2023-02-07 17:07:49 +01:00
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! ---
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BEGIN_PROVIDER [ double precision, natorb_tc_reigvec_mo, (mo_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, natorb_tc_leigvec_mo, (mo_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, natorb_tc_eigval, (mo_num)]
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BEGIN_DOC
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!
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! natorb_tc_reigvec_mo : RIGHT eigenvectors of the ground state transition matrix (equivalent of natural orbitals)
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! natorb_tc_leigvec_mo : LEFT eigenvectors of the ground state transition matrix (equivalent of natural orbitals)
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! natorb_tc_eigval : eigenvalues of the ground state transition matrix (equivalent of the occupation numbers). WARNINING :: can be negative !!
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!
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END_DOC
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implicit none
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integer :: i, j, k
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double precision :: thr_d, thr_nd, thr_deg, accu
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double precision :: accu_d, accu_nd
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double precision, allocatable :: dm_tmp(:,:), fock_diag(:)
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allocate(dm_tmp(mo_num,mo_num), fock_diag(mo_num))
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2023-02-23 16:12:00 +01:00
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dm_tmp(1:mo_num,1:mo_num) = -tc_transition_matrix_mo(1:mo_num,1:mo_num,1,1)
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2023-02-07 17:07:49 +01:00
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print *, ' dm_tmp'
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do i = 1, mo_num
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fock_diag(i) = fock_matrix_tc_mo_tot(i,i)
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write(*, '(100(F16.10,X))') -dm_tmp(:,i)
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enddo
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thr_d = 1.d-6
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thr_nd = 1.d-6
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thr_deg = 1.d-3
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call diag_mat_per_fock_degen( fock_diag, dm_tmp, mo_num, thr_d, thr_nd, thr_deg &
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, natorb_tc_leigvec_mo, natorb_tc_reigvec_mo, natorb_tc_eigval)
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! call non_hrmt_bieig( mo_num, dm_tmp&
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! , natorb_tc_leigvec_mo, natorb_tc_reigvec_mo&
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! , mo_num, natorb_tc_eigval )
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accu = 0.d0
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do i = 1, mo_num
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print*,'natorb_tc_eigval(i) = ',-natorb_tc_eigval(i)
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accu += -natorb_tc_eigval(i)
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enddo
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print *, ' accu = ', accu
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dm_tmp = 0.d0
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do i = 1, mo_num
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accu = 0.d0
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do k = 1, mo_num
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accu += natorb_tc_reigvec_mo(k,i) * natorb_tc_leigvec_mo(k,i)
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enddo
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accu = 1.d0/dsqrt(dabs(accu))
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natorb_tc_reigvec_mo(:,i) *= accu
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natorb_tc_leigvec_mo(:,i) *= accu
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do j = 1, mo_num
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do k = 1, mo_num
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dm_tmp(j,i) += natorb_tc_reigvec_mo(k,i) * natorb_tc_leigvec_mo(k,j)
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enddo
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enddo
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enddo
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accu_d = 0.d0
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accu_nd = 0.d0
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do i = 1, mo_num
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accu_d += dm_tmp(i,i)
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!write(*,'(100(F16.10,X))')dm_tmp(:,i)
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do j = 1, mo_num
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if(i==j)cycle
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accu_nd += dabs(dm_tmp(j,i))
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enddo
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enddo
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print *, ' Trace of the overlap between TC natural orbitals ', accu_d
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print *, ' L1 norm of extra diagonal elements of overlap matrix ', accu_nd
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deallocate(dm_tmp, fock_diag)
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END_PROVIDER
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! ---
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BEGIN_PROVIDER [ double precision, fock_diag_sorted_r_natorb, (mo_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, fock_diag_sorted_l_natorb, (mo_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, fock_diag_sorted_v_natorb, (mo_num)]
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implicit none
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integer :: i,j,k
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integer, allocatable :: iorder(:)
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double precision, allocatable :: fock_diag(:)
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print *, ' Diagonal elements of the Fock matrix before '
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do i = 1, mo_num
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write(*,*) i, Fock_matrix_tc_mo_tot(i,i)
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enddo
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allocate(fock_diag(mo_num))
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fock_diag = 0.d0
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do i = 1, mo_num
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fock_diag(i) = 0.d0
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do j = 1, mo_num
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do k = 1, mo_num
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fock_diag(i) += natorb_tc_leigvec_mo(k,i) * Fock_matrix_tc_mo_tot(k,j) * natorb_tc_reigvec_mo(j,i)
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enddo
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enddo
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enddo
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allocate(iorder(mo_num))
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do i = 1, mo_num
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iorder(i) = i
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enddo
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call dsort(fock_diag, iorder, mo_num)
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print *, ' Diagonal elements of the Fock matrix after '
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do i = 1, mo_num
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write(*,*) i, fock_diag(i)
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enddo
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deallocate(fock_diag)
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do i = 1, mo_num
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fock_diag_sorted_v_natorb(i) = natorb_tc_eigval(iorder(i))
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do j = 1, mo_num
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fock_diag_sorted_r_natorb(j,i) = natorb_tc_reigvec_mo(j,iorder(i))
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fock_diag_sorted_l_natorb(j,i) = natorb_tc_leigvec_mo(j,iorder(i))
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enddo
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enddo
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deallocate(iorder)
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END_PROVIDER
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! ---
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BEGIN_PROVIDER [ double precision, natorb_tc_reigvec_ao, (ao_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, natorb_tc_leigvec_ao, (ao_num, mo_num)]
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&BEGIN_PROVIDER [ double precision, overlap_natorb_tc_eigvec_ao, (mo_num, mo_num) ]
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BEGIN_DOC
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! EIGENVECTORS OF FOCK MATRIX ON THE AO BASIS and their OVERLAP
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!
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! THE OVERLAP SHOULD BE THE SAME AS overlap_natorb_tc_eigvec_mo
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END_DOC
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implicit none
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integer :: i, j, k, q, p
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double precision :: accu, accu_d
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double precision, allocatable :: tmp(:,:)
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! ! MO_R x R
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call dgemm( 'N', 'N', ao_num, mo_num, mo_num, 1.d0 &
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, mo_r_coef, size(mo_r_coef, 1) &
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, fock_diag_sorted_r_natorb, size(fock_diag_sorted_r_natorb, 1) &
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, 0.d0, natorb_tc_reigvec_ao, size(natorb_tc_reigvec_ao, 1) )
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!
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! MO_L x L
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call dgemm( 'N', 'N', ao_num, mo_num, mo_num, 1.d0 &
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, mo_l_coef, size(mo_l_coef, 1) &
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, fock_diag_sorted_l_natorb, size(fock_diag_sorted_l_natorb, 1) &
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, 0.d0, natorb_tc_leigvec_ao, size(natorb_tc_leigvec_ao, 1) )
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allocate( tmp(mo_num,ao_num) )
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! tmp <-- L.T x S_ao
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call dgemm( "T", "N", mo_num, ao_num, ao_num, 1.d0 &
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, natorb_tc_leigvec_ao, size(natorb_tc_leigvec_ao, 1), ao_overlap, size(ao_overlap, 1) &
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, 0.d0, tmp, size(tmp, 1) )
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! S <-- tmp x R
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call dgemm( "N", "N", mo_num, mo_num, ao_num, 1.d0 &
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, tmp, size(tmp, 1), natorb_tc_reigvec_ao, size(natorb_tc_reigvec_ao, 1) &
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, 0.d0, overlap_natorb_tc_eigvec_ao, size(overlap_natorb_tc_eigvec_ao, 1) )
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deallocate( tmp )
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! ---
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double precision :: norm
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do i = 1, mo_num
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norm = 1.d0/dsqrt(dabs(overlap_natorb_tc_eigvec_ao(i,i)))
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do j = 1, mo_num
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natorb_tc_reigvec_ao(j,i) *= norm
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natorb_tc_leigvec_ao(j,i) *= norm
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enddo
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enddo
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allocate( tmp(mo_num,ao_num) )
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! tmp <-- L.T x S_ao
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call dgemm( "T", "N", mo_num, ao_num, ao_num, 1.d0 &
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, natorb_tc_leigvec_ao, size(natorb_tc_leigvec_ao, 1), ao_overlap, size(ao_overlap, 1) &
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, 0.d0, tmp, size(tmp, 1) )
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! S <-- tmp x R
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call dgemm( "N", "N", mo_num, mo_num, ao_num, 1.d0 &
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, tmp, size(tmp, 1), natorb_tc_reigvec_ao, size(natorb_tc_reigvec_ao, 1) &
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, 0.d0, overlap_natorb_tc_eigvec_ao, size(overlap_natorb_tc_eigvec_ao, 1) )
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deallocate( tmp )
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accu_d = 0.d0
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accu = 0.d0
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do i = 1, mo_num
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accu_d += overlap_natorb_tc_eigvec_ao(i,i)
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do j = 1, mo_num
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if(i==j)cycle
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accu += dabs(overlap_natorb_tc_eigvec_ao(j,i))
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enddo
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enddo
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print*,'Trace of the overlap_natorb_tc_eigvec_ao = ',accu_d
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print*,'mo_num = ',mo_num
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print*,'L1 norm of extra diagonal elements of overlap matrix ',accu
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accu = accu / dble(mo_num**2)
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END_PROVIDER
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