qs_cdft_utils.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
! **************************************************************************************************
!> \brief Utility subroutines for CDFT calculations
!> \par   History
!>                 separated from et_coupling [03.2017]
!> \author Nico Holmberg [03.2017]
! **************************************************************************************************
MODULE qs_cdft_utils
   USE ao_util,                         ONLY: exp_radius_very_extended
   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind
   USE bibliography,                    ONLY: becke1988b,&
                                              holmberg2017,&
                                              holmberg2018,&
                                              cite_reference
   USE cell_types,                      ONLY: cell_type,&
                                              pbc
   USE cp_control_types,                ONLY: dft_control_type,&
                                              qs_control_type
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_type,&
                                              cp_to_string
   USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
                                              cp_print_key_unit_nr
   USE cp_realspace_grid_cube,          ONLY: cp_pw_to_cube
   USE cp_units,                        ONLY: cp_unit_from_cp2k
   USE grid_api,                        ONLY: grid_func_ab,&
                                              collocate_pgf_product
   USE hirshfeld_methods,               ONLY: create_shape_function
   USE hirshfeld_types,                 ONLY: create_hirshfeld_type,&
                                              hirshfeld_type,&
                                              set_hirshfeld_info
   USE input_constants,                 ONLY: &
        becke_cutoff_element, becke_cutoff_global, cdft_charge_constraint, &
        outer_scf_becke_constraint, outer_scf_cdft_constraint, outer_scf_hirshfeld_constraint, &
        outer_scf_none, radius_user, shape_function_gaussian
   USE input_section_types,             ONLY: section_get_ivals,&
                                              section_vals_get,&
                                              section_vals_get_subs_vals,&
                                              section_vals_type,&
                                              section_vals_val_get
   USE kinds,                           ONLY: default_path_length,&
                                              dp
   USE memory_utilities,                ONLY: reallocate
   USE message_passing,                 ONLY: mp_para_env_type
   USE outer_scf_control_types,         ONLY: outer_scf_read_parameters
   USE particle_list_types,             ONLY: particle_list_type
   USE particle_types,                  ONLY: particle_type
   USE pw_env_types,                    ONLY: pw_env_get,&
                                              pw_env_type
   USE pw_methods,                      ONLY: pw_zero
   USE pw_pool_types,                   ONLY: pw_pool_type
   USE qs_cdft_types,                   ONLY: becke_constraint_type,&
                                              cdft_control_type,&
                                              cdft_group_type,&
                                              hirshfeld_constraint_type
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_kind_types,                   ONLY: get_qs_kind,&
                                              qs_kind_type
   USE qs_scf_output,                   ONLY: qs_scf_cdft_constraint_info
   USE qs_subsys_types,                 ONLY: qs_subsys_get,&
                                              qs_subsys_type
   USE realspace_grid_types,            ONLY: realspace_grid_type,&
                                              rs_grid_zero,&
                                              transfer_rs2pw
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
 
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'qs_cdft_utils'
   LOGICAL, PARAMETER, PRIVATE          :: debug_this_module = .false.
 
! *** Public subroutines ***
   PUBLIC :: becke_constraint_init, read_becke_section, read_cdft_control_section
   PUBLIC :: hfun_scale, hirshfeld_constraint_init, cdft_constraint_print, &
             cdft_print_hirshfeld_density, cdft_print_weight_function
 
CONTAINS
 
! **************************************************************************************************
!> \brief Initializes the Becke constraint environment
!> \param qs_env the qs_env where to build the constraint
!> \par   History
!>        Created 01.2007 [fschiff]
!>        Extended functionality 12/15-12/16 [Nico Holmberg]
! **************************************************************************************************
   SUBROUTINE becke_constraint_init(qs_env)
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(len=*), PARAMETER :: routinen = 'becke_constraint_init'
 
      CHARACTER(len=2)                                   :: element_symbol
      INTEGER :: atom_a, bounds(2), handle, i, iatom, iex, igroup, ikind, ip, ithread, iw, j, &
         jatom, katom, natom, nkind, npme, nthread, numexp, unit_nr
      INTEGER, DIMENSION(2, 3)                           :: bo
      INTEGER, DIMENSION(:), POINTER                     :: atom_list, cores, stride
      LOGICAL                                            :: build, in_memory, mpi_io
      LOGICAL, ALLOCATABLE, DIMENSION(:)                 :: is_constraint
      REAL(kind=dp)                                      :: alpha, chi, coef, eps_cavity, ircov, &
                                                            jrcov, radius, uij
      REAL(kind=dp), DIMENSION(3)                        :: cell_v, dist_vec, r, r1, ra
      REAL(kind=dp), DIMENSION(:), POINTER               :: radii_list
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: pab
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(becke_constraint_type), POINTER               :: becke_control
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(cdft_group_type), DIMENSION(:), POINTER       :: group
      TYPE(cell_type), POINTER                           :: cell
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(hirshfeld_type), POINTER                      :: cavity_env
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_list_type), POINTER                  :: particles
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(qs_subsys_type), POINTER                      :: subsys
      TYPE(realspace_grid_type), POINTER                 :: rs_cavity
      TYPE(section_vals_type), POINTER                   :: cdft_constraint_section
 
      NULLIFY (cores, stride, atom_list, cell, para_env, dft_control, &
               particle_set, logger, cdft_constraint_section, qs_kind_set, &
               particles, subsys, pab, pw_env, rs_cavity, cavity_env, &
               auxbas_pw_pool, atomic_kind_set, group, radii_list, cdft_control)
      logger => cp_get_default_logger()
      CALL timeset(routinen, handle)
      CALL get_qs_env(qs_env, &
                      cell=cell, &
                      particle_set=particle_set, &
                      natom=natom, &
                      dft_control=dft_control, &
                      para_env=para_env)
      cdft_constraint_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS%CDFT")
      iw = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", extension=".cdftLog")
      cdft_control => dft_control%qs_control%cdft_control
      becke_control => cdft_control%becke_control
      group => cdft_control%group
      in_memory = .false.
      IF (cdft_control%save_pot) THEN
         in_memory = becke_control%in_memory
      END IF
      IF (becke_control%cavity_confine) THEN
         ALLOCATE (is_constraint(natom))
         is_constraint = .false.
         DO i = 1, cdft_control%natoms
            ! Notice that here is_constraint=.TRUE. also for dummy atoms to properly compute their Becke charges
            ! A subsequent check (atom_in_group) ensures that the gradients of these dummy atoms are correct
            is_constraint(cdft_control%atoms(i)) = .true.
         END DO
      END IF
      eps_cavity = becke_control%eps_cavity
      ! Setup atomic radii for adjusting cell boundaries
      IF (becke_control%adjust) THEN
         IF (.NOT. ASSOCIATED(becke_control%radii)) THEN
            CALL get_qs_env(qs_env, atomic_kind_set=atomic_kind_set)
            IF (.NOT. SIZE(atomic_kind_set) == SIZE(becke_control%radii_tmp)) &
               CALL cp_abort(__location__, &
                             "Length of keyword BECKE_CONSTRAINT\ATOMIC_RADII does not "// &
                             "match number of atomic kinds in the input coordinate file.")
            ALLOCATE (becke_control%radii(SIZE(atomic_kind_set)))
            becke_control%radii(:) = becke_control%radii_tmp(:)
            DEALLOCATE (becke_control%radii_tmp)
         END IF
      END IF
      ! Setup cutoff scheme
      IF (.NOT. ASSOCIATED(becke_control%cutoffs)) THEN
         CALL get_qs_env(qs_env, atomic_kind_set=atomic_kind_set)
         ALLOCATE (becke_control%cutoffs(natom))
         SELECT CASE (becke_control%cutoff_type)
         CASE (becke_cutoff_global)
            becke_control%cutoffs(:) = becke_control%rglobal
         CASE (becke_cutoff_element)
            IF (.NOT. SIZE(atomic_kind_set) == SIZE(becke_control%cutoffs_tmp)) &
               CALL cp_abort(__location__, &
                             "Length of keyword BECKE_CONSTRAINT\ELEMENT_CUTOFFS does not "// &
                             "match number of atomic kinds in the input coordinate file.")
            DO ikind = 1, SIZE(atomic_kind_set)
               CALL get_atomic_kind(atomic_kind_set(ikind), natom=katom, atom_list=atom_list)
               DO iatom = 1, katom
                  atom_a = atom_list(iatom)
                  becke_control%cutoffs(atom_a) = becke_control%cutoffs_tmp(ikind)
               END DO
            END DO
            DEALLOCATE (becke_control%cutoffs_tmp)
         END SELECT
      END IF
      ! Zero weight functions
      DO igroup = 1, SIZE(group)
         CALL pw_zero(group(igroup)%weight)
      END DO
      IF (cdft_control%atomic_charges) THEN
         DO iatom = 1, cdft_control%natoms
            CALL pw_zero(cdft_control%charge(iatom))
         END DO
      END IF
      ! Allocate storage for cell adjustment coefficients and needed distance vectors
      build = .false.
      IF (becke_control%adjust .AND. .NOT. ASSOCIATED(becke_control%aij)) THEN
         ALLOCATE (becke_control%aij(natom, natom))
         build = .true.
      END IF
      IF (becke_control%vector_buffer%store_vectors) THEN
         ALLOCATE (becke_control%vector_buffer%distances(natom))
         ALLOCATE (becke_control%vector_buffer%distance_vecs(3, natom))
         IF (in_memory) ALLOCATE (becke_control%vector_buffer%pair_dist_vecs(3, natom, natom))
         ALLOCATE (becke_control%vector_buffer%position_vecs(3, natom))
      END IF
      ALLOCATE (becke_control%vector_buffer%R12(natom, natom))
      ! Calculate pairwise distances between each atom pair
      DO i = 1, 3
         cell_v(i) = cell%hmat(i, i)
      END DO
      DO iatom = 1, natom - 1
         DO jatom = iatom + 1, natom
            r = particle_set(iatom)%r
            r1 = particle_set(jatom)%r
            DO i = 1, 3
               r(i) = modulo(r(i), cell%hmat(i, i)) - cell%hmat(i, i)/2._dp
               r1(i) = modulo(r1(i), cell%hmat(i, i)) - cell%hmat(i, i)/2._dp
            END DO
            dist_vec = (r - r1) - anint((r - r1)/cell_v)*cell_v
            ! Store pbc corrected position and pairwise distance vectors for later reuse
            IF (becke_control%vector_buffer%store_vectors) THEN
               becke_control%vector_buffer%position_vecs(:, iatom) = r(:)
               IF (iatom == 1 .AND. jatom == natom) becke_control%vector_buffer%position_vecs(:, jatom) = r1(:)
               IF (in_memory) THEN
                  becke_control%vector_buffer%pair_dist_vecs(:, iatom, jatom) = dist_vec(:)
                  becke_control%vector_buffer%pair_dist_vecs(:, jatom, iatom) = -dist_vec(:)
               END IF
            END IF
            becke_control%vector_buffer%R12(iatom, jatom) = sqrt(dot_product(dist_vec, dist_vec))
            becke_control%vector_buffer%R12(jatom, iatom) = becke_control%vector_buffer%R12(iatom, jatom)
            ! Set up heteronuclear cell partitioning using user defined radii
            IF (build) THEN
               CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, kind_number=ikind)
               ircov = becke_control%radii(ikind)
               CALL get_atomic_kind(atomic_kind=particle_set(jatom)%atomic_kind, kind_number=ikind)
               jrcov = becke_control%radii(ikind)
               IF (ircov .NE. jrcov) THEN
                  chi = ircov/jrcov
                  uij = (chi - 1.0_dp)/(chi + 1.0_dp)
                  becke_control%aij(iatom, jatom) = uij/(uij**2 - 1.0_dp)
                  IF (becke_control%aij(iatom, jatom) .GT. 0.5_dp) THEN
                     becke_control%aij(iatom, jatom) = 0.5_dp
                  ELSE IF (becke_control%aij(iatom, jatom) .LT. -0.5_dp) THEN
                     becke_control%aij(iatom, jatom) = -0.5_dp
                  END IF
               ELSE
                  becke_control%aij(iatom, jatom) = 0.0_dp
               END IF
               ! Note change of sign
               becke_control%aij(jatom, iatom) = -becke_control%aij(iatom, jatom)
            END IF
         END DO
      END DO
      ! Dump some additional information about the calculation
      IF (cdft_control%first_iteration) THEN
         IF (iw > 0) THEN
            WRITE (iw, '(/,T3,A)') &
               '----------------------- Becke atomic parameters ------------------------'
            IF (becke_control%adjust) THEN
               WRITE (iw, '(T3,A)') &
                  'Atom   Element           Cutoff (angstrom)        CDFT Radius (angstrom)'
               DO iatom = 1, natom
                  CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, element_symbol=element_symbol, &
                                       kind_number=ikind)
                  ircov = cp_unit_from_cp2k(becke_control%radii(ikind), "angstrom")
                  WRITE (iw, "(i6,T15,A2,T37,F8.3,T67,F8.3)") &
                     iatom, adjustr(element_symbol), cp_unit_from_cp2k(becke_control%cutoffs(iatom), "angstrom"), &
                     ircov
               END DO
            ELSE
               WRITE (iw, '(T3,A)') &
                  'Atom   Element           Cutoff (angstrom)'
               DO iatom = 1, natom
                  CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, element_symbol=element_symbol)
                  WRITE (iw, "(i7,T15,A2,T37,F8.3)") &
                     iatom, adjustr(element_symbol), cp_unit_from_cp2k(becke_control%cutoffs(iatom), "angstrom")
               END DO
            END IF
            WRITE (iw, '(T3,A)') &
               '------------------------------------------------------------------------'
            WRITE (iw, '(/,T3,A,T60)') &
               '----------------------- Becke group definitions ------------------------'
            DO igroup = 1, SIZE(group)
               IF (igroup > 1) WRITE (iw, '(T3,A)') ' '
               WRITE (iw, '(T5,A,I5,A,I5)') &
                  'Atomic group', igroup, ' of ', SIZE(group)
               WRITE (iw, '(T5,A)') 'Atom  Element  Coefficient'
               DO ip = 1, SIZE(group(igroup)%atoms)
                  iatom = group(igroup)%atoms(ip)
                  CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, element_symbol=element_symbol)
                  WRITE (iw, '(i8,T16,A2,T23,F8.3)') iatom, adjustr(element_symbol), group(igroup)%coeff(ip)
               END DO
            END DO
            WRITE (iw, '(T3,A)') &
               '------------------------------------------------------------------------'
         END IF
         cdft_control%first_iteration = .false.
      END IF
      ! Setup cavity confinement using spherical Gaussians
      IF (becke_control%cavity_confine) THEN
         cavity_env => becke_control%cavity_env
         CALL get_qs_env(qs_env, atomic_kind_set=atomic_kind_set, pw_env=pw_env, qs_kind_set=qs_kind_set)
         cpassert(ASSOCIATED(qs_kind_set))
         nkind = SIZE(qs_kind_set)
         ! Setup the Gaussian shape function
         IF (.NOT. ASSOCIATED(cavity_env%kind_shape_fn)) THEN
            IF (ASSOCIATED(becke_control%radii)) THEN
               ALLOCATE (radii_list(SIZE(becke_control%radii)))
               DO ikind = 1, SIZE(becke_control%radii)
                  IF (cavity_env%use_bohr) THEN
                     radii_list(ikind) = becke_control%radii(ikind)
                  ELSE
                     radii_list(ikind) = cp_unit_from_cp2k(becke_control%radii(ikind), "angstrom")
                  END IF
               END DO
            END IF
            CALL create_shape_function(cavity_env, qs_kind_set, atomic_kind_set, &
                                       radius=becke_control%rcavity, &
                                       radii_list=radii_list)
            IF (ASSOCIATED(radii_list)) &
               DEALLOCATE (radii_list)
         END IF
         ! Form cavity by summing isolated Gaussian densities over constraint atoms
         NULLIFY (rs_cavity)
         CALL pw_env_get(pw_env, auxbas_rs_grid=rs_cavity, auxbas_pw_pool=auxbas_pw_pool)
         CALL rs_grid_zero(rs_cavity)
         ALLOCATE (pab(1, 1))
         nthread = 1
         ithread = 0
         DO ikind = 1, SIZE(atomic_kind_set)
            numexp = cavity_env%kind_shape_fn(ikind)%numexp
            IF (numexp <= 0) cycle
            CALL get_atomic_kind(atomic_kind_set(ikind), natom=katom, atom_list=atom_list)
            ALLOCATE (cores(katom))
            DO iex = 1, numexp
               alpha = cavity_env%kind_shape_fn(ikind)%zet(iex)
               coef = cavity_env%kind_shape_fn(ikind)%coef(iex)
               npme = 0
               cores = 0
               DO iatom = 1, katom
                  IF (rs_cavity%desc%parallel .AND. .NOT. rs_cavity%desc%distributed) THEN
                     ! replicated realspace grid, split the atoms up between procs
                     IF (modulo(iatom, rs_cavity%desc%group_size) == rs_cavity%desc%my_pos) THEN
                        npme = npme + 1
                        cores(npme) = iatom
                     END IF
                  ELSE
                     npme = npme + 1
                     cores(npme) = iatom
                  END IF
               END DO
               DO j = 1, npme
                  iatom = cores(j)
                  atom_a = atom_list(iatom)
                  pab(1, 1) = coef
                  IF (becke_control%vector_buffer%store_vectors) THEN
                     ra(:) = becke_control%vector_buffer%position_vecs(:, atom_a) + cell_v(:)/2._dp
                  ELSE
                     ra(:) = pbc(particle_set(atom_a)%r, cell)
                  END IF
                  IF (is_constraint(atom_a)) THEN
                     radius = exp_radius_very_extended(la_min=0, la_max=0, lb_min=0, lb_max=0, &
                                                       ra=ra, rb=ra, rp=ra, zetp=alpha, &
                                                       eps=dft_control%qs_control%eps_rho_rspace, &
                                                       pab=pab, o1=0, o2=0, &  ! without map_consistent
                                                       prefactor=1.0_dp, cutoff=0.0_dp)
 
                     CALL collocate_pgf_product(0, alpha, 0, 0, 0.0_dp, 0, ra, &
                                                (/0.0_dp, 0.0_dp, 0.0_dp/), 1.0_dp, &
                                                pab, 0, 0, rs_cavity, &
                                                radius=radius, ga_gb_function=grid_func_ab, &
                                                use_subpatch=.true., subpatch_pattern=0)
                  END IF
               END DO
            END DO
            DEALLOCATE (cores)
         END DO
         DEALLOCATE (pab)
         CALL auxbas_pw_pool%create_pw(becke_control%cavity)
         CALL transfer_rs2pw(rs_cavity, becke_control%cavity)
         ! Grid points where the Gaussian density falls below eps_cavity are ignored
         ! We can calculate the smallest/largest values along z-direction outside
         ! which the cavity is zero at every point (x, y)
         ! If gradients are needed storage needs to be allocated only for grid points within
         ! these bounds
         IF (in_memory .OR. cdft_control%save_pot) THEN
            CALL hfun_zero(becke_control%cavity%array, eps_cavity, just_bounds=.true., bounds=bounds)
            ! Save bounds (first nonzero grid point indices)
            bo = group(1)%weight%pw_grid%bounds_local
            IF (bounds(2) .LT. bo(2, 3)) THEN
               bounds(2) = bounds(2) - 1
            ELSE
               bounds(2) = bo(2, 3)
            END IF
            IF (bounds(1) .GT. bo(1, 3)) THEN
               ! In the special case bounds(1) == bounds(2) == bo(2, 3), after this check
               ! bounds(1) > bounds(2) and the subsequent gradient allocation (:, :, :, bounds(1):bounds(2))
               ! will correctly allocate a 0-sized array
               bounds(1) = bounds(1) + 1
            ELSE
               bounds(1) = bo(1, 3)
            END IF
            becke_control%confine_bounds = bounds
         END IF
         ! Optional printing of cavity (meant for testing, so options currently hardcoded...)
         IF (becke_control%print_cavity) THEN
            CALL hfun_zero(becke_control%cavity%array, eps_cavity, just_bounds=.false.)
            ALLOCATE (stride(3))
            stride = (/2, 2, 2/)
            mpi_io = .true.
            ! Note PROGRAM_RUN_INFO section neeeds to be active!
            unit_nr = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", &
                                           middle_name="BECKE_CAVITY", &
                                           extension=".cube", file_position="REWIND", &
                                           log_filename=.false., mpi_io=mpi_io)
            IF (para_env%is_source() .AND. unit_nr .LT. 1) &
               CALL cp_abort(__location__, &
                             "Please turn on PROGRAM_RUN_INFO to print cavity")
            CALL get_qs_env(qs_env, subsys=subsys)
            CALL qs_subsys_get(subsys, particles=particles)
            CALL cp_pw_to_cube(becke_control%cavity, unit_nr, "CAVITY", particles=particles, stride=stride, mpi_io=mpi_io)
            CALL cp_print_key_finished_output(unit_nr, logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io)
            DEALLOCATE (stride)
         END IF
      END IF
      IF (ALLOCATED(is_constraint)) &
         DEALLOCATE (is_constraint)
      CALL timestop(handle)
 
   END SUBROUTINE becke_constraint_init
 
! **************************************************************************************************
!> \brief reads the input parameters specific to Becke-based CDFT constraints
!> \param cdft_control the cdft_control which holds the Becke control type
!> \param becke_section the input section containing Becke constraint information
!> \par   History
!>        Created 01.2007 [fschiff]
!>        Merged Becke into CDFT 09.2018 [Nico Holmberg]
!> \author Nico Holmberg [09.2018]
! **************************************************************************************************
   SUBROUTINE read_becke_section(cdft_control, becke_section)
 
      TYPE(cdft_control_type), INTENT(INOUT)             :: cdft_control
      TYPE(section_vals_type), POINTER                   :: becke_section
 
      INTEGER                                            :: j
      LOGICAL                                            :: exists
      REAL(kind=dp), DIMENSION(:), POINTER               :: rtmplist
      TYPE(becke_constraint_type), POINTER               :: becke_control
 
      NULLIFY (rtmplist)
      becke_control => cdft_control%becke_control
      cpassert(ASSOCIATED(becke_control))
 
      ! Atomic size corrections
      CALL section_vals_val_get(becke_section, "ADJUST_SIZE", l_val=becke_control%adjust)
      IF (becke_control%adjust) THEN
         CALL section_vals_val_get(becke_section, "ATOMIC_RADII", explicit=exists)
         IF (.NOT. exists) cpabort("Keyword ATOMIC_RADII is missing.")
         CALL section_vals_val_get(becke_section, "ATOMIC_RADII", r_vals=rtmplist)
         cpassert(SIZE(rtmplist) > 0)
         ALLOCATE (becke_control%radii_tmp(SIZE(rtmplist)))
         DO j = 1, SIZE(rtmplist)
            becke_control%radii_tmp(j) = rtmplist(j)
         END DO
      END IF
 
      ! Cutoff scheme
      CALL section_vals_val_get(becke_section, "CUTOFF_TYPE", i_val=becke_control%cutoff_type)
      SELECT CASE (becke_control%cutoff_type)
      CASE (becke_cutoff_global)
         CALL section_vals_val_get(becke_section, "GLOBAL_CUTOFF", r_val=becke_control%rglobal)
      CASE (becke_cutoff_element)
         CALL section_vals_val_get(becke_section, "ELEMENT_CUTOFF", r_vals=rtmplist)
         cpassert(SIZE(rtmplist) > 0)
         ALLOCATE (becke_control%cutoffs_tmp(SIZE(rtmplist)))
         DO j = 1, SIZE(rtmplist)
            becke_control%cutoffs_tmp(j) = rtmplist(j)
         END DO
      END SELECT
 
      ! Gaussian cavity confinement
      CALL section_vals_val_get(becke_section, "CAVITY_CONFINE", l_val=becke_control%cavity_confine)
      CALL section_vals_val_get(becke_section, "SHOULD_SKIP", l_val=becke_control%should_skip)
      CALL section_vals_val_get(becke_section, "IN_MEMORY", l_val=becke_control%in_memory)
      IF (cdft_control%becke_control%cavity_confine) THEN
         CALL section_vals_val_get(becke_section, "CAVITY_SHAPE", i_val=becke_control%cavity_shape)
         IF (becke_control%cavity_shape == radius_user .AND. .NOT. becke_control%adjust) &
            CALL cp_abort(__location__, &
                          "Activate keyword ADJUST_SIZE to use cavity shape USER.")
         CALL section_vals_val_get(becke_section, "CAVITY_RADIUS", r_val=becke_control%rcavity)
         CALL section_vals_val_get(becke_section, "EPS_CAVITY", r_val=becke_control%eps_cavity)
         CALL section_vals_val_get(becke_section, "CAVITY_PRINT", l_val=becke_control%print_cavity)
         CALL section_vals_val_get(becke_section, "CAVITY_USE_BOHR", l_val=becke_control%use_bohr)
         IF (.NOT. cdft_control%becke_control%use_bohr) THEN
            becke_control%rcavity = cp_unit_from_cp2k(becke_control%rcavity, "angstrom")
         END IF
         CALL create_hirshfeld_type(becke_control%cavity_env)
         CALL set_hirshfeld_info(becke_control%cavity_env, &
                                 shape_function_type=shape_function_gaussian, iterative=.false., &
                                 radius_type=becke_control%cavity_shape, &
                                 use_bohr=becke_control%use_bohr)
      END IF
 
      CALL cite_reference(becke1988b)
 
   END SUBROUTINE read_becke_section
 
! **************************************************************************************************
!> \brief reads the input parameters needed to define CDFT constraints
!> \param cdft_control the object which holds the CDFT control type
!> \param cdft_control_section the input section containing CDFT constraint information
!> \author Nico Holmberg [09.2018]
! **************************************************************************************************
   SUBROUTINE read_constraint_definitions(cdft_control, cdft_control_section)
 
      TYPE(cdft_control_type), INTENT(INOUT)             :: cdft_control
      TYPE(section_vals_type), INTENT(INOUT), POINTER    :: cdft_control_section
 
      INTEGER                                            :: i, j, jj, k, n_rep, natoms, nvar, &
                                                            tot_natoms
      INTEGER, DIMENSION(:), POINTER                     :: atomlist, dummylist, tmplist
      LOGICAL                                            :: exists, is_duplicate
      REAL(kind=dp), DIMENSION(:), POINTER               :: rtmplist
      TYPE(section_vals_type), POINTER                   :: group_section
 
      NULLIFY (tmplist, rtmplist, atomlist, dummylist, group_section)
 
      group_section => section_vals_get_subs_vals(cdft_control_section, "ATOM_GROUP")
      CALL section_vals_get(group_section, n_repetition=nvar, explicit=exists)
      IF (.NOT. exists) cpabort("Section ATOM_GROUP is missing.")
      ALLOCATE (cdft_control%group(nvar))
      tot_natoms = 0
      ! Parse all ATOM_GROUP sections
      DO k = 1, nvar
         ! First determine how much storage is needed
         natoms = 0
         CALL section_vals_val_get(group_section, "ATOMS", i_rep_section=k, n_rep_val=n_rep)
         DO j = 1, n_rep
            CALL section_vals_val_get(group_section, "ATOMS", i_rep_section=k, i_rep_val=j, i_vals=tmplist)
            IF (SIZE(tmplist) < 1) &
               cpabort("Each ATOM_GROUP must contain at least 1 atom.")
            natoms = natoms + SIZE(tmplist)
         END DO
         ALLOCATE (cdft_control%group(k)%atoms(natoms))
         ALLOCATE (cdft_control%group(k)%coeff(natoms))
         NULLIFY (cdft_control%group(k)%weight)
         NULLIFY (cdft_control%group(k)%integrated)
         tot_natoms = tot_natoms + natoms
         ! Now parse
         jj = 0
         DO j = 1, n_rep
            CALL section_vals_val_get(group_section, "ATOMS", i_rep_section=k, i_rep_val=j, i_vals=tmplist)
            DO i = 1, SIZE(tmplist)
               jj = jj + 1
               cdft_control%group(k)%atoms(jj) = tmplist(i)
            END DO
         END DO
         CALL section_vals_val_get(group_section, "COEFF", i_rep_section=k, n_rep_val=n_rep)
         jj = 0
         DO j = 1, n_rep
            CALL section_vals_val_get(group_section, "COEFF", i_rep_section=k, i_rep_val=j, r_vals=rtmplist)
            DO i = 1, SIZE(rtmplist)
               jj = jj + 1
               IF (jj > natoms) cpabort("Length of keywords ATOMS and COEFF must match.")
               IF (abs(rtmplist(i)) /= 1.0_dp) cpabort("Keyword COEFF accepts only values +/-1.0")
               cdft_control%group(k)%coeff(jj) = rtmplist(i)
            END DO
         END DO
         IF (jj < natoms) cpabort("Length of keywords ATOMS and COEFF must match.")
         CALL section_vals_val_get(group_section, "CONSTRAINT_TYPE", i_rep_section=k, &
                                   i_val=cdft_control%group(k)%constraint_type)
         CALL section_vals_val_get(group_section, "FRAGMENT_CONSTRAINT", i_rep_section=k, &
                                   l_val=cdft_control%group(k)%is_fragment_constraint)
         IF (cdft_control%group(k)%is_fragment_constraint) cdft_control%fragment_density = .true.
      END DO
      ! Create a list containing all constraint atoms
      ALLOCATE (atomlist(tot_natoms))
      atomlist = -1
      jj = 0
      DO k = 1, nvar
         DO j = 1, SIZE(cdft_control%group(k)%atoms)
            is_duplicate = .false.
            DO i = 1, jj + 1
               IF (cdft_control%group(k)%atoms(j) == atomlist(i)) THEN
                  is_duplicate = .true.
                  EXIT
               END IF
            END DO
            IF (.NOT. is_duplicate) THEN
               jj = jj + 1
               atomlist(jj) = cdft_control%group(k)%atoms(j)
            END IF
         END DO
      END DO
      CALL reallocate(atomlist, 1, jj)
      CALL section_vals_val_get(cdft_control_section, "ATOMIC_CHARGES", &
                                l_val=cdft_control%atomic_charges)
      ! Parse any dummy atoms (no constraint, just charges)
      IF (cdft_control%atomic_charges) THEN
         group_section => section_vals_get_subs_vals(cdft_control_section, "DUMMY_ATOMS")
         CALL section_vals_get(group_section, explicit=exists)
         IF (exists) THEN
            ! First determine how many atoms there are
            natoms = 0
            CALL section_vals_val_get(group_section, "ATOMS", n_rep_val=n_rep)
            DO j = 1, n_rep
               CALL section_vals_val_get(group_section, "ATOMS", i_rep_val=j, i_vals=tmplist)
               IF (SIZE(tmplist) < 1) &
                  cpabort("DUMMY_ATOMS must contain at least 1 atom.")
               natoms = natoms + SIZE(tmplist)
            END DO
            ALLOCATE (dummylist(natoms))
            ! Now parse
            jj = 0
            DO j = 1, n_rep
               CALL section_vals_val_get(group_section, "ATOMS", i_rep_val=j, i_vals=tmplist)
               DO i = 1, SIZE(tmplist)
                  jj = jj + 1
                  dummylist(jj) = tmplist(i)
               END DO
            END DO
            ! Check for duplicates
            DO j = 1, natoms
               DO i = j + 1, natoms
                  IF (dummylist(i) == dummylist(j)) &
                     cpabort("Duplicate atoms defined in section DUMMY_ATOMS.")
               END DO
            END DO
            ! Check that a dummy atom is not included in any ATOM_GROUP
            DO j = 1, SIZE(atomlist)
               DO i = 1, SIZE(dummylist)
                  IF (dummylist(i) == atomlist(j)) &
                     CALL cp_abort(__location__, &
                                   "Duplicate atoms defined in sections ATOM_GROUP and DUMMY_ATOMS.")
               END DO
            END DO
         END IF
      END IF
      ! Join dummy atoms and constraint atoms into one list
      IF (ASSOCIATED(dummylist)) THEN
         cdft_control%natoms = SIZE(atomlist) + SIZE(dummylist)
      ELSE
         cdft_control%natoms = SIZE(atomlist)
      END IF
      ALLOCATE (cdft_control%atoms(cdft_control%natoms))
      ALLOCATE (cdft_control%is_constraint(cdft_control%natoms))
      IF (cdft_control%atomic_charges) ALLOCATE (cdft_control%charge(cdft_control%natoms))
      cdft_control%atoms(1:SIZE(atomlist)) = atomlist
      IF (ASSOCIATED(dummylist)) THEN
         cdft_control%atoms(1 + SIZE(atomlist):) = dummylist
         DEALLOCATE (dummylist)
      END IF
      cdft_control%is_constraint = .false.
      cdft_control%is_constraint(1:SIZE(atomlist)) = .true.
      DEALLOCATE (atomlist)
      ! Get constraint potential definitions from input
      ALLOCATE (cdft_control%strength(nvar))
      ALLOCATE (cdft_control%value(nvar))
      ALLOCATE (cdft_control%target(nvar))
      CALL section_vals_val_get(cdft_control_section, "STRENGTH", r_vals=rtmplist)
      IF (SIZE(rtmplist) /= nvar) &
         CALL cp_abort(__location__, &
                       "The length of keyword STRENGTH is incorrect. "// &
                       "Expected "//trim(adjustl(cp_to_string(nvar)))// &
                       " value(s), got "// &
                       trim(adjustl(cp_to_string(SIZE(rtmplist))))//" value(s).")
      DO j = 1, nvar
         cdft_control%strength(j) = rtmplist(j)
      END DO
      CALL section_vals_val_get(cdft_control_section, "TARGET", r_vals=rtmplist)
      IF (SIZE(rtmplist) /= nvar) &
         CALL cp_abort(__location__, &
                       "The length of keyword TARGET is incorrect. "// &
                       "Expected "//trim(adjustl(cp_to_string(nvar)))// &
                       " value(s), got "// &
                       trim(adjustl(cp_to_string(SIZE(rtmplist))))//" value(s).")
      DO j = 1, nvar
         cdft_control%target(j) = rtmplist(j)
      END DO
      ! Read fragment constraint definitions
      IF (cdft_control%fragment_density) THEN
         CALL section_vals_val_get(cdft_control_section, "FRAGMENT_A_FILE_NAME", &
                                   c_val=cdft_control%fragment_a_fname)
         CALL section_vals_val_get(cdft_control_section, "FRAGMENT_B_FILE_NAME", &
                                   c_val=cdft_control%fragment_b_fname)
         CALL section_vals_val_get(cdft_control_section, "FRAGMENT_A_SPIN_FILE", &
                                   c_val=cdft_control%fragment_a_spin_fname)
         CALL section_vals_val_get(cdft_control_section, "FRAGMENT_B_SPIN_FILE", &
                                   c_val=cdft_control%fragment_b_spin_fname)
         CALL section_vals_val_get(cdft_control_section, "FLIP_FRAGMENT_A", &
                                   l_val=cdft_control%flip_fragment(1))
         CALL section_vals_val_get(cdft_control_section, "FLIP_FRAGMENT_B", &
                                   l_val=cdft_control%flip_fragment(2))
      END IF
 
   END SUBROUTINE read_constraint_definitions
 
! **************************************************************************************************
!> \brief reads the input parameters needed for CDFT with OT
!> \param qs_control the qs_control which holds the CDFT control type
!> \param cdft_control_section the input section for CDFT
!> \author Nico Holmberg [12.2015]
! **************************************************************************************************
   SUBROUTINE read_cdft_control_section(qs_control, cdft_control_section)
      TYPE(qs_control_type), INTENT(INOUT)               :: qs_control
      TYPE(section_vals_type), POINTER                   :: cdft_control_section
 
      INTEGER                                            :: k, nvar
      LOGICAL                                            :: exists
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(section_vals_type), POINTER                   :: becke_constraint_section, group_section, &
                                                            hirshfeld_constraint_section, &
                                                            outer_scf_section, print_section
 
      NULLIFY (outer_scf_section, hirshfeld_constraint_section, becke_constraint_section, &
               print_section, group_section)
      cdft_control => qs_control%cdft_control
      cpassert(ASSOCIATED(cdft_control))
      group_section => section_vals_get_subs_vals(cdft_control_section, "ATOM_GROUP")
      CALL section_vals_get(group_section, n_repetition=nvar, explicit=exists)
 
      CALL section_vals_val_get(cdft_control_section, "TYPE_OF_CONSTRAINT", &
                                i_val=qs_control%cdft_control%type)
 
      IF (cdft_control%type /= outer_scf_none) THEN
         CALL section_vals_val_get(cdft_control_section, "REUSE_PRECOND", &
                                   l_val=cdft_control%reuse_precond)
         CALL section_vals_val_get(cdft_control_section, "PRECOND_FREQ", &
                                   i_val=cdft_control%precond_freq)
         CALL section_vals_val_get(cdft_control_section, "MAX_REUSE", &
                                   i_val=cdft_control%max_reuse)
         CALL section_vals_val_get(cdft_control_section, "PURGE_HISTORY", &
                                   l_val=cdft_control%purge_history)
         CALL section_vals_val_get(cdft_control_section, "PURGE_FREQ", &
                                   i_val=cdft_control%purge_freq)
         CALL section_vals_val_get(cdft_control_section, "PURGE_OFFSET", &
                                   i_val=cdft_control%purge_offset)
         CALL section_vals_val_get(cdft_control_section, "COUNTER", &
                                   i_val=cdft_control%ienergy)
         print_section => section_vals_get_subs_vals(cdft_control_section, "PROGRAM_RUN_INFO%WEIGHT_FUNCTION")
         CALL section_vals_get(print_section, explicit=cdft_control%print_weight)
 
         outer_scf_section => section_vals_get_subs_vals(cdft_control_section, "OUTER_SCF")
         CALL outer_scf_read_parameters(cdft_control%constraint_control, outer_scf_section)
         IF (cdft_control%constraint_control%have_scf) THEN
            IF (cdft_control%constraint_control%type /= outer_scf_cdft_constraint) &
               cpabort("Unsupported CDFT constraint.")
            ! Constraint definitions
            CALL read_constraint_definitions(cdft_control, cdft_control_section)
            ! Constraint-specific initializations
            SELECT CASE (cdft_control%type)
            CASE (outer_scf_becke_constraint)
               becke_constraint_section => section_vals_get_subs_vals(cdft_control_section, "BECKE_CONSTRAINT")
               CALL section_vals_get(becke_constraint_section, explicit=exists)
               IF (.NOT. exists) cpabort("BECKE_CONSTRAINT section is missing.")
               DO k = 1, nvar
                  NULLIFY (cdft_control%group(k)%gradients)
               END DO
               CALL read_becke_section(cdft_control, becke_constraint_section)
            CASE (outer_scf_hirshfeld_constraint)
               hirshfeld_constraint_section => section_vals_get_subs_vals(cdft_control_section, "HIRSHFELD_CONSTRAINT")
               CALL section_vals_get(hirshfeld_constraint_section, explicit=exists)
               IF (.NOT. exists) cpabort("HIRSHFELD_CONSTRAINT section is missing.")
               DO k = 1, nvar
                  NULLIFY (cdft_control%group(k)%gradients_x)
                  NULLIFY (cdft_control%group(k)%gradients_y)
                  NULLIFY (cdft_control%group(k)%gradients_z)
               END DO
               CALL read_hirshfeld_constraint_section(cdft_control, hirshfeld_constraint_section)
            CASE DEFAULT
               cpabort("Unknown constraint type.")
            END SELECT
 
            CALL cite_reference(holmberg2017)
            CALL cite_reference(holmberg2018)
         ELSE
            qs_control%cdft = .false.
         END IF
      ELSE
         qs_control%cdft = .false.
      END IF
 
   END SUBROUTINE read_cdft_control_section
 
! **************************************************************************************************
!> \brief reads the input parameters needed for Hirshfeld constraint
!> \param cdft_control the cdft_control which holds the Hirshfeld constraint
!> \param hirshfeld_section the input section for a Hirshfeld constraint
! **************************************************************************************************
   SUBROUTINE read_hirshfeld_constraint_section(cdft_control, hirshfeld_section)
      TYPE(cdft_control_type), INTENT(INOUT)             :: cdft_control
      TYPE(section_vals_type), POINTER                   :: hirshfeld_section
 
      LOGICAL                                            :: exists
      REAL(kind=dp), DIMENSION(:), POINTER               :: rtmplist
      TYPE(hirshfeld_constraint_type), POINTER           :: hirshfeld_control
 
      NULLIFY (rtmplist)
      hirshfeld_control => cdft_control%hirshfeld_control
      cpassert(ASSOCIATED(hirshfeld_control))
 
      CALL section_vals_val_get(hirshfeld_section, "SHAPE_FUNCTION", i_val=hirshfeld_control%shape_function)
      CALL section_vals_val_get(hirshfeld_section, "GAUSSIAN_SHAPE", i_val=hirshfeld_control%gaussian_shape)
      CALL section_vals_val_get(hirshfeld_section, "GAUSSIAN_RADIUS", r_val=hirshfeld_control%radius)
      CALL section_vals_val_get(hirshfeld_section, "USE_BOHR", l_val=hirshfeld_control%use_bohr)
      CALL section_vals_val_get(hirshfeld_section, "USE_ATOMIC_CUTOFF", l_val=hirshfeld_control%use_atomic_cutoff)
      CALL section_vals_val_get(hirshfeld_section, "PRINT_DENSITY", l_val=hirshfeld_control%print_density)
      CALL section_vals_val_get(hirshfeld_section, "EPS_CUTOFF", r_val=hirshfeld_control%eps_cutoff)
      CALL section_vals_val_get(hirshfeld_section, "ATOMIC_CUTOFF", r_val=hirshfeld_control%atomic_cutoff)
 
      IF (.NOT. hirshfeld_control%use_bohr) THEN
         hirshfeld_control%radius = cp_unit_from_cp2k(hirshfeld_control%radius, "angstrom")
      END IF
 
      IF (hirshfeld_control%shape_function == shape_function_gaussian .AND. &
          hirshfeld_control%gaussian_shape == radius_user) THEN
         CALL section_vals_val_get(hirshfeld_section, "ATOMIC_RADII", explicit=exists)
         IF (.NOT. exists) cpabort("Keyword ATOMIC_RADII is missing.")
         CALL section_vals_val_get(hirshfeld_section, "ATOMIC_RADII", r_vals=rtmplist)
         cpassert(SIZE(rtmplist) > 0)
         ALLOCATE (hirshfeld_control%radii(SIZE(rtmplist)))
         hirshfeld_control%radii(:) = rtmplist
      END IF
 
      CALL create_hirshfeld_type(hirshfeld_control%hirshfeld_env)
      CALL set_hirshfeld_info(hirshfeld_control%hirshfeld_env, &
                              shape_function_type=hirshfeld_control%shape_function, &
                              iterative=.false., &
                              radius_type=hirshfeld_control%gaussian_shape, &
                              use_bohr=hirshfeld_control%use_bohr)
 
   END SUBROUTINE read_hirshfeld_constraint_section
 
! **************************************************************************************************
!> \brief Calculate fout = fun1/fun2 or fout = fun1*fun2
!> \param fout the output 3D potential
!> \param fun1 the first input 3D potential
!> \param fun2 the second input 3D potential
!> \param divide logical that decides whether to divide or multiply the input potentials
!> \param small customisable parameter to determine lower bound of division
! **************************************************************************************************
   SUBROUTINE hfun_scale(fout, fun1, fun2, divide, small)
      REAL(kind=dp), DIMENSION(:, :, :), INTENT(OUT)     :: fout
      REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN)      :: fun1, fun2
      LOGICAL, INTENT(IN)                                :: divide
      REAL(kind=dp), INTENT(IN)                          :: small
 
      INTEGER                                            :: i1, i2, i3, n1, n2, n3
 
      n1 = SIZE(fout, 1)
      n2 = SIZE(fout, 2)
      n3 = SIZE(fout, 3)
      cpassert(n1 == SIZE(fun1, 1))
      cpassert(n2 == SIZE(fun1, 2))
      cpassert(n3 == SIZE(fun1, 3))
      cpassert(n1 == SIZE(fun2, 1))
      cpassert(n2 == SIZE(fun2, 2))
      cpassert(n3 == SIZE(fun2, 3))
 
      IF (divide) THEN
         DO i3 = 1, n3
            DO i2 = 1, n2
               DO i1 = 1, n1
                  IF (fun2(i1, i2, i3) > small) THEN
                     fout(i1, i2, i3) = fun1(i1, i2, i3)/fun2(i1, i2, i3)
                  ELSE
                     fout(i1, i2, i3) = 0.0_dp
                  END IF
               END DO
            END DO
         END DO
      ELSE
         DO i3 = 1, n3
            DO i2 = 1, n2
               DO i1 = 1, n1
                  fout(i1, i2, i3) = fun1(i1, i2, i3)*fun2(i1, i2, i3)
               END DO
            END DO
         END DO
      END IF
 
   END SUBROUTINE hfun_scale
 
! **************************************************************************************************
!> \brief Determine confinement bounds along confinement dir (hardcoded to be z)
!>        and optionally zero entries below a given threshold
!> \param fun input 3D potential (real space)
!> \param th threshold for screening values
!> \param just_bounds if the bounds should be computed without zeroing values
!> \param bounds the confinement bounds: fun is nonzero only between these values along 3rd dimension
! **************************************************************************************************
   SUBROUTINE hfun_zero(fun, th, just_bounds, bounds)
      REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT)   :: fun
      REAL(kind=dp), INTENT(IN)                          :: th
      LOGICAL                                            :: just_bounds
      INTEGER, OPTIONAL                                  :: bounds(2)
 
      INTEGER                                            :: i1, i2, i3, lb, n1, n2, n3, nzeroed, &
                                                            nzeroed_inner, ub
      LOGICAL                                            :: lb_final, ub_final
 
      n1 = SIZE(fun, 1)
      n2 = SIZE(fun, 2)
      n3 = SIZE(fun, 3)
      IF (just_bounds) THEN
         cpassert(PRESENT(bounds))
         lb = 1
         lb_final = .false.
         ub_final = .false.
      END IF
 
      DO i3 = 1, n3
         IF (just_bounds) nzeroed = 0
         DO i2 = 1, n2
            IF (just_bounds) nzeroed_inner = 0
            DO i1 = 1, n1
               IF (fun(i1, i2, i3) < th) THEN
                  IF (just_bounds) THEN
                     nzeroed_inner = nzeroed_inner + 1
                  ELSE
                     fun(i1, i2, i3) = 0.0_dp
                  END IF
               ELSE
                  IF (just_bounds) EXIT
               END IF
            END DO
            IF (just_bounds) THEN
               IF (nzeroed_inner < n1) EXIT
               nzeroed = nzeroed + nzeroed_inner
            END IF
         END DO
         IF (just_bounds) THEN
            IF (nzeroed == (n2*n1)) THEN
               IF (.NOT. lb_final) THEN
                  lb = i3
               ELSE IF (.NOT. ub_final) THEN
                  ub = i3
                  ub_final = .true.
               END IF
            ELSE
               IF (.NOT. lb_final) lb_final = .true.
               IF (ub_final) ub_final = .false. ! Safeguard against "holes"
            END IF
         END IF
      END DO
      IF (just_bounds) THEN
         IF (.NOT. ub_final) ub = n3
         bounds(1) = lb
         bounds(2) = ub
         bounds = bounds - (n3/2) - 1
      END IF
 
   END SUBROUTINE hfun_zero
 
! **************************************************************************************************
!> \brief Initializes Gaussian Hirshfeld constraints
!> \param qs_env the qs_env where to build the constraint
!> \author  Nico Holmberg (09.2018)
! **************************************************************************************************
   SUBROUTINE hirshfeld_constraint_init(qs_env)
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(len=*), PARAMETER :: routinen = 'hirshfeld_constraint_init'
 
      CHARACTER(len=2)                                   :: element_symbol
      INTEGER                                            :: handle, iat, iatom, igroup, ikind, ip, &
                                                            iw, natom, nkind
      INTEGER, DIMENSION(:), POINTER                     :: atom_list
      REAL(kind=dp)                                      :: zeff
      REAL(kind=dp), DIMENSION(:), POINTER               :: radii_list
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(atomic_kind_type), POINTER                    :: atomic_kind
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(cdft_group_type), DIMENSION(:), POINTER       :: group
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(hirshfeld_constraint_type), POINTER           :: hirshfeld_control
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(section_vals_type), POINTER                   :: print_section
 
      NULLIFY (cdft_control, hirshfeld_control, hirshfeld_env, qs_kind_set, atomic_kind_set, &
               radii_list, dft_control, group, atomic_kind, atom_list)
      CALL timeset(routinen, handle)
 
      logger => cp_get_default_logger()
      print_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS%CDFT")
      iw = cp_print_key_unit_nr(logger, print_section, "PROGRAM_RUN_INFO", extension=".cdftLog")
 
      CALL get_qs_env(qs_env, dft_control=dft_control)
      cdft_control => dft_control%qs_control%cdft_control
      hirshfeld_control => cdft_control%hirshfeld_control
      hirshfeld_env => hirshfeld_control%hirshfeld_env
 
      ! Setup the Hirshfeld shape function
      IF (.NOT. ASSOCIATED(hirshfeld_env%kind_shape_fn)) THEN
         hirshfeld_env => hirshfeld_control%hirshfeld_env
         CALL get_qs_env(qs_env, atomic_kind_set=atomic_kind_set, qs_kind_set=qs_kind_set)
         cpassert(ASSOCIATED(qs_kind_set))
         nkind = SIZE(qs_kind_set)
         ! Parse atomic radii for setting up Gaussian shape function
         IF (ASSOCIATED(hirshfeld_control%radii)) THEN
            IF (.NOT. SIZE(atomic_kind_set) == SIZE(hirshfeld_control%radii)) &
               CALL cp_abort(__location__, &
                             "Length of keyword HIRSHFELD_CONSTRAINT\ATOMIC_RADII does not "// &
                             "match number of atomic kinds in the input coordinate file.")
 
            ALLOCATE (radii_list(SIZE(hirshfeld_control%radii)))
            DO ikind = 1, SIZE(hirshfeld_control%radii)
               IF (hirshfeld_control%use_bohr) THEN
                  radii_list(ikind) = hirshfeld_control%radii(ikind)
               ELSE
                  radii_list(ikind) = cp_unit_from_cp2k(hirshfeld_control%radii(ikind), "angstrom")
               END IF
            END DO
         END IF
         ! radius/radii_list parameters are optional for shape_function_density
         CALL create_shape_function(hirshfeld_env, qs_kind_set, atomic_kind_set, &
                                    radius=hirshfeld_control%radius, &
                                    radii_list=radii_list)
         IF (ASSOCIATED(radii_list)) DEALLOCATE (radii_list)
      END IF
 
      ! Atomic reference charges (Mulliken not supported)
      IF (.NOT. ASSOCIATED(hirshfeld_env%charges)) THEN
         CALL get_qs_env(qs_env, qs_kind_set=qs_kind_set, atomic_kind_set=atomic_kind_set, &
                         nkind=nkind, natom=natom)
         ALLOCATE (hirshfeld_env%charges(natom))
         DO ikind = 1, nkind
            CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, atom_list=atom_list)
            DO iat = 1, SIZE(atom_list)
               iatom = atom_list(iat)
               hirshfeld_env%charges(iatom) = zeff
            END DO
         END DO
      END IF
 
      ! Print some additional information about the calculation on the first iteration
      IF (cdft_control%first_iteration) THEN
         IF (iw > 0) THEN
            group => cdft_control%group
            CALL get_qs_env(qs_env, particle_set=particle_set)
            IF (ASSOCIATED(hirshfeld_control%radii)) THEN
               WRITE (iw, '(T3,A)') &
                  'Atom   Element  Gaussian radius (angstrom)'
               DO iatom = 1, natom
                  CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, element_symbol=element_symbol)
                  WRITE (iw, "(i7,T15,A2,T37,F8.3)") &
                     iatom, adjustr(element_symbol), cp_unit_from_cp2k(hirshfeld_control%radii(iatom), "angstrom")
               END DO
               WRITE (iw, '(T3,A)') &
                  '------------------------------------------------------------------------'
            END IF
            WRITE (iw, '(/,T3,A,T60)') &
               '----------------------- CDFT group definitions -------------------------'
            DO igroup = 1, SIZE(group)
               IF (igroup > 1) WRITE (iw, '(T3,A)') ' '
               WRITE (iw, '(T5,A,I5,A,I5)') &
                  'Atomic group', igroup, ' of ', SIZE(group)
               WRITE (iw, '(T5,A)') 'Atom  Element  Coefficient'
               DO ip = 1, SIZE(group(igroup)%atoms)
                  iatom = group(igroup)%atoms(ip)
                  CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, element_symbol=element_symbol)
                  WRITE (iw, '(i8,T16,A2,T23,F8.3)') iatom, adjustr(element_symbol), group(igroup)%coeff(ip)
               END DO
            END DO
            WRITE (iw, '(T3,A)') &
               '------------------------------------------------------------------------'
         END IF
         cdft_control%first_iteration = .false.
      END IF
 
      ! Radii no longer needed
      IF (ASSOCIATED(hirshfeld_control%radii)) DEALLOCATE (hirshfeld_control%radii)
      CALL timestop(handle)
 
   END SUBROUTINE hirshfeld_constraint_init
 
! **************************************************************************************************
!> \brief Prints information about CDFT constraints
!> \param qs_env the qs_env where to build the constraint
!> \param electronic_charge the CDFT charges
!> \par   History
!>        Created 9.2018 [Nico Holmberg]
! **************************************************************************************************
   SUBROUTINE cdft_constraint_print(qs_env, electronic_charge)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: electronic_charge
 
      CHARACTER(len=2)                                   :: element_symbol
      INTEGER                                            :: iatom, ikind, iw, jatom
      REAL(kind=dp)                                      :: tc(2), zeff
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(section_vals_type), POINTER                   :: cdft_constraint_section
 
      NULLIFY (cdft_constraint_section, logger, particle_set, dft_control, qs_kind_set)
      logger => cp_get_default_logger()
 
      CALL get_qs_env(qs_env, &
                      particle_set=particle_set, &
                      dft_control=dft_control, &
                      qs_kind_set=qs_kind_set)
      cpassert(ASSOCIATED(qs_kind_set))
 
      cdft_constraint_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS%CDFT")
      iw = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", extension=".cdftLog")
      cdft_control => dft_control%qs_control%cdft_control
 
      ! Print constraint information
      CALL qs_scf_cdft_constraint_info(iw, cdft_control)
 
      ! Print weight function(s) to cube file(s) whenever weight is (re)built
      IF (cdft_control%print_weight .AND. cdft_control%need_pot) &
         CALL cdft_print_weight_function(qs_env)
 
      ! Print atomic CDFT charges
      IF (iw > 0 .AND. cdft_control%atomic_charges) THEN
         IF (.NOT. cdft_control%fragment_density) THEN
            IF (dft_control%nspins == 1) THEN
               WRITE (iw, '(/,T3,A)') &
                  '-------------------------------- CDFT atomic charges --------------------------------'
               WRITE (iw, '(T3,A,A)') &
                  '#Atom  Element   Is_constraint', '   Core charge    Population (total)'// &
                  '          Net charge'
               tc = 0.0_dp
               DO iatom = 1, cdft_control%natoms
                  jatom = cdft_control%atoms(iatom)
                  CALL get_atomic_kind(atomic_kind=particle_set(jatom)%atomic_kind, &
                                       element_symbol=element_symbol, &
                                       kind_number=ikind)
                  CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
                  WRITE (iw, "(i7,T15,A2,T23,L10,T39,F8.3,T61,F8.3,T81,F8.3)") &
                     jatom, adjustr(element_symbol), cdft_control%is_constraint(iatom), zeff, electronic_charge(iatom, 1), &
                     (zeff - electronic_charge(iatom, 1))
                  tc(1) = tc(1) + (zeff - electronic_charge(iatom, 1))
               END DO
               WRITE (iw, '(/,T3,A,T81,F8.3,/)') "Total Charge: ", tc(1)
            ELSE
               WRITE (iw, '(/,T3,A)') &
                  '------------------------------------------ CDFT atomic charges -------------------------------------------'
               WRITE (iw, '(T3,A,A)') &
                  '#Atom  Element   Is_constraint', '   Core charge    Population (alpha, beta)'// &
                  '    Net charge      Spin population'
               tc = 0.0_dp
               DO iatom = 1, cdft_control%natoms
                  jatom = cdft_control%atoms(iatom)
                  CALL get_atomic_kind(atomic_kind=particle_set(jatom)%atomic_kind, &
                                       element_symbol=element_symbol, &
                                       kind_number=ikind)
                  CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
                  WRITE (iw, "(i7,T15,A2,T23,L10,T39,F8.3,T53,F8.3,T67,F8.3,T81,F8.3,T102,F8.3)") &
                     jatom, adjustr(element_symbol), &
                     cdft_control%is_constraint(iatom), &
                     zeff, electronic_charge(iatom, 1), electronic_charge(iatom, 2), &
                     (zeff - electronic_charge(iatom, 1) - electronic_charge(iatom, 2)), &
                     electronic_charge(iatom, 1) - electronic_charge(iatom, 2)
                  tc(1) = tc(1) + (zeff - electronic_charge(iatom, 1) - electronic_charge(iatom, 2))
                  tc(2) = tc(2) + (electronic_charge(iatom, 1) - electronic_charge(iatom, 2))
               END DO
               WRITE (iw, '(/,T3,A,T81,F8.3,T102,F8.3/)') "Total Charge and Spin Moment: ", tc(1), tc(2)
            END IF
         ELSE
            IF (all(cdft_control%group(:)%constraint_type == cdft_charge_constraint)) THEN
               WRITE (iw, '(/,T3,A)') &
                  '-------------------------------- CDFT atomic charges --------------------------------'
               IF (dft_control%nspins == 1) THEN
                  WRITE (iw, '(T3,A,A)') &
                     '#Atom  Element   Is_constraint', '   Fragment charge    Population (total)'// &
                     '      Net charge'
               ELSE
                  WRITE (iw, '(T3,A,A)') &
                     '#Atom  Element   Is_constraint', '   Fragment charge  Population (alpha, beta)'// &
                     '  Net charge'
               END IF
               tc = 0.0_dp
               DO iatom = 1, cdft_control%natoms
                  jatom = cdft_control%atoms(iatom)
                  CALL get_atomic_kind(atomic_kind=particle_set(jatom)%atomic_kind, &
                                       element_symbol=element_symbol, &
                                       kind_number=ikind)
                  IF (dft_control%nspins == 1) THEN
                     WRITE (iw, "(i7,T15,A2,T23,L10,T43,F8.3,T65,F8.3,T81,F8.3)") &
                        jatom, adjustr(element_symbol), &
                        cdft_control%is_constraint(iatom), &
                        cdft_control%charges_fragment(iatom, 1), &
                        electronic_charge(iatom, 1), &
                        (electronic_charge(iatom, 1) - &
                         cdft_control%charges_fragment(iatom, 1))
                     tc(1) = tc(1) + (electronic_charge(iatom, 1) - &
                                      cdft_control%charges_fragment(iatom, 1))
                  ELSE
                     WRITE (iw, "(i7,T15,A2,T23,L10,T43,F8.3,T57,F8.3,T69,F8.3,T81,F8.3)") &
                        jatom, adjustr(element_symbol), &
                        cdft_control%is_constraint(iatom), &
                        cdft_control%charges_fragment(iatom, 1), &
                        electronic_charge(iatom, 1), electronic_charge(iatom, 2), &
                        (electronic_charge(iatom, 1) + electronic_charge(iatom, 2) - &
                         cdft_control%charges_fragment(iatom, 1))
                     tc(1) = tc(1) + (electronic_charge(iatom, 1) + electronic_charge(iatom, 2) - &
                                      cdft_control%charges_fragment(iatom, 1))
                  END IF
               END DO
               WRITE (iw, '(/,T3,A,T81,F8.3,/)') "Total Charge: ", tc(1)
            ELSE
               WRITE (iw, '(/,T3,A)') &
                  '------------------------------------------ CDFT atomic charges -------------------------------------------'
               WRITE (iw, '(T3,A,A)') &
                  '#Atom  Element  Is_constraint', ' Fragment charge/spin moment'// &
                  '  Population (alpha, beta)  Net charge/spin moment'
               tc = 0.0_dp
               DO iatom = 1, cdft_control%natoms
                  jatom = cdft_control%atoms(iatom)
                  CALL get_atomic_kind(atomic_kind=particle_set(jatom)%atomic_kind, &
                                       element_symbol=element_symbol, &
                                       kind_number=ikind)
                  WRITE (iw, "(i7,T15,A2,T22,L10,T40,F8.3,T52,F8.3,T66,F8.3,T78,F8.3,T90,F8.3,T102,F8.3)") &
                     jatom, adjustr(element_symbol), &
                     cdft_control%is_constraint(iatom), &
                     cdft_control%charges_fragment(iatom, 1), &
                     cdft_control%charges_fragment(iatom, 2), &
                     electronic_charge(iatom, 1), electronic_charge(iatom, 2), &
                     (electronic_charge(iatom, 1) + electronic_charge(iatom, 2) - &
                      cdft_control%charges_fragment(iatom, 1)), &
                     (electronic_charge(iatom, 1) - electronic_charge(iatom, 2) - &
                      cdft_control%charges_fragment(iatom, 2))
                  tc(1) = tc(1) + (electronic_charge(iatom, 1) + electronic_charge(iatom, 2) - &
                                   cdft_control%charges_fragment(iatom, 1))
                  tc(2) = tc(2) + (electronic_charge(iatom, 1) - electronic_charge(iatom, 2) - &
                                   cdft_control%charges_fragment(iatom, 2))
               END DO
               WRITE (iw, '(/,T3,A,T90,F8.3,T102,F8.3/)') "Total Charge and Spin Moment: ", tc(1), tc(2)
            END IF
         END IF
      END IF
 
   END SUBROUTINE cdft_constraint_print
 
! **************************************************************************************************
!> \brief Prints CDFT weight functions to cube files
!> \param qs_env ...
! **************************************************************************************************
   SUBROUTINE cdft_print_weight_function(qs_env)
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(LEN=default_path_length)                 :: middle_name
      INTEGER                                            :: igroup, unit_nr
      LOGICAL                                            :: mpi_io
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_list_type), POINTER                  :: particles
      TYPE(qs_subsys_type), POINTER                      :: subsys
      TYPE(section_vals_type), POINTER                   :: cdft_constraint_section
 
      NULLIFY (cdft_constraint_section, logger, particles, dft_control, &
               para_env, subsys, cdft_control)
      logger => cp_get_default_logger()
 
      CALL get_qs_env(qs_env, subsys=subsys, para_env=para_env, dft_control=dft_control)
      CALL qs_subsys_get(subsys, particles=particles)
      cdft_control => dft_control%qs_control%cdft_control
      cdft_constraint_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS%CDFT")
 
      DO igroup = 1, SIZE(cdft_control%group)
         mpi_io = .true.
         middle_name = "cdft_weight_"//trim(adjustl(cp_to_string(igroup)))
         unit_nr = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", &
                                        middle_name=middle_name, &
                                        extension=".cube", file_position="REWIND", &
                                        log_filename=.false., mpi_io=mpi_io)
         ! Note PROGRAM_RUN_INFO section neeeds to be active!
         IF (para_env%is_source() .AND. unit_nr .LT. 1) &
            CALL cp_abort(__location__, &
                          "Please turn on PROGRAM_RUN_INFO to print CDFT weight function.")
 
         CALL cp_pw_to_cube(cdft_control%group(igroup)%weight, &
                            unit_nr, &
                            "CDFT Weight Function", &
                            particles=particles, &
                            stride=section_get_ivals(cdft_constraint_section, "PROGRAM_RUN_INFO%WEIGHT_FUNCTION%STRIDE"), &
                            mpi_io=mpi_io)
         CALL cp_print_key_finished_output(unit_nr, logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io)
      END DO
 
   END SUBROUTINE cdft_print_weight_function
 
! **************************************************************************************************
!> \brief Prints Hirshfeld weight function and promolecule density
!> \param qs_env ...
! **************************************************************************************************
   SUBROUTINE cdft_print_hirshfeld_density(qs_env)
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(LEN=default_path_length)                 :: middle_name
      INTEGER                                            :: iatom, igroup, unit_nr
      LOGICAL                                            :: mpi_io
      TYPE(cdft_control_type), POINTER                   :: cdft_control
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_list_type), POINTER                  :: particles
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(qs_subsys_type), POINTER                      :: subsys
      TYPE(section_vals_type), POINTER                   :: cdft_constraint_section
 
      NULLIFY (cdft_constraint_section, logger, particles, dft_control, &
               para_env, subsys, cdft_control, pw_env)
      logger => cp_get_default_logger()
 
      CALL get_qs_env(qs_env, subsys=subsys, para_env=para_env, dft_control=dft_control, pw_env=pw_env)
      CALL qs_subsys_get(subsys, particles=particles)
      cdft_control => dft_control%qs_control%cdft_control
      cdft_constraint_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS%CDFT")
 
      mpi_io = .true.
 
      DO igroup = 1, SIZE(cdft_control%group)
 
         middle_name = "hw_rho_total"//trim(adjustl(cp_to_string(igroup)))
         unit_nr = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io, &
                                        file_position="REWIND", middle_name=middle_name, extension=".cube")
 
         CALL cp_pw_to_cube(cdft_control%group(igroup)%hw_rho_total, unit_nr, "CDFT Weight Function", mpi_io=mpi_io, &
                  particles=particles, stride=section_get_ivals(cdft_constraint_section, "PROGRAM_RUN_INFO%WEIGHT_FUNCTION%STRIDE"))
 
         CALL cp_print_key_finished_output(unit_nr, logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io)
 
      END DO
 
      DO igroup = 1, SIZE(cdft_control%group)
 
         middle_name = "hw_rho_total_constraint_"//trim(adjustl(cp_to_string(igroup)))
         unit_nr = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io, &
                                        file_position="REWIND", middle_name=middle_name, extension=".cube")
 
         CALL cp_pw_to_cube(cdft_control%group(igroup)%hw_rho_total_constraint, unit_nr, &
                            "CDFT Weight Function", mpi_io=mpi_io, particles=particles, &
                            stride=section_get_ivals(cdft_constraint_section, "PROGRAM_RUN_INFO%WEIGHT_FUNCTION%STRIDE"))
 
         CALL cp_print_key_finished_output(unit_nr, logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io)
 
      END DO
 
      DO igroup = 1, SIZE(cdft_control%group)
         DO iatom = 1, (cdft_control%natoms)
 
            middle_name = "hw_rho_atomic_"//trim(adjustl(cp_to_string(iatom)))
            unit_nr = cp_print_key_unit_nr(logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io, &
                                           file_position="REWIND", middle_name=middle_name, extension=".cube")
 
            CALL cp_pw_to_cube(cdft_control%group(igroup)%hw_rho_atomic(iatom), unit_nr, &
                               "CDFT Weight Function", mpi_io=mpi_io, particles=particles, &
                               stride=section_get_ivals(cdft_constraint_section, "PROGRAM_RUN_INFO%WEIGHT_FUNCTION%STRIDE"))
 
            CALL cp_print_key_finished_output(unit_nr, logger, cdft_constraint_section, "PROGRAM_RUN_INFO", mpi_io=mpi_io)
 
         END DO
      END DO
 
   END SUBROUTINE cdft_print_hirshfeld_density
 
END MODULE qs_cdft_utils