LCOV - code coverage report
Current view: top level - src - optimize_embedding_potential.F (source / functions) Hit Total Coverage
Test: CP2K Regtests (git:b8e0b09) Lines: 1065 1312 81.2 %
Date: 2024-08-31 06:31:37 Functions: 38 41 92.7 %

          Line data    Source code
       1             : !--------------------------------------------------------------------------------------------------!
       2             : !   CP2K: A general program to perform molecular dynamics simulations                              !
       3             : !   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
       4             : !                                                                                                  !
       5             : !   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
       6             : !--------------------------------------------------------------------------------------------------!
       7             : 
       8             : MODULE optimize_embedding_potential
       9             : 
      10             :    USE atomic_kind_types,               ONLY: atomic_kind_type,&
      11             :                                               get_atomic_kind,&
      12             :                                               get_atomic_kind_set
      13             :    USE cell_types,                      ONLY: cell_type
      14             :    USE cp_blacs_env,                    ONLY: cp_blacs_env_create,&
      15             :                                               cp_blacs_env_release,&
      16             :                                               cp_blacs_env_type
      17             :    USE cp_control_types,                ONLY: dft_control_type
      18             :    USE cp_dbcsr_api,                    ONLY: dbcsr_p_type
      19             :    USE cp_dbcsr_operations,             ONLY: copy_dbcsr_to_fm,&
      20             :                                               dbcsr_deallocate_matrix_set
      21             :    USE cp_files,                        ONLY: close_file,&
      22             :                                               open_file
      23             :    USE cp_fm_basic_linalg,              ONLY: cp_fm_column_scale,&
      24             :                                               cp_fm_scale,&
      25             :                                               cp_fm_scale_and_add,&
      26             :                                               cp_fm_trace
      27             :    USE cp_fm_diag,                      ONLY: choose_eigv_solver
      28             :    USE cp_fm_struct,                    ONLY: cp_fm_struct_create,&
      29             :                                               cp_fm_struct_release,&
      30             :                                               cp_fm_struct_type
      31             :    USE cp_fm_types,                     ONLY: &
      32             :         cp_fm_copy_general, cp_fm_create, cp_fm_get_element, cp_fm_get_info, cp_fm_release, &
      33             :         cp_fm_set_all, cp_fm_to_fm, cp_fm_to_fm_submat, cp_fm_type, cp_fm_write_unformatted
      34             :    USE cp_log_handling,                 ONLY: cp_get_default_logger,&
      35             :                                               cp_logger_type
      36             :    USE cp_output_handling,              ONLY: cp_p_file,&
      37             :                                               cp_print_key_finished_output,&
      38             :                                               cp_print_key_should_output,&
      39             :                                               cp_print_key_unit_nr
      40             :    USE cp_realspace_grid_cube,          ONLY: cp_cube_to_pw,&
      41             :                                               cp_pw_to_cube,&
      42             :                                               cp_pw_to_simple_volumetric
      43             :    USE embed_types,                     ONLY: opt_embed_pot_type
      44             :    USE force_env_types,                 ONLY: force_env_type
      45             :    USE input_constants,                 ONLY: &
      46             :         embed_diff, embed_fa, embed_grid_angstrom, embed_grid_bohr, embed_level_shift, embed_none, &
      47             :         embed_quasi_newton, embed_resp, embed_steep_desc
      48             :    USE input_section_types,             ONLY: section_get_ival,&
      49             :                                               section_get_ivals,&
      50             :                                               section_get_rval,&
      51             :                                               section_vals_get_subs_vals,&
      52             :                                               section_vals_type,&
      53             :                                               section_vals_val_get
      54             :    USE kinds,                           ONLY: default_path_length,&
      55             :                                               dp
      56             :    USE lri_environment_types,           ONLY: lri_kind_type
      57             :    USE mathconstants,                   ONLY: pi
      58             :    USE message_passing,                 ONLY: mp_para_env_type
      59             :    USE mixed_environment_utils,         ONLY: get_subsys_map_index
      60             :    USE parallel_gemm_api,               ONLY: parallel_gemm
      61             :    USE particle_list_types,             ONLY: particle_list_type
      62             :    USE particle_types,                  ONLY: particle_type
      63             :    USE pw_env_types,                    ONLY: pw_env_get,&
      64             :                                               pw_env_type
      65             :    USE pw_methods,                      ONLY: &
      66             :         pw_axpy, pw_copy, pw_derive, pw_dr2, pw_integral_ab, pw_integrate_function, pw_scale, &
      67             :         pw_transfer, pw_zero
      68             :    USE pw_poisson_methods,              ONLY: pw_poisson_solve
      69             :    USE pw_poisson_types,                ONLY: pw_poisson_type
      70             :    USE pw_pool_types,                   ONLY: pw_pool_type
      71             :    USE pw_types,                        ONLY: pw_c1d_gs_type,&
      72             :                                               pw_r3d_rs_type
      73             :    USE qs_collocate_density,            ONLY: calculate_rho_resp_all,&
      74             :                                               calculate_wavefunction,&
      75             :                                               collocate_function
      76             :    USE qs_environment_types,            ONLY: get_qs_env,&
      77             :                                               qs_environment_type,&
      78             :                                               set_qs_env
      79             :    USE qs_integrate_potential_single,   ONLY: integrate_v_rspace_one_center
      80             :    USE qs_kind_types,                   ONLY: get_qs_kind,&
      81             :                                               qs_kind_type
      82             :    USE qs_kinetic,                      ONLY: build_kinetic_matrix
      83             :    USE qs_ks_types,                     ONLY: qs_ks_env_type
      84             :    USE qs_mo_types,                     ONLY: get_mo_set,&
      85             :                                               mo_set_type
      86             :    USE qs_neighbor_list_types,          ONLY: neighbor_list_set_p_type
      87             :    USE qs_rho_types,                    ONLY: qs_rho_get,&
      88             :                                               qs_rho_type
      89             :    USE qs_subsys_types,                 ONLY: qs_subsys_get,&
      90             :                                               qs_subsys_type
      91             :    USE xc,                              ONLY: smooth_cutoff
      92             :    USE xc_rho_cflags_types,             ONLY: xc_rho_cflags_setall,&
      93             :                                               xc_rho_cflags_type
      94             :    USE xc_rho_set_types,                ONLY: xc_rho_set_create,&
      95             :                                               xc_rho_set_release,&
      96             :                                               xc_rho_set_type,&
      97             :                                               xc_rho_set_update
      98             : #include "./base/base_uses.f90"
      99             : 
     100             :    IMPLICIT NONE
     101             : 
     102             :    PRIVATE
     103             : 
     104             :    CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'optimize_embedding_potential'
     105             : 
     106             :    PUBLIC :: prepare_embed_opt, init_embed_pot, release_opt_embed, calculate_embed_pot_grad, &
     107             :              opt_embed_step, print_rho_diff, step_control, max_dens_diff, print_emb_opt_info, &
     108             :              conv_check_embed, make_subsys_embed_pot, print_embed_restart, find_aux_dimen, &
     109             :              read_embed_pot, understand_spin_states, given_embed_pot, print_rho_spin_diff, &
     110             :              print_pot_simple_grid, get_prev_density, get_max_subsys_diff, Coulomb_guess
     111             : 
     112             : CONTAINS
     113             : 
     114             : ! **************************************************************************************************
     115             : !> \brief Find out whether we need to swap alpha- and beta- spind densities in the second subsystem
     116             : !> \brief It's only needed because by default alpha-spins go first in a subsystem.
     117             : !> \brief By swapping we impose the constraint:
     118             : !> \brief rho_1(alpha) + rho_2(alpha) = rho_total(alpha)
     119             : !> \brief rho_1(beta) + rho_2(beta) = rho_total(beta)
     120             : !> \param force_env ...
     121             : !> \param ref_subsys_number ...
     122             : !> \param change_spin ...
     123             : !> \param open_shell_embed ...
     124             : !> \param all_nspins ...
     125             : !> \return ...
     126             : !> \author Vladimir Rybkin
     127             : ! **************************************************************************************************
     128          24 :    SUBROUTINE understand_spin_states(force_env, ref_subsys_number, change_spin, open_shell_embed, all_nspins)
     129             :       TYPE(force_env_type), POINTER                      :: force_env
     130             :       INTEGER                                            :: ref_subsys_number
     131             :       LOGICAL                                            :: change_spin, open_shell_embed
     132             :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: all_nspins
     133             : 
     134             :       INTEGER                                            :: i_force_eval, nspins, sub_spin_1, &
     135             :                                                             sub_spin_2, total_spin
     136             :       INTEGER, DIMENSION(2)                              :: nelectron_spin
     137             :       INTEGER, DIMENSION(2, 3)                           :: all_spins
     138             :       TYPE(dft_control_type), POINTER                    :: dft_control
     139             : 
     140          24 :       change_spin = .FALSE.
     141          24 :       open_shell_embed = .FALSE.
     142          72 :       ALLOCATE (all_nspins(ref_subsys_number))
     143          24 :       IF (ref_subsys_number .EQ. 3) THEN
     144          24 :          all_spins = 0
     145          96 :          DO i_force_eval = 1, ref_subsys_number
     146             :             CALL get_qs_env(qs_env=force_env%sub_force_env(i_force_eval)%force_env%qs_env, &
     147          72 :                             nelectron_spin=nelectron_spin, dft_control=dft_control)
     148         216 :             all_spins(:, i_force_eval) = nelectron_spin
     149          72 :             nspins = dft_control%nspins
     150          96 :             all_nspins(i_force_eval) = nspins
     151             :          END DO
     152             : 
     153             :          ! Find out whether we need a spin-dependend embedding potential
     154          24 :          IF (.NOT. ((all_nspins(1) .EQ. 1) .AND. (all_nspins(2) .EQ. 1) .AND. (all_nspins(3) .EQ. 1))) &
     155          12 :             open_shell_embed = .TRUE.
     156             : 
     157             :          ! If it's open shell, we need to check spin states
     158          24 :          IF (open_shell_embed) THEN
     159             : 
     160          12 :             IF (all_nspins(3) .EQ. 1) THEN
     161             :                total_spin = 0
     162             :             ELSE
     163          10 :                total_spin = all_spins(1, 3) - all_spins(2, 3)
     164             :             END IF
     165          12 :             IF (all_nspins(1) .EQ. 1) THEN
     166             :                sub_spin_1 = 0
     167             :             ELSE
     168          12 :                sub_spin_1 = all_spins(1, 1) - all_spins(2, 1)
     169             :             END IF
     170          12 :             IF (all_nspins(2) .EQ. 1) THEN
     171             :                sub_spin_2 = 0
     172             :             ELSE
     173          12 :                sub_spin_2 = all_spins(1, 2) - all_spins(2, 2)
     174             :             END IF
     175          12 :             IF ((sub_spin_1 + sub_spin_2) .EQ. total_spin) THEN
     176          10 :                change_spin = .FALSE.
     177             :             ELSE
     178           2 :                IF (ABS(sub_spin_1 - sub_spin_2) .EQ. total_spin) THEN
     179           2 :                   change_spin = .TRUE.
     180             :                ELSE
     181           0 :                   CPABORT("Spin states of subsystems are not compatible.")
     182             :                END IF
     183             :             END IF
     184             : 
     185             :          END IF ! not open_shell
     186             :       ELSE
     187           0 :          CPABORT("Reference subsystem must be the third FORCE_EVAL.")
     188             :       END IF
     189             : 
     190          24 :    END SUBROUTINE understand_spin_states
     191             : 
     192             : ! **************************************************************************************************
     193             : !> \brief ...
     194             : !> \param qs_env ...
     195             : !> \param embed_pot ...
     196             : !> \param add_const_pot ...
     197             : !> \param Fermi_Amaldi ...
     198             : !> \param const_pot ...
     199             : !> \param open_shell_embed ...
     200             : !> \param spin_embed_pot ...
     201             : !> \param pot_diff ...
     202             : !> \param Coulomb_guess ...
     203             : !> \param grid_opt ...
     204             : ! **************************************************************************************************
     205          24 :    SUBROUTINE init_embed_pot(qs_env, embed_pot, add_const_pot, Fermi_Amaldi, const_pot, open_shell_embed, &
     206             :                              spin_embed_pot, pot_diff, Coulomb_guess, grid_opt)
     207             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     208             :       TYPE(pw_r3d_rs_type), POINTER                      :: embed_pot
     209             :       LOGICAL                                            :: add_const_pot, Fermi_Amaldi
     210             :       TYPE(pw_r3d_rs_type), POINTER                      :: const_pot
     211             :       LOGICAL                                            :: open_shell_embed
     212             :       TYPE(pw_r3d_rs_type), POINTER                      :: spin_embed_pot, pot_diff
     213             :       LOGICAL                                            :: Coulomb_guess, grid_opt
     214             : 
     215             :       INTEGER                                            :: nelectrons
     216             :       INTEGER, DIMENSION(2)                              :: nelectron_spin
     217             :       REAL(KIND=dp)                                      :: factor
     218             :       TYPE(pw_env_type), POINTER                         :: pw_env
     219             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
     220             :       TYPE(pw_r3d_rs_type), POINTER                      :: v_hartree_r_space
     221             : 
     222             :       ! Extract  plane waves environment
     223             :       CALL get_qs_env(qs_env=qs_env, pw_env=pw_env, &
     224             :                       nelectron_spin=nelectron_spin, &
     225          24 :                       v_hartree_rspace=v_hartree_r_space)
     226             : 
     227             :       ! Prepare plane-waves pool
     228          24 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
     229             : 
     230             :       ! Create embedding potential and set to zero
     231             :       NULLIFY (embed_pot)
     232          24 :       ALLOCATE (embed_pot)
     233          24 :       CALL auxbas_pw_pool%create_pw(embed_pot)
     234          24 :       CALL pw_zero(embed_pot)
     235             : 
     236             :       ! Spin embedding potential if asked
     237          24 :       IF (open_shell_embed) THEN
     238             :          NULLIFY (spin_embed_pot)
     239          12 :          ALLOCATE (spin_embed_pot)
     240          12 :          CALL auxbas_pw_pool%create_pw(spin_embed_pot)
     241          12 :          CALL pw_zero(spin_embed_pot)
     242             :       END IF
     243             : 
     244             :       ! Coulomb guess/constant potential
     245          24 :       IF (Coulomb_guess) THEN
     246             :          NULLIFY (pot_diff)
     247           2 :          ALLOCATE (pot_diff)
     248           2 :          CALL auxbas_pw_pool%create_pw(pot_diff)
     249           2 :          CALL pw_zero(pot_diff)
     250             :       END IF
     251             : 
     252             :       ! Initialize constant part of the embedding potential
     253          24 :       IF (add_const_pot .AND. (.NOT. grid_opt)) THEN
     254             :          ! Now the constant potential is the Coulomb one
     255             :          NULLIFY (const_pot)
     256           4 :          ALLOCATE (const_pot)
     257           4 :          CALL auxbas_pw_pool%create_pw(const_pot)
     258           4 :          CALL pw_zero(const_pot)
     259             :       END IF
     260             : 
     261             :       ! Add Fermi-Amaldi potential if requested
     262          24 :       IF (Fermi_Amaldi) THEN
     263             : 
     264             :          ! Extract  Hartree potential
     265           6 :          NULLIFY (v_hartree_r_space)
     266             :          CALL get_qs_env(qs_env=qs_env, pw_env=pw_env, &
     267           6 :                          v_hartree_rspace=v_hartree_r_space)
     268           6 :          CALL pw_copy(v_hartree_r_space, embed_pot)
     269             : 
     270             :          ! Calculate the number of electrons
     271           6 :          nelectrons = nelectron_spin(1) + nelectron_spin(2)
     272           6 :          factor = (REAL(nelectrons, dp) - 1.0_dp)/(REAL(nelectrons, dp))
     273             : 
     274             :          ! Scale the Hartree potential to get Fermi-Amaldi
     275           6 :          CALL pw_scale(embed_pot, a=factor)
     276             : 
     277             :          ! Copy Fermi-Amaldi to embedding potential for basis-based optimization
     278           6 :          IF (.NOT. grid_opt) CALL pw_copy(embed_pot, embed_pot)
     279             : 
     280             :       END IF
     281             : 
     282          24 :    END SUBROUTINE init_embed_pot
     283             : 
     284             : ! **************************************************************************************************
     285             : !> \brief Creates and allocates objects for optimization of embedding potential
     286             : !> \param qs_env ...
     287             : !> \param opt_embed ...
     288             : !> \param opt_embed_section ...
     289             : !> \author Vladimir Rybkin
     290             : ! **************************************************************************************************
     291          24 :    SUBROUTINE prepare_embed_opt(qs_env, opt_embed, opt_embed_section)
     292             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     293             :       TYPE(opt_embed_pot_type)                           :: opt_embed
     294             :       TYPE(section_vals_type), POINTER                   :: opt_embed_section
     295             : 
     296             :       INTEGER                                            :: diff_size, i_dens, size_prev_dens
     297             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
     298             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
     299             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     300             :       TYPE(pw_env_type), POINTER                         :: pw_env
     301             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
     302             : 
     303             :       !TYPE(pw_env_type), POINTER                         :: pw_env
     304             :       !TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
     305             : 
     306             :       ! First, read the input
     307             : 
     308          24 :       CALL read_opt_embed_section(opt_embed, opt_embed_section)
     309             : 
     310             :       ! All these are needed for optimization in a finite Gaussian basis
     311          24 :       IF (.NOT. opt_embed%grid_opt) THEN
     312             :          ! Create blacs environment
     313             :          CALL get_qs_env(qs_env=qs_env, &
     314          14 :                          para_env=para_env)
     315          14 :          NULLIFY (blacs_env)
     316          14 :          CALL cp_blacs_env_create(blacs_env=blacs_env, para_env=para_env)
     317             : 
     318             :          ! Reveal the dimension of the RI basis
     319          14 :          CALL find_aux_dimen(qs_env, opt_embed%dimen_aux)
     320             : 
     321             :          ! Prepare the object for integrals
     322          14 :          CALL make_lri_object(qs_env, opt_embed%lri)
     323             : 
     324             :          ! In case if spin embedding potential has to be optimized,
     325             :          ! the dimension of variational space is two times larger
     326          14 :          IF (opt_embed%open_shell_embed) THEN
     327           6 :             opt_embed%dimen_var_aux = 2*opt_embed%dimen_aux
     328             :          ELSE
     329           8 :             opt_embed%dimen_var_aux = opt_embed%dimen_aux
     330             :          END IF
     331             : 
     332             :          ! Allocate expansion coefficients and gradient
     333          14 :          NULLIFY (opt_embed%embed_pot_grad, opt_embed%embed_pot_coef, opt_embed%step, fm_struct)
     334             : 
     335          14 :          NULLIFY (opt_embed%prev_embed_pot_grad, opt_embed%prev_embed_pot_coef, opt_embed%prev_step)
     336             :          CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
     337          14 :                                   nrow_global=opt_embed%dimen_var_aux, ncol_global=1)
     338             :          ALLOCATE (opt_embed%embed_pot_grad, opt_embed%embed_pot_coef, &
     339             :                    opt_embed%prev_embed_pot_grad, opt_embed%prev_embed_pot_coef, &
     340          14 :                    opt_embed%step, opt_embed%prev_step)
     341          14 :          CALL cp_fm_create(opt_embed%embed_pot_grad, fm_struct, name="pot_grad")
     342          14 :          CALL cp_fm_create(opt_embed%embed_pot_coef, fm_struct, name="pot_coef")
     343          14 :          CALL cp_fm_create(opt_embed%prev_embed_pot_grad, fm_struct, name="prev_pot_grad")
     344          14 :          CALL cp_fm_create(opt_embed%prev_embed_pot_coef, fm_struct, name="prev_pot_coef")
     345          14 :          CALL cp_fm_create(opt_embed%step, fm_struct, name="step")
     346          14 :          CALL cp_fm_create(opt_embed%prev_step, fm_struct, name="prev_step")
     347             : 
     348          14 :          CALL cp_fm_struct_release(fm_struct)
     349          14 :          CALL cp_fm_set_all(opt_embed%embed_pot_grad, 0.0_dp)
     350          14 :          CALL cp_fm_set_all(opt_embed%prev_embed_pot_grad, 0.0_dp)
     351          14 :          CALL cp_fm_set_all(opt_embed%embed_pot_coef, 0.0_dp)
     352          14 :          CALL cp_fm_set_all(opt_embed%prev_embed_pot_coef, 0.0_dp)
     353          14 :          CALL cp_fm_set_all(opt_embed%step, 0.0_dp)
     354             : 
     355          14 :          CALL cp_fm_set_all(opt_embed%prev_step, 0.0_dp)
     356             : 
     357             :          ! Allocate Hessian
     358          14 :          NULLIFY (opt_embed%embed_pot_hess, opt_embed%prev_embed_pot_hess, fm_struct)
     359             :          CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
     360          14 :                                   nrow_global=opt_embed%dimen_var_aux, ncol_global=opt_embed%dimen_var_aux)
     361          14 :          ALLOCATE (opt_embed%embed_pot_hess, opt_embed%prev_embed_pot_hess)
     362          14 :          CALL cp_fm_create(opt_embed%embed_pot_hess, fm_struct, name="pot_Hess")
     363          14 :          CALL cp_fm_create(opt_embed%prev_embed_pot_hess, fm_struct, name="prev_pot_Hess")
     364          14 :          CALL cp_fm_struct_release(fm_struct)
     365             : 
     366             :          ! Special structure for the kinetic energy matrix
     367          14 :          NULLIFY (fm_struct, opt_embed%kinetic_mat)
     368             :          CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
     369          14 :                                   nrow_global=opt_embed%dimen_aux, ncol_global=opt_embed%dimen_aux)
     370          14 :          ALLOCATE (opt_embed%kinetic_mat)
     371          14 :          CALL cp_fm_create(opt_embed%kinetic_mat, fm_struct, name="kinetic_mat")
     372          14 :          CALL cp_fm_struct_release(fm_struct)
     373          14 :          CALL cp_fm_set_all(opt_embed%kinetic_mat, 0.0_dp)
     374             : 
     375             :          ! Hessian is set as a unit matrix
     376          14 :          CALL cp_fm_set_all(opt_embed%embed_pot_hess, 0.0_dp, -1.0_dp)
     377          14 :          CALL cp_fm_set_all(opt_embed%prev_embed_pot_hess, 0.0_dp, -1.0_dp)
     378             : 
     379             :          ! Release blacs environment
     380          14 :          CALL cp_blacs_env_release(blacs_env)
     381             : 
     382             :       END IF
     383             : 
     384          24 :       CALL get_qs_env(qs_env=qs_env, pw_env=pw_env)
     385          24 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
     386          24 :       NULLIFY (opt_embed%prev_subsys_dens)
     387          72 :       size_prev_dens = SUM(opt_embed%all_nspins(1:(SIZE(opt_embed%all_nspins) - 1)))
     388         144 :       ALLOCATE (opt_embed%prev_subsys_dens(size_prev_dens))
     389          96 :       DO i_dens = 1, size_prev_dens
     390          72 :          CALL auxbas_pw_pool%create_pw(opt_embed%prev_subsys_dens(i_dens))
     391          96 :          CALL pw_zero(opt_embed%prev_subsys_dens(i_dens))
     392             :       END DO
     393          72 :       ALLOCATE (opt_embed%max_subsys_dens_diff(size_prev_dens))
     394             : 
     395             :       ! Array to store functional values
     396          72 :       ALLOCATE (opt_embed%w_func(opt_embed%n_iter))
     397        1136 :       opt_embed%w_func = 0.0_dp
     398             : 
     399             :       ! Allocate max_diff and int_diff
     400          24 :       diff_size = 1
     401          24 :       IF (opt_embed%open_shell_embed) diff_size = 2
     402          48 :       ALLOCATE (opt_embed%max_diff(diff_size))
     403          48 :       ALLOCATE (opt_embed%int_diff(diff_size))
     404          48 :       ALLOCATE (opt_embed%int_diff_square(diff_size))
     405             : 
     406             :       ! FAB update
     407          24 :       IF (opt_embed%fab) THEN
     408             :          NULLIFY (opt_embed%prev_embed_pot)
     409           2 :          ALLOCATE (opt_embed%prev_embed_pot)
     410           2 :          CALL auxbas_pw_pool%create_pw(opt_embed%prev_embed_pot)
     411           2 :          CALL pw_zero(opt_embed%prev_embed_pot)
     412           2 :          IF (opt_embed%open_shell_embed) THEN
     413             :             NULLIFY (opt_embed%prev_spin_embed_pot)
     414           0 :             ALLOCATE (opt_embed%prev_spin_embed_pot)
     415           0 :             CALL auxbas_pw_pool%create_pw(opt_embed%prev_spin_embed_pot)
     416           0 :             CALL pw_zero(opt_embed%prev_spin_embed_pot)
     417             :          END IF
     418             :       END IF
     419             : 
     420             :       ! Set allowed energy decrease parameter
     421          24 :       opt_embed%allowed_decrease = 0.0001_dp
     422             : 
     423             :       ! Regularization contribution is set to zero
     424          24 :       opt_embed%reg_term = 0.0_dp
     425             : 
     426             :       ! Step is accepted in the beginning
     427          24 :       opt_embed%accept_step = .TRUE.
     428          24 :       opt_embed%newton_step = .FALSE.
     429          24 :       opt_embed%last_accepted = 1
     430             : 
     431             :       ! Set maximum and minimum trust radii
     432          24 :       opt_embed%max_trad = opt_embed%trust_rad*7.900_dp
     433          24 :       opt_embed%min_trad = opt_embed%trust_rad*0.125*0.065_dp
     434             : 
     435          24 :    END SUBROUTINE prepare_embed_opt
     436             : 
     437             : ! **************************************************************************************************
     438             : !> \brief ...
     439             : !> \param opt_embed ...
     440             : !> \param opt_embed_section ...
     441             : ! **************************************************************************************************
     442          72 :    SUBROUTINE read_opt_embed_section(opt_embed, opt_embed_section)
     443             :       TYPE(opt_embed_pot_type)                           :: opt_embed
     444             :       TYPE(section_vals_type), POINTER                   :: opt_embed_section
     445             : 
     446             :       INTEGER                                            :: embed_guess, embed_optimizer
     447             : 
     448             :       ! Read keywords
     449             :       CALL section_vals_val_get(opt_embed_section, "REG_LAMBDA", &
     450          24 :                                 r_val=opt_embed%lambda)
     451             : 
     452             :       CALL section_vals_val_get(opt_embed_section, "N_ITER", &
     453          24 :                                 i_val=opt_embed%n_iter)
     454             : 
     455             :       CALL section_vals_val_get(opt_embed_section, "TRUST_RAD", &
     456          24 :                                 r_val=opt_embed%trust_rad)
     457             : 
     458             :       CALL section_vals_val_get(opt_embed_section, "DENS_CONV_MAX", &
     459          24 :                                 r_val=opt_embed%conv_max)
     460             : 
     461             :       CALL section_vals_val_get(opt_embed_section, "DENS_CONV_INT", &
     462          24 :                                 r_val=opt_embed%conv_int)
     463             : 
     464             :       CALL section_vals_val_get(opt_embed_section, "SPIN_DENS_CONV_MAX", &
     465          24 :                                 r_val=opt_embed%conv_max_spin)
     466             : 
     467             :       CALL section_vals_val_get(opt_embed_section, "SPIN_DENS_CONV_INT", &
     468          24 :                                 r_val=opt_embed%conv_int_spin)
     469             : 
     470             :       CALL section_vals_val_get(opt_embed_section, "CHARGE_DISTR_WIDTH", &
     471          24 :                                 r_val=opt_embed%eta)
     472             : 
     473             :       CALL section_vals_val_get(opt_embed_section, "READ_EMBED_POT", &
     474          24 :                                 l_val=opt_embed%read_embed_pot)
     475             : 
     476             :       CALL section_vals_val_get(opt_embed_section, "READ_EMBED_POT_CUBE", &
     477          24 :                                 l_val=opt_embed%read_embed_pot_cube)
     478             : 
     479             :       CALL section_vals_val_get(opt_embed_section, "GRID_OPT", &
     480          24 :                                 l_val=opt_embed%grid_opt)
     481             : 
     482             :       CALL section_vals_val_get(opt_embed_section, "LEEUWEN-BAERENDS", &
     483          24 :                                 l_val=opt_embed%leeuwen)
     484             : 
     485             :       CALL section_vals_val_get(opt_embed_section, "FAB", &
     486          24 :                                 l_val=opt_embed%fab)
     487             : 
     488             :       CALL section_vals_val_get(opt_embed_section, "VW_CUTOFF", &
     489          24 :                                 r_val=opt_embed%vw_cutoff)
     490             : 
     491             :       CALL section_vals_val_get(opt_embed_section, "VW_SMOOTH_CUT_RANGE", &
     492          24 :                                 r_val=opt_embed%vw_smooth_cutoff_range)
     493             : 
     494          24 :       CALL section_vals_val_get(opt_embed_section, "OPTIMIZER", i_val=embed_optimizer)
     495          14 :       SELECT CASE (embed_optimizer)
     496             :       CASE (embed_steep_desc)
     497          14 :          opt_embed%steep_desc = .TRUE.
     498             :       CASE (embed_quasi_newton)
     499           4 :          opt_embed%steep_desc = .FALSE.
     500           4 :          opt_embed%level_shift = .FALSE.
     501             :       CASE (embed_level_shift)
     502           6 :          opt_embed%steep_desc = .FALSE.
     503           6 :          opt_embed%level_shift = .TRUE.
     504             :       CASE DEFAULT
     505          24 :          opt_embed%steep_desc = .TRUE.
     506             :       END SELECT
     507             : 
     508          24 :       CALL section_vals_val_get(opt_embed_section, "POT_GUESS", i_val=embed_guess)
     509          16 :       SELECT CASE (embed_guess)
     510             :       CASE (embed_none)
     511          16 :          opt_embed%add_const_pot = .FALSE.
     512          16 :          opt_embed%Fermi_Amaldi = .FALSE.
     513          16 :          opt_embed%Coulomb_guess = .FALSE.
     514          16 :          opt_embed%diff_guess = .FALSE.
     515             :       CASE (embed_diff)
     516           2 :          opt_embed%add_const_pot = .TRUE.
     517           2 :          opt_embed%Fermi_Amaldi = .FALSE.
     518           2 :          opt_embed%Coulomb_guess = .FALSE.
     519           2 :          opt_embed%diff_guess = .TRUE.
     520             :       CASE (embed_fa)
     521           4 :          opt_embed%add_const_pot = .TRUE.
     522           4 :          opt_embed%Fermi_Amaldi = .TRUE.
     523           4 :          opt_embed%Coulomb_guess = .FALSE.
     524           4 :          opt_embed%diff_guess = .FALSE.
     525             :       CASE (embed_resp)
     526           2 :          opt_embed%add_const_pot = .TRUE.
     527           2 :          opt_embed%Fermi_Amaldi = .TRUE.
     528           2 :          opt_embed%Coulomb_guess = .TRUE.
     529           2 :          opt_embed%diff_guess = .FALSE.
     530             :       CASE DEFAULT
     531           0 :          opt_embed%add_const_pot = .FALSE.
     532           0 :          opt_embed%Fermi_Amaldi = .FALSE.
     533           0 :          opt_embed%Coulomb_guess = .FALSE.
     534          24 :          opt_embed%diff_guess = .FALSE.
     535             :       END SELECT
     536             : 
     537          24 :    END SUBROUTINE read_opt_embed_section
     538             : 
     539             : ! **************************************************************************************************
     540             : !> \brief Find the dimension of the auxiliary basis for the expansion of the embedding potential
     541             : !> \param qs_env ...
     542             : !> \param dimen_aux ...
     543             : ! **************************************************************************************************
     544          18 :    SUBROUTINE find_aux_dimen(qs_env, dimen_aux)
     545             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     546             :       INTEGER                                            :: dimen_aux
     547             : 
     548             :       INTEGER                                            :: iatom, ikind, nsgf
     549          18 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of
     550          18 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     551          18 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     552          18 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     553             : 
     554             :       ! First, reveal the dimension of the RI basis
     555             :       CALL get_qs_env(qs_env=qs_env, &
     556             :                       particle_set=particle_set, &
     557             :                       qs_kind_set=qs_kind_set, &
     558          18 :                       atomic_kind_set=atomic_kind_set)
     559             : 
     560          18 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of)
     561             : 
     562          18 :       dimen_aux = 0
     563          82 :       DO iatom = 1, SIZE(particle_set)
     564          64 :          ikind = kind_of(iatom)
     565          64 :          CALL get_qs_kind(qs_kind=qs_kind_set(ikind), nsgf=nsgf, basis_type="RI_AUX")
     566          82 :          dimen_aux = dimen_aux + nsgf
     567             :       END DO
     568             : 
     569          36 :    END SUBROUTINE find_aux_dimen
     570             : 
     571             : ! **************************************************************************************************
     572             : !> \brief Prepare the lri_kind_type object for integrals between density and aux. basis functions
     573             : !> \param qs_env ...
     574             : !> \param lri ...
     575             : ! **************************************************************************************************
     576          14 :    SUBROUTINE make_lri_object(qs_env, lri)
     577             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     578             :       TYPE(lri_kind_type), DIMENSION(:), POINTER         :: lri
     579             : 
     580             :       INTEGER                                            :: ikind, natom, nkind, nsgf
     581          14 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     582             :       TYPE(atomic_kind_type), POINTER                    :: atomic_kind
     583          14 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     584             : 
     585          14 :       NULLIFY (atomic_kind, lri)
     586             :       CALL get_qs_env(qs_env=qs_env, atomic_kind_set=atomic_kind_set, &
     587          14 :                       qs_kind_set=qs_kind_set)
     588          14 :       nkind = SIZE(atomic_kind_set)
     589             : 
     590          62 :       ALLOCATE (lri(nkind))
     591             :       ! Here we need only v_int and acoef (the latter as dummies)
     592          34 :       DO ikind = 1, nkind
     593          20 :          NULLIFY (lri(ikind)%acoef)
     594          20 :          NULLIFY (lri(ikind)%v_int)
     595          20 :          atomic_kind => atomic_kind_set(ikind)
     596          20 :          CALL get_atomic_kind(atomic_kind=atomic_kind, natom=natom)
     597          20 :          CALL get_qs_kind(qs_kind=qs_kind_set(ikind), nsgf=nsgf, basis_type="RI_AUX")
     598          80 :          ALLOCATE (lri(ikind)%acoef(natom, nsgf))
     599        2672 :          lri(ikind)%acoef = 0._dp
     600          60 :          ALLOCATE (lri(ikind)%v_int(natom, nsgf))
     601        2706 :          lri(ikind)%v_int = 0._dp
     602             :       END DO
     603             : 
     604          14 :    END SUBROUTINE make_lri_object
     605             : 
     606             : ! **************************************************************************************************
     607             : !> \brief Read the external embedding potential, not to be optimized
     608             : !> \param qs_env ...
     609             : ! **************************************************************************************************
     610           2 :    SUBROUTINE given_embed_pot(qs_env)
     611             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     612             : 
     613             :       LOGICAL                                            :: open_shell_embed
     614             :       TYPE(dft_control_type), POINTER                    :: dft_control
     615             :       TYPE(pw_env_type), POINTER                         :: pw_env
     616             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool_subsys
     617             :       TYPE(pw_r3d_rs_type), POINTER                      :: embed_pot, spin_embed_pot
     618             :       TYPE(section_vals_type), POINTER                   :: input, qs_section
     619             : 
     620           2 :       qs_env%given_embed_pot = .TRUE.
     621           2 :       NULLIFY (input, dft_control, embed_pot, spin_embed_pot, embed_pot, spin_embed_pot, &
     622           2 :                qs_section)
     623             :       CALL get_qs_env(qs_env=qs_env, &
     624             :                       input=input, &
     625             :                       dft_control=dft_control, &
     626           2 :                       pw_env=pw_env)
     627           2 :       qs_section => section_vals_get_subs_vals(input, "DFT%QS")
     628           2 :       open_shell_embed = .FALSE.
     629           2 :       IF (dft_control%nspins .EQ. 2) open_shell_embed = .TRUE.
     630             : 
     631             :       ! Prepare plane-waves pool
     632           2 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool_subsys)
     633             : 
     634             :       ! Create embedding potential
     635             :       !CALL get_qs_env(qs_env=qs_env, &
     636             :       !                embed_pot=embed_pot)
     637           2 :       ALLOCATE (embed_pot)
     638           2 :       CALL auxbas_pw_pool_subsys%create_pw(embed_pot)
     639           2 :       IF (open_shell_embed) THEN
     640             :          ! Create spin embedding potential
     641           2 :          ALLOCATE (spin_embed_pot)
     642           2 :          CALL auxbas_pw_pool_subsys%create_pw(spin_embed_pot)
     643             :       END IF
     644             :       ! Read the cubes
     645           2 :       CALL read_embed_pot_cube(embed_pot, spin_embed_pot, qs_section, open_shell_embed)
     646             : 
     647           2 :       IF (.NOT. open_shell_embed) THEN
     648           0 :          CALL set_qs_env(qs_env=qs_env, embed_pot=embed_pot)
     649             :       ELSE
     650           2 :          CALL set_qs_env(qs_env=qs_env, embed_pot=embed_pot, spin_embed_pot=spin_embed_pot)
     651             :       END IF
     652             : 
     653           2 :    END SUBROUTINE given_embed_pot
     654             : 
     655             : ! **************************************************************************************************
     656             : !> \brief ...
     657             : !> \param qs_env ...
     658             : !> \param embed_pot ...
     659             : !> \param spin_embed_pot ...
     660             : !> \param section ...
     661             : !> \param opt_embed ...
     662             : ! **************************************************************************************************
     663           6 :    SUBROUTINE read_embed_pot(qs_env, embed_pot, spin_embed_pot, section, opt_embed)
     664             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     665             :       TYPE(pw_r3d_rs_type), POINTER                      :: embed_pot, spin_embed_pot
     666             :       TYPE(section_vals_type), POINTER                   :: section
     667             :       TYPE(opt_embed_pot_type)                           :: opt_embed
     668             : 
     669             :       ! Read the potential as a vector in the auxiliary basis
     670           6 :       IF (opt_embed%read_embed_pot) &
     671             :          CALL read_embed_pot_vector(qs_env, embed_pot, spin_embed_pot, section, &
     672           4 :                                     opt_embed%embed_pot_coef, opt_embed%open_shell_embed)
     673             :       ! Read the potential as a cube (two cubes for open shell)
     674           6 :       IF (opt_embed%read_embed_pot_cube) &
     675           2 :          CALL read_embed_pot_cube(embed_pot, spin_embed_pot, section, opt_embed%open_shell_embed)
     676             : 
     677           6 :    END SUBROUTINE read_embed_pot
     678             : 
     679             : ! **************************************************************************************************
     680             : !> \brief ...
     681             : !> \param embed_pot ...
     682             : !> \param spin_embed_pot ...
     683             : !> \param section ...
     684             : !> \param open_shell_embed ...
     685             : ! **************************************************************************************************
     686           4 :    SUBROUTINE read_embed_pot_cube(embed_pot, spin_embed_pot, section, open_shell_embed)
     687             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: embed_pot, spin_embed_pot
     688             :       TYPE(section_vals_type), POINTER                   :: section
     689             :       LOGICAL                                            :: open_shell_embed
     690             : 
     691             :       CHARACTER(LEN=default_path_length)                 :: filename
     692             :       LOGICAL                                            :: exist
     693             :       REAL(KIND=dp)                                      :: scaling_factor
     694             : 
     695           4 :       exist = .FALSE.
     696           4 :       CALL section_vals_val_get(section, "EMBED_CUBE_FILE_NAME", c_val=filename)
     697           4 :       INQUIRE (FILE=filename, exist=exist)
     698           4 :       IF (.NOT. exist) &
     699           0 :          CPABORT("Embedding cube file not found. ")
     700             : 
     701           4 :       scaling_factor = 1.0_dp
     702           4 :       CALL cp_cube_to_pw(embed_pot, filename, scaling_factor)
     703             : 
     704             :       ! Spin-dependent part of the potential
     705           4 :       IF (open_shell_embed) THEN
     706           4 :          exist = .FALSE.
     707           4 :          CALL section_vals_val_get(section, "EMBED_SPIN_CUBE_FILE_NAME", c_val=filename)
     708           4 :          INQUIRE (FILE=filename, exist=exist)
     709           4 :          IF (.NOT. exist) &
     710           0 :             CPABORT("Embedding spin cube file not found. ")
     711             : 
     712             :          scaling_factor = 1.0_dp
     713           4 :          CALL cp_cube_to_pw(spin_embed_pot, filename, scaling_factor)
     714             :       END IF
     715             : 
     716           4 :    END SUBROUTINE read_embed_pot_cube
     717             : 
     718             : ! **************************************************************************************************
     719             : !> \brief Read the embedding potential from the binary file
     720             : !> \param qs_env ...
     721             : !> \param embed_pot ...
     722             : !> \param spin_embed_pot ...
     723             : !> \param section ...
     724             : !> \param embed_pot_coef ...
     725             : !> \param open_shell_embed ...
     726             : ! **************************************************************************************************
     727           4 :    SUBROUTINE read_embed_pot_vector(qs_env, embed_pot, spin_embed_pot, section, embed_pot_coef, open_shell_embed)
     728             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     729             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
     730             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
     731             :       TYPE(section_vals_type), POINTER                   :: section
     732             :       TYPE(cp_fm_type), INTENT(IN)                       :: embed_pot_coef
     733             :       LOGICAL, INTENT(IN)                                :: open_shell_embed
     734             : 
     735             :       CHARACTER(LEN=default_path_length)                 :: filename
     736             :       INTEGER                                            :: dimen_aux, dimen_restart_basis, &
     737             :                                                             dimen_var_aux, l_global, LLL, &
     738             :                                                             nrow_local, restart_unit
     739           4 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
     740           4 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: coef, coef_read
     741             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
     742             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
     743             :       TYPE(cp_fm_type)                                   :: my_embed_pot_coef
     744             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     745             : 
     746             :       ! Get the vector dimension
     747           4 :       CALL find_aux_dimen(qs_env, dimen_aux)
     748           4 :       IF (open_shell_embed) THEN
     749           2 :          dimen_var_aux = dimen_aux*2
     750             :       ELSE
     751           2 :          dimen_var_aux = dimen_aux
     752             :       END IF
     753             : 
     754             :       ! We need a temporary vector of coefficients
     755             :       CALL get_qs_env(qs_env=qs_env, &
     756           4 :                       para_env=para_env)
     757           4 :       NULLIFY (blacs_env)
     758           4 :       NULLIFY (fm_struct)
     759           4 :       CALL cp_blacs_env_create(blacs_env=blacs_env, para_env=para_env)
     760             :       CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
     761           4 :                                nrow_global=dimen_var_aux, ncol_global=1)
     762           4 :       CALL cp_fm_create(my_embed_pot_coef, fm_struct, name="my_pot_coef")
     763             : 
     764           4 :       CALL cp_fm_struct_release(fm_struct)
     765           4 :       CALL cp_fm_set_all(my_embed_pot_coef, 0.0_dp)
     766             : 
     767             :       ! Read the coefficients vector
     768           4 :       restart_unit = -1
     769             : 
     770             :       ! Allocate the attay to read the coefficients
     771          12 :       ALLOCATE (coef(dimen_var_aux))
     772         636 :       coef = 0.0_dp
     773             : 
     774           4 :       IF (para_env%is_source()) THEN
     775             : 
     776             :          ! Get the restart file name
     777           2 :          CALL embed_restart_file_name(filename, section)
     778             : 
     779             :          CALL open_file(file_name=filename, &
     780             :                         file_action="READ", &
     781             :                         file_form="UNFORMATTED", &
     782             :                         file_status="OLD", &
     783           2 :                         unit_number=restart_unit)
     784             : 
     785           2 :          READ (restart_unit) dimen_restart_basis
     786             :          ! Check the dimensions of the bases: the actual and the restart one
     787           2 :          IF (.NOT. (dimen_restart_basis == dimen_aux)) &
     788           0 :             CPABORT("Wrong dimension of the embedding basis in the restart file.")
     789             : 
     790           4 :          ALLOCATE (coef_read(dimen_var_aux))
     791         318 :          coef_read = 0.0_dp
     792             : 
     793           2 :          READ (restart_unit) coef_read
     794         318 :          coef(:) = coef_read(:)
     795           2 :          DEALLOCATE (coef_read)
     796             : 
     797             :          ! Close restart file
     798           2 :          CALL close_file(unit_number=restart_unit)
     799             : 
     800             :       END IF
     801             : 
     802             :       ! Broadcast the coefficients on all processes
     803           4 :       CALL para_env%bcast(coef)
     804             : 
     805             :       ! Copy to fm_type structure
     806             :       ! Information about full matrix gradient
     807             :       CALL cp_fm_get_info(matrix=my_embed_pot_coef, &
     808             :                           nrow_local=nrow_local, &
     809           4 :                           row_indices=row_indices)
     810             : 
     811         320 :       DO LLL = 1, nrow_local
     812         316 :          l_global = row_indices(LLL)
     813         320 :          my_embed_pot_coef%local_data(LLL, 1) = coef(l_global)
     814             :       END DO
     815             : 
     816           4 :       DEALLOCATE (coef)
     817             : 
     818             :       ! Copy to the my_embed_pot_coef to embed_pot_coef
     819           4 :       CALL cp_fm_copy_general(my_embed_pot_coef, embed_pot_coef, para_env)
     820             : 
     821             :       ! Build the embedding potential on the grid
     822             :       CALL update_embed_pot(embed_pot_coef, dimen_aux, embed_pot, spin_embed_pot, &
     823           4 :                             qs_env, .FALSE., open_shell_embed)
     824             : 
     825             :       ! Release my_embed_pot_coef
     826           4 :       CALL cp_fm_release(my_embed_pot_coef)
     827             : 
     828             :       ! Release blacs environment
     829           4 :       CALL cp_blacs_env_release(blacs_env)
     830             : 
     831          16 :    END SUBROUTINE read_embed_pot_vector
     832             : 
     833             : ! **************************************************************************************************
     834             : !> \brief Find the embedding restart file name
     835             : !> \param filename ...
     836             : !> \param section ...
     837             : ! **************************************************************************************************
     838           2 :    SUBROUTINE embed_restart_file_name(filename, section)
     839             :       CHARACTER(LEN=default_path_length), INTENT(OUT)    :: filename
     840             :       TYPE(section_vals_type), POINTER                   :: section
     841             : 
     842             :       LOGICAL                                            :: exist
     843             : 
     844           2 :       exist = .FALSE.
     845           2 :       CALL section_vals_val_get(section, "EMBED_RESTART_FILE_NAME", c_val=filename)
     846           2 :       INQUIRE (FILE=filename, exist=exist)
     847           2 :       IF (.NOT. exist) &
     848           0 :          CPABORT("Embedding restart file not found. ")
     849             : 
     850           2 :    END SUBROUTINE embed_restart_file_name
     851             : 
     852             : ! **************************************************************************************************
     853             : !> \brief Deallocate stuff for optimizing embedding potential
     854             : !> \param opt_embed ...
     855             : ! **************************************************************************************************
     856          24 :    SUBROUTINE release_opt_embed(opt_embed)
     857             :       TYPE(opt_embed_pot_type)                           :: opt_embed
     858             : 
     859             :       INTEGER                                            :: i_dens, i_spin, ikind
     860             : 
     861          24 :       IF (.NOT. opt_embed%grid_opt) THEN
     862          14 :          CALL cp_fm_release(opt_embed%embed_pot_grad)
     863          14 :          CALL cp_fm_release(opt_embed%embed_pot_coef)
     864          14 :          CALL cp_fm_release(opt_embed%step)
     865          14 :          CALL cp_fm_release(opt_embed%prev_step)
     866          14 :          CALL cp_fm_release(opt_embed%embed_pot_hess)
     867          14 :          CALL cp_fm_release(opt_embed%prev_embed_pot_grad)
     868          14 :          CALL cp_fm_release(opt_embed%prev_embed_pot_coef)
     869          14 :          CALL cp_fm_release(opt_embed%prev_embed_pot_hess)
     870          14 :          CALL cp_fm_release(opt_embed%kinetic_mat)
     871           0 :          DEALLOCATE (opt_embed%embed_pot_grad, opt_embed%embed_pot_coef, &
     872           0 :                      opt_embed%step, opt_embed%prev_step, opt_embed%embed_pot_hess, &
     873           0 :                      opt_embed%prev_embed_pot_grad, opt_embed%prev_embed_pot_coef, &
     874          14 :                      opt_embed%prev_embed_pot_hess, opt_embed%kinetic_mat)
     875          14 :          DEALLOCATE (opt_embed%w_func)
     876          14 :          DEALLOCATE (opt_embed%max_diff)
     877          14 :          DEALLOCATE (opt_embed%int_diff)
     878             : 
     879          34 :          DO ikind = 1, SIZE(opt_embed%lri)
     880          20 :             DEALLOCATE (opt_embed%lri(ikind)%v_int)
     881          34 :             DEALLOCATE (opt_embed%lri(ikind)%acoef)
     882             :          END DO
     883          14 :          DEALLOCATE (opt_embed%lri)
     884             :       END IF
     885             : 
     886          24 :       IF (ASSOCIATED(opt_embed%prev_subsys_dens)) THEN
     887          96 :          DO i_dens = 1, SIZE(opt_embed%prev_subsys_dens)
     888          96 :             CALL opt_embed%prev_subsys_dens(i_dens)%release()
     889             :          END DO
     890          24 :          DEALLOCATE (opt_embed%prev_subsys_dens)
     891             :       END IF
     892          24 :       DEALLOCATE (opt_embed%max_subsys_dens_diff)
     893             : 
     894          24 :       DEALLOCATE (opt_embed%all_nspins)
     895             : 
     896          24 :       IF (ASSOCIATED(opt_embed%const_pot)) THEN
     897           4 :          CALL opt_embed%const_pot%release()
     898           4 :          DEALLOCATE (opt_embed%const_pot)
     899             :       END IF
     900             : 
     901          24 :       IF (ASSOCIATED(opt_embed%pot_diff)) THEN
     902           2 :          CALL opt_embed%pot_diff%release()
     903           2 :          DEALLOCATE (opt_embed%pot_diff)
     904             :       END IF
     905             : 
     906          24 :       IF (ASSOCIATED(opt_embed%prev_embed_pot)) THEN
     907           2 :          CALL opt_embed%prev_embed_pot%release()
     908           2 :          DEALLOCATE (opt_embed%prev_embed_pot)
     909             :       END IF
     910          24 :       IF (ASSOCIATED(opt_embed%prev_spin_embed_pot)) THEN
     911           0 :          CALL opt_embed%prev_spin_embed_pot%release()
     912           0 :          DEALLOCATE (opt_embed%prev_spin_embed_pot)
     913             :       END IF
     914          24 :       IF (ASSOCIATED(opt_embed%v_w)) THEN
     915           4 :          DO i_spin = 1, SIZE(opt_embed%v_w)
     916           4 :             CALL opt_embed%v_w(i_spin)%release()
     917             :          END DO
     918           2 :          DEALLOCATE (opt_embed%v_w)
     919             :       END IF
     920             : 
     921          24 :    END SUBROUTINE release_opt_embed
     922             : 
     923             : ! **************************************************************************************************
     924             : !> \brief Calculates subsystem Coulomb potential from the RESP charges of the total system
     925             : !> \param v_rspace ...
     926             : !> \param rhs ...
     927             : !> \param mapping_section ...
     928             : !> \param qs_env ...
     929             : !> \param nforce_eval ...
     930             : !> \param iforce_eval ...
     931             : !> \param eta ...
     932             : ! **************************************************************************************************
     933           4 :    SUBROUTINE Coulomb_guess(v_rspace, rhs, mapping_section, qs_env, nforce_eval, iforce_eval, eta)
     934             :       TYPE(pw_r3d_rs_type)                               :: v_rspace
     935             :       REAL(KIND=dp), DIMENSION(:), POINTER               :: rhs
     936             :       TYPE(section_vals_type), POINTER                   :: mapping_section
     937             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     938             :       INTEGER                                            :: nforce_eval, iforce_eval
     939             :       REAL(KIND=dp)                                      :: eta
     940             : 
     941             :       INTEGER                                            :: iparticle, jparticle, natom
     942           4 :       INTEGER, DIMENSION(:), POINTER                     :: map_index
     943             :       REAL(KIND=dp)                                      :: dvol, normalize_factor
     944           4 :       REAL(KIND=dp), DIMENSION(:), POINTER               :: rhs_subsys
     945             :       TYPE(particle_list_type), POINTER                  :: particles
     946             :       TYPE(pw_c1d_gs_type)                               :: v_resp_gspace
     947             :       TYPE(pw_env_type), POINTER                         :: pw_env
     948             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
     949             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
     950             :       TYPE(pw_r3d_rs_type)                               :: rho_resp, v_resp_rspace
     951             :       TYPE(qs_subsys_type), POINTER                      :: subsys
     952             : 
     953             :       ! Get available particles
     954           4 :       NULLIFY (subsys)
     955           4 :       CALL get_qs_env(qs_env=qs_env, subsys=subsys, pw_env=pw_env)
     956           4 :       CALL qs_subsys_get(subsys, particles=particles)
     957           4 :       natom = particles%n_els
     958             : 
     959          12 :       ALLOCATE (rhs_subsys(natom))
     960             : 
     961           4 :       NULLIFY (map_index)
     962             :       CALL get_subsys_map_index(mapping_section, natom, iforce_eval, nforce_eval, &
     963           4 :                                 map_index, .TRUE.)
     964             : 
     965             :       ! Mapping particles from iforce_eval environment to the embed env
     966          14 :       DO iparticle = 1, natom
     967          10 :          jparticle = map_index(iparticle)
     968          14 :          rhs_subsys(iparticle) = rhs(jparticle)
     969             :       END DO
     970             : 
     971             :       ! Prepare plane waves
     972           4 :       NULLIFY (auxbas_pw_pool)
     973             : 
     974             :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool, &
     975           4 :                       poisson_env=poisson_env)
     976             : 
     977           4 :       CALL auxbas_pw_pool%create_pw(v_resp_gspace)
     978             : 
     979           4 :       CALL auxbas_pw_pool%create_pw(v_resp_rspace)
     980             : 
     981           4 :       CALL auxbas_pw_pool%create_pw(rho_resp)
     982             : 
     983             :       ! Calculate charge density
     984           4 :       CALL pw_zero(rho_resp)
     985           4 :       CALL calculate_rho_resp_all(rho_resp, rhs_subsys, natom, eta, qs_env)
     986             : 
     987             :       ! Calculate potential
     988             :       CALL pw_poisson_solve(poisson_env, rho_resp, &
     989           4 :                             vhartree=v_resp_rspace)
     990           4 :       dvol = v_resp_rspace%pw_grid%dvol
     991           4 :       CALL pw_scale(v_resp_rspace, dvol)
     992           4 :       normalize_factor = SQRT((eta/pi)**3)
     993             :       !normalize_factor = -2.0_dp
     994           4 :       CALL pw_scale(v_resp_rspace, normalize_factor)
     995             : 
     996             :       ! Hard copy potential
     997           4 :       CALL pw_copy(v_resp_rspace, v_rspace)
     998             : 
     999             :       ! Release plane waves
    1000           4 :       CALL v_resp_gspace%release()
    1001           4 :       CALL v_resp_rspace%release()
    1002           4 :       CALL rho_resp%release()
    1003             : 
    1004             :       ! Deallocate map_index array
    1005           4 :       DEALLOCATE (map_index)
    1006             :       ! Deallocate charges
    1007           4 :       DEALLOCATE (rhs_subsys)
    1008             : 
    1009           4 :    END SUBROUTINE Coulomb_guess
    1010             : 
    1011             : ! **************************************************************************************************
    1012             : !> \brief Creates a subsystem embedding potential
    1013             : !> \param qs_env ...
    1014             : !> \param embed_pot ...
    1015             : !> \param embed_pot_subsys ...
    1016             : !> \param spin_embed_pot ...
    1017             : !> \param spin_embed_pot_subsys ...
    1018             : !> \param open_shell_embed ...
    1019             : !> \param change_spin_sign ...
    1020             : !> \author Vladimir Rybkin
    1021             : ! **************************************************************************************************
    1022         120 :    SUBROUTINE make_subsys_embed_pot(qs_env, embed_pot, embed_pot_subsys, &
    1023             :                                     spin_embed_pot, spin_embed_pot_subsys, open_shell_embed, &
    1024             :                                     change_spin_sign)
    1025             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1026             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: embed_pot
    1027             :       TYPE(pw_r3d_rs_type), POINTER                      :: embed_pot_subsys
    1028             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
    1029             :       TYPE(pw_r3d_rs_type), POINTER                      :: spin_embed_pot_subsys
    1030             :       LOGICAL                                            :: open_shell_embed, change_spin_sign
    1031             : 
    1032             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1033             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool_subsys
    1034             : 
    1035             :       ! Extract  plane waves environment
    1036         120 :       CALL get_qs_env(qs_env, pw_env=pw_env)
    1037             : 
    1038             :       ! Prepare plane-waves pool
    1039         120 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool_subsys)
    1040             : 
    1041             :       ! Create embedding potential and set to zero
    1042             :       NULLIFY (embed_pot_subsys)
    1043         120 :       ALLOCATE (embed_pot_subsys)
    1044         120 :       CALL auxbas_pw_pool_subsys%create_pw(embed_pot_subsys)
    1045             : 
    1046             :       ! Hard copy the grid
    1047         120 :       CALL pw_copy(embed_pot, embed_pot_subsys)
    1048             : 
    1049         120 :       IF (open_shell_embed) THEN
    1050             :          NULLIFY (spin_embed_pot_subsys)
    1051          64 :          ALLOCATE (spin_embed_pot_subsys)
    1052          64 :          CALL auxbas_pw_pool_subsys%create_pw(spin_embed_pot_subsys)
    1053             :          ! Hard copy the grid
    1054          64 :          IF (change_spin_sign) THEN
    1055           8 :             CALL pw_axpy(spin_embed_pot, spin_embed_pot_subsys, -1.0_dp, 0.0_dp, allow_noncompatible_grids=.TRUE.)
    1056             :          ELSE
    1057          56 :             CALL pw_copy(spin_embed_pot, spin_embed_pot_subsys)
    1058             :          END IF
    1059             :       END IF
    1060             : 
    1061         120 :    END SUBROUTINE make_subsys_embed_pot
    1062             : 
    1063             : ! **************************************************************************************************
    1064             : !> \brief Calculates the derivative of the embedding potential wrt to the expansion coefficients
    1065             : !> \param qs_env ...
    1066             : !> \param diff_rho_r ...
    1067             : !> \param diff_rho_spin ...
    1068             : !> \param opt_embed ...
    1069             : !> \author Vladimir Rybkin
    1070             : ! **************************************************************************************************
    1071             : 
    1072          32 :    SUBROUTINE calculate_embed_pot_grad(qs_env, diff_rho_r, diff_rho_spin, opt_embed)
    1073             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1074             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r, diff_rho_spin
    1075             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    1076             : 
    1077             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_embed_pot_grad'
    1078             : 
    1079             :       INTEGER                                            :: handle
    1080             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
    1081             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    1082             :       TYPE(cp_fm_type)                                   :: embed_pot_coeff_spin, &
    1083             :                                                             embed_pot_coeff_spinless, &
    1084             :                                                             regular_term, spin_reg, spinless_reg
    1085             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1086             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1087             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    1088             : 
    1089          16 :       CALL timeset(routineN, handle)
    1090             : 
    1091             :       ! We destroy the previous gradient and Hessian:
    1092             :       ! current data are now previous data
    1093          16 :       CALL cp_fm_to_fm(opt_embed%embed_pot_grad, opt_embed%prev_embed_pot_grad)
    1094          16 :       CALL cp_fm_to_fm(opt_embed%embed_pot_Hess, opt_embed%prev_embed_pot_Hess)
    1095             : 
    1096          16 :       NULLIFY (pw_env)
    1097             : 
    1098          16 :       CALL get_qs_env(qs_env=qs_env, pw_env=pw_env, para_env=para_env)
    1099             : 
    1100             :       ! Get plane waves pool
    1101          16 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    1102             : 
    1103             :       ! Calculate potential gradient coefficients
    1104             :       CALL calculate_embed_pot_grad_inner(qs_env, opt_embed%dimen_aux, diff_rho_r, diff_rho_spin, &
    1105             :                                           opt_embed%embed_pot_grad, &
    1106          16 :                                           opt_embed%open_shell_embed, opt_embed%lri)
    1107             : 
    1108             :       ! Add regularization with kinetic matrix
    1109          16 :       IF (opt_embed%i_iter .EQ. 1) THEN ! Else it is kept in memory
    1110          12 :          CALL compute_kinetic_mat(qs_env, opt_embed%kinetic_mat)
    1111             :       END IF
    1112             : 
    1113             :       CALL cp_fm_get_info(matrix=opt_embed%embed_pot_grad, &
    1114          16 :                           matrix_struct=fm_struct)
    1115          16 :       CALL cp_fm_create(regular_term, fm_struct, name="regular_term")
    1116          16 :       CALL cp_fm_set_all(regular_term, 0.0_dp)
    1117             : 
    1118             :       ! In case of open shell embedding we need two terms of dimen_aux=dimen_var_aux/2 for
    1119             :       ! the spinless and the spin parts
    1120          16 :       IF (opt_embed%open_shell_embed) THEN
    1121             :          ! Prepare auxiliary full matrices
    1122          10 :          NULLIFY (fm_struct, blacs_env)
    1123             : 
    1124             :          !CALL cp_blacs_env_create(blacs_env=blacs_env, para_env=para_env)
    1125             : 
    1126          10 :          CALL cp_fm_get_info(matrix=opt_embed%embed_pot_coef, context=blacs_env)
    1127             :          CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
    1128          10 :                                   nrow_global=opt_embed%dimen_aux, ncol_global=1)
    1129          10 :          CALL cp_fm_create(embed_pot_coeff_spinless, fm_struct, name="pot_coeff_spinless")
    1130          10 :          CALL cp_fm_create(embed_pot_coeff_spin, fm_struct, name="pot_coeff_spin")
    1131          10 :          CALL cp_fm_create(spinless_reg, fm_struct, name="spinless_reg")
    1132          10 :          CALL cp_fm_create(spin_reg, fm_struct, name="spin_reg")
    1133          10 :          CALL cp_fm_set_all(embed_pot_coeff_spinless, 0.0_dp)
    1134          10 :          CALL cp_fm_set_all(embed_pot_coeff_spin, 0.0_dp)
    1135          10 :          CALL cp_fm_set_all(spinless_reg, 0.0_dp)
    1136          10 :          CALL cp_fm_set_all(spin_reg, 0.0_dp)
    1137          10 :          CALL cp_fm_struct_release(fm_struct)
    1138             : 
    1139             :          ! Copy coefficients to the auxiliary structures
    1140             :          CALL cp_fm_to_fm_submat(msource=opt_embed%embed_pot_coef, &
    1141             :                                  mtarget=embed_pot_coeff_spinless, &
    1142             :                                  nrow=opt_embed%dimen_aux, ncol=1, &
    1143             :                                  s_firstrow=1, s_firstcol=1, &
    1144          10 :                                  t_firstrow=1, t_firstcol=1)
    1145             :          CALL cp_fm_to_fm_submat(msource=opt_embed%embed_pot_coef, &
    1146             :                                  mtarget=embed_pot_coeff_spin, &
    1147             :                                  nrow=opt_embed%dimen_aux, ncol=1, &
    1148             :                                  s_firstrow=opt_embed%dimen_aux + 1, s_firstcol=1, &
    1149          10 :                                  t_firstrow=1, t_firstcol=1)
    1150             :          ! Multiply
    1151             :          CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_aux, n=1, &
    1152             :                             k=opt_embed%dimen_aux, alpha=1.0_dp, &
    1153             :                             matrix_a=opt_embed%kinetic_mat, matrix_b=embed_pot_coeff_spinless, &
    1154          10 :                             beta=0.0_dp, matrix_c=spinless_reg)
    1155             :          CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_aux, n=1, &
    1156             :                             k=opt_embed%dimen_aux, alpha=1.0_dp, &
    1157             :                             matrix_a=opt_embed%kinetic_mat, matrix_b=embed_pot_coeff_spin, &
    1158          10 :                             beta=0.0_dp, matrix_c=spin_reg)
    1159             :          ! Copy from the auxiliary structures to the full regularization term
    1160             :          CALL cp_fm_to_fm_submat(msource=spinless_reg, &
    1161             :                                  mtarget=regular_term, &
    1162             :                                  nrow=opt_embed%dimen_aux, ncol=1, &
    1163             :                                  s_firstrow=1, s_firstcol=1, &
    1164          10 :                                  t_firstrow=1, t_firstcol=1)
    1165             :          CALL cp_fm_to_fm_submat(msource=spin_reg, &
    1166             :                                  mtarget=regular_term, &
    1167             :                                  nrow=opt_embed%dimen_aux, ncol=1, &
    1168             :                                  s_firstrow=1, s_firstcol=1, &
    1169          10 :                                  t_firstrow=opt_embed%dimen_aux + 1, t_firstcol=1)
    1170             :          ! Release internally used auxiliary structures
    1171          10 :          CALL cp_fm_release(embed_pot_coeff_spinless)
    1172          10 :          CALL cp_fm_release(embed_pot_coeff_spin)
    1173          10 :          CALL cp_fm_release(spin_reg)
    1174          10 :          CALL cp_fm_release(spinless_reg)
    1175             : 
    1176             :       ELSE ! Simply multiply
    1177             :          CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_var_aux, n=1, &
    1178             :                             k=opt_embed%dimen_var_aux, alpha=1.0_dp, &
    1179             :                             matrix_a=opt_embed%kinetic_mat, matrix_b=opt_embed%embed_pot_coef, &
    1180           6 :                             beta=0.0_dp, matrix_c=regular_term)
    1181             :       END IF
    1182             : 
    1183             :       ! Scale by the regularization parameter and add to the gradient
    1184          16 :       CALL cp_fm_scale_and_add(1.0_dp, opt_embed%embed_pot_grad, 4.0_dp*opt_embed%lambda, regular_term)
    1185             : 
    1186             :       ! Calculate the regularization contribution to the energy functional
    1187          16 :       CALL cp_fm_trace(opt_embed%embed_pot_coef, regular_term, opt_embed%reg_term)
    1188          16 :       opt_embed%reg_term = 2.0_dp*opt_embed%lambda*opt_embed%reg_term
    1189             : 
    1190             :       ! Deallocate regular term
    1191          16 :       CALL cp_fm_release(regular_term)
    1192             : 
    1193          16 :       CALL timestop(handle)
    1194             : 
    1195          16 :    END SUBROUTINE calculate_embed_pot_grad
    1196             : 
    1197             : ! **************************************************************************************************
    1198             : !> \brief Performs integration for the embedding potential gradient
    1199             : !> \param qs_env ...
    1200             : !> \param dimen_aux ...
    1201             : !> \param rho_r ...
    1202             : !> \param rho_spin ...
    1203             : !> \param embed_pot_grad ...
    1204             : !> \param open_shell_embed ...
    1205             : !> \param lri ...
    1206             : !> \author Vladimir Rybkin
    1207             : ! **************************************************************************************************
    1208          16 :    SUBROUTINE calculate_embed_pot_grad_inner(qs_env, dimen_aux, rho_r, rho_spin, embed_pot_grad, &
    1209             :                                              open_shell_embed, lri)
    1210             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1211             :       INTEGER                                            :: dimen_aux
    1212             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: rho_r, rho_spin
    1213             :       TYPE(cp_fm_type), INTENT(IN)                       :: embed_pot_grad
    1214             :       LOGICAL                                            :: open_shell_embed
    1215             :       TYPE(lri_kind_type), DIMENSION(:), POINTER         :: lri
    1216             : 
    1217             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_embed_pot_grad_inner'
    1218             : 
    1219             :       INTEGER                                            :: handle, iatom, ikind, l_global, LLL, &
    1220             :                                                             nrow_local, nsgf, start_pos
    1221          16 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
    1222          16 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: pot_grad
    1223          16 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    1224             :       TYPE(cell_type), POINTER                           :: cell
    1225             :       TYPE(dft_control_type), POINTER                    :: dft_control
    1226             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1227          16 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    1228          16 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    1229             : 
    1230             : ! Needed to store integrals
    1231             : 
    1232          16 :       CALL timeset(routineN, handle)
    1233             : 
    1234             :       CALL get_qs_env(qs_env=qs_env, &
    1235             :                       particle_set=particle_set, &
    1236             :                       qs_kind_set=qs_kind_set, &
    1237             :                       dft_control=dft_control, &
    1238             :                       cell=cell, &
    1239             :                       atomic_kind_set=atomic_kind_set, &
    1240          16 :                       para_env=para_env)
    1241             : 
    1242             :       ! Create wf_vector and gradient
    1243          16 :       IF (open_shell_embed) THEN
    1244          30 :          ALLOCATE (pot_grad(dimen_aux*2))
    1245             :       ELSE
    1246          18 :          ALLOCATE (pot_grad(dimen_aux))
    1247             :       END IF
    1248             : 
    1249             :       ! Use lri subroutine
    1250          38 :       DO ikind = 1, SIZE(lri)
    1251        2750 :          lri(ikind)%v_int = 0.0_dp
    1252             :       END DO
    1253             : 
    1254             :       CALL integrate_v_rspace_one_center(rho_r, qs_env, lri, &
    1255          16 :                                          .FALSE., "RI_AUX")
    1256          38 :       DO ikind = 1, SIZE(lri)
    1257        5462 :          CALL para_env%sum(lri(ikind)%v_int)
    1258             :       END DO
    1259             : 
    1260        2392 :       pot_grad = 0.0_dp
    1261          16 :       start_pos = 1
    1262          38 :       DO ikind = 1, SIZE(lri)
    1263          88 :          DO iatom = 1, SIZE(lri(ikind)%v_int, DIM=1)
    1264          50 :             nsgf = SIZE(lri(ikind)%v_int(iatom, :))
    1265        1826 :             pot_grad(start_pos:start_pos + nsgf - 1) = lri(ikind)%v_int(iatom, :)
    1266          72 :             start_pos = start_pos + nsgf
    1267             :          END DO
    1268             :       END DO
    1269             : 
    1270             :       ! Open-shell embedding
    1271          16 :       IF (open_shell_embed) THEN
    1272          20 :          DO ikind = 1, SIZE(lri)
    1273         920 :             lri(ikind)%v_int = 0.0_dp
    1274             :          END DO
    1275             : 
    1276             :          CALL integrate_v_rspace_one_center(rho_spin, qs_env, lri, &
    1277          10 :                                             .FALSE., "RI_AUX")
    1278          20 :          DO ikind = 1, SIZE(lri)
    1279        1820 :             CALL para_env%sum(lri(ikind)%v_int)
    1280             :          END DO
    1281             : 
    1282          10 :          start_pos = dimen_aux + 1
    1283          20 :          DO ikind = 1, SIZE(lri)
    1284          40 :             DO iatom = 1, SIZE(lri(ikind)%v_int, DIM=1)
    1285          20 :                nsgf = SIZE(lri(ikind)%v_int(iatom, :))
    1286         620 :                pot_grad(start_pos:start_pos + nsgf - 1) = lri(ikind)%v_int(iatom, :)
    1287          30 :                start_pos = start_pos + nsgf
    1288             :             END DO
    1289             :          END DO
    1290             :       END IF
    1291             : 
    1292             :       ! Scale by the cell volume
    1293        2392 :       pot_grad = pot_grad*rho_r%pw_grid%dvol
    1294             : 
    1295             :       ! Information about full matrix gradient
    1296             :       CALL cp_fm_get_info(matrix=embed_pot_grad, &
    1297             :                           nrow_local=nrow_local, &
    1298          16 :                           row_indices=row_indices)
    1299             : 
    1300             :       ! Copy the gradient into the full matrix
    1301        1204 :       DO LLL = 1, nrow_local
    1302        1188 :          l_global = row_indices(LLL)
    1303        1204 :          embed_pot_grad%local_data(LLL, 1) = pot_grad(l_global)
    1304             :       END DO
    1305             : 
    1306          16 :       DEALLOCATE (pot_grad)
    1307             : 
    1308          16 :       CALL timestop(handle)
    1309             : 
    1310          16 :    END SUBROUTINE calculate_embed_pot_grad_inner
    1311             : 
    1312             : ! **************************************************************************************************
    1313             : !> \brief Calculates kinetic energy matrix in auxiliary basis in the fm format
    1314             : !> \param qs_env ...
    1315             : !> \param kinetic_mat ...
    1316             : !> \author Vladimir Rybkin
    1317             : ! **************************************************************************************************
    1318          12 :    SUBROUTINE compute_kinetic_mat(qs_env, kinetic_mat)
    1319             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1320             :       TYPE(cp_fm_type), INTENT(IN)                       :: kinetic_mat
    1321             : 
    1322             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_kinetic_mat'
    1323             : 
    1324             :       INTEGER                                            :: handle
    1325          12 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_t
    1326             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
    1327          12 :          POINTER                                         :: sab_orb
    1328             :       TYPE(qs_ks_env_type), POINTER                      :: ks_env
    1329             : 
    1330          12 :       CALL timeset(routineN, handle)
    1331             : 
    1332          12 :       NULLIFY (ks_env, sab_orb, matrix_t)
    1333             : 
    1334             :       ! First, get the dbcsr structure from the overlap matrix
    1335          12 :       CALL get_qs_env(qs_env=qs_env, ks_env=ks_env, sab_orb=sab_orb)
    1336             : 
    1337             :       ! Calculate kinetic matrix
    1338             :       CALL build_kinetic_matrix(ks_env, matrix_t=matrix_t, &
    1339             :                                 matrix_name="KINETIC ENERGY MATRIX", &
    1340             :                                 basis_type="RI_AUX", &
    1341          12 :                                 sab_nl=sab_orb, calculate_forces=.FALSE.)
    1342             : 
    1343             :       ! Change to the fm format
    1344          12 :       CALL copy_dbcsr_to_fm(matrix_t(1)%matrix, kinetic_mat)
    1345             : 
    1346             :       ! Release memory
    1347          12 :       CALL dbcsr_deallocate_matrix_set(matrix_t)
    1348             : 
    1349          12 :       CALL timestop(handle)
    1350             : 
    1351          12 :    END SUBROUTINE compute_kinetic_mat
    1352             : 
    1353             : ! **************************************************************************************************
    1354             : !> \brief Regularizes the Wu-Yang potential on the grid
    1355             : !> \param potential ...
    1356             : !> \param pw_env ...
    1357             : !> \param lambda ...
    1358             : !> \param reg_term ...
    1359             : ! **************************************************************************************************
    1360           6 :    SUBROUTINE grid_regularize(potential, pw_env, lambda, reg_term)
    1361             : 
    1362             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: potential
    1363             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1364             :       REAL(KIND=dp)                                      :: lambda, reg_term
    1365             : 
    1366             :       INTEGER                                            :: i, j, k
    1367             :       INTEGER, DIMENSION(3)                              :: lb, n, ub
    1368             :       TYPE(pw_c1d_gs_type)                               :: dr2_pot, grid_reg_g, potential_g
    1369          24 :       TYPE(pw_c1d_gs_type), DIMENSION(3)                 :: dpot_g
    1370             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    1371             :       TYPE(pw_r3d_rs_type)                               :: grid_reg, square_norm_dpot
    1372          24 :       TYPE(pw_r3d_rs_type), DIMENSION(3)                 :: dpot
    1373             : 
    1374             :       !
    1375             :       ! First, the contribution to the gradient
    1376             :       !
    1377             : 
    1378             :       ! Get some of the grids ready
    1379           6 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    1380             : 
    1381           6 :       CALL auxbas_pw_pool%create_pw(potential_g)
    1382             : 
    1383           6 :       CALL auxbas_pw_pool%create_pw(dr2_pot)
    1384             : 
    1385           6 :       CALL auxbas_pw_pool%create_pw(grid_reg)
    1386             : 
    1387           6 :       CALL auxbas_pw_pool%create_pw(grid_reg_g)
    1388           6 :       CALL pw_zero(grid_reg_g)
    1389             : 
    1390             :       ! Transfer potential to the reciprocal space
    1391           6 :       CALL pw_transfer(potential, potential_g)
    1392             : 
    1393             :       ! Calculate second derivatives: dx^2, dy^2, dz^2
    1394          24 :       DO i = 1, 3
    1395          18 :          CALL pw_dr2(potential_g, dr2_pot, i, i)
    1396          24 :          CALL pw_axpy(dr2_pot, grid_reg_g, 1.0_dp)
    1397             :       END DO
    1398             :       ! Transfer potential to the real space
    1399           6 :       CALL pw_transfer(grid_reg_g, grid_reg)
    1400             : 
    1401             :       ! Update the potential with a regularization term
    1402           6 :       CALL pw_axpy(grid_reg, potential, -4.0_dp*lambda)
    1403             : 
    1404             :       !
    1405             :       ! Second, the contribution to the functional
    1406             :       !
    1407          24 :       DO i = 1, 3
    1408          18 :          CALL auxbas_pw_pool%create_pw(dpot(i))
    1409          24 :          CALL auxbas_pw_pool%create_pw(dpot_g(i))
    1410             :       END DO
    1411             : 
    1412           6 :       CALL auxbas_pw_pool%create_pw(square_norm_dpot)
    1413             : 
    1414          24 :       DO i = 1, 3
    1415          18 :          n(:) = 0
    1416          18 :          n(i) = 1
    1417          18 :          CALL pw_copy(potential_g, dpot_g(i))
    1418          18 :          CALL pw_derive(dpot_g(i), n(:))
    1419          24 :          CALL pw_transfer(dpot_g(i), dpot(i))
    1420             :       END DO
    1421             : 
    1422          24 :       lb(1:3) = square_norm_dpot%pw_grid%bounds_local(1, 1:3)
    1423          24 :       ub(1:3) = square_norm_dpot%pw_grid%bounds_local(2, 1:3)
    1424             : !$OMP PARALLEL DO DEFAULT(NONE) &
    1425             : !$OMP             PRIVATE(i,j,k) &
    1426           6 : !$OMP             SHARED(dpot, lb, square_norm_dpot, ub)
    1427             :       DO k = lb(3), ub(3)
    1428             :          DO j = lb(2), ub(2)
    1429             :             DO i = lb(1), ub(1)
    1430             :                square_norm_dpot%array(i, j, k) = (dpot(1)%array(i, j, k)* &
    1431             :                                                   dpot(1)%array(i, j, k) + &
    1432             :                                                   dpot(2)%array(i, j, k)* &
    1433             :                                                   dpot(2)%array(i, j, k) + &
    1434             :                                                   dpot(3)%array(i, j, k)* &
    1435             :                                                   dpot(3)%array(i, j, k))
    1436             :             END DO
    1437             :          END DO
    1438             :       END DO
    1439             : !$OMP END PARALLEL DO
    1440             : 
    1441           6 :       reg_term = 2*lambda*pw_integrate_function(fun=square_norm_dpot)
    1442             : 
    1443             :       ! Release
    1444           6 :       CALL auxbas_pw_pool%give_back_pw(potential_g)
    1445           6 :       CALL auxbas_pw_pool%give_back_pw(dr2_pot)
    1446           6 :       CALL auxbas_pw_pool%give_back_pw(grid_reg)
    1447           6 :       CALL auxbas_pw_pool%give_back_pw(grid_reg_g)
    1448           6 :       CALL auxbas_pw_pool%give_back_pw(square_norm_dpot)
    1449          24 :       DO i = 1, 3
    1450          18 :          CALL auxbas_pw_pool%give_back_pw(dpot(i))
    1451          24 :          CALL auxbas_pw_pool%give_back_pw(dpot_g(i))
    1452             :       END DO
    1453             : 
    1454           6 :    END SUBROUTINE grid_regularize
    1455             : 
    1456             : ! **************************************************************************************************
    1457             : !> \brief Takes maximization step in embedding potential optimization
    1458             : !> \param diff_rho_r ...
    1459             : !> \param diff_rho_spin ...
    1460             : !> \param opt_embed ...
    1461             : !> \param embed_pot ...
    1462             : !> \param spin_embed_pot ...
    1463             : !> \param rho_r_ref ...
    1464             : !> \param qs_env ...
    1465             : !> \author Vladimir Rybkin
    1466             : ! **************************************************************************************************
    1467          24 :    SUBROUTINE opt_embed_step(diff_rho_r, diff_rho_spin, opt_embed, embed_pot, spin_embed_pot, rho_r_ref, qs_env)
    1468             : 
    1469             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: diff_rho_r, diff_rho_spin
    1470             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    1471             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
    1472             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
    1473             :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r_ref
    1474             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1475             : 
    1476             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'opt_embed_step'
    1477             :       REAL(KIND=dp), PARAMETER                           :: thresh = 0.000001_dp
    1478             : 
    1479             :       INTEGER                                            :: handle, l_global, LLL, nrow_local
    1480          24 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
    1481          24 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: eigenval
    1482             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    1483             :       TYPE(cp_fm_type)                                   :: diag_grad, diag_step, fm_U, fm_U_scale
    1484             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1485             : 
    1486          24 :       CALL timeset(routineN, handle)
    1487             : 
    1488          24 :       IF (opt_embed%grid_opt) THEN ! Grid based optimization
    1489             : 
    1490           8 :          opt_embed%step_len = opt_embed%trust_rad
    1491           8 :          CALL get_qs_env(qs_env=qs_env, pw_env=pw_env)
    1492           8 :          IF (opt_embed%leeuwen) THEN
    1493             :             CALL Leeuwen_Baerends_potential_update(pw_env, embed_pot, spin_embed_pot, diff_rho_r, diff_rho_spin, &
    1494           2 :                                                    rho_r_ref, opt_embed%open_shell_embed, opt_embed%trust_rad)
    1495             :          ELSE
    1496           6 :             IF (opt_embed%fab) THEN
    1497             :                CALL FAB_update(qs_env, rho_r_ref, opt_embed%prev_embed_pot, opt_embed%prev_spin_embed_pot, &
    1498             :                                embed_pot, spin_embed_pot, &
    1499             :                                diff_rho_r, diff_rho_spin, opt_embed%v_w, opt_embed%i_iter, opt_embed%trust_rad, &
    1500           2 :                                opt_embed%open_shell_embed, opt_embed%vw_cutoff, opt_embed%vw_smooth_cutoff_range)
    1501             :             ELSE
    1502           4 :                CALL grid_based_step(diff_rho_r, diff_rho_spin, pw_env, opt_embed, embed_pot, spin_embed_pot)
    1503             :             END IF
    1504             :          END IF
    1505             : 
    1506             :       ELSE ! Finite basis optimization
    1507             :          ! If the previous step has been rejected, we go back to the previous expansion coefficients
    1508          16 :          IF (.NOT. opt_embed%accept_step) &
    1509           0 :             CALL cp_fm_scale_and_add(1.0_dp, opt_embed%embed_pot_coef, -1.0_dp, opt_embed%step)
    1510             : 
    1511             :          ! Do a simple steepest descent
    1512          16 :          IF (opt_embed%steep_desc) THEN
    1513           6 :             IF (opt_embed%i_iter .GT. 2) &
    1514             :                opt_embed%trust_rad = Barzilai_Borwein(opt_embed%step, opt_embed%prev_step, &
    1515           0 :                                                       opt_embed%embed_pot_grad, opt_embed%prev_embed_pot_grad)
    1516           6 :             IF (ABS(opt_embed%trust_rad) .GT. opt_embed%max_trad) THEN
    1517           0 :                IF (opt_embed%trust_rad .GT. 0.0_dp) THEN
    1518           0 :                   opt_embed%trust_rad = opt_embed%max_trad
    1519             :                ELSE
    1520           0 :                   opt_embed%trust_rad = -opt_embed%max_trad
    1521             :                END IF
    1522             :             END IF
    1523             : 
    1524           6 :             CALL cp_fm_to_fm(opt_embed%step, opt_embed%prev_step)
    1525           6 :             CALL cp_fm_scale_and_add(0.0_dp, opt_embed%prev_step, 1.0_dp, opt_embed%step)
    1526           6 :             CALL cp_fm_set_all(opt_embed%step, 0.0_dp)
    1527           6 :             CALL cp_fm_scale_and_add(1.0_dp, opt_embed%step, opt_embed%trust_rad, opt_embed%embed_pot_grad)
    1528           6 :             opt_embed%step_len = opt_embed%trust_rad
    1529             :          ELSE
    1530             : 
    1531             :             ! First, update the Hessian inverse if needed
    1532          10 :             IF (opt_embed%i_iter > 1) THEN
    1533           2 :                IF (opt_embed%accept_step) & ! We don't update Hessian if the step has been rejected
    1534             :                   CALL symm_rank_one_update(opt_embed%embed_pot_grad, opt_embed%prev_embed_pot_grad, &
    1535           2 :                                             opt_embed%step, opt_embed%prev_embed_pot_Hess, opt_embed%embed_pot_Hess)
    1536             :             END IF
    1537             : 
    1538             :             ! Add regularization term to the Hessian
    1539             :             !CALL cp_fm_scale_and_add(1.0_dp, opt_embed%embed_pot_Hess, 4.0_dp*opt_embed%lambda, &
    1540             :             !                         opt_embed%kinetic_mat)
    1541             : 
    1542             :             ! Else use the first initial Hessian. Now it's just the unit matrix: embed_pot_hess
    1543             :             ! Second, invert the Hessian
    1544          30 :             ALLOCATE (eigenval(opt_embed%dimen_var_aux))
    1545        1666 :             eigenval = 0.0_dp
    1546             :             CALL cp_fm_get_info(matrix=opt_embed%embed_pot_hess, &
    1547          10 :                                 matrix_struct=fm_struct)
    1548          10 :             CALL cp_fm_create(fm_U, fm_struct, name="fm_U")
    1549          10 :             CALL cp_fm_create(fm_U_scale, fm_struct, name="fm_U")
    1550          10 :             CALL cp_fm_set_all(fm_U, 0.0_dp)
    1551          10 :             CALL cp_fm_set_all(fm_U_scale, 0.0_dp)
    1552             :             CALL cp_fm_get_info(matrix=opt_embed%embed_pot_grad, &
    1553          10 :                                 matrix_struct=fm_struct)
    1554          10 :             CALL cp_fm_create(diag_grad, fm_struct, name="diag_grad")
    1555          10 :             CALL cp_fm_set_all(diag_grad, 0.0_dp)
    1556          10 :             CALL cp_fm_create(diag_step, fm_struct, name="diag_step")
    1557          10 :             CALL cp_fm_set_all(diag_step, 0.0_dp)
    1558             : 
    1559             :             ! Store the Hessian as it will be destroyed in diagonalization: use fm_U_scal for it
    1560          10 :             CALL cp_fm_to_fm(opt_embed%embed_pot_hess, fm_U_scale)
    1561             : 
    1562             :             ! Diagonalize Hessian
    1563          10 :             CALL choose_eigv_solver(opt_embed%embed_pot_hess, fm_U, eigenval)
    1564             : 
    1565             :             ! Copy the Hessian back
    1566          10 :             CALL cp_fm_to_fm(fm_U_scale, opt_embed%embed_pot_hess)
    1567             : 
    1568             :             ! Find the step in diagonal representation, begin with gradient
    1569             :             CALL parallel_gemm(transa="T", transb="N", m=opt_embed%dimen_var_aux, n=1, &
    1570             :                                k=opt_embed%dimen_var_aux, alpha=1.0_dp, &
    1571             :                                matrix_a=fm_U, matrix_b=opt_embed%embed_pot_grad, beta=0.0_dp, &
    1572          10 :                                matrix_c=diag_grad)
    1573             : 
    1574             :             CALL cp_fm_get_info(matrix=opt_embed%embed_pot_coef, &
    1575             :                                 nrow_local=nrow_local, &
    1576          10 :                                 row_indices=row_indices)
    1577             : 
    1578         838 :             DO LLL = 1, nrow_local
    1579         828 :                l_global = row_indices(LLL)
    1580         838 :                IF (ABS(eigenval(l_global)) .GE. thresh) THEN
    1581             :                   diag_step%local_data(LLL, 1) = &
    1582         828 :                      -diag_grad%local_data(LLL, 1)/(eigenval(l_global))
    1583             :                ELSE
    1584           0 :                   diag_step%local_data(LLL, 1) = 0.0_dp
    1585             :                END IF
    1586             :             END DO
    1587          10 :             CALL cp_fm_trace(diag_step, diag_step, opt_embed%step_len)
    1588             : 
    1589             :             ! Transform step to a non-diagonal representation
    1590             :             CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_var_aux, n=1, &
    1591             :                                k=opt_embed%dimen_var_aux, alpha=1.0_dp, &
    1592             :                                matrix_a=fm_U, matrix_b=diag_step, beta=0.0_dp, &
    1593          10 :                                matrix_c=opt_embed%step)
    1594             : 
    1595             :             ! Now use fm_U_scale for scaled eigenvectors
    1596          10 :             CALL cp_fm_to_fm(fm_U, fm_U_scale)
    1597          10 :             CALL cp_fm_column_scale(fm_U_scale, eigenval)
    1598             : 
    1599          10 :             CALL cp_fm_release(fm_U_scale)
    1600             : 
    1601             :             ! Scale the step to fit within the trust radius: it it's less already,
    1602             :             ! then take the Newton step
    1603          10 :             CALL cp_fm_trace(opt_embed%step, opt_embed%step, opt_embed%step_len)
    1604          10 :             IF (opt_embed%step_len .GT. opt_embed%trust_rad) THEN
    1605             : 
    1606           2 :                IF (opt_embed%level_shift) THEN
    1607             :                   ! Find a level shift parameter and apply it
    1608           2 :                   CALL level_shift(opt_embed, diag_grad, eigenval, diag_step)
    1609             :                ELSE ! Just scale
    1610           0 :                   CALL cp_fm_trace(diag_step, diag_step, opt_embed%step_len)
    1611           0 :                   CALL cp_fm_scale(opt_embed%trust_rad/opt_embed%step_len, diag_step)
    1612             :                END IF
    1613           2 :                CALL cp_fm_trace(diag_step, diag_step, opt_embed%step_len)
    1614             :                ! Transform step to a non-diagonal representation
    1615             :                CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_var_aux, n=1, &
    1616             :                                   k=opt_embed%dimen_var_aux, alpha=1.0_dp, &
    1617             :                                   matrix_a=fm_U, matrix_b=diag_step, beta=0.0_dp, &
    1618           2 :                                   matrix_c=opt_embed%step)
    1619           2 :                CALL cp_fm_trace(opt_embed%step, opt_embed%step, opt_embed%step_len)
    1620             : 
    1621             :                ! Recalculate step in diagonal representation
    1622           2 :                opt_embed%newton_step = .FALSE.
    1623             :             ELSE
    1624           8 :                opt_embed%newton_step = .TRUE.
    1625             :             END IF
    1626             : 
    1627             :             ! Release some memory
    1628          10 :             DEALLOCATE (eigenval)
    1629             :             ! Release more memory
    1630          10 :             CALL cp_fm_release(diag_grad)
    1631          10 :             CALL cp_fm_release(diag_step)
    1632          50 :             CALL cp_fm_release(fm_U)
    1633             : 
    1634             :          END IF ! grad_descent
    1635             : 
    1636             :          ! Update the coefficients
    1637          16 :          CALL cp_fm_scale_and_add(1.0_dp, opt_embed%embed_pot_coef, 1.0_dp, opt_embed%step)
    1638             : 
    1639             :          ! Update the embedding potential
    1640             :          CALL update_embed_pot(opt_embed%embed_pot_coef, opt_embed%dimen_aux, embed_pot, &
    1641             :                                spin_embed_pot, qs_env, opt_embed%add_const_pot, &
    1642          16 :                                opt_embed%open_shell_embed, opt_embed%const_pot)
    1643             :       END IF ! Grid-based optimization
    1644             : 
    1645          24 :       CALL timestop(handle)
    1646             : 
    1647          48 :    END SUBROUTINE opt_embed_step
    1648             : 
    1649             : !
    1650             : ! **************************************************************************************************
    1651             : !> \brief ...
    1652             : !> \param diff_rho_r ...
    1653             : !> \param diff_rho_spin ...
    1654             : !> \param pw_env ...
    1655             : !> \param opt_embed ...
    1656             : !> \param embed_pot ...
    1657             : !> \param spin_embed_pot ...
    1658             : ! **************************************************************************************************
    1659           4 :    SUBROUTINE grid_based_step(diff_rho_r, diff_rho_spin, pw_env, opt_embed, embed_pot, spin_embed_pot)
    1660             : 
    1661             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: diff_rho_r, diff_rho_spin
    1662             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1663             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    1664             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
    1665             :       TYPE(pw_r3d_rs_type), POINTER                      :: spin_embed_pot
    1666             : 
    1667             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'grid_based_step'
    1668             : 
    1669             :       INTEGER                                            :: handle
    1670             :       REAL(KIND=dp)                                      :: my_reg_term
    1671             : 
    1672           4 :       CALL timeset(routineN, handle)
    1673             : 
    1674             :       ! Take the step for spin-free part
    1675           4 :       CALL pw_axpy(diff_rho_r, embed_pot, opt_embed%step_len)
    1676             :       ! Regularize
    1677           4 :       CALL grid_regularize(embed_pot, pw_env, opt_embed%lambda, my_reg_term)
    1678           4 :       opt_embed%reg_term = opt_embed%reg_term + my_reg_term
    1679             : 
    1680           4 :       IF (opt_embed%open_shell_embed) THEN
    1681           2 :          CALL pw_axpy(diff_rho_spin, spin_embed_pot, opt_embed%step_len)
    1682           2 :          CALL grid_regularize(spin_embed_pot, pw_env, opt_embed%lambda, my_reg_term)
    1683           2 :          opt_embed%reg_term = opt_embed%reg_term + my_reg_term
    1684             :       END IF
    1685             : 
    1686           4 :       CALL timestop(handle)
    1687             : 
    1688           4 :    END SUBROUTINE grid_based_step
    1689             : 
    1690             : ! **************************************************************************************************
    1691             : !> \brief ... Adds variable part of to the embedding potential
    1692             : !> \param embed_pot_coef ...
    1693             : !> \param dimen_aux ...
    1694             : !> \param embed_pot ...
    1695             : !> \param spin_embed_pot ...
    1696             : !> \param qs_env ...
    1697             : !> \param add_const_pot ...
    1698             : !> \param open_shell_embed ...
    1699             : !> \param const_pot ...
    1700             : !> \author Vladimir Rybkin
    1701             : ! **************************************************************************************************
    1702             : 
    1703          20 :    SUBROUTINE update_embed_pot(embed_pot_coef, dimen_aux, embed_pot, spin_embed_pot, &
    1704             :                                qs_env, add_const_pot, open_shell_embed, const_pot)
    1705             :       TYPE(cp_fm_type), INTENT(IN)                       :: embed_pot_coef
    1706             :       INTEGER                                            :: dimen_aux
    1707             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
    1708             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
    1709             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1710             :       LOGICAL                                            :: add_const_pot, open_shell_embed
    1711             :       TYPE(pw_r3d_rs_type), INTENT(IN), OPTIONAL         :: const_pot
    1712             : 
    1713             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'update_embed_pot'
    1714             : 
    1715             :       INTEGER                                            :: handle, l_global, LLL, nrow_local
    1716          20 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
    1717             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: wf_vector
    1718          20 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    1719             :       TYPE(cell_type), POINTER                           :: cell
    1720             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
    1721             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    1722             :       TYPE(cp_fm_type)                                   :: embed_pot_coef_spin, &
    1723             :                                                             embed_pot_coef_spinless
    1724             :       TYPE(cp_fm_type), POINTER                          :: mo_coeff
    1725             :       TYPE(dft_control_type), POINTER                    :: dft_control
    1726          20 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    1727             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1728          20 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    1729             :       TYPE(pw_c1d_gs_type)                               :: rho_g
    1730             :       TYPE(pw_env_type), POINTER                         :: pw_env
    1731             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    1732             :       TYPE(pw_r3d_rs_type)                               :: psi_L
    1733          20 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    1734             : 
    1735          20 :       CALL timeset(routineN, handle)
    1736             :       ! Get MO coefficients: we need only the structure, therefore don't care about the spin
    1737             :       CALL get_qs_env(qs_env=qs_env, &
    1738             :                       particle_set=particle_set, &
    1739             :                       qs_kind_set=qs_kind_set, &
    1740             :                       dft_control=dft_control, &
    1741             :                       cell=cell, &
    1742             :                       atomic_kind_set=atomic_kind_set, &
    1743          20 :                       pw_env=pw_env, mos=mos, para_env=para_env)
    1744          20 :       CALL get_mo_set(mo_set=mos(1), mo_coeff=mo_coeff)
    1745             : 
    1746             :       ! Get plane waves pool
    1747          20 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    1748             : 
    1749             :       ! get some of the grids ready
    1750          20 :       CALL auxbas_pw_pool%create_pw(rho_g)
    1751             : 
    1752          20 :       CALL auxbas_pw_pool%create_pw(psi_L)
    1753             : 
    1754             :       ! Create wf_vector and auxiliary wave functions
    1755          60 :       ALLOCATE (wf_vector(dimen_aux))
    1756        2308 :       wf_vector = 0.0_dp
    1757             : 
    1758             :       ! Create auxiliary full matrices for open-shell case
    1759          20 :       IF (open_shell_embed) THEN
    1760          12 :          NULLIFY (blacs_env)
    1761          12 :          CALL cp_fm_get_info(matrix=embed_pot_coef, context=blacs_env)
    1762             :          CALL cp_fm_struct_create(fm_struct, para_env=para_env, context=blacs_env, &
    1763          12 :                                   nrow_global=dimen_aux, ncol_global=1)
    1764          12 :          CALL cp_fm_create(embed_pot_coef_spinless, fm_struct, name="pot_coeff_spinless")
    1765          12 :          CALL cp_fm_create(embed_pot_coef_spin, fm_struct, name="pot_coeff_spin")
    1766          12 :          CALL cp_fm_set_all(embed_pot_coef_spinless, 0.0_dp)
    1767          12 :          CALL cp_fm_set_all(embed_pot_coef_spin, 0.0_dp)
    1768          12 :          CALL cp_fm_struct_release(fm_struct)
    1769             : 
    1770             :          ! Copy coefficients to the auxiliary structures
    1771             :          CALL cp_fm_to_fm_submat(embed_pot_coef, &
    1772             :                                  mtarget=embed_pot_coef_spinless, &
    1773             :                                  nrow=dimen_aux, ncol=1, &
    1774             :                                  s_firstrow=1, s_firstcol=1, &
    1775          12 :                                  t_firstrow=1, t_firstcol=1)
    1776             :          CALL cp_fm_to_fm_submat(embed_pot_coef, &
    1777             :                                  mtarget=embed_pot_coef_spin, &
    1778             :                                  nrow=dimen_aux, ncol=1, &
    1779             :                                  s_firstrow=dimen_aux + 1, s_firstcol=1, &
    1780          12 :                                  t_firstrow=1, t_firstcol=1)
    1781             : 
    1782             :          ! Spinless potential
    1783             :          CALL cp_fm_get_info(matrix=embed_pot_coef_spinless, &
    1784             :                              nrow_local=nrow_local, &
    1785          12 :                              row_indices=row_indices)
    1786             : 
    1787             :          ! Copy fm_coeff to an array
    1788         372 :          DO LLL = 1, nrow_local
    1789         360 :             l_global = row_indices(LLL)
    1790         372 :             wf_vector(l_global) = embed_pot_coef_spinless%local_data(LLL, 1)
    1791             :          END DO
    1792          12 :          CALL para_env%sum(wf_vector)
    1793             : 
    1794             :          ! Calculate the variable part of the embedding potential
    1795             :          CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, &
    1796             :                                  qs_kind_set, cell, particle_set, pw_env, &
    1797             :                                  dft_control%qs_control%eps_rho_rspace, &
    1798          12 :                                  basis_type="RI_AUX")
    1799             :          ! Update the full embedding potential
    1800          12 :          IF (add_const_pot) THEN
    1801           0 :             CALL pw_copy(const_pot, embed_pot)
    1802             :          ELSE
    1803          12 :             CALL pw_zero(embed_pot)
    1804             :          END IF
    1805             : 
    1806          12 :          CALL pw_axpy(psi_L, embed_pot)
    1807             : 
    1808             :          ! Spin-dependent potential
    1809         732 :          wf_vector = 0.0_dp
    1810             :          CALL cp_fm_get_info(matrix=embed_pot_coef_spin, &
    1811             :                              nrow_local=nrow_local, &
    1812          12 :                              row_indices=row_indices)
    1813             : 
    1814             :          ! Copy fm_coeff to an array
    1815         372 :          DO LLL = 1, nrow_local
    1816         360 :             l_global = row_indices(LLL)
    1817         372 :             wf_vector(l_global) = embed_pot_coef_spin%local_data(LLL, 1)
    1818             :          END DO
    1819          12 :          CALL para_env%sum(wf_vector)
    1820             : 
    1821             :          ! Calculate the variable part of the embedding potential
    1822             :          CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, &
    1823             :                                  qs_kind_set, cell, particle_set, pw_env, &
    1824             :                                  dft_control%qs_control%eps_rho_rspace, &
    1825          12 :                                  basis_type="RI_AUX")
    1826             :          ! No constant potential for spin-dependent potential
    1827          12 :          CALL pw_zero(spin_embed_pot)
    1828          12 :          CALL pw_axpy(psi_L, spin_embed_pot)
    1829             : 
    1830             :       ELSE ! Closed shell
    1831             : 
    1832             :          CALL cp_fm_get_info(matrix=embed_pot_coef, &
    1833             :                              nrow_local=nrow_local, &
    1834           8 :                              row_indices=row_indices)
    1835             : 
    1836             :          ! Copy fm_coeff to an array
    1837         792 :          DO LLL = 1, nrow_local
    1838         784 :             l_global = row_indices(LLL)
    1839         792 :             wf_vector(l_global) = embed_pot_coef%local_data(LLL, 1)
    1840             :          END DO
    1841           8 :          CALL para_env%sum(wf_vector)
    1842             : 
    1843             :          ! Calculate the variable part of the embedding potential
    1844             :          CALL calculate_wavefunction(mo_coeff, 1, psi_L, rho_g, atomic_kind_set, &
    1845           8 :                                      qs_kind_set, cell, dft_control, particle_set, pw_env)
    1846             : 
    1847             :          CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, &
    1848             :                                  qs_kind_set, cell, particle_set, pw_env, &
    1849             :                                  dft_control%qs_control%eps_rho_rspace, &
    1850           8 :                                  basis_type="RI_AUX")
    1851             : 
    1852             :          ! Update the full embedding potential
    1853           8 :          IF (add_const_pot) THEN
    1854           2 :             CALL pw_copy(const_pot, embed_pot)
    1855             :          ELSE
    1856           6 :             CALL pw_zero(embed_pot)
    1857             :          END IF
    1858             : 
    1859           8 :          CALL pw_axpy(psi_L, embed_pot)
    1860             :       END IF ! Open/closed shell
    1861             : 
    1862             :       ! Deallocate memory and release objects
    1863          20 :       DEALLOCATE (wf_vector)
    1864          20 :       CALL auxbas_pw_pool%give_back_pw(psi_L)
    1865          20 :       CALL auxbas_pw_pool%give_back_pw(rho_g)
    1866             : 
    1867          20 :       IF (open_shell_embed) THEN
    1868          12 :          CALL cp_fm_release(embed_pot_coef_spin)
    1869          12 :          CALL cp_fm_release(embed_pot_coef_spinless)
    1870             :       END IF
    1871             : 
    1872          20 :       CALL timestop(handle)
    1873             : 
    1874          20 :    END SUBROUTINE update_embed_pot
    1875             : 
    1876             : ! **************************************************************************************************
    1877             : !> \brief BFGS update of the inverse Hessian in the full matrix format
    1878             : !> \param grad ...
    1879             : !> \param prev_grad ...
    1880             : !> \param step ...
    1881             : !> \param prev_inv_Hess ...
    1882             : !> \param inv_Hess ...
    1883             : !> \author Vladimir Rybkin
    1884             : ! **************************************************************************************************
    1885           0 :    SUBROUTINE inv_Hessian_update(grad, prev_grad, step, prev_inv_Hess, inv_Hess)
    1886             :       TYPE(cp_fm_type), INTENT(IN)                       :: grad, prev_grad, step, prev_inv_Hess, &
    1887             :                                                             inv_Hess
    1888             : 
    1889             :       INTEGER                                            :: mat_size
    1890             :       REAL(KIND=dp)                                      :: factor1, s_dot_y, y_dot_B_inv_y
    1891             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct_mat, fm_struct_vec
    1892             :       TYPE(cp_fm_type)                                   :: B_inv_y, B_inv_y_s, s_s, s_y, s_y_B_inv, &
    1893             :                                                             y
    1894             : 
    1895             :       ! Recover the dimension
    1896             :       CALL cp_fm_get_info(matrix=inv_Hess, &
    1897           0 :                           nrow_global=mat_size)
    1898             : 
    1899           0 :       CALL cp_fm_set_all(inv_Hess, 0.0_dp)
    1900           0 :       CALL cp_fm_to_fm(prev_inv_Hess, inv_Hess)
    1901             : 
    1902             :       ! Get full matrix structures
    1903           0 :       NULLIFY (fm_struct_mat, fm_struct_vec)
    1904             : 
    1905             :       CALL cp_fm_get_info(matrix=prev_inv_Hess, &
    1906           0 :                           matrix_struct=fm_struct_mat)
    1907             :       CALL cp_fm_get_info(matrix=grad, &
    1908           0 :                           matrix_struct=fm_struct_vec)
    1909             : 
    1910             :       ! Allocate intermediates
    1911           0 :       CALL cp_fm_create(B_inv_y, fm_struct_vec, name="B_inv_y")
    1912           0 :       CALL cp_fm_create(y, fm_struct_vec, name="y")
    1913             : 
    1914           0 :       CALL cp_fm_create(s_s, fm_struct_mat, name="s_s")
    1915           0 :       CALL cp_fm_create(s_y, fm_struct_mat, name="s_y")
    1916           0 :       CALL cp_fm_create(B_inv_y_s, fm_struct_mat, name="B_inv_y_s")
    1917           0 :       CALL cp_fm_create(s_y_B_inv, fm_struct_mat, name="s_y_B_inv")
    1918             : 
    1919           0 :       CALL cp_fm_set_all(B_inv_y, 0.0_dp)
    1920           0 :       CALL cp_fm_set_all(s_s, 0.0_dp)
    1921           0 :       CALL cp_fm_set_all(s_y, 0.0_dp)
    1922           0 :       CALL cp_fm_set_all(B_inv_y_s, 0.0_dp)
    1923           0 :       CALL cp_fm_set_all(s_y_B_inv, 0.0_dp)
    1924             : 
    1925             :       ! Calculate intermediates
    1926             :       ! y the is gradient difference
    1927           0 :       CALL cp_fm_get_info(matrix=grad)
    1928           0 :       CALL cp_fm_to_fm(grad, y)
    1929           0 :       CALL cp_fm_scale_and_add(1.0_dp, y, -1.0_dp, prev_grad)
    1930             : 
    1931             :       ! First term
    1932             :       CALL parallel_gemm(transa="N", transb="N", m=mat_size, n=1, &
    1933             :                          k=mat_size, alpha=1.0_dp, &
    1934             :                          matrix_a=prev_inv_Hess, matrix_b=y, beta=0.0_dp, &
    1935           0 :                          matrix_c=B_inv_y)
    1936             : 
    1937             :       CALL parallel_gemm(transa="N", transb="T", m=mat_size, n=mat_size, &
    1938             :                          k=1, alpha=1.0_dp, &
    1939             :                          matrix_a=step, matrix_b=step, beta=0.0_dp, &
    1940           0 :                          matrix_c=s_s)
    1941             : 
    1942             :       CALL parallel_gemm(transa="N", transb="T", m=mat_size, n=mat_size, &
    1943             :                          k=1, alpha=1.0_dp, &
    1944             :                          matrix_a=step, matrix_b=y, beta=0.0_dp, &
    1945           0 :                          matrix_c=s_y)
    1946             : 
    1947           0 :       CALL cp_fm_trace(step, y, s_dot_y)
    1948             : 
    1949           0 :       CALL cp_fm_trace(y, y, s_dot_y)
    1950           0 :       CALL cp_fm_trace(step, step, s_dot_y)
    1951             : 
    1952           0 :       CALL cp_fm_trace(y, B_inv_y, y_dot_B_inv_y)
    1953             : 
    1954           0 :       factor1 = (s_dot_y + y_dot_B_inv_y)/(s_dot_y)**2
    1955             : 
    1956           0 :       CALL cp_fm_scale_and_add(1.0_dp, inv_Hess, factor1, s_s)
    1957             : 
    1958             :       ! Second term
    1959             :       CALL parallel_gemm(transa="N", transb="T", m=mat_size, n=mat_size, &
    1960             :                          k=1, alpha=1.0_dp, &
    1961             :                          matrix_a=B_inv_y, matrix_b=step, beta=0.0_dp, &
    1962           0 :                          matrix_c=B_inv_y_s)
    1963             : 
    1964             :       CALL parallel_gemm(transa="N", transb="N", m=mat_size, n=mat_size, &
    1965             :                          k=mat_size, alpha=1.0_dp, &
    1966             :                          matrix_a=s_y, matrix_b=prev_inv_Hess, beta=0.0_dp, &
    1967           0 :                          matrix_c=s_y_B_inv)
    1968             : 
    1969           0 :       CALL cp_fm_scale_and_add(1.0_dp, B_inv_y_s, 1.0_dp, s_y_B_inv)
    1970             : 
    1971             :       ! Assemble the new inverse Hessian
    1972           0 :       CALL cp_fm_scale_and_add(1.0_dp, inv_Hess, -s_dot_y, B_inv_y_s)
    1973             : 
    1974             :       ! Deallocate intermediates
    1975           0 :       CALL cp_fm_release(y)
    1976           0 :       CALL cp_fm_release(B_inv_y)
    1977           0 :       CALL cp_fm_release(s_s)
    1978           0 :       CALL cp_fm_release(s_y)
    1979           0 :       CALL cp_fm_release(B_inv_y_s)
    1980           0 :       CALL cp_fm_release(s_y_B_inv)
    1981             : 
    1982           0 :    END SUBROUTINE inv_Hessian_update
    1983             : 
    1984             : ! **************************************************************************************************
    1985             : !> \brief ...
    1986             : !> \param grad ...
    1987             : !> \param prev_grad ...
    1988             : !> \param step ...
    1989             : !> \param prev_Hess ...
    1990             : !> \param Hess ...
    1991             : ! **************************************************************************************************
    1992           0 :    SUBROUTINE Hessian_update(grad, prev_grad, step, prev_Hess, Hess)
    1993             :       TYPE(cp_fm_type), INTENT(IN)                       :: grad, prev_grad, step, prev_Hess, Hess
    1994             : 
    1995             :       INTEGER                                            :: mat_size
    1996             :       REAL(KIND=dp)                                      :: s_b_s, y_t_s
    1997             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
    1998             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct_mat, fm_struct_vec, &
    1999             :                                                             fm_struct_vec_t
    2000             :       TYPE(cp_fm_type)                                   :: B_s, B_s_s_B, s_t_B, y, y_y_t
    2001             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    2002             : 
    2003             :       ! Recover the dimension
    2004             :       CALL cp_fm_get_info(matrix=Hess, &
    2005           0 :                           nrow_global=mat_size, para_env=para_env)
    2006             : 
    2007           0 :       CALL cp_fm_set_all(Hess, 0.0_dp)
    2008           0 :       CALL cp_fm_to_fm(prev_Hess, Hess)
    2009             : 
    2010             :       ! WARNING: our Hessian must be negative-definite, whereas BFGS makes it positive-definite!
    2011             :       ! Therefore, we change sign in the beginning and in the end.
    2012           0 :       CALL cp_fm_scale(-1.0_dp, Hess)
    2013             : 
    2014             :       ! Create blacs environment
    2015           0 :       NULLIFY (blacs_env)
    2016           0 :       CALL cp_blacs_env_create(blacs_env=blacs_env, para_env=para_env)
    2017             : 
    2018             :       ! Get full matrix structures
    2019           0 :       NULLIFY (fm_struct_mat, fm_struct_vec, fm_struct_vec_t)
    2020             : 
    2021             :       CALL cp_fm_get_info(matrix=prev_Hess, &
    2022           0 :                           matrix_struct=fm_struct_mat)
    2023             :       CALL cp_fm_get_info(matrix=grad, &
    2024           0 :                           matrix_struct=fm_struct_vec)
    2025             :       CALL cp_fm_struct_create(fm_struct_vec_t, para_env=para_env, context=blacs_env, &
    2026           0 :                                nrow_global=1, ncol_global=mat_size)
    2027             : 
    2028             :       ! Allocate intermediates
    2029           0 :       CALL cp_fm_create(B_s, fm_struct_vec, name="B_s")
    2030           0 :       CALL cp_fm_create(s_t_B, fm_struct_vec_t, name="s_t_B")
    2031           0 :       CALL cp_fm_create(y, fm_struct_vec, name="y")
    2032             : 
    2033           0 :       CALL cp_fm_create(y_y_t, fm_struct_mat, name="y_y_t")
    2034           0 :       CALL cp_fm_create(B_s_s_B, fm_struct_mat, name="B_s_s_B")
    2035             : 
    2036           0 :       CALL cp_fm_set_all(y_y_t, 0.0_dp)
    2037           0 :       CALL cp_fm_set_all(y, 0.0_dp)
    2038           0 :       CALL cp_fm_set_all(B_s_s_B, 0.0_dp)
    2039           0 :       CALL cp_fm_set_all(B_s, 0.0_dp)
    2040           0 :       CALL cp_fm_set_all(s_t_B, 0.0_dp)
    2041             : 
    2042             :       ! Release the structure created only here
    2043           0 :       CALL cp_fm_struct_release(fm_struct_vec_t)
    2044             : 
    2045             :       ! Calculate intermediates
    2046             :       ! y the is gradient difference
    2047           0 :       CALL cp_fm_to_fm(grad, y)
    2048           0 :       CALL cp_fm_scale_and_add(1.0_dp, y, -1.0_dp, prev_grad)
    2049             : 
    2050             :       ! First term
    2051             :       CALL parallel_gemm(transa="N", transb="T", m=mat_size, n=mat_size, &
    2052             :                          k=1, alpha=1.0_dp, &
    2053             :                          matrix_a=y, matrix_b=y, beta=0.0_dp, &
    2054           0 :                          matrix_c=y_y_t)
    2055             : 
    2056           0 :       CALL cp_fm_trace(y, step, y_t_s)
    2057             : 
    2058           0 :       CALL cp_fm_scale_and_add(1.0_dp, Hess, (1.0_dp/y_t_s), y_y_t)
    2059             : 
    2060             :       ! Second term
    2061             :       CALL parallel_gemm(transa="N", transb="N", m=mat_size, n=1, &
    2062             :                          k=mat_size, alpha=1.0_dp, &
    2063             :                          matrix_a=Hess, matrix_b=step, beta=0.0_dp, &
    2064           0 :                          matrix_c=B_s)
    2065             : 
    2066           0 :       CALL cp_fm_trace(B_s, step, s_B_s)
    2067             : 
    2068             :       CALL parallel_gemm(transa="T", transb="N", m=1, n=mat_size, &
    2069             :                          k=mat_size, alpha=1.0_dp, &
    2070             :                          matrix_a=step, matrix_b=Hess, beta=0.0_dp, &
    2071           0 :                          matrix_c=s_t_B)
    2072             : 
    2073             :       CALL parallel_gemm(transa="N", transb="N", m=mat_size, n=mat_size, &
    2074             :                          k=1, alpha=1.0_dp, &
    2075             :                          matrix_a=B_s, matrix_b=s_t_B, beta=0.0_dp, &
    2076           0 :                          matrix_c=B_s_s_B)
    2077             : 
    2078           0 :       CALL cp_fm_scale_and_add(1.0_dp, Hess, -(1.0_dp/s_B_s), B_s_s_B)
    2079             : 
    2080             :       ! WARNING: our Hessian must be negative-definite, whereas BFGS makes it positive-definite!
    2081             :       ! Therefore, we change sign in the beginning and in the end.
    2082           0 :       CALL cp_fm_scale(-1.0_dp, Hess)
    2083             : 
    2084             :       ! Release blacs environment
    2085           0 :       CALL cp_blacs_env_release(blacs_env)
    2086             : 
    2087             :       ! Deallocate intermediates
    2088           0 :       CALL cp_fm_release(y_y_t)
    2089           0 :       CALL cp_fm_release(B_s_s_B)
    2090           0 :       CALL cp_fm_release(B_s)
    2091           0 :       CALL cp_fm_release(s_t_B)
    2092           0 :       CALL cp_fm_release(y)
    2093             : 
    2094           0 :    END SUBROUTINE Hessian_update
    2095             : 
    2096             : ! **************************************************************************************************
    2097             : !> \brief ...
    2098             : !> \param grad ...
    2099             : !> \param prev_grad ...
    2100             : !> \param step ...
    2101             : !> \param prev_Hess ...
    2102             : !> \param Hess ...
    2103             : ! **************************************************************************************************
    2104          10 :    SUBROUTINE symm_rank_one_update(grad, prev_grad, step, prev_Hess, Hess)
    2105             :       TYPE(cp_fm_type), INTENT(IN)                       :: grad, prev_grad, step, prev_Hess, Hess
    2106             : 
    2107             :       INTEGER                                            :: mat_size
    2108             :       REAL(KIND=dp)                                      :: factor
    2109             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct_mat, fm_struct_vec
    2110             :       TYPE(cp_fm_type)                                   :: B_x, y, y_B_x_y_B_x
    2111             : 
    2112             :       ! Recover the dimension
    2113           2 :       CALL cp_fm_get_info(matrix=Hess, nrow_global=mat_size)
    2114             : 
    2115           2 :       CALL cp_fm_set_all(Hess, 0.0_dp)
    2116           2 :       CALL cp_fm_to_fm(prev_Hess, Hess)
    2117             : 
    2118             :       ! Get full matrix structures
    2119           2 :       NULLIFY (fm_struct_mat, fm_struct_vec)
    2120             : 
    2121             :       CALL cp_fm_get_info(matrix=prev_Hess, &
    2122           2 :                           matrix_struct=fm_struct_mat)
    2123             :       CALL cp_fm_get_info(matrix=grad, &
    2124           2 :                           matrix_struct=fm_struct_vec)
    2125             : 
    2126             :       ! Allocate intermediates
    2127           2 :       CALL cp_fm_create(y, fm_struct_vec, name="y")
    2128           2 :       CALL cp_fm_create(B_x, fm_struct_vec, name="B_x")
    2129           2 :       CALL cp_fm_create(y_B_x_y_B_x, fm_struct_mat, name="y_B_x_y_B_x")
    2130             : 
    2131           2 :       CALL cp_fm_set_all(y, 0.0_dp)
    2132           2 :       CALL cp_fm_set_all(B_x, 0.0_dp)
    2133           2 :       CALL cp_fm_set_all(y_B_x_y_B_x, 0.0_dp)
    2134             : 
    2135             :       ! Calculate intermediates
    2136             :       ! y the is gradient difference
    2137           2 :       CALL cp_fm_to_fm(grad, y)
    2138           2 :       CALL cp_fm_scale_and_add(1.0_dp, y, -1.0_dp, prev_grad)
    2139             : 
    2140             :       CALL parallel_gemm(transa="N", transb="N", m=mat_size, n=1, &
    2141             :                          k=mat_size, alpha=1.0_dp, &
    2142             :                          matrix_a=Hess, matrix_b=step, beta=0.0_dp, &
    2143           2 :                          matrix_c=B_x)
    2144             : 
    2145           2 :       CALL cp_fm_scale_and_add(1.0_dp, y, -1.0_dp, B_x)
    2146             : 
    2147             :       CALL parallel_gemm(transa="N", transb="T", m=mat_size, n=mat_size, &
    2148             :                          k=1, alpha=1.0_dp, &
    2149             :                          matrix_a=y, matrix_b=y, beta=0.0_dp, &
    2150           2 :                          matrix_c=y_B_x_y_B_x)
    2151             : 
    2152             :       ! Scaling factor
    2153           2 :       CALL cp_fm_trace(y, step, factor)
    2154             : 
    2155             :       ! Assemble the Hessian
    2156           2 :       CALL cp_fm_scale_and_add(1.0_dp, Hess, (1.0_dp/factor), y_B_x_y_B_x)
    2157             : 
    2158             :       ! Deallocate intermediates
    2159           2 :       CALL cp_fm_release(y)
    2160           2 :       CALL cp_fm_release(B_x)
    2161           2 :       CALL cp_fm_release(y_B_x_y_B_x)
    2162             : 
    2163           2 :    END SUBROUTINE symm_rank_one_update
    2164             : 
    2165             : ! **************************************************************************************************
    2166             : !> \brief Controls the step, changes the trust radius if needed in maximization of the V_emb
    2167             : !> \param opt_embed ...
    2168             : !> \author Vladimir Rybkin
    2169             : ! **************************************************************************************************
    2170           8 :    SUBROUTINE step_control(opt_embed)
    2171             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    2172             : 
    2173             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'step_control'
    2174             : 
    2175             :       INTEGER                                            :: handle
    2176             :       REAL(KIND=dp)                                      :: actual_ener_change, ener_ratio, &
    2177             :                                                             lin_term, pred_ener_change, quad_term
    2178             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    2179             :       TYPE(cp_fm_type)                                   :: H_b
    2180             : 
    2181           2 :       CALL timeset(routineN, handle)
    2182             : 
    2183           2 :       NULLIFY (fm_struct)
    2184             :       CALL cp_fm_get_info(matrix=opt_embed%embed_pot_grad, &
    2185           2 :                           matrix_struct=fm_struct)
    2186           2 :       CALL cp_fm_create(H_b, fm_struct, name="H_b")
    2187           2 :       CALL cp_fm_set_all(H_b, 0.0_dp)
    2188             : 
    2189             :       ! Calculate the quadratic estimate for the energy
    2190             :       ! Linear term
    2191           2 :       CALL cp_fm_trace(opt_embed%step, opt_embed%embed_pot_grad, lin_term)
    2192             : 
    2193             :       ! Quadratic term
    2194             :       CALL parallel_gemm(transa="N", transb="N", m=opt_embed%dimen_aux, n=1, &
    2195             :                          k=opt_embed%dimen_aux, alpha=1.0_dp, &
    2196             :                          matrix_a=opt_embed%embed_pot_Hess, matrix_b=opt_embed%step, &
    2197           2 :                          beta=0.0_dp, matrix_c=H_b)
    2198           2 :       CALL cp_fm_trace(opt_embed%step, H_b, quad_term)
    2199             : 
    2200           2 :       pred_ener_change = lin_term + 0.5_dp*quad_term
    2201             : 
    2202             :       ! Reveal actual energy change
    2203             :       actual_ener_change = opt_embed%w_func(opt_embed%i_iter) - &
    2204           2 :                            opt_embed%w_func(opt_embed%last_accepted)
    2205             : 
    2206           2 :       ener_ratio = actual_ener_change/pred_ener_change
    2207             : 
    2208           2 :       CALL cp_fm_release(H_b)
    2209             : 
    2210           2 :       IF (actual_ener_change .GT. 0.0_dp) THEN ! If energy increases
    2211             :          ! We accept step
    2212           2 :          opt_embed%accept_step = .TRUE.
    2213             :          ! If energy change is larger than the predicted one, increase trust radius twice
    2214             :          ! Else (between 0 and 1) leave as it is, unless Newton step has been taken and if the step is less than max
    2215           2 :          IF ((ener_ratio .GT. 1.0_dp) .AND. (.NOT. opt_embed%newton_step) .AND. &
    2216             :              (opt_embed%trust_rad .LT. opt_embed%max_trad)) &
    2217           0 :             opt_embed%trust_rad = 2.0_dp*opt_embed%trust_rad
    2218             :       ELSE ! Energy decreases
    2219             :          ! If the decrease is not too large we allow this step to be taken
    2220             :          ! Otherwise, the step is rejected
    2221           0 :          IF (ABS(actual_ener_change) .GE. opt_embed%allowed_decrease) THEN
    2222           0 :             opt_embed%accept_step = .FALSE.
    2223             :          END IF
    2224             :          ! Trust radius is decreased 4 times unless it's smaller than the minimal allowed value
    2225           0 :          IF (opt_embed%trust_rad .GE. opt_embed%min_trad) &
    2226           0 :             opt_embed%trust_rad = 0.25_dp*opt_embed%trust_rad
    2227             :       END IF
    2228             : 
    2229           2 :       IF (opt_embed%accept_step) opt_embed%last_accepted = opt_embed%i_iter
    2230             : 
    2231           2 :       CALL timestop(handle)
    2232             : 
    2233           2 :    END SUBROUTINE step_control
    2234             : 
    2235             : ! **************************************************************************************************
    2236             : !> \brief ...
    2237             : !> \param opt_embed ...
    2238             : !> \param diag_grad ...
    2239             : !> \param eigenval ...
    2240             : !> \param diag_step ...
    2241             : ! **************************************************************************************************
    2242           2 :    SUBROUTINE level_shift(opt_embed, diag_grad, eigenval, diag_step)
    2243             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    2244             :       TYPE(cp_fm_type), INTENT(IN)                       :: diag_grad
    2245             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: eigenval
    2246             :       TYPE(cp_fm_type), INTENT(IN)                       :: diag_step
    2247             : 
    2248             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'level_shift'
    2249             :       INTEGER, PARAMETER                                 :: max_iter = 25
    2250             :       REAL(KIND=dp), PARAMETER                           :: thresh = 0.00001_dp
    2251             : 
    2252             :       INTEGER                                            :: handle, i_iter, l_global, LLL, &
    2253             :                                                             min_index, nrow_local
    2254           2 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: red_eigenval_map
    2255           2 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
    2256             :       LOGICAL                                            :: converged, do_shift
    2257             :       REAL(KIND=dp) :: diag_grad_norm, grad_min, hess_min, shift, shift_max, shift_min, step_len, &
    2258             :          step_minus_trad, step_minus_trad_first, step_minus_trad_max, step_minus_trad_min
    2259             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    2260             : 
    2261           2 :       CALL timeset(routineN, handle)
    2262             : 
    2263             :       ! Array properties
    2264             :       CALL cp_fm_get_info(matrix=opt_embed%embed_pot_coef, &
    2265             :                           nrow_local=nrow_local, &
    2266             :                           row_indices=row_indices, &
    2267           2 :                           para_env=para_env)
    2268             : 
    2269         242 :       min_index = MINLOC(ABS(eigenval), dim=1)
    2270           2 :       hess_min = eigenval(min_index)
    2271           2 :       CALL cp_fm_get_element(diag_grad, min_index, 1, grad_min)
    2272             : 
    2273           2 :       CALL cp_fm_trace(diag_grad, diag_grad, diag_grad_norm)
    2274             : 
    2275           2 :       IF (hess_min .LT. 0.0_dp) THEN
    2276             :          !shift_min = -2.0_dp*(diag_grad_norm/opt_embed%trust_rad - min(hess_min, 0.0_dp))
    2277             :          !shift_max = max(0.0_dp, -hess_min + 0.5_dp*grad_min/opt_embed%trust_rad)
    2278             :          !shift_max = MIN(-hess_min+0.5_dp*grad_min/opt_embed%trust_rad, 0.0_dp)
    2279           2 :          shift_max = hess_min + 0.1
    2280             :          shift_min = diag_grad_norm/opt_embed%trust_rad
    2281           2 :          shift_min = 10.0_dp
    2282             :          !If (abs(shift_max) .LE. thresh) then
    2283             :          !   shift_min = -20.0_dp*(diag_grad_norm/opt_embed%trust_rad - min(hess_min, 0.0_dp))
    2284             :          !Else
    2285             :          !   shift_min = 20.0_dp*shift_max
    2286             :          !Endif
    2287             : 
    2288             :          ! The boundary values
    2289           2 :          step_minus_trad_max = shifted_step(diag_grad, eigenval, shift_max, opt_embed%trust_rad)
    2290           2 :          step_minus_trad_min = shifted_step(diag_grad, eigenval, shift_min, opt_embed%trust_rad)
    2291             : 
    2292             :          ! Find zero by bisection
    2293           2 :          converged = .FALSE.
    2294           2 :          do_shift = .FALSE.
    2295           2 :          IF (ABS(step_minus_trad_max) .LE. thresh) THEN
    2296           0 :             shift = shift_max
    2297             :          ELSE
    2298           2 :             IF (ABS(step_minus_trad_min) .LE. thresh) THEN
    2299           0 :                shift = shift_min
    2300             :             ELSE
    2301          28 :                DO i_iter = 1, max_iter
    2302          28 :                   shift = 0.5_dp*(shift_max + shift_min)
    2303          28 :                   step_minus_trad = shifted_step(diag_grad, eigenval, shift, opt_embed%trust_rad)
    2304          28 :                   IF (i_iter .EQ. 1) step_minus_trad_first = step_minus_trad
    2305          28 :                   IF (step_minus_trad .GT. 0.0_dp) shift_max = shift
    2306          28 :                   IF (step_minus_trad .LT. 0.0_dp) shift_min = shift
    2307             :                   !IF (ABS(shift_max-shift_min) .LT. thresh) converged = .TRUE.
    2308          28 :                   IF (ABS(step_minus_trad) .LT. thresh) converged = .TRUE.
    2309          26 :                   IF (converged) EXIT
    2310             :                END DO
    2311           2 :                IF (ABS(step_minus_trad) .LT. ABS(step_minus_trad_first)) do_shift = .TRUE.
    2312             :             END IF
    2313             :          END IF
    2314             :          ! Apply level-shifting
    2315           2 :          IF (converged .OR. do_shift) THEN
    2316         122 :             DO LLL = 1, nrow_local
    2317         120 :                l_global = row_indices(LLL)
    2318         122 :                IF (ABS(eigenval(l_global)) .GE. thresh) THEN
    2319             :                   diag_step%local_data(LLL, 1) = &
    2320         120 :                      -diag_grad%local_data(LLL, 1)/(eigenval(l_global) - shift)
    2321             :                ELSE
    2322           0 :                   diag_step%local_data(LLL, 1) = 0.0_dp
    2323             :                END IF
    2324             :             END DO
    2325             :          END IF
    2326           2 :          IF (.NOT. converged) THEN ! Scale if shift has not been found
    2327           0 :             CALL cp_fm_trace(diag_step, diag_step, step_len)
    2328           0 :             CALL cp_fm_scale(opt_embed%trust_rad/step_len, diag_step)
    2329             :          END IF
    2330             : 
    2331             :          ! Special case
    2332             :       ELSE ! Hess min .LT. 0.0_dp
    2333             :          ! First, find all positive eigenvalues
    2334           0 :          ALLOCATE (red_eigenval_map(opt_embed%dimen_var_aux))
    2335           0 :          red_eigenval_map = 0
    2336           0 :          DO LLL = 1, nrow_local
    2337           0 :             l_global = row_indices(LLL)
    2338           0 :             IF (eigenval(l_global) .GE. 0.0_dp) THEN
    2339           0 :                red_eigenval_map(l_global) = 1
    2340             :             END IF
    2341             :          END DO
    2342           0 :          CALL para_env%sum(red_eigenval_map)
    2343             : 
    2344             :          ! Set shift as -hess_min and find step on the reduced space of negative-value
    2345             :          ! eigenvectors
    2346           0 :          shift = -hess_min
    2347           0 :          DO LLL = 1, nrow_local
    2348           0 :             l_global = row_indices(LLL)
    2349           0 :             IF (red_eigenval_map(l_global) .EQ. 0) THEN
    2350           0 :                IF (ABS(eigenval(l_global)) .GE. thresh) THEN
    2351             :                   diag_step%local_data(LLL, 1) = &
    2352           0 :                      -diag_grad%local_data(LLL, 1)/(eigenval(l_global) - shift)
    2353             :                ELSE
    2354           0 :                   diag_step%local_data(LLL, 1) = 0.0_dp
    2355             :                END IF
    2356             :             ELSE
    2357           0 :                diag_step%local_data(LLL, 1) = 0.0_dp
    2358             :             END IF
    2359             :          END DO
    2360             : 
    2361             :          ! Find the step length of such a step
    2362           0 :          CALL cp_fm_trace(diag_step, diag_step, step_len)
    2363             : 
    2364             :       END IF
    2365             : 
    2366           2 :       CALL timestop(handle)
    2367             : 
    2368           4 :    END SUBROUTINE level_shift
    2369             : 
    2370             : ! **************************************************************************************************
    2371             : !> \brief ...
    2372             : !> \param diag_grad ...
    2373             : !> \param eigenval ...
    2374             : !> \param shift ...
    2375             : !> \param trust_rad ...
    2376             : !> \return ...
    2377             : ! **************************************************************************************************
    2378          32 :    FUNCTION shifted_step(diag_grad, eigenval, shift, trust_rad) RESULT(step_minus_trad)
    2379             :       TYPE(cp_fm_type), INTENT(IN)                       :: diag_grad
    2380             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
    2381             :          INTENT(IN)                                      :: eigenval
    2382             :       REAL(KIND=dp), INTENT(IN)                          :: shift, trust_rad
    2383             :       REAL(KIND=dp)                                      :: step_minus_trad
    2384             : 
    2385             :       REAL(KIND=dp), PARAMETER                           :: thresh = 0.000001_dp
    2386             : 
    2387             :       INTEGER                                            :: l_global, LLL, nrow_local
    2388          32 :       INTEGER, DIMENSION(:), POINTER                     :: row_indices
    2389             :       REAL(KIND=dp)                                      :: step, step_1d
    2390             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    2391             : 
    2392             :       CALL cp_fm_get_info(matrix=diag_grad, &
    2393             :                           nrow_local=nrow_local, &
    2394             :                           row_indices=row_indices, &
    2395          32 :                           para_env=para_env)
    2396             : 
    2397          32 :       step = 0.0_dp
    2398        1952 :       DO LLL = 1, nrow_local
    2399        1920 :          l_global = row_indices(LLL)
    2400        1952 :          IF ((ABS(eigenval(l_global)) .GE. thresh) .AND. (ABS(diag_grad%local_data(LLL, 1)) .GE. thresh)) THEN
    2401          16 :             step_1d = -diag_grad%local_data(LLL, 1)/(eigenval(l_global) + shift)
    2402          16 :             step = step + step_1d**2
    2403             :          END IF
    2404             :       END DO
    2405             : 
    2406          32 :       CALL para_env%sum(step)
    2407             : 
    2408          32 :       step_minus_trad = SQRT(step) - trust_rad
    2409             : 
    2410          32 :    END FUNCTION shifted_step
    2411             : 
    2412             : ! **************************************************************************************************
    2413             : !> \brief ...
    2414             : !> \param step ...
    2415             : !> \param prev_step ...
    2416             : !> \param grad ...
    2417             : !> \param prev_grad ...
    2418             : !> \return ...
    2419             : !> \retval length ...
    2420             : ! **************************************************************************************************
    2421           0 :    FUNCTION Barzilai_Borwein(step, prev_step, grad, prev_grad) RESULT(length)
    2422             :       TYPE(cp_fm_type), INTENT(IN)                       :: step, prev_step, grad, prev_grad
    2423             :       REAL(KIND=dp)                                      :: length
    2424             : 
    2425             :       REAL(KIND=dp)                                      :: denominator, numerator
    2426             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    2427             :       TYPE(cp_fm_type)                                   :: grad_diff, step_diff
    2428             : 
    2429             :       ! Get full matrix structures
    2430           0 :       NULLIFY (fm_struct)
    2431             : 
    2432             :       CALL cp_fm_get_info(matrix=grad, &
    2433           0 :                           matrix_struct=fm_struct)
    2434             : 
    2435             :       ! Allocate intermediates
    2436           0 :       CALL cp_fm_create(grad_diff, fm_struct, name="grad_diff")
    2437           0 :       CALL cp_fm_create(step_diff, fm_struct, name="step_diff")
    2438             : 
    2439             :       ! Calculate intermediates
    2440           0 :       CALL cp_fm_to_fm(grad, grad_diff)
    2441           0 :       CALL cp_fm_to_fm(step, step_diff)
    2442             : 
    2443           0 :       CALL cp_fm_scale_and_add(1.0_dp, grad_diff, -1.0_dp, prev_grad)
    2444           0 :       CALL cp_fm_scale_and_add(1.0_dp, step_diff, -1.0_dp, prev_step)
    2445             : 
    2446           0 :       CALL cp_fm_trace(step_diff, grad_diff, numerator)
    2447           0 :       CALL cp_fm_trace(grad_diff, grad_diff, denominator)
    2448             : 
    2449             :       ! Release intermediates
    2450           0 :       CALL cp_fm_release(grad_diff)
    2451           0 :       CALL cp_fm_release(step_diff)
    2452             : 
    2453           0 :       length = numerator/denominator
    2454             : 
    2455           0 :    END FUNCTION Barzilai_Borwein
    2456             : 
    2457             : ! **************************************************************************************************
    2458             : !> \brief ...
    2459             : !> \param pw_env ...
    2460             : !> \param embed_pot ...
    2461             : !> \param spin_embed_pot ...
    2462             : !> \param diff_rho_r ...
    2463             : !> \param diff_rho_spin ...
    2464             : !> \param rho_r_ref ...
    2465             : !> \param open_shell_embed ...
    2466             : !> \param step_len ...
    2467             : ! **************************************************************************************************
    2468           2 :    SUBROUTINE Leeuwen_Baerends_potential_update(pw_env, embed_pot, spin_embed_pot, diff_rho_r, diff_rho_spin, &
    2469             :                                                 rho_r_ref, open_shell_embed, step_len)
    2470             :       TYPE(pw_env_type), POINTER                         :: pw_env
    2471             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
    2472             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
    2473             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r, diff_rho_spin
    2474             :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r_ref
    2475             :       LOGICAL, INTENT(IN)                                :: open_shell_embed
    2476             :       REAL(KIND=dp), INTENT(IN)                          :: step_len
    2477             : 
    2478             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'Leeuwen_Baerends_potential_update'
    2479             : 
    2480             :       INTEGER                                            :: handle, i, i_spin, j, k, nspins
    2481             :       INTEGER, DIMENSION(3)                              :: lb, ub
    2482             :       REAL(KIND=dp)                                      :: my_rho, rho_cutoff
    2483             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2484           2 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: new_embed_pot, rho_n_1, temp_embed_pot
    2485             : 
    2486           2 :       CALL timeset(routineN, handle)
    2487             : 
    2488           2 :       rho_cutoff = EPSILON(0.0_dp)
    2489             : 
    2490             :       ! Prepare plane-waves pool
    2491           2 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    2492           2 :       NULLIFY (new_embed_pot)
    2493             : 
    2494           2 :       nspins = 1
    2495           2 :       IF (open_shell_embed) nspins = 2
    2496             :       NULLIFY (new_embed_pot)
    2497           8 :       ALLOCATE (new_embed_pot(nspins))
    2498           6 :       DO i_spin = 1, nspins
    2499           4 :          CALL auxbas_pw_pool%create_pw(new_embed_pot(i_spin))
    2500           6 :          CALL pw_zero(new_embed_pot(i_spin))
    2501             :       END DO
    2502             : 
    2503           8 :       lb(1:3) = embed_pot%pw_grid%bounds_local(1, 1:3)
    2504           8 :       ub(1:3) = embed_pot%pw_grid%bounds_local(2, 1:3)
    2505             : 
    2506           2 :       IF (.NOT. open_shell_embed) THEN
    2507             : !$OMP    PARALLEL DO DEFAULT(NONE) &
    2508             : !$OMP                PRIVATE(i,j,k, my_rho) &
    2509           0 : !$OMP                SHARED(new_embed_pot, embed_pot, diff_rho_r, rho_r_ref, lb, ub, rho_cutoff, step_len)
    2510             :          DO k = lb(3), ub(3)
    2511             :             DO j = lb(2), ub(2)
    2512             :                DO i = lb(1), ub(1)
    2513             :                   IF (rho_r_ref(1)%array(i, j, k) .GT. rho_cutoff) THEN
    2514             :                      my_rho = rho_r_ref(1)%array(i, j, k)
    2515             :                   ELSE
    2516             :                      my_rho = rho_cutoff
    2517             :                   END IF
    2518             :                   new_embed_pot(1)%array(i, j, k) = step_len*embed_pot%array(i, j, k)* &
    2519             :                                                     (diff_rho_r%array(i, j, k) + rho_r_ref(1)%array(i, j, k))/my_rho
    2520             :                END DO
    2521             :             END DO
    2522             :          END DO
    2523             : !$OMP    END PARALLEL DO
    2524           0 :          CALL pw_copy(new_embed_pot(1), embed_pot)
    2525             : 
    2526             :       ELSE
    2527             :          ! One has to work with spin components rather than with total and spin density
    2528           2 :          NULLIFY (rho_n_1)
    2529           8 :          ALLOCATE (rho_n_1(nspins))
    2530           2 :          NULLIFY (temp_embed_pot)
    2531           8 :          ALLOCATE (temp_embed_pot(nspins))
    2532           6 :          DO i_spin = 1, nspins
    2533           4 :             CALL auxbas_pw_pool%create_pw(rho_n_1(i_spin))
    2534           4 :             CALL pw_zero(rho_n_1(i_spin))
    2535           4 :             CALL auxbas_pw_pool%create_pw(temp_embed_pot(i_spin))
    2536           6 :             CALL pw_zero(temp_embed_pot(i_spin))
    2537             :          END DO
    2538           2 :          CALL pw_copy(diff_rho_r, rho_n_1(1))
    2539           2 :          CALL pw_copy(diff_rho_r, rho_n_1(2))
    2540           2 :          CALL pw_axpy(diff_rho_spin, rho_n_1(1), 1.0_dp)
    2541           2 :          CALL pw_axpy(diff_rho_spin, rho_n_1(2), -1.0_dp)
    2542           2 :          CALL pw_scale(rho_n_1(1), a=0.5_dp)
    2543           2 :          CALL pw_scale(rho_n_1(2), a=0.5_dp)
    2544             : 
    2545           2 :          CALL pw_copy(embed_pot, temp_embed_pot(1))
    2546           2 :          CALL pw_copy(embed_pot, temp_embed_pot(2))
    2547           2 :          CALL pw_axpy(spin_embed_pot, temp_embed_pot(1), 1.0_dp)
    2548           2 :          CALL pw_axpy(spin_embed_pot, temp_embed_pot(2), -1.0_dp)
    2549             : 
    2550           2 :          IF (SIZE(rho_r_ref) .EQ. 2) THEN
    2551           2 :             CALL pw_axpy(rho_r_ref(1), rho_n_1(1), 1.0_dp)
    2552           2 :             CALL pw_axpy(rho_r_ref(2), rho_n_1(2), 1.0_dp)
    2553             : 
    2554             : !$OMP    PARALLEL DO DEFAULT(NONE) &
    2555             : !$OMP                PRIVATE(i,j,k, my_rho) &
    2556           2 : !$OMP                SHARED(new_embed_pot, temp_embed_pot, rho_r_ref, rho_n_1, lb, ub, rho_cutoff, step_len)
    2557             :             DO k = lb(3), ub(3)
    2558             :                DO j = lb(2), ub(2)
    2559             :                   DO i = lb(1), ub(1)
    2560             :                      IF (rho_r_ref(1)%array(i, j, k) .GT. rho_cutoff) THEN
    2561             :                         my_rho = rho_r_ref(1)%array(i, j, k)
    2562             :                      ELSE
    2563             :                         my_rho = rho_cutoff
    2564             :                      END IF
    2565             :                      new_embed_pot(1)%array(i, j, k) = step_len*temp_embed_pot(1)%array(i, j, k)* &
    2566             :                                                        (rho_n_1(1)%array(i, j, k))/my_rho
    2567             :                      IF (rho_r_ref(2)%array(i, j, k) .GT. rho_cutoff) THEN
    2568             :                         my_rho = rho_r_ref(2)%array(i, j, k)
    2569             :                      ELSE
    2570             :                         my_rho = rho_cutoff
    2571             :                      END IF
    2572             :                      new_embed_pot(2)%array(i, j, k) = step_len*temp_embed_pot(2)%array(i, j, k)* &
    2573             :                                                        (rho_n_1(2)%array(i, j, k))/my_rho
    2574             :                   END DO
    2575             :                END DO
    2576             :             END DO
    2577             : !$OMP    END PARALLEL DO
    2578             : 
    2579             :          ELSE ! Reference system is closed-shell
    2580           0 :             CALL pw_axpy(rho_r_ref(1), rho_n_1(1), 1.0_dp)
    2581             :             ! The beta spin component is here equal to the difference: nothing to do
    2582             : 
    2583             : !$OMP    PARALLEL DO DEFAULT(NONE) &
    2584             : !$OMP                PRIVATE(i,j,k, my_rho) &
    2585           0 : !$OMP                SHARED(new_embed_pot, rho_r_ref, temp_embed_pot, rho_n_1, lb, ub, rho_cutoff, step_len)
    2586             :             DO k = lb(3), ub(3)
    2587             :                DO j = lb(2), ub(2)
    2588             :                   DO i = lb(1), ub(1)
    2589             :                      IF (rho_r_ref(1)%array(i, j, k) .GT. rho_cutoff) THEN
    2590             :                         my_rho = 0.5_dp*rho_r_ref(1)%array(i, j, k)
    2591             :                      ELSE
    2592             :                         my_rho = rho_cutoff
    2593             :                      END IF
    2594             :                      new_embed_pot(1)%array(i, j, k) = step_len*temp_embed_pot(1)%array(i, j, k)* &
    2595             :                                                        (rho_n_1(1)%array(i, j, k))/my_rho
    2596             :                      new_embed_pot(2)%array(i, j, k) = step_len*temp_embed_pot(2)%array(i, j, k)* &
    2597             :                                                        (rho_n_1(2)%array(i, j, k))/my_rho
    2598             :                   END DO
    2599             :                END DO
    2600             :             END DO
    2601             : !$OMP    END PARALLEL DO
    2602             :          END IF
    2603             : 
    2604           2 :          CALL pw_copy(new_embed_pot(1), embed_pot)
    2605           2 :          CALL pw_axpy(new_embed_pot(2), embed_pot, 1.0_dp)
    2606           2 :          CALL pw_scale(embed_pot, a=0.5_dp)
    2607           2 :          CALL pw_copy(new_embed_pot(1), spin_embed_pot)
    2608           2 :          CALL pw_axpy(new_embed_pot(2), spin_embed_pot, -1.0_dp)
    2609           2 :          CALL pw_scale(spin_embed_pot, a=0.5_dp)
    2610             : 
    2611           6 :          DO i_spin = 1, nspins
    2612           4 :             CALL rho_n_1(i_spin)%release()
    2613           6 :             CALL temp_embed_pot(i_spin)%release()
    2614             :          END DO
    2615           2 :          DEALLOCATE (rho_n_1)
    2616           2 :          DEALLOCATE (temp_embed_pot)
    2617             :       END IF
    2618             : 
    2619           6 :       DO i_spin = 1, nspins
    2620           6 :          CALL new_embed_pot(i_spin)%release()
    2621             :       END DO
    2622             : 
    2623           2 :       DEALLOCATE (new_embed_pot)
    2624             : 
    2625           2 :       CALL timestop(handle)
    2626             : 
    2627           2 :    END SUBROUTINE Leeuwen_Baerends_potential_update
    2628             : 
    2629             : ! **************************************************************************************************
    2630             : !> \brief ...
    2631             : !> \param qs_env ...
    2632             : !> \param rho_r_ref ...
    2633             : !> \param prev_embed_pot ...
    2634             : !> \param prev_spin_embed_pot ...
    2635             : !> \param embed_pot ...
    2636             : !> \param spin_embed_pot ...
    2637             : !> \param diff_rho_r ...
    2638             : !> \param diff_rho_spin ...
    2639             : !> \param v_w_ref ...
    2640             : !> \param i_iter ...
    2641             : !> \param step_len ...
    2642             : !> \param open_shell_embed ...
    2643             : !> \param vw_cutoff ...
    2644             : !> \param vw_smooth_cutoff_range ...
    2645             : ! **************************************************************************************************
    2646           2 :    SUBROUTINE FAB_update(qs_env, rho_r_ref, prev_embed_pot, prev_spin_embed_pot, embed_pot, spin_embed_pot, &
    2647             :                          diff_rho_r, diff_rho_spin, v_w_ref, i_iter, step_len, open_shell_embed, &
    2648             :                          vw_cutoff, vw_smooth_cutoff_range)
    2649             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2650             :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r_ref
    2651             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: prev_embed_pot
    2652             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: prev_spin_embed_pot
    2653             :       TYPE(pw_r3d_rs_type), INTENT(INOUT)                :: embed_pot
    2654             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: spin_embed_pot
    2655             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r, diff_rho_spin
    2656             :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: v_w_ref
    2657             :       INTEGER, INTENT(IN)                                :: i_iter
    2658             :       REAL(KIND=dp)                                      :: step_len
    2659             :       LOGICAL                                            :: open_shell_embed
    2660             :       REAL(KIND=dp)                                      :: vw_cutoff, vw_smooth_cutoff_range
    2661             : 
    2662             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'FAB_update'
    2663             : 
    2664             :       INTEGER                                            :: handle, i_spin, nspins
    2665             :       TYPE(pw_env_type), POINTER                         :: pw_env
    2666             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2667           2 :       TYPE(pw_r3d_rs_type), ALLOCATABLE, DIMENSION(:)    :: new_embed_pot, temp_embed_pot, v_w
    2668           2 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: curr_rho
    2669             : 
    2670           2 :       CALL timeset(routineN, handle)
    2671             : 
    2672             :       ! Update formula: v(n+1) = v(n-1) - v_w(ref) + v_w(n)
    2673             : 
    2674             :       CALL get_qs_env(qs_env=qs_env, &
    2675           2 :                       pw_env=pw_env)
    2676             :       ! Get plane waves pool
    2677           2 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    2678             : 
    2679             :       ! We calculate von Weizsaecker potential for the reference density
    2680             :       ! only at the first iteration
    2681           2 :       IF (i_iter .LE. 1) THEN
    2682           2 :          nspins = SIZE(rho_r_ref)
    2683           2 :          NULLIFY (v_w_ref)
    2684           8 :          ALLOCATE (v_w_ref(nspins))
    2685           4 :          DO i_spin = 1, nspins
    2686           4 :             CALL auxbas_pw_pool%create_pw(v_w_ref(i_spin))
    2687             :          END DO
    2688           2 :          CALL Von_Weizsacker(rho_r_ref, v_w_ref, qs_env, vw_cutoff, vw_smooth_cutoff_range)
    2689             :          ! For the first step previous are set to current
    2690           2 :          CALL pw_copy(embed_pot, prev_embed_pot)
    2691           2 :          CALL pw_axpy(diff_rho_r, embed_pot, 0.5_dp)
    2692           2 :          IF (open_shell_embed) THEN
    2693           0 :             CALL pw_copy(spin_embed_pot, prev_spin_embed_pot)
    2694           0 :             CALL pw_axpy(diff_rho_r, embed_pot, 0.5_dp)
    2695             :          END IF
    2696             : 
    2697             :       ELSE
    2698             : 
    2699             :          ! Reference can be closed shell, but total embedding - open shell:
    2700             :          ! redefine nspins
    2701           0 :          nspins = 1
    2702           0 :          IF (open_shell_embed) nspins = 2
    2703           0 :          ALLOCATE (new_embed_pot(nspins))
    2704           0 :          ALLOCATE (v_w(nspins))
    2705           0 :          NULLIFY (curr_rho)
    2706           0 :          ALLOCATE (curr_rho(nspins))
    2707           0 :          DO i_spin = 1, nspins
    2708           0 :             CALL auxbas_pw_pool%create_pw(new_embed_pot(i_spin))
    2709           0 :             CALL pw_zero(new_embed_pot(i_spin))
    2710             : 
    2711           0 :             CALL auxbas_pw_pool%create_pw(v_w(i_spin))
    2712           0 :             CALL pw_zero(v_w(i_spin))
    2713             : 
    2714           0 :             CALL auxbas_pw_pool%create_pw(curr_rho(i_spin))
    2715           0 :             CALL pw_zero(curr_rho(i_spin))
    2716             :          END DO
    2717             : 
    2718             :          ! Now, deal with the current density
    2719             : 
    2720           0 :          IF (.NOT. open_shell_embed) THEN
    2721             :             ! Reconstruct current density
    2722           0 :             CALL pw_copy(diff_rho_r, curr_rho(1))
    2723           0 :             CALL pw_axpy(rho_r_ref(1), curr_rho(1), 1.0_dp)
    2724             :             ! Compute von Weizsaecker potential
    2725           0 :             CALL Von_Weizsacker(curr_rho, v_w, qs_env, vw_cutoff, vw_smooth_cutoff_range)
    2726             :             ! Compute new embedding potential
    2727           0 :             CALL pw_copy(prev_embed_pot, new_embed_pot(1))
    2728           0 :             CALL pw_axpy(v_w(1), new_embed_pot(1), step_len)
    2729           0 :             CALL pw_axpy(v_w_ref(1), new_embed_pot(1), -step_len)
    2730             :             ! Copy the potentials
    2731             : 
    2732           0 :             CALL pw_copy(embed_pot, prev_embed_pot)
    2733           0 :             CALL pw_copy(new_embed_pot(1), embed_pot)
    2734             : 
    2735             :          ELSE
    2736             :             ! Reconstruct current density
    2737           0 :             CALL pw_copy(diff_rho_r, curr_rho(1))
    2738           0 :             CALL pw_copy(diff_rho_r, curr_rho(2))
    2739           0 :             CALL pw_axpy(diff_rho_spin, curr_rho(1), 1.0_dp)
    2740           0 :             CALL pw_axpy(diff_rho_spin, curr_rho(2), -1.0_dp)
    2741           0 :             CALL pw_scale(curr_rho(1), a=0.5_dp)
    2742           0 :             CALL pw_scale(curr_rho(2), a=0.5_dp)
    2743             : 
    2744           0 :             IF (SIZE(rho_r_ref) .EQ. 1) THEN ! If reference system is closed-shell
    2745           0 :                CALL pw_axpy(rho_r_ref(1), curr_rho(1), 0.5_dp)
    2746           0 :                CALL pw_axpy(rho_r_ref(1), curr_rho(2), 0.5_dp)
    2747             :             ELSE ! If reference system is open-shell
    2748           0 :                CALL pw_axpy(rho_r_ref(1), curr_rho(1), 1.0_dp)
    2749           0 :                CALL pw_axpy(rho_r_ref(2), curr_rho(2), 1.0_dp)
    2750             :             END IF
    2751             : 
    2752             :             ! Compute von Weizsaecker potential
    2753           0 :             CALL Von_Weizsacker(curr_rho, v_w, qs_env, vw_cutoff, vw_smooth_cutoff_range)
    2754             : 
    2755             :             ! Reconstruct corrent spin components of the potential
    2756           0 :             ALLOCATE (temp_embed_pot(nspins))
    2757           0 :             DO i_spin = 1, nspins
    2758           0 :                CALL auxbas_pw_pool%create_pw(temp_embed_pot(i_spin))
    2759           0 :                CALL pw_zero(temp_embed_pot(i_spin))
    2760             :             END DO
    2761           0 :             CALL pw_copy(embed_pot, temp_embed_pot(1))
    2762           0 :             CALL pw_copy(embed_pot, temp_embed_pot(2))
    2763           0 :             CALL pw_axpy(spin_embed_pot, temp_embed_pot(1), 1.0_dp)
    2764           0 :             CALL pw_axpy(spin_embed_pot, temp_embed_pot(2), -1.0_dp)
    2765             : 
    2766             :             ! Compute new embedding potential
    2767           0 :             IF (SIZE(v_w_ref) .EQ. 1) THEN ! Reference system is closed-shell
    2768           0 :                CALL pw_copy(temp_embed_pot(1), new_embed_pot(1))
    2769           0 :                CALL pw_axpy(v_w(1), new_embed_pot(1), 0.5_dp*step_len)
    2770           0 :                CALL pw_axpy(v_w_ref(1), new_embed_pot(1), -0.5_dp*step_len)
    2771             : 
    2772           0 :                CALL pw_copy(temp_embed_pot(2), new_embed_pot(2))
    2773           0 :                CALL pw_axpy(v_w(2), new_embed_pot(2), 0.5_dp)
    2774           0 :                CALL pw_axpy(v_w_ref(1), new_embed_pot(2), -0.5_dp)
    2775             : 
    2776             :             ELSE ! Reference system is open-shell
    2777             : 
    2778           0 :                DO i_spin = 1, nspins
    2779           0 :                   CALL pw_copy(temp_embed_pot(i_spin), new_embed_pot(i_spin))
    2780           0 :                   CALL pw_axpy(v_w(1), new_embed_pot(i_spin), step_len)
    2781           0 :                   CALL pw_axpy(v_w_ref(i_spin), new_embed_pot(i_spin), -step_len)
    2782             :                END DO
    2783             :             END IF
    2784             : 
    2785             :             ! Update embedding potentials
    2786           0 :             CALL pw_copy(embed_pot, prev_embed_pot)
    2787           0 :             CALL pw_copy(spin_embed_pot, prev_spin_embed_pot)
    2788             : 
    2789           0 :             CALL pw_copy(new_embed_pot(1), embed_pot)
    2790           0 :             CALL pw_axpy(new_embed_pot(2), embed_pot, 1.0_dp)
    2791           0 :             CALL pw_scale(embed_pot, a=0.5_dp)
    2792           0 :             CALL pw_copy(new_embed_pot(1), spin_embed_pot)
    2793           0 :             CALL pw_axpy(new_embed_pot(2), spin_embed_pot, -1.0_dp)
    2794           0 :             CALL pw_scale(spin_embed_pot, a=0.5_dp)
    2795             : 
    2796           0 :             DO i_spin = 1, nspins
    2797           0 :                CALL temp_embed_pot(i_spin)%release()
    2798             :             END DO
    2799           0 :             DEALLOCATE (temp_embed_pot)
    2800             : 
    2801             :          END IF
    2802             : 
    2803           0 :          DO i_spin = 1, nspins
    2804           0 :             CALL curr_rho(i_spin)%release()
    2805           0 :             CALL new_embed_pot(i_spin)%release()
    2806           0 :             CALL v_w(i_spin)%release()
    2807             :          END DO
    2808             : 
    2809           0 :          DEALLOCATE (new_embed_pot)
    2810           0 :          DEALLOCATE (v_w)
    2811           0 :          DEALLOCATE (curr_rho)
    2812             : 
    2813             :       END IF
    2814             : 
    2815           2 :       CALL timestop(handle)
    2816             : 
    2817           4 :    END SUBROUTINE FAB_update
    2818             : 
    2819             : ! **************************************************************************************************
    2820             : !> \brief ...
    2821             : !> \param rho_r ...
    2822             : !> \param v_w ...
    2823             : !> \param qs_env ...
    2824             : !> \param vw_cutoff ...
    2825             : !> \param vw_smooth_cutoff_range ...
    2826             : ! **************************************************************************************************
    2827           2 :    SUBROUTINE Von_Weizsacker(rho_r, v_w, qs_env, vw_cutoff, vw_smooth_cutoff_range)
    2828             :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r
    2829             :       TYPE(pw_r3d_rs_type), DIMENSION(:), INTENT(IN)     :: v_w
    2830             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2831             :       REAL(KIND=dp), INTENT(IN)                          :: vw_cutoff, vw_smooth_cutoff_range
    2832             : 
    2833             :       REAL(KIND=dp), PARAMETER                           :: one_4 = 0.25_dp, one_8 = 0.125_dp
    2834             : 
    2835             :       INTEGER                                            :: i, i_spin, j, k, nspins
    2836             :       INTEGER, DIMENSION(3)                              :: lb, ub
    2837             :       REAL(KIND=dp)                                      :: density_smooth_cut_range, my_rho, &
    2838             :                                                             rho_cutoff
    2839           2 :       REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: rhoa, rhob
    2840           2 :       TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER        :: rho_g
    2841             :       TYPE(pw_env_type), POINTER                         :: pw_env
    2842             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2843           2 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: tau
    2844             :       TYPE(section_vals_type), POINTER                   :: input, xc_section
    2845             :       TYPE(xc_rho_cflags_type)                           :: needs
    2846             :       TYPE(xc_rho_set_type)                              :: rho_set
    2847             : 
    2848           2 :       rho_cutoff = EPSILON(0.0_dp)
    2849             : 
    2850           2 :       nspins = SIZE(rho_r)
    2851             : 
    2852           2 :       NULLIFY (xc_section)
    2853             : 
    2854             :       CALL get_qs_env(qs_env=qs_env, &
    2855             :                       pw_env=pw_env, &
    2856           2 :                       input=input)
    2857             : 
    2858             :       ! Get plane waves pool
    2859           2 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    2860             : 
    2861             :       ! get some of the grids ready
    2862           2 :       NULLIFY (rho_g)
    2863           8 :       ALLOCATE (rho_g(nspins))
    2864           4 :       DO i_spin = 1, nspins
    2865           2 :          CALL auxbas_pw_pool%create_pw(rho_g(i_spin))
    2866           4 :          CALL pw_transfer(rho_r(i_spin), rho_g(i_spin))
    2867             :       END DO
    2868             : 
    2869           2 :       xc_section => section_vals_get_subs_vals(input, "DFT%XC")
    2870             : 
    2871             :       CALL xc_rho_set_create(rho_set, &
    2872             :                              rho_r(1)%pw_grid%bounds_local, &
    2873             :                              rho_cutoff=section_get_rval(xc_section, "density_cutoff"), &
    2874             :                              drho_cutoff=section_get_rval(xc_section, "gradient_cutoff"), &
    2875           2 :                              tau_cutoff=section_get_rval(xc_section, "tau_cutoff"))
    2876             : 
    2877           2 :       CALL xc_rho_cflags_setall(needs, .FALSE.)
    2878             : 
    2879           2 :       IF (nspins .EQ. 2) THEN
    2880           0 :          needs%rho_spin = .TRUE.
    2881           0 :          needs%norm_drho_spin = .TRUE.
    2882           0 :          needs%laplace_rho_spin = .TRUE.
    2883             :       ELSE
    2884           2 :          needs%rho = .TRUE.
    2885           2 :          needs%norm_drho = .TRUE.
    2886           2 :          needs%laplace_rho = .TRUE.
    2887             :       END IF
    2888             : 
    2889             :       CALL xc_rho_set_update(rho_set, rho_r, rho_g, tau, needs, &
    2890             :                              section_get_ival(xc_section, "XC_GRID%XC_DERIV"), &
    2891             :                              section_get_ival(xc_section, "XC_GRID%XC_SMOOTH_RHO"), &
    2892           2 :                              auxbas_pw_pool)
    2893             : 
    2894             :       CALL section_vals_val_get(xc_section, "DENSITY_CUTOFF", &
    2895           2 :                                 r_val=rho_cutoff)
    2896             :       CALL section_vals_val_get(xc_section, "DENSITY_SMOOTH_CUTOFF_RANGE", &
    2897           2 :                                 r_val=density_smooth_cut_range)
    2898             : 
    2899           8 :       lb(1:3) = rho_r(1)%pw_grid%bounds_local(1, 1:3)
    2900           8 :       ub(1:3) = rho_r(1)%pw_grid%bounds_local(2, 1:3)
    2901             : 
    2902           2 :       IF (nspins .EQ. 2) THEN
    2903             : !$OMP    PARALLEL DO DEFAULT(NONE) &
    2904             : !$OMP                PRIVATE(i,j,k, my_rho) &
    2905           0 : !$OMP                SHARED(v_w, rho_r, rho_set, lb, ub, rho_cutoff)
    2906             :          DO k = lb(3), ub(3)
    2907             :             DO j = lb(2), ub(2)
    2908             :                DO i = lb(1), ub(1)
    2909             :                   IF (rho_r(1)%array(i, j, k) .GT. rho_cutoff) THEN
    2910             :                      my_rho = rho_r(1)%array(i, j, k)
    2911             :                   ELSE
    2912             :                      my_rho = rho_cutoff
    2913             :                   END IF
    2914             :                   v_w(1)%array(i, j, k) = one_8*rho_set%norm_drhoa(i, j, k)**2/my_rho**2 - &
    2915             :                                           one_4*rho_set%laplace_rhoa(i, j, k)/my_rho
    2916             : 
    2917             :                   IF (rho_r(2)%array(i, j, k) .GT. rho_cutoff) THEN
    2918             :                      my_rho = rho_r(2)%array(i, j, k)
    2919             :                   ELSE
    2920             :                      my_rho = rho_cutoff
    2921             :                   END IF
    2922             :                   v_w(2)%array(i, j, k) = one_8*rho_set%norm_drhob(i, j, k)**2/my_rho**2 - &
    2923             :                                           one_4*rho_set%laplace_rhob(i, j, k)/my_rho
    2924             :                END DO
    2925             :             END DO
    2926             :          END DO
    2927             : !$OMP    END PARALLEL DO
    2928             :       ELSE
    2929             : !$OMP    PARALLEL DO DEFAULT(NONE) &
    2930             : !$OMP                PRIVATE(i,j,k, my_rho) &
    2931           2 : !$OMP                SHARED(v_w, rho_r, rho_set, lb, ub, rho_cutoff)
    2932             :          DO k = lb(3), ub(3)
    2933             :             DO j = lb(2), ub(2)
    2934             :                DO i = lb(1), ub(1)
    2935             :                   IF (rho_r(1)%array(i, j, k) .GT. rho_cutoff) THEN
    2936             :                      my_rho = rho_r(1)%array(i, j, k)
    2937             :                      v_w(1)%array(i, j, k) = one_8*rho_set%norm_drho(i, j, k)**2/my_rho**2 - &
    2938             :                                              one_4*rho_set%laplace_rho(i, j, k)/my_rho
    2939             :                   ELSE
    2940             :                      v_w(1)%array(i, j, k) = 0.0_dp
    2941             :                   END IF
    2942             :                END DO
    2943             :             END DO
    2944             :          END DO
    2945             : !$OMP    END PARALLEL DO
    2946             : 
    2947             :       END IF
    2948             : 
    2949             :       ! Smoothen the von Weizsaecker potential
    2950           2 :       IF (nspins == 2) THEN
    2951           0 :          density_smooth_cut_range = 0.5_dp*density_smooth_cut_range
    2952           0 :          rho_cutoff = 0.5_dp*rho_cutoff
    2953             :       END IF
    2954           4 :       DO i_spin = 1, nspins
    2955             :          CALL smooth_cutoff(pot=v_w(i_spin)%array, rho=rho_r(i_spin)%array, rhoa=rhoa, rhob=rhob, &
    2956             :                             rho_cutoff=vw_cutoff, &
    2957           4 :                             rho_smooth_cutoff_range=vw_smooth_cutoff_range)
    2958             :       END DO
    2959             : 
    2960           2 :       CALL xc_rho_set_release(rho_set, pw_pool=auxbas_pw_pool)
    2961             : 
    2962           4 :       DO i_spin = 1, nspins
    2963           4 :          CALL rho_g(i_spin)%release()
    2964             :       END DO
    2965           2 :       DEALLOCATE (rho_g)
    2966             : 
    2967          46 :    END SUBROUTINE Von_Weizsacker
    2968             : 
    2969             : ! **************************************************************************************************
    2970             : !> \brief ...
    2971             : !> \param diff_rho_r ...
    2972             : !> \return ...
    2973             : ! **************************************************************************************************
    2974         222 :    FUNCTION max_dens_diff(diff_rho_r) RESULT(total_max_diff)
    2975             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r
    2976             :       REAL(KIND=dp)                                      :: total_max_diff
    2977             : 
    2978             :       INTEGER                                            :: size_x, size_y, size_z
    2979             :       REAL(KIND=dp)                                      :: max_diff
    2980         222 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: grid_3d
    2981             : 
    2982             :       !, i_x, i_y, i_z
    2983             : 
    2984             :       ! Get the sizes
    2985         222 :       size_x = SIZE(diff_rho_r%array, 1)
    2986         222 :       size_y = SIZE(diff_rho_r%array, 2)
    2987         222 :       size_z = SIZE(diff_rho_r%array, 3)
    2988             : 
    2989             :       ! Allocate the density
    2990        1110 :       ALLOCATE (grid_3d(size_x, size_y, size_z))
    2991             : 
    2992             :       ! Copy density
    2993     4589181 :       grid_3d(:, :, :) = diff_rho_r%array(:, :, :)
    2994             : 
    2995             :       ! Find the maximum absolute value
    2996     4589181 :       max_diff = MAXVAL(ABS(grid_3d))
    2997         222 :       total_max_diff = max_diff
    2998         222 :       CALL diff_rho_r%pw_grid%para%group%max(total_max_diff)
    2999             : 
    3000             :       ! Deallocate the density
    3001         222 :       DEALLOCATE (grid_3d)
    3002             : 
    3003         222 :    END FUNCTION max_dens_diff
    3004             : 
    3005             : ! **************************************************************************************************
    3006             : !> \brief Prints a cube for the (rho_A + rho_B - rho_ref) to be minimized in embedding
    3007             : !> \param diff_rho_r ...
    3008             : !> \param i_iter ...
    3009             : !> \param qs_env ...
    3010             : !> \param final_one ...
    3011             : !> \author Vladimir Rybkin
    3012             : ! **************************************************************************************************
    3013          48 :    SUBROUTINE print_rho_diff(diff_rho_r, i_iter, qs_env, final_one)
    3014             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r
    3015             :       INTEGER, INTENT(IN)                                :: i_iter
    3016             :       TYPE(qs_environment_type), INTENT(IN), POINTER     :: qs_env
    3017             :       LOGICAL, INTENT(IN)                                :: final_one
    3018             : 
    3019             :       CHARACTER(LEN=default_path_length)                 :: filename, my_pos_cube, title
    3020             :       INTEGER                                            :: unit_nr
    3021             :       TYPE(cp_logger_type), POINTER                      :: logger
    3022             :       TYPE(particle_list_type), POINTER                  :: particles
    3023             :       TYPE(qs_subsys_type), POINTER                      :: subsys
    3024             :       TYPE(section_vals_type), POINTER                   :: dft_section, input
    3025             : 
    3026          48 :       NULLIFY (subsys, input)
    3027             : 
    3028             :       CALL get_qs_env(qs_env=qs_env, &
    3029             :                       subsys=subsys, &
    3030          48 :                       input=input)
    3031          48 :       dft_section => section_vals_get_subs_vals(input, "DFT")
    3032          48 :       CALL qs_subsys_get(subsys, particles=particles)
    3033             : 
    3034          48 :       logger => cp_get_default_logger()
    3035          48 :       IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3036             :                                            "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF"), cp_p_file)) THEN
    3037          10 :          my_pos_cube = "REWIND"
    3038          10 :          IF (.NOT. final_one) THEN
    3039          10 :             WRITE (filename, '(a5,I3.3,a1,I1.1)') "DIFF_", i_iter
    3040             :          ELSE
    3041           0 :             WRITE (filename, '(a5,I3.3,a1,I1.1)') "DIFF"
    3042             :          END IF
    3043             :          unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF", &
    3044             :                                         extension=".cube", middle_name=TRIM(filename), file_position=my_pos_cube, &
    3045          10 :                                         log_filename=.FALSE.)
    3046             : 
    3047          10 :          WRITE (title, *) "EMBEDDING DENSITY DIFFERENCE ", " optimization step ", i_iter
    3048             :          CALL cp_pw_to_cube(diff_rho_r, unit_nr, title, particles=particles, &
    3049          10 :                             stride=section_get_ivals(dft_section, "QS%OPT_EMBED%EMBED_DENS_DIFF%STRIDE"))
    3050             :          CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3051          10 :                                            "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF")
    3052             :       END IF
    3053             : 
    3054          48 :    END SUBROUTINE print_rho_diff
    3055             : 
    3056             : ! **************************************************************************************************
    3057             : !> \brief Prints a cube for the (spin_rho_A + spin_rho_B - spin_rho_ref) to be minimized in embedding
    3058             : !> \param spin_diff_rho_r ...
    3059             : !> \param i_iter ...
    3060             : !> \param qs_env ...
    3061             : !> \param final_one ...
    3062             : !> \author Vladimir Rybkin
    3063             : ! **************************************************************************************************
    3064          38 :    SUBROUTINE print_rho_spin_diff(spin_diff_rho_r, i_iter, qs_env, final_one)
    3065             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: spin_diff_rho_r
    3066             :       INTEGER, INTENT(IN)                                :: i_iter
    3067             :       TYPE(qs_environment_type), INTENT(IN), POINTER     :: qs_env
    3068             :       LOGICAL, INTENT(IN)                                :: final_one
    3069             : 
    3070             :       CHARACTER(LEN=default_path_length)                 :: filename, my_pos_cube, title
    3071             :       INTEGER                                            :: unit_nr
    3072             :       TYPE(cp_logger_type), POINTER                      :: logger
    3073             :       TYPE(particle_list_type), POINTER                  :: particles
    3074             :       TYPE(qs_subsys_type), POINTER                      :: subsys
    3075             :       TYPE(section_vals_type), POINTER                   :: dft_section, input
    3076             : 
    3077          38 :       NULLIFY (subsys, input)
    3078             : 
    3079             :       CALL get_qs_env(qs_env=qs_env, &
    3080             :                       subsys=subsys, &
    3081          38 :                       input=input)
    3082          38 :       dft_section => section_vals_get_subs_vals(input, "DFT")
    3083          38 :       CALL qs_subsys_get(subsys, particles=particles)
    3084             : 
    3085          38 :       logger => cp_get_default_logger()
    3086          38 :       IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3087             :                                            "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF"), cp_p_file)) THEN
    3088           0 :          my_pos_cube = "REWIND"
    3089           0 :          IF (.NOT. final_one) THEN
    3090           0 :             WRITE (filename, '(a5,I3.3,a1,I1.1)') "SPIN_DIFF_", i_iter
    3091             :          ELSE
    3092           0 :             WRITE (filename, '(a9,I3.3,a1,I1.1)') "SPIN_DIFF"
    3093             :          END IF
    3094             :          unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF", &
    3095             :                                         extension=".cube", middle_name=TRIM(filename), file_position=my_pos_cube, &
    3096           0 :                                         log_filename=.FALSE.)
    3097             : 
    3098           0 :          WRITE (title, *) "EMBEDDING SPIN DENSITY DIFFERENCE ", " optimization step ", i_iter
    3099             :          CALL cp_pw_to_cube(spin_diff_rho_r, unit_nr, title, particles=particles, &
    3100           0 :                             stride=section_get_ivals(dft_section, "QS%OPT_EMBED%EMBED_DENS_DIFF%STRIDE"))
    3101             :          CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3102           0 :                                            "DFT%QS%OPT_EMBED%EMBED_DENS_DIFF")
    3103             :       END IF
    3104             : 
    3105          38 :    END SUBROUTINE print_rho_spin_diff
    3106             : ! **************************************************************************************************
    3107             : !> \brief Print embedding potential as a cube and as a binary (for restarting)
    3108             : !> \param qs_env ...
    3109             : !> \param dimen_aux ...
    3110             : !> \param embed_pot_coef ...
    3111             : !> \param embed_pot ...
    3112             : !> \param i_iter ...
    3113             : !> \param embed_pot_spin ...
    3114             : !> \param open_shell_embed ...
    3115             : !> \param grid_opt ...
    3116             : !> \param final_one ...
    3117             : ! **************************************************************************************************
    3118          72 :    SUBROUTINE print_embed_restart(qs_env, dimen_aux, embed_pot_coef, embed_pot, i_iter, &
    3119             :                                   embed_pot_spin, open_shell_embed, grid_opt, final_one)
    3120             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3121             :       INTEGER                                            :: dimen_aux
    3122             :       TYPE(cp_fm_type), INTENT(IN), POINTER              :: embed_pot_coef
    3123             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: embed_pot
    3124             :       INTEGER                                            :: i_iter
    3125             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: embed_pot_spin
    3126             :       LOGICAL                                            :: open_shell_embed, grid_opt, final_one
    3127             : 
    3128             :       CHARACTER(LEN=default_path_length)                 :: filename, my_pos_cube, title
    3129             :       INTEGER                                            :: unit_nr
    3130             :       TYPE(cp_logger_type), POINTER                      :: logger
    3131             :       TYPE(particle_list_type), POINTER                  :: particles
    3132             :       TYPE(qs_subsys_type), POINTER                      :: subsys
    3133             :       TYPE(section_vals_type), POINTER                   :: dft_section, input
    3134             : 
    3135          72 :       NULLIFY (input)
    3136             :       CALL get_qs_env(qs_env=qs_env, subsys=subsys, &
    3137          72 :                       input=input)
    3138             : 
    3139             :       ! First we print an unformatted file
    3140          72 :       IF (.NOT. grid_opt) THEN ! Only for finite basis optimization
    3141          44 :          logger => cp_get_default_logger()
    3142          44 :          IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3143             :                                               "DFT%QS%OPT_EMBED%EMBED_POT_VECTOR"), cp_p_file)) THEN
    3144          44 :             IF (.NOT. final_one) THEN
    3145          30 :                WRITE (filename, '(a10,I3.3)') "embed_pot_", i_iter
    3146             :             ELSE
    3147          14 :                WRITE (filename, '(a10,I3.3)') "embed_pot"
    3148             :             END IF
    3149             :             unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%EMBED_POT_VECTOR", extension=".wfn", &
    3150          44 :                                            file_form="UNFORMATTED", middle_name=TRIM(filename), file_position="REWIND")
    3151          44 :             IF (unit_nr > 0) THEN
    3152          22 :                WRITE (unit_nr) dimen_aux
    3153             :             END IF
    3154          44 :             CALL cp_fm_write_unformatted(embed_pot_coef, unit_nr)
    3155          44 :             IF (unit_nr > 0) THEN
    3156          22 :                CALL close_file(unit_nr)
    3157             :             END IF
    3158             :          END IF
    3159             :       END IF
    3160             : 
    3161             :       ! Second, cube files
    3162          72 :       dft_section => section_vals_get_subs_vals(input, "DFT")
    3163          72 :       CALL qs_subsys_get(subsys, particles=particles)
    3164             : 
    3165          72 :       logger => cp_get_default_logger()
    3166          72 :       IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3167             :                                            "DFT%QS%OPT_EMBED%EMBED_POT_CUBE"), cp_p_file)) THEN
    3168          32 :          my_pos_cube = "REWIND"
    3169          32 :          IF (.NOT. final_one) THEN
    3170          20 :             WRITE (filename, '(a10,I3.3)') "embed_pot_", i_iter
    3171             :          ELSE
    3172          12 :             WRITE (filename, '(a10,I3.3)') "embed_pot"
    3173             :          END IF
    3174             :          unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%EMBED_POT_CUBE", &
    3175             :                                         extension=".cube", middle_name=TRIM(filename), file_position=my_pos_cube, &
    3176          32 :                                         log_filename=.FALSE.)
    3177             : 
    3178          32 :          WRITE (title, *) "EMBEDDING POTENTIAL at optimization step ", i_iter
    3179          32 :          CALL cp_pw_to_cube(embed_pot, unit_nr, title, particles=particles)
    3180             : !, &
    3181             : !                            stride=section_get_ivals(dft_section, "QS%OPT_EMBED%EMBED_POT_CUBE%STRIDE"))
    3182             :          CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3183          32 :                                            "DFT%QS%OPT_EMBED%EMBED_POT_CUBE")
    3184          32 :          IF (open_shell_embed) THEN ! Print spin part of the embedding potential
    3185          16 :             my_pos_cube = "REWIND"
    3186          16 :             IF (.NOT. final_one) THEN
    3187          10 :                WRITE (filename, '(a15,I3.3)') "spin_embed_pot_", i_iter
    3188             :             ELSE
    3189           6 :                WRITE (filename, '(a15,I3.3)') "spin_embed_pot"
    3190             :             END IF
    3191             :             unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%EMBED_POT_CUBE", &
    3192             :                                            extension=".cube", middle_name=TRIM(filename), file_position=my_pos_cube, &
    3193          16 :                                            log_filename=.FALSE.)
    3194             : 
    3195          16 :             WRITE (title, *) "SPIN EMBEDDING POTENTIAL at optimization step ", i_iter
    3196          16 :             CALL cp_pw_to_cube(embed_pot_spin, unit_nr, title, particles=particles)
    3197             : !,  &
    3198             : !                               stride=section_get_ivals(dft_section, "QS%OPT_EMBED%EMBED_POT_CUBE%STRIDE"))
    3199             :             CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3200          16 :                                               "DFT%QS%OPT_EMBED%EMBED_POT_CUBE")
    3201             :          END IF
    3202             :       END IF
    3203             : 
    3204          72 :    END SUBROUTINE print_embed_restart
    3205             : 
    3206             : ! **************************************************************************************************
    3207             : !> \brief Prints a volumetric file: X Y Z value for interfacing with external programs.
    3208             : !> \param qs_env ...
    3209             : !> \param embed_pot ...
    3210             : !> \param embed_pot_spin ...
    3211             : !> \param i_iter ...
    3212             : !> \param open_shell_embed ...
    3213             : !> \param final_one ...
    3214             : !> \param qs_env_cluster ...
    3215             : ! **************************************************************************************************
    3216          72 :    SUBROUTINE print_pot_simple_grid(qs_env, embed_pot, embed_pot_spin, i_iter, open_shell_embed, &
    3217             :                                     final_one, qs_env_cluster)
    3218             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3219             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: embed_pot
    3220             :       TYPE(pw_r3d_rs_type), INTENT(IN), POINTER          :: embed_pot_spin
    3221             :       INTEGER                                            :: i_iter
    3222             :       LOGICAL                                            :: open_shell_embed, final_one
    3223             :       TYPE(qs_environment_type), POINTER                 :: qs_env_cluster
    3224             : 
    3225             :       CHARACTER(LEN=default_path_length)                 :: filename
    3226             :       INTEGER                                            :: my_units, unit_nr
    3227             :       LOGICAL                                            :: angstrom, bohr
    3228             :       TYPE(cp_logger_type), POINTER                      :: logger
    3229             :       TYPE(pw_env_type), POINTER                         :: pw_env
    3230             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    3231             :       TYPE(pw_r3d_rs_type)                               :: pot_alpha, pot_beta
    3232             :       TYPE(section_vals_type), POINTER                   :: dft_section, input
    3233             : 
    3234          72 :       NULLIFY (input)
    3235          72 :       CALL get_qs_env(qs_env=qs_env, input=input, pw_env=pw_env)
    3236             : 
    3237             :       ! Second, cube files
    3238          72 :       dft_section => section_vals_get_subs_vals(input, "DFT")
    3239             : 
    3240          72 :       NULLIFY (logger)
    3241          72 :       logger => cp_get_default_logger()
    3242          72 :       IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3243             :                                            "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID"), cp_p_file)) THEN
    3244             : 
    3245             :          ! Figure out the units
    3246          16 :          angstrom = .FALSE.
    3247          16 :          bohr = .TRUE.
    3248          16 :          CALL section_vals_val_get(dft_section, "QS%OPT_EMBED%WRITE_SIMPLE_GRID%UNITS", i_val=my_units)
    3249             :          SELECT CASE (my_units)
    3250             :          CASE (embed_grid_bohr)
    3251          16 :             bohr = .TRUE.
    3252          16 :             angstrom = .FALSE.
    3253             :          CASE (embed_grid_angstrom)
    3254             :             bohr = .FALSE.
    3255             :             angstrom = .TRUE.
    3256             :          CASE DEFAULT
    3257             :             bohr = .TRUE.
    3258             :             angstrom = .FALSE.
    3259             :          END SELECT
    3260             : 
    3261             :          ! Get alpha and beta potentials
    3262             :          ! Prepare plane-waves pool
    3263          16 :          CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool)
    3264             : 
    3265             :          ! Create embedding potential and set to zero
    3266          16 :          CALL auxbas_pw_pool%create_pw(pot_alpha)
    3267          16 :          CALL pw_zero(pot_alpha)
    3268             : 
    3269          16 :          CALL pw_copy(embed_pot, pot_alpha)
    3270             : 
    3271          16 :          IF (open_shell_embed) THEN
    3272           0 :             CALL auxbas_pw_pool%create_pw(pot_beta)
    3273           0 :             CALL pw_copy(embed_pot, pot_beta)
    3274             :             ! Add spin potential to the alpha, and subtract from the beta part
    3275           0 :             CALL pw_axpy(embed_pot_spin, pot_alpha, 1.0_dp)
    3276           0 :             CALL pw_axpy(embed_pot_spin, pot_beta, -1.0_dp)
    3277             :          END IF
    3278             : 
    3279          16 :          IF (.NOT. final_one) THEN
    3280          10 :             WRITE (filename, '(a10,I3.3)') "embed_pot_", i_iter
    3281             :          ELSE
    3282           6 :             WRITE (filename, '(a10,I3.3)') "embed_pot"
    3283             :          END IF
    3284             :          unit_nr = cp_print_key_unit_nr(logger, input, "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID", extension=".dat", &
    3285          16 :                                         middle_name=TRIM(filename), file_form="FORMATTED", file_position="REWIND")
    3286             : 
    3287          16 :          IF (open_shell_embed) THEN ! Print spin part of the embedding potential
    3288             :             CALL cp_pw_to_simple_volumetric(pw=pot_alpha, unit_nr=unit_nr, &
    3289             :                                             stride=section_get_ivals(dft_section, "QS%OPT_EMBED%WRITE_SIMPLE_GRID%STRIDE"), &
    3290           0 :                                             pw2=pot_beta)
    3291             :          ELSE
    3292             :             CALL cp_pw_to_simple_volumetric(pot_alpha, unit_nr, &
    3293          16 :                                             stride=section_get_ivals(dft_section, "QS%OPT_EMBED%WRITE_SIMPLE_GRID%STRIDE"))
    3294             :          END IF
    3295             : 
    3296             :          CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3297          16 :                                            "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID")
    3298             :          ! Release structures
    3299          16 :          CALL pot_alpha%release()
    3300          16 :          IF (open_shell_embed) THEN
    3301           0 :             CALL pot_beta%release()
    3302             :          END IF
    3303             : 
    3304             :       END IF
    3305             : 
    3306             :       ! Fold the coordinates and write into separate file: needed to have the grid correspond to coordinates
    3307             :       ! Needed for external software.
    3308          72 :       CALL print_folded_coordinates(qs_env_cluster, input)
    3309             : 
    3310          72 :    END SUBROUTINE print_pot_simple_grid
    3311             : 
    3312             : ! **************************************************************************************************
    3313             : !> \brief ...
    3314             : !> \param qs_env ...
    3315             : !> \param input ...
    3316             : ! **************************************************************************************************
    3317          72 :    SUBROUTINE print_folded_coordinates(qs_env, input)
    3318             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3319             :       TYPE(section_vals_type), POINTER                   :: input
    3320             : 
    3321          72 :       CHARACTER(LEN=2), ALLOCATABLE, DIMENSION(:)        :: particles_el
    3322             :       CHARACTER(LEN=default_path_length)                 :: filename
    3323             :       INTEGER                                            :: iat, n, unit_nr
    3324          72 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: particles_r
    3325             :       REAL(KIND=dp), DIMENSION(3)                        :: center, r_pbc, s
    3326             :       TYPE(cell_type), POINTER                           :: cell
    3327             :       TYPE(cp_logger_type), POINTER                      :: logger
    3328             :       TYPE(particle_list_type), POINTER                  :: particles
    3329             :       TYPE(qs_subsys_type), POINTER                      :: subsys
    3330             : 
    3331          72 :       NULLIFY (logger)
    3332          72 :       logger => cp_get_default_logger()
    3333          72 :       IF (BTEST(cp_print_key_should_output(logger%iter_info, input, &
    3334             :                                            "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID/FOLD_COORD"), cp_p_file)) THEN
    3335          16 :          CALL get_qs_env(qs_env=qs_env, cell=cell, subsys=subsys)
    3336          16 :          CALL qs_subsys_get(subsys=subsys, particles=particles)
    3337             : 
    3338             :          ! Prepare the file
    3339          16 :          WRITE (filename, '(a14)') "folded_cluster"
    3340             :          unit_nr = cp_print_key_unit_nr(logger, input, &
    3341             :                                         "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID/FOLD_COORD", extension=".dat", &
    3342          16 :                                         middle_name=TRIM(filename), file_form="FORMATTED", file_position="REWIND")
    3343          16 :          IF (unit_nr > 0) THEN
    3344             : 
    3345           8 :             n = particles%n_els
    3346          16 :             ALLOCATE (particles_el(n))
    3347          24 :             ALLOCATE (particles_r(3, n))
    3348          24 :             DO iat = 1, n
    3349          16 :                CALL get_atomic_kind(particles%els(iat)%atomic_kind, element_symbol=particles_el(iat))
    3350          72 :                particles_r(:, iat) = particles%els(iat)%r(:)
    3351             :             END DO
    3352             : 
    3353             :             ! Fold the coordinates
    3354          32 :             center(:) = cell%hmat(:, 1)/2.0_dp + cell%hmat(:, 2)/2.0_dp + cell%hmat(:, 3)/2.0_dp
    3355             : 
    3356             :             ! Print folded coordinates to file
    3357          24 :             DO iat = 1, SIZE(particles_el)
    3358          64 :                r_pbc(:) = particles_r(:, iat) - center
    3359         208 :                s = MATMUL(cell%h_inv, r_pbc)
    3360          64 :                s = s - ANINT(s)
    3361         208 :                r_pbc = MATMUL(cell%hmat, s)
    3362          64 :                r_pbc = r_pbc + center
    3363          24 :                WRITE (unit_nr, '(a4,4f12.6)') particles_el(iat), r_pbc(:)
    3364             :             END DO
    3365             : 
    3366             :             CALL cp_print_key_finished_output(unit_nr, logger, input, &
    3367           8 :                                               "DFT%QS%OPT_EMBED%WRITE_SIMPLE_GRID/FOLD_COORD")
    3368             : 
    3369           8 :             DEALLOCATE (particles_el)
    3370           8 :             DEALLOCATE (particles_r)
    3371             :          END IF
    3372             : 
    3373             :       END IF ! Should output
    3374             : 
    3375          72 :    END SUBROUTINE print_folded_coordinates
    3376             : 
    3377             : ! **************************************************************************************************
    3378             : !> \brief ...
    3379             : !> \param output_unit ...
    3380             : !> \param step_num ...
    3381             : !> \param opt_embed ...
    3382             : ! **************************************************************************************************
    3383          48 :    SUBROUTINE print_emb_opt_info(output_unit, step_num, opt_embed)
    3384             :       INTEGER                                            :: output_unit, step_num
    3385             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    3386             : 
    3387          48 :       IF (output_unit > 0) THEN
    3388             :          WRITE (UNIT=output_unit, FMT="(/,T2,8('-'),A,I5,1X,12('-'))") &
    3389          24 :             "  Optimize embedding potential info at step = ", step_num
    3390             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3391          24 :             " Functional value         = ", opt_embed%w_func(step_num)
    3392          24 :          IF (step_num .GT. 1) THEN
    3393             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3394          12 :                " Real energy change         = ", opt_embed%w_func(step_num) - &
    3395          24 :                opt_embed%w_func(step_num - 1)
    3396             : 
    3397             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3398          12 :                " Step size                  = ", opt_embed%step_len
    3399             : 
    3400             :          END IF
    3401             : 
    3402             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3403          24 :             " Trust radius               = ", opt_embed%trust_rad
    3404             : 
    3405          24 :          WRITE (UNIT=output_unit, FMT="(T2,51('-'))")
    3406             :       END IF
    3407             : 
    3408          48 :    END SUBROUTINE print_emb_opt_info
    3409             : 
    3410             : ! **************************************************************************************************
    3411             : !> \brief ...
    3412             : !> \param opt_embed ...
    3413             : !> \param force_env ...
    3414             : !> \param subsys_num ...
    3415             : ! **************************************************************************************************
    3416          96 :    SUBROUTINE get_prev_density(opt_embed, force_env, subsys_num)
    3417             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    3418             :       TYPE(force_env_type), POINTER                      :: force_env
    3419             :       INTEGER                                            :: subsys_num
    3420             : 
    3421             :       INTEGER                                            :: i_dens_start, i_spin, nspins
    3422          96 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r
    3423             :       TYPE(qs_rho_type), POINTER                         :: rho
    3424             : 
    3425          96 :       NULLIFY (rho_r, rho)
    3426          96 :       CALL get_qs_env(force_env%qs_env, rho=rho)
    3427          96 :       CALL qs_rho_get(rho_struct=rho, rho_r=rho_r)
    3428             : 
    3429          96 :       nspins = opt_embed%all_nspins(subsys_num)
    3430             : 
    3431         240 :       i_dens_start = SUM(opt_embed%all_nspins(1:subsys_num)) - nspins + 1
    3432             : 
    3433         244 :       DO i_spin = 1, nspins
    3434             :          opt_embed%prev_subsys_dens(i_dens_start + i_spin - 1)%array(:, :, :) = &
    3435     3059550 :             rho_r(i_spin)%array(:, :, :)
    3436             :       END DO
    3437             : 
    3438          96 :    END SUBROUTINE get_prev_density
    3439             : 
    3440             : ! **************************************************************************************************
    3441             : !> \brief ...
    3442             : !> \param opt_embed ...
    3443             : !> \param force_env ...
    3444             : !> \param subsys_num ...
    3445             : ! **************************************************************************************************
    3446          96 :    SUBROUTINE get_max_subsys_diff(opt_embed, force_env, subsys_num)
    3447             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    3448             :       TYPE(force_env_type), POINTER                      :: force_env
    3449             :       INTEGER                                            :: subsys_num
    3450             : 
    3451             :       INTEGER                                            :: i_dens_start, i_spin, nspins
    3452          96 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rho_r
    3453             :       TYPE(qs_rho_type), POINTER                         :: rho
    3454             : 
    3455          96 :       NULLIFY (rho_r, rho)
    3456          96 :       CALL get_qs_env(force_env%qs_env, rho=rho)
    3457          96 :       CALL qs_rho_get(rho_struct=rho, rho_r=rho_r)
    3458             : 
    3459          96 :       nspins = opt_embed%all_nspins(subsys_num)
    3460             : 
    3461         240 :       i_dens_start = SUM(opt_embed%all_nspins(1:subsys_num)) - nspins + 1
    3462             : 
    3463         244 :       DO i_spin = 1, nspins
    3464             :          CALL pw_axpy(rho_r(i_spin), opt_embed%prev_subsys_dens(i_dens_start + i_spin - 1), 1.0_dp, -1.0_dp, &
    3465         148 :                       allow_noncompatible_grids=.TRUE.)
    3466             :          opt_embed%max_subsys_dens_diff(i_dens_start + i_spin - 1) = &
    3467         244 :             max_dens_diff(opt_embed%prev_subsys_dens(i_dens_start + i_spin - 1))
    3468             :       END DO
    3469             : 
    3470          96 :    END SUBROUTINE get_max_subsys_diff
    3471             : 
    3472             : ! **************************************************************************************************
    3473             : !> \brief ...
    3474             : !> \param opt_embed ...
    3475             : !> \param diff_rho_r ...
    3476             : !> \param diff_rho_spin ...
    3477             : !> \param output_unit ...
    3478             : ! **************************************************************************************************
    3479          48 :    SUBROUTINE conv_check_embed(opt_embed, diff_rho_r, diff_rho_spin, output_unit)
    3480             :       TYPE(opt_embed_pot_type)                           :: opt_embed
    3481             :       TYPE(pw_r3d_rs_type), INTENT(IN)                   :: diff_rho_r, diff_rho_spin
    3482             :       INTEGER                                            :: output_unit
    3483             : 
    3484             :       INTEGER                                            :: i_dens, i_dens_start, i_spin
    3485             :       LOGICAL                                            :: conv_int_diff, conv_max_diff
    3486             :       REAL(KIND=dp)                                      :: int_diff, int_diff_spin, &
    3487             :                                                             int_diff_square, int_diff_square_spin, &
    3488             :                                                             max_diff, max_diff_spin
    3489             : 
    3490             :       ! Calculate the convergence target values
    3491          48 :       opt_embed%max_diff(1) = max_dens_diff(diff_rho_r)
    3492          48 :       opt_embed%int_diff(1) = pw_integrate_function(fun=diff_rho_r, oprt='ABS')
    3493          48 :       opt_embed%int_diff_square(1) = pw_integral_ab(diff_rho_r, diff_rho_r)
    3494          48 :       IF (opt_embed%open_shell_embed) THEN
    3495          26 :          opt_embed%max_diff(2) = max_dens_diff(diff_rho_spin)
    3496          26 :          opt_embed%int_diff(2) = pw_integrate_function(fun=diff_rho_spin, oprt='ABS')
    3497          26 :          opt_embed%int_diff_square(2) = pw_integral_ab(diff_rho_spin, diff_rho_spin)
    3498             :       END IF
    3499             : 
    3500             :       ! Find out the convergence
    3501          48 :       max_diff = opt_embed%max_diff(1)
    3502             : 
    3503             :       ! Maximum value criterium
    3504             :       ! Open shell
    3505          48 :       IF (opt_embed%open_shell_embed) THEN
    3506          26 :          max_diff_spin = opt_embed%max_diff(2)
    3507          26 :          IF ((max_diff .LE. opt_embed%conv_max) .AND. (max_diff_spin .LE. opt_embed%conv_max_spin)) THEN
    3508             :             conv_max_diff = .TRUE.
    3509             :          ELSE
    3510          12 :             conv_max_diff = .FALSE.
    3511             :          END IF
    3512             :       ELSE
    3513             :          ! Closed shell
    3514          22 :          IF (max_diff .LE. opt_embed%conv_max) THEN
    3515             :             conv_max_diff = .TRUE.
    3516             :          ELSE
    3517           8 :             conv_max_diff = .FALSE.
    3518             :          END IF
    3519             :       END IF
    3520             : 
    3521             :       ! Integrated value criterium
    3522          48 :       int_diff = opt_embed%int_diff(1)
    3523             :       ! Open shell
    3524          48 :       IF (opt_embed%open_shell_embed) THEN
    3525          26 :          int_diff_spin = opt_embed%int_diff(2)
    3526          26 :          IF ((int_diff .LE. opt_embed%conv_int) .AND. (int_diff_spin .LE. opt_embed%conv_int_spin)) THEN
    3527             :             conv_int_diff = .TRUE.
    3528             :          ELSE
    3529           6 :             conv_int_diff = .FALSE.
    3530             :          END IF
    3531             :       ELSE
    3532             :          ! Closed shell
    3533          22 :          IF (int_diff .LE. opt_embed%conv_int) THEN
    3534             :             conv_int_diff = .TRUE.
    3535             :          ELSE
    3536          10 :             conv_int_diff = .FALSE.
    3537             :          END IF
    3538             :       END IF
    3539             : 
    3540             :       ! Integrated squared value criterium
    3541          48 :       int_diff_square = opt_embed%int_diff_square(1)
    3542             :       ! Open shell
    3543          48 :       IF (opt_embed%open_shell_embed) int_diff_square_spin = opt_embed%int_diff_square(2)
    3544             : 
    3545          48 :       IF ((conv_max_diff) .AND. (conv_int_diff)) THEN
    3546          24 :          opt_embed%converged = .TRUE.
    3547             :       ELSE
    3548          24 :          opt_embed%converged = .FALSE.
    3549             :       END IF
    3550             : 
    3551             :       ! Print the information
    3552          48 :       IF (output_unit > 0) THEN
    3553             :          WRITE (UNIT=output_unit, FMT="(/,T2,A)") &
    3554          24 :             " Convergence check :"
    3555             : 
    3556             :          ! Maximum value of density
    3557             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3558          24 :             " Maximum density difference                = ", max_diff
    3559             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3560          24 :             " Convergence limit for max. density diff.  = ", opt_embed%conv_max
    3561             : 
    3562          24 :          IF (opt_embed%open_shell_embed) THEN
    3563             : 
    3564             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3565          13 :                " Maximum spin density difference           = ", max_diff_spin
    3566             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3567          13 :                " Convergence limit for max. spin dens.diff.= ", opt_embed%conv_max_spin
    3568             : 
    3569             :          END IF
    3570             : 
    3571          24 :          IF (conv_max_diff) THEN
    3572             :             WRITE (UNIT=output_unit, FMT="(T2,2A)") &
    3573          14 :                " Convergence in max. density diff.    =     ", &
    3574          28 :                "             YES"
    3575             :          ELSE
    3576             :             WRITE (UNIT=output_unit, FMT="(T2,2A)") &
    3577          10 :                " Convergence in max. density diff.    =     ", &
    3578          20 :                "              NO"
    3579             :          END IF
    3580             : 
    3581             :          ! Integrated abs. value of density
    3582             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3583          24 :             " Integrated density difference             = ", int_diff
    3584             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3585          24 :             " Conv. limit for integrated density diff.  = ", opt_embed%conv_int
    3586          24 :          IF (opt_embed%open_shell_embed) THEN
    3587             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3588          13 :                " Integrated spin density difference        = ", int_diff_spin
    3589             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3590          13 :                " Conv. limit for integrated spin dens.diff.= ", opt_embed%conv_int_spin
    3591             :          END IF
    3592             : 
    3593          24 :          IF (conv_int_diff) THEN
    3594             :             WRITE (UNIT=output_unit, FMT="(T2,2A)") &
    3595          16 :                " Convergence in integrated density diff.    =     ", &
    3596          32 :                "             YES"
    3597             :          ELSE
    3598             :             WRITE (UNIT=output_unit, FMT="(T2,2A)") &
    3599           8 :                " Convergence in integrated density diff.    =     ", &
    3600          16 :                "              NO"
    3601             :          END IF
    3602             : 
    3603             :          ! Integrated squared value of density
    3604             :          WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3605          24 :             " Integrated squared density difference     = ", int_diff_square
    3606          24 :          IF (opt_embed%open_shell_embed) THEN
    3607             :             WRITE (UNIT=output_unit, FMT="(T2,A,F20.10)") &
    3608          13 :                " Integrated squared spin density difference= ", int_diff_square_spin
    3609             :          END IF
    3610             : 
    3611             :          ! Maximum subsystem density change
    3612             :          WRITE (UNIT=output_unit, FMT="(/,T2,A)") &
    3613          24 :             " Maximum density change in:"
    3614          72 :          DO i_dens = 1, (SIZE(opt_embed%all_nspins) - 1)
    3615         120 :             i_dens_start = SUM(opt_embed%all_nspins(1:i_dens)) - opt_embed%all_nspins(i_dens) + 1
    3616         146 :             DO i_spin = 1, opt_embed%all_nspins(i_dens)
    3617             :                WRITE (UNIT=output_unit, FMT="(T4,A10,I3,A6,I3,A1,F20.10)") &
    3618          74 :                   " subsystem ", i_dens, ', spin', i_spin, ":", &
    3619         196 :                   opt_embed%max_subsys_dens_diff(i_dens_start + i_spin - 1)
    3620             :             END DO
    3621             :          END DO
    3622             : 
    3623             :       END IF
    3624             : 
    3625          48 :       IF ((opt_embed%converged) .AND. (output_unit > 0)) THEN
    3626          12 :          WRITE (UNIT=output_unit, FMT="(/,T2,A)") REPEAT("*", 79)
    3627             :          WRITE (UNIT=output_unit, FMT="(T2,A,T25,A,T78,A)") &
    3628          12 :             "***", "EMBEDDING POTENTIAL OPTIMIZATION COMPLETED", "***"
    3629          12 :          WRITE (UNIT=output_unit, FMT="(T2,A)") REPEAT("*", 79)
    3630             :       END IF
    3631             : 
    3632          48 :    END SUBROUTINE conv_check_embed
    3633             : 
    3634             : END MODULE optimize_embedding_potential

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