do i = 1, nstates do j =i+1,nstates accu = 0.5d0 * (s2(i,j) + s2(j,i)) s2(i,j) = accu s2(j,i) = accu enddo enddo end subroutine diagonalize_s2_betweenstates(keys_tmp,u_0,n,nmax_keys,nmax_coefs,nstates,s2_eigvalues) BEGIN_DOC ! You enter with nstates vectors in u_0 that may be coupled by S^2 ! The subroutine diagonalize the S^2 operator in the basis of these states. ! The vectors that you obtain in output are no more coupled by S^2, ! which does not necessary mean that they are eigenfunction of S^2. ! n,nmax,nstates = number of determinants, physical dimension of the arrays and number of states ! keys_tmp = array of integer(bit_kind) that represents the determinants ! psi_coefs(i,j) = coeff of the ith determinant in the jth state ! VECTORS ARE SUPPOSED TO BE ORTHONORMAL IN INPUT END_DOC implicit none use bitmasks integer, intent(in) :: n,nmax_keys,nmax_coefs,nstates integer(bit_kind), intent(in) :: keys_tmp(N_int,2,nmax_keys) double precision, intent(inout) :: u_0(nmax_coefs,nstates) double precision, intent(out) :: s2_eigvalues(nstates) double precision,allocatable :: s2(:,:),overlap(:,:) double precision, allocatable :: eigvectors(:,:,:) integer :: i,j,k double precision, allocatable :: psi_coefs_tmp(:,:) double precision :: accu,coef_contract double precision :: u_dot_u,u_dot_v print*,'' print*,'*********************************************************************' print*,'Cleaning the various vectors by diagonalization of the S^2 matrix ...' print*,'' print*,'nstates = ',nstates allocate(s2(nstates,nstates),overlap(nstates,nstates)) overlap = 0.d0 call dgemm('T','N',nstates,nstates,n, 1.d0, u_0, size(u_0,1), & u_0, size(u_0,1), 0.d0, overlap, size(overlap,1)) call ortho_lowdin(overlap,size(overlap,1),nstates,u_0,size(u_0,1),n) double precision, allocatable :: v_0(:,:) allocate ( v_0(size(u_0,1),nstates) ) call S2_u_0_nstates(v_0,u_0,n,keys_tmp,N_int,nstates,size(u_0,1)) call dgemm('T','N',nstates,nstates,n, 1.d0, u_0, size(u_0,1), & v_0, size(v_0,1), 0.d0, s2, size(s2,1)) print*,'S^2 matrix in the basis of the states considered' do i = 1, nstates write(*,'(100(F5.2,X))')s2(i,:) enddo double precision :: accu_precision_diag,accu_precision_of_diag accu_precision_diag = 0.d0 accu_precision_of_diag = 0.d0 do i = 1, nstates ! Do not combine states of the same spin symmetry do j = i+1, nstates if( dabs(s2(i,i) - s2(j,j)) .le.0.5d0) then s2(i,j) = 0.d0 s2(j,i) = 0.d0 endif enddo ! Do not rotate if the diagonal is correct if( dabs(s2(i,i) - expected_s2).le.5.d-3) then do j = 1, nstates if (j==i) cycle s2(i,j) = 0.d0 s2(j,i) = 0.d0 enddo endif enddo print*,'Modified S^2 matrix that will be diagonalized' do i = 1, nstates write(*,'(10(F5.2,X))')s2(i,:) s2(i,i) = s2(i,i) enddo allocate(eigvectors(nstates,nstates,2)) ! call svd(s2, size(s2,1), eigvectors, size(eigvectors,1), s2_eigvalues,& ! eigvectors(1,1,2), size(eigvectors,1), nstates, nstates) call lapack_diagd(s2_eigvalues,eigvectors,s2,nstates,nstates) print*,'Eigenvalues' double precision :: t(nstates) integer :: iorder(nstates) do i = 1, nstates t(i) = dabs(s2_eigvalues(i)) iorder(i) = i enddo call dsort(t,iorder,nstates) do i = 1, nstates s2_eigvalues(i) = t(i) do j=1,nstates eigvectors(j,i,2) = eigvectors(j,iorder(i),1) enddo print*,'s2 = ',s2_eigvalues(i) enddo allocate(psi_coefs_tmp(nmax_coefs,nstates)) psi_coefs_tmp = 0.d0 do j = 1, nstates do k = 1, nstates coef_contract = eigvectors(k,j,2) ! do i = 1, n_det psi_coefs_tmp(i,j) += u_0(i,k) * coef_contract enddo enddo enddo do j = 1, nstates accu = 1.d0/u_dot_u(psi_coefs_tmp(1,j),n_det) do i = 1, n_det u_0(i,j) = psi_coefs_tmp(i,j) * accu enddo enddo deallocate(s2,v_0,eigvectors,psi_coefs_tmp,overlap ) end