tdtdm.F90

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!! Copyright (C) 2019-2021 N. Tancogne-Dejean
!!
!! This program is free software; you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation; either version 2, or (at your option)
!! any later version.
!!
!! This program is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with this program; if not, write to the Free Software
!! Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
!! 02110-1301, USA.
!!
 
#include "global.h"
 
program tdtdm
  use batch_oct_m
  use calc_mode_par_oct_m
  use comm_oct_m
  use debug_oct_m
  use electrons_oct_m
  use electron_space_oct_m
  use fft_oct_m
  use global_oct_m
  use grid_oct_m
  use hamiltonian_elec_oct_m
  use io_oct_m
  use io_function_oct_m
  use kpoints_oct_m
  use lalg_basic_oct_m
  use messages_oct_m
  use mesh_oct_m
  use mesh_function_oct_m
  use mpi_oct_m
  use multicomm_oct_m
  use namespace_oct_m
  use parser_oct_m
  use profiling_oct_m
  use restart_oct_m
  use spectrum_oct_m
  use states_elec_oct_m
  use states_elec_dim_oct_m
  use states_elec_restart_oct_m
  use symmetries_oct_m
  use symm_op_oct_m
  use types_oct_m
  use unit_oct_m
  use unit_system_oct_m
  use xc_oct_m
 
  implicit none
 
  integer :: in_file, ii, jj, kk, ierr, ip_h, irow, ifreq, nrow, it
  integer :: ik, ist, uist, istep, ikpoint, irep, out_file, iop, idim
  integer :: time_steps, energy_steps, istart, iend, ntiter, Nreplica, Ntrans
  real(real64)   :: dt, tt, weight, kpoint(3), kpoint_sym(3), kred(3), kred_sym(3)
  real(real64)   :: xx_h_sym(3)
  integer :: irep_h, ip_h_sym, rankmin
  real(real64)   :: start_time, dmin
  real(real64), allocatable :: Et(:), ftreal(:, :, :), ftimag(:, :, :), tmp(:), omega(:)
  complex(real64), allocatable :: Xiak(:,:,:), Yiak(:,:,:)
  real(real64), allocatable :: proj_r(:,:,:,:), proj_i(:,:,:,:)
  real(real64), allocatable :: proj_r_corr(:,:), proj_i_corr(:,:), centers(:,:)
  complex(real64), allocatable :: tdm(:,:), tdm_1D(:,:,:,:)
  complex(real64), allocatable, target :: psi(:,:), upsi(:,:)
  complex(real64), allocatable ::  phase(:,:,:), ftcmplx(:,:)
  complex(real64), pointer :: psi_sym(:,:), upsi_sym(:,:)
  type(spectrum_t)  :: spectrum
  type(electrons_t), pointer :: sys
  type(batch_t)     :: projb_r, projb_i, ftrealb, ftimagb
  character(len=MAX_PATH_LEN) :: fname
  type(states_elec_t), pointer :: st
  type(states_elec_t) :: gs_st
  type(restart_t) :: restart
  type(unit_t) :: fn_unit
  integer :: kpt_start, kpt_end, supercell(3), nomega, ncols
  type(block_t) :: blk
  real(real64) :: pos_h(3), norm
 
  ! Initializion
  call global_init()
  call parser_init()
 
  call messages_init()
  call io_init()
 
  call profiling_init(global_namespace)
 
  call messages_experimental("oct-tdtdm utility")
  call fft_all_init(global_namespace)
  call unit_system_init(global_namespace)
  call restart_module_init(global_namespace)
 
  call calc_mode_par%set_parallelization(p_strategy_states, default = .false.)
  sys => electrons_t(global_namespace)
  call sys%init_parallelization(mpi_world)
 
  call spectrum_init(spectrum, global_namespace)
 
  st => sys%st
 
  if(sys%st%d%ispin == spinors) then
    call messages_not_implemented('oct-tdtdm with spinors')
  end if
 
  if(st%parallel_in_states) then
    call messages_not_implemented("oct-tdtdm with states parallelization")
  end if
 
  if(sys%gr%parallel_in_domains) then
    call messages_not_implemented("oct-tdtdm with domain parallelization")
  end if
 
  !%Variable TDTDMFrequencies
  !%Type block
  !%Section Utilities::oct-tdtdm
  !%Description
  !% This block defines for which frequencies the analysis is performed.
  !%
  !% Each row of the block indicates a frequency.
  !%End
  if (parse_block(global_namespace, 'TDTDMFrequencies', blk) == 0) then
 
    nrow = parse_block_n(blk)
    nomega = nrow
 
    safe_allocate(omega(1:nrow))
    !read frequencies
    do irow = 0, nrow-1
      call parse_block_float(blk, irow, 0, omega(irow+1))
    end do
 
    call parse_block_end(blk)
  else
    message(1) = "oct-tdtdm: TDTDMFrequencies must be defined."
    call messages_fatal(1)
  end if
 
  ! We check that the resonant and antiresonant transitions are contained in the
  ! energy range of the Fourier transforms
  if(any(omega > spectrum%max_energy)) then
    message(1) = "One requested frequecy is larger than PropagationSpectrumMaxEnergy."
    message(2) = "Please increase the value of PropagationSpectrumMaxEnergy."
    call messages_fatal(2)
  end if
  if(any(omega > -spectrum%min_energy)) then
    message(1) = "One requested frequency is larger than -PropagationSpectrumMinEnergy."
    message(2) = "Please decrease the value of PropagationSpectrumMinEnergy."
    call messages_fatal(2)
  end if
 
 
  call states_elec_copy(gs_st, st, exclude_wfns = .true., exclude_eigenval = .true.)
 
  safe_deallocate_a(gs_st%node)
 
  call restart_init(restart, global_namespace, restart_proj, restart_type_load, sys%mc, ierr, mesh=sys%gr)
  if(ierr == 0) call states_elec_look(restart, ii, jj, gs_st%nst, ierr)
  if(ierr /= 0) then
    message(1) = "oct-tdtdm: Unable to read states information."
    call messages_fatal(1)
  end if
 
  ! allocate memory
  safe_allocate(gs_st%occ(1:gs_st%nst, 1:gs_st%nik))
  safe_allocate(gs_st%eigenval(1:gs_st%nst, 1:gs_st%nik))
 
  ! We want all the task to have all the states
  ! States can be distibuted for the states we propagate.
  safe_allocate(gs_st%node(1:gs_st%nst))
  gs_st%node(:)  = 0
  call kpoints_distribute(gs_st, sys%mc)
  call states_elec_distribute_nodes(gs_st, global_namespace, sys%mc)
 
  kpt_start = gs_st%d%kpt%start
  kpt_end = gs_st%d%kpt%end
 
  kpoint = m_zero
 
  gs_st%eigenval = huge(gs_st%eigenval)
  gs_st%occ      = m_zero
  if(gs_st%d%ispin == spinors) then
    safe_deallocate_a(gs_st%spin)
    safe_allocate(gs_st%spin(1:3, 1:gs_st%nst, 1:gs_st%nik))
  end if
 
  call states_elec_allocate_wfns(gs_st, sys%gr, type_cmplx)
  call states_elec_load(restart, global_namespace, sys%space, gs_st, sys%gr, sys%kpoints, fixed_occ=.true., ierr=ierr)
  if(ierr /= 0 .and. ierr /= (gs_st%st_end-gs_st%st_start+1)*(kpt_end-kpt_start+1)*gs_st%d%dim) then
    message(1) = "oct-tdtdm: Unable to read wavefunctions for TDOutput."
    call messages_fatal(1)
  end if
  call restart_end(restart)
 
 
  in_file = io_open('td.general/projections', action='read', status='old')
  call io_skip_header(in_file)
  call spectrum_count_time_steps(global_namespace, in_file, time_steps, dt)
  dt = units_to_atomic(units_out%time, dt)
 
 
  safe_allocate(tmp(1:st%nst*gs_st%nst*st%nik*2))
  safe_allocate(proj_r(1:time_steps, 1:gs_st%nst, 1:st%nst, 1:st%nik))
  safe_allocate(proj_i(1:time_steps, 1:gs_st%nst, 1:st%nst, 1:st%nik))
 
 
  call io_skip_header(in_file)
 
  do ii = 1, time_steps
    read(in_file, *) jj, tt, (tmp(kk), kk = 1, st%nst*gs_st%nst*st%nik*2)
    do ik = 1, st%nik
      do ist = 1, st%nst
        do uist = 1, gs_st%nst
          jj  = (ik-1)*st%nst*gs_st%nst + (ist-1)*gs_st%nst + uist
          proj_r(ii, uist, ist, ik) = tmp((jj-1)*2+1)
          ! Here we add a minus sign, as we want to get <\phi_0 | \psi(t)>
          ! and td_occup computes the complex conjugaute of this
          proj_i(ii, uist, ist, ik) = -tmp((jj-1)*2+2)
        end do
      end do
    end do
  end do
  safe_deallocate_a(tmp)
 
  call io_close(in_file)
 
  write(message(1), '(a, i7, a)') "oct-tdtdm: Read ", time_steps, " steps from file '"// &
    trim(io_workpath('td.general/projections'))//"'"
  call messages_info(1)
 
  start_time = spectrum%start_time
 
  ! Phase correction of the projections before doing the Fourier transforms
  ! See Eq. (5) of Williams et al., JCTC 17, 1795 (2021)
  ! We need to multiply C_ik(t)e^{-ie_kt} (the projection of \phi_i(t) on \phi_k^GS)
  ! by e^{ie_it}, which is obtained by the cc of the projection of \phi_i(t) on \phi_i^GS
  ! Here we only care about optical transitions (so TD occupied to GS unocc)
  safe_allocate(proj_r_corr(1:time_steps, 1:gs_st%nst*st%nst*(kpt_end-kpt_start+1)))
  safe_allocate(proj_i_corr(1:time_steps, 1:gs_st%nst*st%nst*(kpt_end-kpt_start+1)))
  proj_r_corr = m_zero
  proj_i_corr = m_zero
  do ik = kpt_start, kpt_end
    do ist = 1, st%nst
      do uist = ist+1, gs_st%nst
        jj = (ik-kpt_start)*st%nst*gs_st%nst+(ist-1)*gs_st%nst+uist
        do ii = 1, time_steps
          norm = hypot(proj_r(ii, ist, ist, ik),proj_i(ii, ist, ist, ik))
          if (norm > m_epsilon) then
            proj_r_corr(ii, jj) = (proj_r(ii, uist, ist, ik) * proj_r(ii, ist, ist, ik) &
              + proj_i(ii, uist, ist, ik) * proj_i(ii, ist, ist, ik))/norm
            proj_i_corr(ii, jj) =(-proj_r(ii, uist, ist, ik) * proj_i(ii, ist, ist, ik) &
              + proj_i(ii, uist, ist, ik) * proj_r(ii, ist, ist, ik))/norm
          else
            proj_r_corr(ii, jj) = m_zero
            proj_i_corr(ii, jj) = m_zero
          end if
        end do
      end do
    end do
  end do
 
  safe_deallocate_a(proj_r)
  safe_deallocate_a(proj_i)
 
  ! Find out the iteration numbers corresponding to the time limits.
  call spectrum_fix_time_limits(spectrum, time_steps, dt, istart, iend, ntiter)
  istart = max(1, istart)
  energy_steps = spectrum_nenergy_steps(spectrum)
 
  safe_allocate(ftreal(1:energy_steps, 1:st%nst*gs_st%nst*(kpt_end-kpt_start+1), 1:2))
  safe_allocate(ftimag(1:energy_steps, 1:st%nst*gs_st%nst*(kpt_end-kpt_start+1), 1:2))
 
  call batch_init(projb_r, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), proj_r_corr)
  call batch_init(projb_i, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), proj_i_corr)
  call batch_init(ftrealb, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), ftreal(:,:,1))
  call batch_init(ftimagb, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), ftimag(:,:,1))
 
  write(message(1), '(a)') "oct-tdtdm: Fourier transforming real part of the projections"
  call messages_info(1)
 
  call spectrum_fourier_transform(spectrum%method, spectrum_transform_cos, spectrum%noise, &
    istart, iend, spectrum%start_time, dt, projb_r, spectrum%min_energy, spectrum%max_energy, spectrum%energy_step, ftrealb)
 
  call spectrum_fourier_transform(spectrum%method, spectrum_transform_sin, spectrum%noise, &
    istart, iend, spectrum%start_time, dt, projb_r, spectrum%min_energy, spectrum%max_energy, spectrum%energy_step, ftimagb)
 
  call ftrealb%end()
  call ftimagb%end()
 
  safe_allocate(ftcmplx(1:energy_steps, 1:st%nst*gs_st%nst*(kpt_end-kpt_start+1)))
  do ii = 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1)
    ftcmplx(1:energy_steps,ii) =  cmplx(ftreal(1:energy_steps,ii,1), ftimag(1:energy_steps,ii,1), real64)
  end do
 
  write(message(1), '(a)') "oct-tdtdm: Fourier transforming imaginary part of the projections"
  call messages_info(1)
 
  call batch_init(ftrealb, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), ftreal(:,:,2))
  call batch_init(ftimagb, 1, 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1), ftimag(:,:,2))
 
  call spectrum_fourier_transform(spectrum%method, spectrum_transform_cos, spectrum%noise, &
    istart, iend, spectrum%start_time, dt, projb_i, spectrum%min_energy, spectrum%max_energy, spectrum%energy_step, ftrealb)
 
  call spectrum_fourier_transform(spectrum%method, spectrum_transform_sin, spectrum%noise, &
    istart, iend, spectrum%start_time, dt, projb_i, spectrum%min_energy, spectrum%max_energy, spectrum%energy_step, ftimagb)
 
  call projb_i%end()
  call projb_r%end()
  call ftrealb%end()
  call ftimagb%end()
  safe_deallocate_a(proj_r_corr)
  safe_deallocate_a(proj_i_corr)
 
  do ii = 1, st%nst*gs_st%nst*(kpt_end-kpt_start+1)
    ftcmplx(1:energy_steps,ii) = ftcmplx(1:energy_steps,ii) + m_zi*ftreal(1:energy_steps,ii,2) - ftimag(1:energy_steps,ii,2)
  end do
 
  safe_deallocate_a(ftreal)
  safe_deallocate_a(ftimag)
 
  write(message(1), '(a)') "oct-tdtdm: Constructing the two-particle wavefunctions."
  call messages_info(1)
 
  !%Variable SupercellDimensions
  !%Type block
  !%Default KPointsGrid
  !%Section Utilities::oct-tdtdm
  !%Description
  !% This block allows to specify the size of the supercell used to plot excitonic wavefunctions.
  !% If not specified, the code uses the number of k-points for defining the size of the supercell.
  !%End
  if (parse_is_defined(sys%namespace, 'SupercellDimensions')) then
    if (parse_block(sys%namespace, 'SupercellDimensions', blk) == 0) then
      ncols = parse_block_cols(blk, 0)
      if (ncols /= sys%space%dim) then
        write(message(1),'(a,i3,a,i3)') 'SupercellDimensions has ', ncols, ' columns but must have ', sys%space%dim
        call messages_fatal(1, namespace=sys%namespace)
      end if
      do ii = 1, sys%space%dim
        call parse_block_integer(blk, 0, ii - 1, supercell(ii))
      end do
 
      call parse_block_end(blk)
    end if
  else
    supercell(1:sys%space%dim) = sys%kpoints%nik_axis(1:sys%space%dim)
  end if
 
  nreplica = product(supercell(1:sys%space%dim))
 
  ! The center of each replica of the unit cell
  safe_allocate(centers(1:sys%space%dim, 1:nreplica))
  irep = 1
  do ii = 0, supercell(1)-1
    do jj = 0, supercell(2)-1
      do kk = 0, supercell(3)-1
        centers(1, irep) = -floor((supercell(1)-1)/m_two)+ii
        centers(2, irep) = -floor((supercell(2)-1)/m_two)+jj
        centers(3, irep) = -floor((supercell(3)-1)/m_two)+kk
        centers(:, irep) = matmul(sys%ions%latt%rlattice, centers(:, irep))
        irep = irep + 1
      end do
    end do
  end do
 
  ! The phase for each center
  irep = 0
  do ik = kpt_start, kpt_end
    ikpoint = gs_st%d%get_kpoint_index(ik)
    irep = max(irep, kpoints_get_num_symmetry_ops(sys%kpoints, ikpoint))
  end do
  safe_allocate(phase(kpt_start:kpt_end, 1:irep, 1:nreplica))
  do irep = 1, nreplica
    do ik = kpt_start, kpt_end
      ikpoint = gs_st%d%get_kpoint_index(ik)
      kpoint(1:sys%space%dim) = sys%kpoints%get_point(ikpoint)
      do ii = 1, kpoints_get_num_symmetry_ops(sys%kpoints, ikpoint)
        iop = kpoints_get_symmetry_ops(sys%kpoints, ikpoint, ii)
 
        if (sys%kpoints%use_symmetries) then !We apply the symmetry
          call kpoints_to_reduced(sys%kpoints%latt, kpoint, kred)
          call symmetries_apply_kpoint_red(sys%kpoints%symm, iop, kred, kred_sym)
          call kpoints_to_absolute(sys%kpoints%latt, kred_sym, kpoint_sym)
        else
          kpoint_sym = kpoint
        end if
        phase(ik, ii, irep) = exp(-m_zi*sum(kpoint_sym(1:sys%space%dim)*centers(:, irep)))
      end do
    end do
  end do
 
  ! Position of the hole, here assumed to be on top of the first atom
  ! To be obtained from the input file
  if(sys%space%dim > 1) then
    call tdtdm_get_hole_position(pos_h, ip_h)
  end if
 
  ntrans = 0
  ! Here we assume that there is a clear gap, so the information at Gamma is enough
  do ist = 1, gs_st%nst
    if(abs(gs_st%occ(ist, 1)) < m_min_occ) cycle
 
    do uist = 1, gs_st%nst
      if(abs(gs_st%occ(uist, 1)) > m_min_occ) cycle
      weight = gs_st%kweights(1) * (gs_st%occ(ist, 1)-gs_st%occ(uist, 1))
      if(abs(weight) < m_min_occ) cycle
      ntrans = ntrans + 1
    end do
  end do
  if(ntrans == 0) then
    write(message(1), '(a)') "oct-tdtdm: No transition found."
    write(message(2), '(a)') "Please check that unoccupied states are included in the ground state calculation."
    call messages_fatal(2)
  end if
 
  safe_allocate(xiak(1:st%nst, 1:gs_st%nst, 1:st%nik))
  safe_allocate(yiak(1:st%nst, 1:gs_st%nst, 1:st%nik))
  safe_allocate(et(1:ntrans*st%nik))
  safe_allocate(psi(1:sys%gr%np, 1:gs_st%d%dim))
  safe_allocate(upsi(1:sys%gr%np, 1:gs_st%d%dim))
 
  if(sys%kpoints%use_symmetries) then
    safe_allocate(psi_sym(1:sys%gr%np, 1:st%d%dim))
    safe_allocate(upsi_sym(1:sys%gr%np, 1:st%d%dim))
  end if
 
  select case(sys%space%dim)
  case(2,3)
    safe_allocate(tdm(1:sys%gr%np, 1:nreplica))
  case(1)
    safe_allocate(tdm_1d(1:sys%gr%np, 1:sys%gr%np, 1:nreplica, 1:nreplica))
  end select
 
  do ifreq = 1, nomega
 
    write(message(1), '(a, f6.4, a)') "oct-tdtdm: Constructing the two-particle wavefunction at ", omega(ifreq), " Ha."
    call messages_info(1)
 
    select case(sys%space%dim)
    case(2,3)
      tdm = m_z0
    case(1)
      tdm_1d = m_z0
    end select
 
    et = m_zero
    xiak = m_z0
    yiak = m_z0
 
    ! Local transition index
    it = (kpt_start-1)*ntrans + 1
 
    do ik = kpt_start, kpt_end
      ikpoint = st%d%get_kpoint_index(ik)
 
      do ist = 1, st%nst
        if(abs(gs_st%occ(ist, ik)) < m_min_occ) cycle
 
        call states_elec_get_state(gs_st, sys%gr, ist, ik, psi)
        if (sys%hm%phase%is_allocated()) then
          call sys%hm%phase%apply_to_single(psi, sys%gr%np, gs_st%d%dim, ik, .false.)
        end if
 
        do uist = 1, gs_st%nst
          if(abs(gs_st%occ(uist, ik)) > m_min_occ) cycle
 
          ! For a given requested frequency, we get the corresponding values of Xia and Yia
          ! One correspond to the +\Omega frequency, the other one to the -\Omega frequency
          ! For Xiak, we use the fact that TF[f*](\Omega) = (TF[f](-\Omega))^*
          jj = (ik-kpt_start)*st%nst*gs_st%nst+(ist-1)*gs_st%nst+uist
          istep = int((+omega(ifreq)-spectrum%min_energy)/spectrum%energy_step)
          xiak(ist, uist, ik) = conjg(ftcmplx(istep, jj))
          istep = int((+omega(ifreq)-spectrum%min_energy)/spectrum%energy_step)
          yiak(ist, uist, ik) = ftcmplx(istep, jj)
 
 
          weight = gs_st%kweights(ik) * (gs_st%occ(ist, ik)-gs_st%occ(uist, ik)) &
            / kpoints_get_num_symmetry_ops(sys%kpoints, ikpoint)
          if(abs(weight) < m_epsilon) cycle
 
          call states_elec_get_state(gs_st, sys%gr, uist, ik, upsi)
          if(sys%hm%phase%is_allocated()) then
            call sys%hm%phase%apply_to_single(upsi, sys%gr%np, st%d%dim, ik, .false.)
          end if
 
          do ii = 1, kpoints_get_num_symmetry_ops(sys%kpoints, ikpoint)
            iop = kpoints_get_symmetry_ops(sys%kpoints, ikpoint, ii)
 
            if(sys%kpoints%use_symmetries) then
              do idim = 1, st%d%dim
                call zgrid_symmetrize_single(sys%gr, iop, psi(:,idim), psi_sym(:,idim))
                call zgrid_symmetrize_single(sys%gr, iop, upsi(:,idim), upsi_sym(:,idim))
              end do
 
              ! We need to get the position of the hole after applying the symmetry operation too
              xx_h_sym = symm_op_apply_cart(sys%kpoints%symm%ops(iop), pos_h)
              xx_h_sym = sys%ions%latt%fold_into_cell(xx_h_sym)
              ! At the moment, we ignore rankmin
              assert(.not.sys%gr%parallel_in_domains)
              ip_h_sym = mesh_nearest_point(sys%gr, xx_h_sym, dmin, rankmin)
            else
              psi_sym => psi
              upsi_sym => upsi
              ip_h_sym = ip_h
            end if
 
            ! We now compute the single mode TDTDM
            ! See Eq. (5) of Williams et al., JCTC 17, 1795 (2021)
            ! We take here the complex conjugate of the 2-body wavefunction
            select case(sys%space%dim)
            case(2,3)
              do irep = 1, nreplica
                call lalg_axpy(sys%gr%np, phase(ik, ii, irep) * weight &
                  * conjg(xiak(ist,uist,ik))*conjg(psi_sym(ip_h_sym,1)), upsi_sym(:, 1), tdm(:,irep))
                call lalg_axpy(sys%gr%np, phase(ik, ii, irep) * weight &
                  * yiak(ist,uist,ik)*conjg(upsi_sym(ip_h_sym,1)), psi_sym(:, 1), tdm(:,irep))
              end do
            case(1)
              ! In the 1D case, we contruct the full TDTDM of r_e, r_h
              do irep_h = 1, nreplica
                do irep = 1, nreplica
                  do ip_h = 1, sys%gr%np
                    call lalg_axpy(sys%gr%np, phase(ik, ii, irep) * conjg(phase(ik, ii, irep_h)) &
                      * weight * conjg(xiak(ist,uist,ik)) * conjg(psi_sym(ip_h,1)), &
                      upsi_sym(:, 1), tdm_1d(:, ip_h, irep, irep_h))
                    call lalg_axpy(sys%gr%np, phase(ik, ii, irep) * conjg(phase(ik, ii, irep_h)) &
                      * weight * conjg(yiak(ist,uist,ik)) * conjg(upsi_sym(ip_h,1)), &
                      psi_sym(:, 1), tdm_1d(:, ip_h, irep, irep_h))
                  end do
                end do
              end do
            end select
 
          end do ! ii
 
          et(it) = gs_st%eigenval(uist, ik) - gs_st%eigenval(ist, ik)
          it = it + 1
        end do
      end do
    end do
 
    if(gs_st%d%kpt%parallel) then
      if(sys%space%dim > 1) then
        call comm_allreduce(gs_st%d%kpt%mpi_grp, tdm)
      else
        call comm_allreduce(gs_st%d%kpt%mpi_grp, tdm_1d)
      end if
      call comm_allreduce(gs_st%d%kpt%mpi_grp, et)
      call comm_allreduce(gs_st%d%kpt%mpi_grp, xiak)
      call comm_allreduce(gs_st%d%kpt%mpi_grp, yiak)
    end if
 
    call tdtdm_output_density()
 
    call tdtdm_excitonic_weight()
 
  end do ! ifreq
 
  safe_deallocate_a(et)
  safe_deallocate_a(xiak)
  safe_deallocate_a(yiak)
  safe_deallocate_a(tdm)
  safe_deallocate_a(tdm_1d)
 
  safe_deallocate_a(psi)
  safe_deallocate_a(upsi)
  if(sys%kpoints%use_symmetries) then
    safe_deallocate_p(psi_sym)
    safe_deallocate_p(upsi_sym)
  end if
  safe_deallocate_a(ftcmplx)
  safe_deallocate_a(centers)
  safe_deallocate_a(phase)
  safe_deallocate_a(omega)
 
  safe_deallocate_p(sys)
  call states_elec_end(gs_st)
  call fft_all_end()
  call io_end()
  call profiling_end(global_namespace)
  call messages_end()
  call parser_end()
  call global_end()
 
contains
 
  ! -----------------------------------------------------------------
  ! Determines the position of the hole, either from the input or using the
  ! first atom in the cell.
  ! This returns the index of the point in the mesh closest to the position.
  subroutine tdtdm_get_hole_position(xx_h, ip_h)
    real(real64),   intent(out) :: xx_h(1:sys%space%dim)
    integer, intent(out) :: ip_h
 
    real(real64) :: dmin
    integer :: idir, rankmin
 
    push_sub(tdtdm_get_hole_position)
 
    !%Variable TDTDMHoleCoordinates
    !%Type float
    !%Section Utilities::oct-tdtdm
    !%Description
    !% The position of the hole used to compute the TDTDM,
    !% in Cartesian coordinates.
    !% Note that the code will use the closest grid point.
    !%
    !% The coordinates of the hole are specified in the following way
    !% <tt>%TDTDMHoleCoordinates
    !% <br>&nbsp;&nbsp;hole_x | hole_y | hole_z
    !% <br>%</tt>
    !%
    !% If TDTDMHoleCoordinates or TDTDMHoleReducedCoordinates are not specified,
    !% the code will use the coordinate of the first atom in the cell.
    !%End
 
    if(parse_block(global_namespace, 'TDTDMHoleCoordinates', blk) == 0) then
      if(parse_block_cols(blk,0) < sys%space%dim) then
        call messages_input_error(global_namespace, 'TDTDMHoleCoordinates')
      end if
      do idir = 1, sys%space%dim
        call parse_block_float(blk, 0, idir - 1, xx_h(idir), units_inp%length)
      end do
      call parse_block_end(blk)
    else
      !%Variable TDTDMHoleReducedCoordinates
      !%Type float
      !%Section Utilities::oct-tdtdm
      !%Description
      !% Same as TDTDMHoleCoordinates, except that coordinates are given in reduced coordinates
      !%End
 
      if(parse_block(global_namespace, 'TDTDMHoleReducedCoordinates', blk) == 0) then
        if(parse_block_cols(blk,0) < sys%space%dim) then
          call messages_input_error(global_namespace, 'TDTDMHoleReducedCoordinates')
        end if
        do idir = 1, sys%space%dim
          call parse_block_float(blk, 0, idir - 1, xx_h(idir))
        end do
        call parse_block_end(blk)
        xx_h = sys%ions%latt%red_to_cart(xx_h)
      else
        xx_h(1:sys%space%dim) = sys%ions%pos(1:sys%space%dim, 1)
      end if
    end if
 
    ! We bring back the hole into the cell
    xx_h = sys%ions%latt%fold_into_cell(xx_h)
 
    ! At the moment, we ignore rankmin
    assert(.not.sys%gr%parallel_in_domains)
    ip_h = mesh_nearest_point(sys%gr, xx_h, dmin, rankmin)
    write(message(1), '(a, 3(1x,f7.4,a))') "oct-tdtdm: Requesting the hole at (", xx_h(1), &
      ",", xx_h(2), ",", xx_h(3), ")."
    call mesh_r(sys%gr, ip_h, dmin, coords=xx_h)
    write(message(2), '(a, 3(1x,f7.4,a))') "oct-tdtdm: Setting the hole at (", xx_h(1), &
      ",", xx_h(2), ",", xx_h(3), ")."
 
    call messages_info(2)
 
    pop_sub(tdtdm_get_hole_position)
  end subroutine tdtdm_get_hole_position
 
  subroutine tdtdm_output_density()
    real(real64), allocatable :: den(:,:), den_1d(:,:,:,:)
    real(real64) :: norm, xx(3), xx_h(3)
    integer :: iunit
 
    push_sub(tdtdm_output_density)
 
    ! We compute the TDM density
    select case(sys%space%dim)
    case(2,3)
      safe_allocate(den(1:sys%gr%np, 1:nreplica))
      do irep = 1, nreplica
        do ii = 1, sys%gr%np
          den(ii, irep) = real(tdm(ii, irep)*conjg(tdm(ii, irep)), real64)
        end do
      end do
 
      ! Here we renormalize to avoid too small numbers in the outputs
      norm = maxval(den)
      call lalg_scal(sys%gr%np, nreplica, m_one/norm, den)
 
    case(1)
      safe_allocate(den_1d(1:sys%gr%np, 1:sys%gr%np, 1:nreplica, 1:nreplica))
      do irep_h = 1, nreplica
        do irep = 1, nreplica
          do ip_h = 1, sys%gr%np
            do ii = 1, sys%gr%np
              tdm_1d(ii, ip_h, irep, irep_h) = conjg(tdm_1d(ii, ip_h, irep, irep_h))
              den_1d(ii, ip_h, irep, irep_h) = real(tdm_1d(ii, ip_h, irep, irep_h)*conjg(tdm_1d(ii,ip_h, irep, irep_h)), real64)
            end do
          end do
        end do
      end do
    end select
 
    fn_unit = units_out%length**(-sys%space%dim)
 
    select case(sys%space%dim)
    case(2,3)
      write(fname, '(a, f0.4)') 'tdm_density-0', omega(ifreq)
      call io_function_output_supercell(io_function_fill_how("XCrySDen"), "td.general", fname, &
        sys%gr, sys%space, sys%ions%latt, den, centers, supercell, fn_unit, &
        ierr, global_namespace, pos=sys%ions%pos, atoms=sys%ions%atom, grp = st%dom_st_kpt_mpi_grp, extra_atom=pos_h)
 
      call io_function_output_supercell(io_function_fill_how("PlaneZ"), "td.general", fname, &
        sys%gr, sys%space, sys%ions%latt, den, centers, supercell, fn_unit, &
        ierr, global_namespace, grp = st%dom_st_kpt_mpi_grp)
 
      safe_deallocate_a(den)
 
    case(1)
 
      call tdtdm_get_hole_position(pos_h, ip_h)
      irep_h = floor(supercell(1)/m_two)
 
      write(fname, '(a, f0.4)') 'tdm_density-0', omega(ifreq)
      call io_function_output_supercell(io_function_fill_how("AxisX"), "td.general", fname, &
        sys%gr, sys%space, sys%ions%latt, &
        den_1d(:,ip_h,:,irep_h), centers, supercell, fn_unit, ierr, global_namespace, &
        grp = st%dom_st_kpt_mpi_grp)
 
      write(fname, '(a, f0.4)') 'tdm_wfn-0', omega(ifreq)
      call io_function_output_supercell(io_function_fill_how("AxisX"), "td.general", fname, &
        sys%gr, sys%space, sys%ions%latt, &
        tdm_1d(:,ip_h,:,irep_h), centers, supercell, fn_unit, ierr, global_namespace, &
        grp = st%dom_st_kpt_mpi_grp)
 
      assert(.not.sys%gr%parallel_in_domains)
      if (mpi_grp_is_root(mpi_world)) then
        write(fname, '(a, f0.4)') 'td.general/tdm_density-0', omega(ifreq)
        iunit = io_open(fname, action='write')
        write(iunit, '(a)', iostat=ierr) '# r_e    r_h    Re(\Psi(r_e,r_h)) Im(\Psi(r_e,r_h)) |\Psi(r_e,r_h)|^2'
 
        do irep_h = 1, nreplica
          do ip_h = 1, sys%gr%np
            xx_h = units_from_atomic(units_out%length, mesh_x_global(sys%gr, i4_to_i8(ip_h)) &
              + centers(1:sys%space%dim, irep_h))
 
            do irep = 1, nreplica
              do ii = 1, sys%gr%np
                xx = units_from_atomic(units_out%length, mesh_x_global(sys%gr, i4_to_i8(ii)) &
                  + centers(1:sys%space%dim, irep))
                write(iunit, '(5es23.14E3)', iostat=ierr) xx(1), xx_h(1), &
                  real(units_from_atomic(fn_unit, tdm_1D(ii, ip_h, irep, irep_h)), real64)  ,&
                  aimag(units_from_atomic(fn_unit, tdm_1D(ii, ip_h, irep, irep_h))), &
                  units_from_atomic(fn_unit, den_1D(ii, ip_h, irep, irep_h))
              end do
            end do
          end do
        end do
      end if
 
      safe_deallocate_a(den_1d)
    end select
 
 
    pop_sub(tdtdm_output_density)
  end subroutine tdtdm_output_density
 
  subroutine tdtdm_excitonic_weight()
    real(real64), allocatable :: weight(:,:)
 
    if (.not. mpi_grp_is_root(mpi_world)) return
 
    push_sub(tdtdm_excitonic_weight)
 
    safe_allocate(weight(1:st%nik, 1:gs_st%nst))
    weight = m_zero
 
    do ik = 1, st%nik
      do ist = 1, st%nst
        if(abs(gs_st%occ(ist, ik)) < m_min_occ) cycle
 
        do uist = ist+1, gs_st%nst
          if(abs(gs_st%occ(uist, ik)) > m_min_occ) cycle
 
          weight(ik, ist)  = weight(ik, ist) + abs(xiak(ist, uist, ik))**2
          weight(ik, uist) = weight(ik,uist) + abs(yiak(ist, uist, ik))**2
        end do
      end do
    end do
 
    write(fname, '(a, f0.4)') 'td.general/tdm_weights-0', omega(ifreq)
    out_file = io_open(fname, action='write')
    write(out_file, '(a)') '# ik - kx - ky - kz - sum weights - eigenval and weights(ist,ik) '
    do ik = 1, st%nik
      ikpoint = st%d%get_kpoint_index(ik)
      kpoint(1:sys%space%dim) = sys%kpoints%reduced%point1BZ(1:sys%space%dim,ikpoint)
      write(out_file, '(i4,4e15.6)', advance='no') ik, kpoint(1:3), sum(weight(ik, 1:gs_st%nst))
      do uist = 1, gs_st%nst-1
        write(out_file, '(2e15.6)', advance='no') gs_st%eigenval(uist, ik), weight(ik, uist)
      end do
      write(out_file, '(e15.6)') weight(ik, uist)
    end do
    call io_close(out_file)
 
    safe_deallocate_a(weight)
 
    pop_sub(tdtdm_excitonic_weight)
  end subroutine tdtdm_excitonic_weight
 
end program tdtdm
 
!! Local Variables:
!! mode: f90
!! coding: utf-8
!! End: