hirshfeld_methods.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 Calculate Hirshfeld charges and related functions
!> \par History
!>      11.2014 created [JGH]
!> \author JGH
! **************************************************************************************************
MODULE hirshfeld_methods
   USE ao_util,                         ONLY: exp_radius_very_extended
   USE atom_kind_orbitals,              ONLY: calculate_atomic_density
   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind
   USE cell_types,                      ONLY: cell_type,&
                                              pbc
   USE cp_control_types,                ONLY: dft_control_type
   USE cp_result_methods,               ONLY: cp_results_erase,&
                                              put_results
   USE cp_result_types,                 ONLY: cp_result_type
   USE cp_units,                        ONLY: cp_unit_to_cp2k
   USE grid_api,                        ONLY: grid_func_ab,&
                                              collocate_pgf_product,&
                                              integrate_pgf_product
   USE hirshfeld_types,                 ONLY: get_hirshfeld_info,&
                                              hirshfeld_type,&
                                              set_hirshfeld_info
   USE input_constants,                 ONLY: radius_covalent,&
                                              radius_default,&
                                              radius_single,&
                                              radius_user,&
                                              radius_vdw,&
                                              shape_function_density,&
                                              shape_function_gaussian
   USE kinds,                           ONLY: default_string_length,&
                                              dp
   USE mathconstants,                   ONLY: pi
   USE message_passing,                 ONLY: mp_para_env_type
   USE particle_types,                  ONLY: particle_type
   USE periodic_table,                  ONLY: get_ptable_info
   USE pw_env_types,                    ONLY: pw_env_get,&
                                              pw_env_type
   USE pw_methods,                      ONLY: pw_integrate_function
   USE pw_pool_types,                   ONLY: pw_pool_type
   USE pw_types,                        ONLY: pw_r3d_rs_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_rho_types,                    ONLY: qs_rho_get,&
                                              qs_rho_type
   USE realspace_grid_types,            ONLY: realspace_grid_desc_type,&
                                              realspace_grid_type,&
                                              rs_grid_zero,&
                                              transfer_pw2rs,&
                                              transfer_rs2pw
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'hirshfeld_methods'
 
   PUBLIC :: create_shape_function, comp_hirshfeld_charges, &
             comp_hirshfeld_i_charges, write_hirshfeld_charges, &
             save_hirshfeld_charges
 
! **************************************************************************************************
 
CONTAINS
 
! **************************************************************************************************
!> \brief ...
!> \param charges ...
!> \param hirshfeld_env ...
!> \param particle_set ...
!> \param qs_kind_set ...
!> \param unit_nr ...
! **************************************************************************************************
   SUBROUTINE write_hirshfeld_charges(charges, hirshfeld_env, particle_set, &
                                      qs_kind_set, unit_nr)
      REAL(kind=dp), DIMENSION(:, :), INTENT(inout)      :: charges
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      INTEGER, INTENT(IN)                                :: unit_nr
 
      CHARACTER(len=2)                                   :: element_symbol
      INTEGER                                            :: iatom, ikind, natom, nspin
      REAL(kind=dp)                                      :: refc, tc1, zeff
 
      natom = SIZE(charges, 1)
      nspin = SIZE(charges, 2)
      WRITE (unit_nr, '(/,T2,A)') '!-----------------------------------------------------------------------------!'
      WRITE (unit=unit_nr, fmt="(T28,A)") "Hirshfeld Charges"
      IF (nspin == 1) THEN
         WRITE (unit=unit_nr, fmt="(/,T3,A,A)") &
            "#Atom  Element  Kind ", " Ref Charge     Population                    Net charge"
      ELSE
         WRITE (unit=unit_nr, fmt="(/,T3,A,A)") &
            "#Atom  Element  Kind ", " Ref Charge     Population       Spin moment  Net charge"
      END IF
      tc1 = 0.0_dp
      DO iatom = 1, natom
         CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, &
                              element_symbol=element_symbol, kind_number=ikind)
         refc = hirshfeld_env%charges(iatom)
         CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
         IF (nspin == 1) THEN
            WRITE (unit=unit_nr, fmt="(i7,T15,A2,T20,i3,T27,F8.3,T42,F8.3,T72,F8.3)") &
               iatom, element_symbol, ikind, refc, charges(iatom, 1), zeff - charges(iatom, 1)
         ELSE
            WRITE (unit=unit_nr, fmt="(i7,T15,A2,T20,i3,T27,F8.3,T36,2F8.3,T61,F8.3,T72,F8.3)") &
               iatom, element_symbol, ikind, refc, charges(iatom, 1), charges(iatom, 2), &
               charges(iatom, 1) - charges(iatom, 2), zeff - sum(charges(iatom, :))
         END IF
         tc1 = tc1 + (zeff - sum(charges(iatom, :)))
      END DO
      WRITE (unit=unit_nr, fmt="(/,T3,A,T72,F8.3)") "Total Charge ", tc1
      WRITE (unit_nr, '(T2,A)') '!-----------------------------------------------------------------------------!'
 
   END SUBROUTINE write_hirshfeld_charges
 
! **************************************************************************************************
!> \brief saves the Hirshfeld charges to the results structure
!> \param charges the calculated Hirshfeld charges
!> \param particle_set the particle set
!> \param qs_kind_set the kind set
!> \param qs_env the environment
! **************************************************************************************************
   SUBROUTINE save_hirshfeld_charges(charges, particle_set, qs_kind_set, qs_env)
      REAL(kind=dp), DIMENSION(:, :), INTENT(inout)      :: charges
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(LEN=default_string_length)               :: description
      INTEGER                                            :: iatom, ikind, natom
      REAL(kind=dp)                                      :: zeff
      REAL(kind=dp), DIMENSION(:), POINTER               :: charges_save
      TYPE(cp_result_type), POINTER                      :: results
 
      NULLIFY (results)
      CALL get_qs_env(qs_env, results=results)
 
      natom = SIZE(charges, 1)
      ALLOCATE (charges_save(natom))
 
      DO iatom = 1, natom
         CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, &
                              kind_number=ikind)
         CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
         charges_save(iatom) = zeff - sum(charges(iatom, :))
      END DO
 
      ! Store charges in results
      description = "[HIRSHFELD-CHARGES]"
      CALL cp_results_erase(results=results, description=description)
      CALL put_results(results=results, description=description, &
                       values=charges_save)
 
      DEALLOCATE (charges_save)
 
   END SUBROUTINE save_hirshfeld_charges
 
! **************************************************************************************************
!> \brief creates kind specific shape functions for Hirshfeld charges
!> \param hirshfeld_env the env that holds information about Hirshfeld
!> \param qs_kind_set the qs_kind_set
!> \param atomic_kind_set the atomic_kind_set
!> \param radius optional radius parameter to use for all atomic kinds
!> \param radii_list optional list of radii to use for different atomic kinds
! **************************************************************************************************
   SUBROUTINE create_shape_function(hirshfeld_env, qs_kind_set, atomic_kind_set, radius, radii_list)
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      REAL(kind=dp), OPTIONAL                            :: radius
      REAL(kind=dp), DIMENSION(:), OPTIONAL, POINTER     :: radii_list
 
      INTEGER, PARAMETER                                 :: ngto = 8
 
      CHARACTER(len=2)                                   :: esym
      INTEGER                                            :: ikind, nkind
      LOGICAL                                            :: found
      REAL(kind=dp)                                      :: al, rco, zeff
      REAL(kind=dp), DIMENSION(ngto, 2)                  :: ppdens
      TYPE(atomic_kind_type), POINTER                    :: atomic_kind
      TYPE(qs_kind_type), POINTER                        :: qs_kind
 
      cpassert(ASSOCIATED(hirshfeld_env))
 
      nkind = SIZE(qs_kind_set)
      ALLOCATE (hirshfeld_env%kind_shape_fn(nkind))
 
      SELECT CASE (hirshfeld_env%shape_function_type)
      CASE (shape_function_gaussian)
         DO ikind = 1, nkind
            hirshfeld_env%kind_shape_fn(ikind)%numexp = 1
            ALLOCATE (hirshfeld_env%kind_shape_fn(ikind)%zet(1))
            ALLOCATE (hirshfeld_env%kind_shape_fn(ikind)%coef(1))
            CALL get_qs_kind(qs_kind_set(ikind), element_symbol=esym)
            rco = 2.0_dp
            SELECT CASE (hirshfeld_env%radius_type)
            CASE (radius_default)
               CALL get_ptable_info(symbol=esym, covalent_radius=rco, found=found)
               rco = max(rco, 1.0_dp)
            CASE (radius_user)
               cpassert(PRESENT(radii_list))
               cpassert(ASSOCIATED(radii_list))
               cpassert(SIZE(radii_list) == nkind)
               ! Note we assume that radii_list is correctly ordered
               rco = radii_list(ikind)
            CASE (radius_vdw)
               CALL get_ptable_info(symbol=esym, vdw_radius=rco, found=found)
               IF (.NOT. found) THEN
                  rco = max(rco, 1.0_dp)
               ELSE
                  IF (hirshfeld_env%use_bohr) &
                     rco = cp_unit_to_cp2k(rco, "angstrom")
               END IF
            CASE (radius_covalent)
               CALL get_ptable_info(symbol=esym, covalent_radius=rco, found=found)
               IF (.NOT. found) THEN
                  rco = max(rco, 1.0_dp)
               ELSE
                  IF (hirshfeld_env%use_bohr) &
                     rco = cp_unit_to_cp2k(rco, "angstrom")
               END IF
            CASE (radius_single)
               cpassert(PRESENT(radius))
               rco = radius
            END SELECT
            al = 0.5_dp/rco**2
            hirshfeld_env%kind_shape_fn(ikind)%zet(1) = al
            hirshfeld_env%kind_shape_fn(ikind)%coef(1) = (al/pi)**1.5_dp
         END DO
      CASE (shape_function_density)
         ! calculate atomic density
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            qs_kind => qs_kind_set(ikind)
            CALL calculate_atomic_density(ppdens(:, :), atomic_kind, qs_kind, ngto, &
                                          confine=.false.)
            hirshfeld_env%kind_shape_fn(ikind)%numexp = ngto
            ALLOCATE (hirshfeld_env%kind_shape_fn(ikind)%zet(ngto))
            ALLOCATE (hirshfeld_env%kind_shape_fn(ikind)%coef(ngto))
            hirshfeld_env%kind_shape_fn(ikind)%zet(:) = ppdens(:, 1)
            CALL get_qs_kind(qs_kind, zeff=zeff)
            hirshfeld_env%kind_shape_fn(ikind)%coef(:) = ppdens(:, 2)/zeff
         END DO
 
      CASE DEFAULT
         cpabort("Unknown shape function")
      END SELECT
 
   END SUBROUTINE create_shape_function
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param hirshfeld_env ...
!> \param charges ...
! **************************************************************************************************
   SUBROUTINE comp_hirshfeld_charges(qs_env, hirshfeld_env, charges)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      REAL(kind=dp), DIMENSION(:, :), INTENT(inout)      :: charges
 
      INTEGER                                            :: is
      LOGICAL                                            :: rho_r_valid
      REAL(kind=dp)                                      :: tnfun
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
      TYPE(pw_r3d_rs_type)                               :: rhonorm
      TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r
      TYPE(qs_rho_type), POINTER                         :: rho
 
      NULLIFY (rho_r)
      ! normalization function on grid
      CALL calculate_hirshfeld_normalization(qs_env, hirshfeld_env)
      ! check normalization
      tnfun = pw_integrate_function(hirshfeld_env%fnorm)
      tnfun = abs(tnfun - sum(hirshfeld_env%charges))
      !
      CALL get_qs_env(qs_env=qs_env, pw_env=pw_env, rho=rho)
      CALL qs_rho_get(rho, rho_r=rho_r, rho_r_valid=rho_r_valid)
      CALL pw_env_get(pw_env=pw_env, auxbas_pw_pool=auxbas_pw_pool)
      CALL auxbas_pw_pool%create_pw(rhonorm)
      ! loop over spins
      DO is = 1, SIZE(rho_r)
         IF (rho_r_valid) THEN
            CALL hfun_scale(rhonorm%array, rho_r(is)%array, &
                            hirshfeld_env%fnorm%array)
         ELSE
            cpabort("We need rho in real space")
         END IF
         CALL hirshfeld_integration(qs_env, hirshfeld_env, rhonorm, charges(:, is))
         charges(:, is) = charges(:, is)*hirshfeld_env%charges(:)
      END DO
      CALL auxbas_pw_pool%give_back_pw(rhonorm)
 
   END SUBROUTINE comp_hirshfeld_charges
! **************************************************************************************************
!> \brief Calculate fout = fun1/fun2
!> \param fout ...
!> \param fun1 ...
!> \param fun2 ...
! **************************************************************************************************
   SUBROUTINE hfun_scale(fout, fun1, fun2)
      REAL(kind=dp), DIMENSION(:, :, :), INTENT(OUT)     :: fout
      REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN)      :: fun1, fun2
 
      REAL(kind=dp), PARAMETER                           :: small = 1.0e-12_dp
 
      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))
 
      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
 
   END SUBROUTINE hfun_scale
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param hirshfeld_env ...
!> \param charges ...
!> \param ounit ...
! **************************************************************************************************
   SUBROUTINE comp_hirshfeld_i_charges(qs_env, hirshfeld_env, charges, ounit)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      REAL(kind=dp), DIMENSION(:, :), INTENT(inout)      :: charges
      INTEGER, INTENT(IN)                                :: ounit
 
      INTEGER, PARAMETER                                 :: maxloop = 100
      REAL(kind=dp), PARAMETER                           :: maxres = 1.0e-2_dp
 
      CHARACTER(len=3)                                   :: yesno
      INTEGER                                            :: iat, iloop, is, natom
      LOGICAL                                            :: rho_r_valid
      REAL(kind=dp)                                      :: res, tnfun
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
      TYPE(pw_r3d_rs_type)                               :: rhonorm
      TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r
      TYPE(qs_rho_type), POINTER                         :: rho
 
      NULLIFY (rho_r)
 
      natom = SIZE(charges, 1)
 
      IF (ounit > 0) WRITE (ounit, "(/,T2,A)") "Hirshfeld charge iterations: Residuals ..."
      !
      CALL get_qs_env(qs_env=qs_env, pw_env=pw_env, rho=rho)
      CALL qs_rho_get(rho, rho_r=rho_r, rho_r_valid=rho_r_valid)
      CALL pw_env_get(pw_env=pw_env, auxbas_pw_pool=auxbas_pw_pool)
      CALL auxbas_pw_pool%create_pw(rhonorm)
      !
      DO iloop = 1, maxloop
 
         ! normalization function on grid
         CALL calculate_hirshfeld_normalization(qs_env, hirshfeld_env)
         ! check normalization
         tnfun = pw_integrate_function(hirshfeld_env%fnorm)
         tnfun = abs(tnfun - sum(hirshfeld_env%charges))
         ! loop over spins
         DO is = 1, SIZE(rho_r)
            IF (rho_r_valid) THEN
               CALL hfun_scale(rhonorm%array, rho_r(is)%array, &
                               hirshfeld_env%fnorm%array)
            ELSE
               cpabort("We need rho in real space")
            END IF
            CALL hirshfeld_integration(qs_env, hirshfeld_env, rhonorm, charges(:, is))
            charges(:, is) = charges(:, is)*hirshfeld_env%charges(:)
         END DO
         ! residual
         res = 0.0_dp
         DO iat = 1, natom
            res = res + (sum(charges(iat, :)) - hirshfeld_env%charges(iat))**2
         END DO
         res = sqrt(res/real(natom, kind=dp))
         IF (ounit > 0) THEN
            yesno = "NO "
            IF (mod(iloop, 10) == 0) yesno = "YES"
            WRITE (ounit, fmt="(F8.3)", advance=yesno) res
         END IF
         ! update
         DO iat = 1, natom
            hirshfeld_env%charges(iat) = sum(charges(iat, :))
         END DO
         IF (res < maxres) EXIT
 
      END DO
      !
      CALL auxbas_pw_pool%give_back_pw(rhonorm)
 
   END SUBROUTINE comp_hirshfeld_i_charges
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param hirshfeld_env ...
! **************************************************************************************************
   SUBROUTINE calculate_hirshfeld_normalization(qs_env, hirshfeld_env)
 
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
 
      CHARACTER(len=*), PARAMETER :: routinen = 'calculate_hirshfeld_normalization'
 
      INTEGER                                            :: atom_a, handle, iatom, iex, ikind, &
                                                            ithread, j, natom, npme, nthread, &
                                                            numexp, subpatch_pattern
      INTEGER, DIMENSION(:), POINTER                     :: atom_list, cores
      REAL(kind=dp)                                      :: alpha, coef, eps_rho_rspace, radius
      REAL(kind=dp), DIMENSION(3)                        :: ra
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: pab
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(cell_type), POINTER                           :: cell
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
      TYPE(pw_r3d_rs_type), POINTER                      :: fnorm
      TYPE(realspace_grid_desc_type), POINTER            :: auxbas_rs_desc
      TYPE(realspace_grid_type), POINTER                 :: rs_rho
 
      CALL timeset(routinen, handle)
 
      CALL get_qs_env(qs_env=qs_env, atomic_kind_set=atomic_kind_set, cell=cell, &
                      dft_control=dft_control, particle_set=particle_set, pw_env=pw_env)
      CALL pw_env_get(pw_env, auxbas_rs_desc=auxbas_rs_desc, auxbas_rs_grid=rs_rho, &
                      auxbas_pw_pool=auxbas_pw_pool)
      ! be careful in parallel nsmax is chosen with multigrid in mind!
      CALL rs_grid_zero(rs_rho)
 
      eps_rho_rspace = dft_control%qs_control%eps_rho_rspace
      ALLOCATE (pab(1, 1))
      nthread = 1
      ithread = 0
 
      DO ikind = 1, SIZE(atomic_kind_set)
         numexp = hirshfeld_env%kind_shape_fn(ikind)%numexp
         IF (numexp <= 0) cycle
         CALL get_atomic_kind(atomic_kind_set(ikind), natom=natom, atom_list=atom_list)
         ALLOCATE (cores(natom))
 
         DO iex = 1, numexp
            alpha = hirshfeld_env%kind_shape_fn(ikind)%zet(iex)
            coef = hirshfeld_env%kind_shape_fn(ikind)%coef(iex)
            npme = 0
            cores = 0
            DO iatom = 1, natom
               atom_a = atom_list(iatom)
               ra(:) = pbc(particle_set(atom_a)%r, cell)
               IF (rs_rho%desc%parallel .AND. .NOT. rs_rho%desc%distributed) THEN
                  ! replicated realspace grid, split the atoms up between procs
                  IF (modulo(iatom, rs_rho%desc%group_size) == rs_rho%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) = hirshfeld_env%charges(atom_a)*coef
               ra(:) = pbc(particle_set(atom_a)%r, cell)
               subpatch_pattern = 0
               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=eps_rho_rspace, &
                                                 pab=pab, o1=0, o2=0, &  ! without map_consistent
                                                 prefactor=1.0_dp, cutoff=0.0_dp)
 
               ! la_max==0 so set lmax_global to 0
               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_rho, &
                                          radius=radius, ga_gb_function=grid_func_ab, &
                                          use_subpatch=.true., subpatch_pattern=subpatch_pattern)
            END DO
         END DO
 
         DEALLOCATE (cores)
      END DO
      DEALLOCATE (pab)
 
      NULLIFY (fnorm)
      CALL get_hirshfeld_info(hirshfeld_env, fnorm=fnorm)
      IF (ASSOCIATED(fnorm)) THEN
         CALL fnorm%release()
         DEALLOCATE (fnorm)
      END IF
      ALLOCATE (fnorm)
      CALL auxbas_pw_pool%create_pw(fnorm)
      CALL set_hirshfeld_info(hirshfeld_env, fnorm=fnorm)
 
      CALL transfer_rs2pw(rs_rho, fnorm)
 
      CALL timestop(handle)
 
   END SUBROUTINE calculate_hirshfeld_normalization
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param hirshfeld_env ...
!> \param rfun ...
!> \param fval ...
!> \param fderiv ...
! **************************************************************************************************
   SUBROUTINE hirshfeld_integration(qs_env, hirshfeld_env, rfun, fval, fderiv)
 
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(hirshfeld_type), POINTER                      :: hirshfeld_env
      TYPE(pw_r3d_rs_type)                               :: rfun
      REAL(kind=dp), DIMENSION(:), INTENT(inout)         :: fval
      REAL(kind=dp), DIMENSION(:, :), INTENT(inout), &
         OPTIONAL                                        :: fderiv
 
      CHARACTER(len=*), PARAMETER :: routinen = 'hirshfeld_integration'
 
      INTEGER                                            :: atom_a, handle, iatom, iex, ikind, &
                                                            ithread, j, natom, npme, nthread, &
                                                            numexp
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: cores
      INTEGER, DIMENSION(:), POINTER                     :: atom_list
      LOGICAL                                            :: do_force
      REAL(kind=dp)                                      :: alpha, coef, dvol, eps_rho_rspace, radius
      REAL(kind=dp), DIMENSION(3)                        :: force_a, force_b, ra
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: hab, pab
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(cell_type), POINTER                           :: cell
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(pw_env_type), POINTER                         :: pw_env
      TYPE(realspace_grid_desc_type), POINTER            :: auxbas_rs_desc
      TYPE(realspace_grid_type), POINTER                 :: rs_v
 
      CALL timeset(routinen, handle)
 
      do_force = PRESENT(fderiv)
      fval = 0.0_dp
      dvol = rfun%pw_grid%dvol
 
      NULLIFY (pw_env, auxbas_rs_desc)
      CALL get_qs_env(qs_env=qs_env, pw_env=pw_env)
      CALL pw_env_get(pw_env=pw_env, auxbas_rs_desc=auxbas_rs_desc, &
                      auxbas_rs_grid=rs_v)
      CALL transfer_pw2rs(rs_v, rfun)
 
      CALL get_qs_env(qs_env=qs_env, atomic_kind_set=atomic_kind_set, cell=cell, &
                      dft_control=dft_control, particle_set=particle_set)
      eps_rho_rspace = dft_control%qs_control%eps_rho_rspace
 
      nthread = 1
      ithread = 0
      ALLOCATE (hab(1, 1), pab(1, 1))
 
      DO ikind = 1, SIZE(atomic_kind_set)
         numexp = hirshfeld_env%kind_shape_fn(ikind)%numexp
         IF (numexp <= 0) cycle
         CALL get_atomic_kind(atomic_kind_set(ikind), natom=natom, atom_list=atom_list)
         ALLOCATE (cores(natom))
 
         DO iex = 1, numexp
            alpha = hirshfeld_env%kind_shape_fn(ikind)%zet(iex)
            coef = hirshfeld_env%kind_shape_fn(ikind)%coef(iex)
            npme = 0
            cores = 0
            DO iatom = 1, natom
               atom_a = atom_list(iatom)
               ra(:) = pbc(particle_set(atom_a)%r, cell)
               IF (rs_v%desc%parallel .AND. .NOT. rs_v%desc%distributed) THEN
                  ! replicated realspace grid, split the atoms up between procs
                  IF (modulo(iatom, rs_v%desc%group_size) == rs_v%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)
               ra(:) = pbc(particle_set(atom_a)%r, cell)
               pab(1, 1) = coef
               hab(1, 1) = 0.0_dp
               force_a(:) = 0.0_dp
               force_b(:) = 0.0_dp
 
               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=eps_rho_rspace, &
                                                 pab=pab, o1=0, o2=0, &  ! without map_consistent
                                                 prefactor=1.0_dp, cutoff=1.0_dp)
 
               CALL integrate_pgf_product(0, alpha, 0, &
                                          0, 0.0_dp, 0, ra, (/0.0_dp, 0.0_dp, 0.0_dp/), &
                                          rs_v, hab, pab=pab, o1=0, o2=0, &
                                          radius=radius, calculate_forces=do_force, &
                                          force_a=force_a, force_b=force_b, use_virial=.false., &
                                          use_subpatch=.true., subpatch_pattern=0)
               fval(atom_a) = fval(atom_a) + hab(1, 1)*dvol*coef
               IF (do_force) THEN
                  fderiv(:, atom_a) = fderiv(:, atom_a) + force_a(:)*dvol
               END IF
            END DO
 
         END DO
         DEALLOCATE (cores)
 
      END DO
 
      DEALLOCATE (hab, pab)
 
      CALL get_qs_env(qs_env=qs_env, para_env=para_env)
      CALL para_env%sum(fval)
 
      CALL timestop(handle)
 
   END SUBROUTINE hirshfeld_integration
 
END MODULE hirshfeld_methods