LCOV - code coverage report
Current view: top level - src - rpa_im_time_force_methods.F (source / functions) Hit Total Coverage
Test: CP2K Regtests (git:dc8eeee) Lines: 1885 1935 97.4 %
Date: 2025-05-15 08:34:30 Functions: 12 12 100.0 %

          Line data    Source code
       1             : !--------------------------------------------------------------------------------------------------!
       2             : !   CP2K: A general program to perform molecular dynamics simulations                              !
       3             : !   Copyright 2000-2025 CP2K developers group <https://cp2k.org>                                   !
       4             : !                                                                                                  !
       5             : !   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
       6             : !--------------------------------------------------------------------------------------------------!
       7             : 
       8             : ! **************************************************************************************************
       9             : !> \brief Routines needed for cubic-scaling RPA and SOS-Laplace-MP2 forces
      10             : !> \author Augustin Bussy
      11             : ! **************************************************************************************************
      12             : MODULE rpa_im_time_force_methods
      13             :    USE admm_methods,                    ONLY: admm_projection_derivative
      14             :    USE admm_types,                      ONLY: admm_type,&
      15             :                                               get_admm_env
      16             :    USE ao_util,                         ONLY: exp_radius_very_extended
      17             :    USE atomic_kind_types,               ONLY: atomic_kind_type,&
      18             :                                               get_atomic_kind_set
      19             :    USE basis_set_types,                 ONLY: gto_basis_set_p_type,&
      20             :                                               gto_basis_set_type
      21             :    USE bibliography,                    ONLY: Bussy2023,&
      22             :                                               cite_reference
      23             :    USE cell_types,                      ONLY: cell_type,&
      24             :                                               pbc
      25             :    USE core_ae,                         ONLY: build_core_ae
      26             :    USE core_ppl,                        ONLY: build_core_ppl
      27             :    USE core_ppnl,                       ONLY: build_core_ppnl
      28             :    USE cp_blacs_env,                    ONLY: cp_blacs_env_type
      29             :    USE cp_control_types,                ONLY: dft_control_type
      30             :    USE cp_dbcsr_api,                    ONLY: &
      31             :         dbcsr_add, dbcsr_clear, dbcsr_complete_redistribute, dbcsr_copy, dbcsr_create, &
      32             :         dbcsr_distribution_new, dbcsr_distribution_release, dbcsr_distribution_type, &
      33             :         dbcsr_get_block_p, dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, &
      34             :         dbcsr_iterator_start, dbcsr_iterator_stop, dbcsr_iterator_type, dbcsr_multiply, &
      35             :         dbcsr_p_type, dbcsr_release, dbcsr_scale, dbcsr_set, dbcsr_type, dbcsr_type_antisymmetric, &
      36             :         dbcsr_type_no_symmetry, dbcsr_type_symmetric
      37             :    USE cp_dbcsr_cholesky,               ONLY: cp_dbcsr_cholesky_decompose,&
      38             :                                               cp_dbcsr_cholesky_invert
      39             :    USE cp_dbcsr_contrib,                ONLY: dbcsr_add_on_diag,&
      40             :                                               dbcsr_frobenius_norm
      41             :    USE cp_dbcsr_diag,                   ONLY: cp_dbcsr_power
      42             :    USE cp_dbcsr_operations,             ONLY: copy_dbcsr_to_fm,&
      43             :                                               copy_fm_to_dbcsr,&
      44             :                                               cp_dbcsr_dist2d_to_dist,&
      45             :                                               cp_dbcsr_sm_fm_multiply,&
      46             :                                               dbcsr_allocate_matrix_set,&
      47             :                                               dbcsr_deallocate_matrix_set
      48             :    USE cp_eri_mme_interface,            ONLY: cp_eri_mme_update_local_counts
      49             :    USE cp_fm_struct,                    ONLY: cp_fm_struct_create,&
      50             :                                               cp_fm_struct_release,&
      51             :                                               cp_fm_struct_type
      52             :    USE cp_fm_types,                     ONLY: cp_fm_create,&
      53             :                                               cp_fm_release,&
      54             :                                               cp_fm_set_all,&
      55             :                                               cp_fm_to_fm,&
      56             :                                               cp_fm_type
      57             :    USE dbt_api,                         ONLY: &
      58             :         dbt_batched_contract_finalize, dbt_batched_contract_init, dbt_clear, dbt_contract, &
      59             :         dbt_copy, dbt_copy_matrix_to_tensor, dbt_copy_tensor_to_matrix, dbt_create, dbt_destroy, &
      60             :         dbt_filter, dbt_get_info, dbt_mp_environ_pgrid, dbt_pgrid_create, dbt_pgrid_destroy, &
      61             :         dbt_pgrid_type, dbt_scale, dbt_type
      62             :    USE distribution_2d_types,           ONLY: distribution_2d_type
      63             :    USE ec_methods,                      ONLY: create_kernel
      64             :    USE gaussian_gridlevels,             ONLY: gaussian_gridlevel
      65             :    USE hfx_admm_utils,                  ONLY: tddft_hfx_matrix
      66             :    USE hfx_derivatives,                 ONLY: derivatives_four_center
      67             :    USE hfx_exx,                         ONLY: add_exx_to_rhs
      68             :    USE hfx_ri,                          ONLY: get_2c_der_force,&
      69             :                                               get_force_from_3c_trace,&
      70             :                                               get_idx_to_atom,&
      71             :                                               hfx_ri_update_forces
      72             :    USE hfx_types,                       ONLY: alloc_containers,&
      73             :                                               block_ind_type,&
      74             :                                               dealloc_containers,&
      75             :                                               hfx_compression_type,&
      76             :                                               hfx_type
      77             :    USE input_constants,                 ONLY: do_admm_aux_exch_func_none,&
      78             :                                               do_eri_gpw,&
      79             :                                               do_eri_mme,&
      80             :                                               do_potential_id,&
      81             :                                               ri_rpa_method_gpw
      82             :    USE input_section_types,             ONLY: section_vals_get,&
      83             :                                               section_vals_get_subs_vals,&
      84             :                                               section_vals_type,&
      85             :                                               section_vals_val_get
      86             :    USE iterate_matrix,                  ONLY: matrix_exponential
      87             :    USE kinds,                           ONLY: dp,&
      88             :                                               int_8
      89             :    USE libint_2c_3c,                    ONLY: libint_potential_type
      90             :    USE machine,                         ONLY: m_flush,&
      91             :                                               m_walltime
      92             :    USE mathconstants,                   ONLY: fourpi
      93             :    USE message_passing,                 ONLY: mp_cart_type,&
      94             :                                               mp_para_env_release,&
      95             :                                               mp_para_env_type
      96             :    USE mp2_eri,                         ONLY: integrate_set_2c
      97             :    USE mp2_eri_gpw,                     ONLY: calc_potential_gpw,&
      98             :                                               cleanup_gpw,&
      99             :                                               prepare_gpw,&
     100             :                                               virial_gpw_potential
     101             :    USE mp2_types,                       ONLY: mp2_type
     102             :    USE orbital_pointers,                ONLY: ncoset
     103             :    USE parallel_gemm_api,               ONLY: parallel_gemm
     104             :    USE particle_methods,                ONLY: get_particle_set
     105             :    USE particle_types,                  ONLY: particle_type
     106             :    USE pw_env_types,                    ONLY: pw_env_get,&
     107             :                                               pw_env_type
     108             :    USE pw_methods,                      ONLY: pw_axpy,&
     109             :                                               pw_copy,&
     110             :                                               pw_integral_ab,&
     111             :                                               pw_scale,&
     112             :                                               pw_transfer,&
     113             :                                               pw_zero
     114             :    USE pw_poisson_methods,              ONLY: pw_poisson_solve
     115             :    USE pw_poisson_types,                ONLY: pw_poisson_type
     116             :    USE pw_pool_types,                   ONLY: pw_pool_type
     117             :    USE pw_types,                        ONLY: pw_c1d_gs_type,&
     118             :                                               pw_r3d_rs_type
     119             :    USE qs_collocate_density,            ONLY: calculate_rho_elec,&
     120             :                                               collocate_function
     121             :    USE qs_density_matrices,             ONLY: calculate_whz_matrix
     122             :    USE qs_environment_types,            ONLY: get_qs_env,&
     123             :                                               qs_environment_type,&
     124             :                                               set_qs_env
     125             :    USE qs_force_types,                  ONLY: qs_force_type
     126             :    USE qs_integral_utils,               ONLY: basis_set_list_setup
     127             :    USE qs_integrate_potential,          ONLY: integrate_pgf_product,&
     128             :                                               integrate_v_core_rspace,&
     129             :                                               integrate_v_rspace
     130             :    USE qs_interactions,                 ONLY: init_interaction_radii_orb_basis
     131             :    USE qs_kind_types,                   ONLY: qs_kind_type
     132             :    USE qs_kinetic,                      ONLY: build_kinetic_matrix
     133             :    USE qs_ks_methods,                   ONLY: calc_rho_tot_gspace
     134             :    USE qs_ks_reference,                 ONLY: ks_ref_potential
     135             :    USE qs_ks_types,                     ONLY: set_ks_env
     136             :    USE qs_linres_types,                 ONLY: linres_control_type
     137             :    USE qs_matrix_w,                     ONLY: compute_matrix_w
     138             :    USE qs_mo_types,                     ONLY: get_mo_set,&
     139             :                                               mo_set_type
     140             :    USE qs_neighbor_list_types,          ONLY: neighbor_list_set_p_type,&
     141             :                                               release_neighbor_list_sets
     142             :    USE qs_overlap,                      ONLY: build_overlap_matrix
     143             :    USE qs_p_env_methods,                ONLY: p_env_create,&
     144             :                                               p_env_psi0_changed
     145             :    USE qs_p_env_types,                  ONLY: p_env_release,&
     146             :                                               qs_p_env_type
     147             :    USE qs_rho_types,                    ONLY: qs_rho_get,&
     148             :                                               qs_rho_type
     149             :    USE qs_tensors,                      ONLY: &
     150             :         build_2c_derivatives, build_2c_integrals, build_2c_neighbor_lists, build_3c_derivatives, &
     151             :         build_3c_neighbor_lists, calc_2c_virial, calc_3c_virial, compress_tensor, &
     152             :         decompress_tensor, get_tensor_occupancy, neighbor_list_3c_destroy
     153             :    USE qs_tensors_types,                ONLY: create_2c_tensor,&
     154             :                                               create_3c_tensor,&
     155             :                                               create_tensor_batches,&
     156             :                                               distribution_3d_create,&
     157             :                                               distribution_3d_type,&
     158             :                                               neighbor_list_3c_type
     159             :    USE realspace_grid_types,            ONLY: map_gaussian_here,&
     160             :                                               realspace_grid_type
     161             :    USE response_solver,                 ONLY: response_equation_new
     162             :    USE rpa_im_time,                     ONLY: compute_mat_dm_global
     163             :    USE rpa_im_time_force_types,         ONLY: im_time_force_type
     164             :    USE rs_pw_interface,                 ONLY: potential_pw2rs
     165             :    USE task_list_types,                 ONLY: task_list_type
     166             :    USE virial_types,                    ONLY: virial_type
     167             : #include "./base/base_uses.f90"
     168             : 
     169             :    IMPLICIT NONE
     170             : 
     171             :    PRIVATE
     172             : 
     173             :    CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'rpa_im_time_force_methods'
     174             : 
     175             :    PUBLIC :: init_im_time_forces, calc_laplace_loop_forces, calc_post_loop_forces, &
     176             :              keep_initial_quad, calc_rpa_loop_forces
     177             : 
     178             : CONTAINS
     179             : 
     180             : ! **************************************************************************************************
     181             : !> \brief Initializes and pre-calculates all needed tensors for the forces
     182             : !> \param force_data ...
     183             : !> \param fm_matrix_PQ ...
     184             : !> \param t_3c_M the 3-center M tensor to be used as a template
     185             : !> \param unit_nr ...
     186             : !> \param mp2_env ...
     187             : !> \param qs_env ...
     188             : ! **************************************************************************************************
     189          50 :    SUBROUTINE init_im_time_forces(force_data, fm_matrix_PQ, t_3c_M, unit_nr, mp2_env, qs_env)
     190             : 
     191             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
     192             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_PQ
     193             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M
     194             :       INTEGER, INTENT(IN)                                :: unit_nr
     195             :       TYPE(mp2_type)                                     :: mp2_env
     196             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     197             : 
     198             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'init_im_time_forces'
     199             : 
     200             :       INTEGER                                            :: handle, i_mem, i_xyz, ibasis, ispin, &
     201             :                                                             n_dependent, n_mem, n_rep, natom, &
     202             :                                                             nkind, nspins
     203             :       INTEGER(int_8)                                     :: nze, nze_tot
     204          50 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: dist1, dist2, dist_AO_1, dist_AO_2, &
     205          50 :                                                             dist_RI, dummy_end, dummy_start, &
     206         100 :                                                             end_blocks, sizes_AO, sizes_RI, &
     207          50 :                                                             start_blocks
     208             :       INTEGER, DIMENSION(2)                              :: pdims_t2c
     209             :       INTEGER, DIMENSION(3)                              :: nblks_total, pcoord, pdims, pdims_t3c
     210         100 :       INTEGER, DIMENSION(:), POINTER                     :: col_bsize, row_bsize
     211             :       LOGICAL                                            :: do_periodic, use_virial
     212             :       REAL(dp)                                           :: compression_factor, eps_pgf_orb, &
     213             :                                                             eps_pgf_orb_old, memory, occ
     214             :       TYPE(cell_type), POINTER                           :: cell
     215             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
     216             :       TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
     217         100 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_s, rho_ao
     218             :       TYPE(dbcsr_type)                                   :: dbcsr_work, dbcsr_work2, dbcsr_work3
     219         100 :       TYPE(dbcsr_type), DIMENSION(1)                     :: t_2c_int_tmp
     220         350 :       TYPE(dbcsr_type), DIMENSION(1, 3)                  :: t_2c_der_tmp
     221         250 :       TYPE(dbt_pgrid_type)                               :: pgrid_t2c, pgrid_t3c
     222        1000 :       TYPE(dbt_type)                                     :: t_2c_template, t_2c_tmp, t_3c_template
     223          50 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:, :, :)    :: t_3c_der_AO_prv, t_3c_der_RI_prv
     224             :       TYPE(dft_control_type), POINTER                    :: dft_control
     225             :       TYPE(distribution_2d_type), POINTER                :: dist_2d
     226             :       TYPE(distribution_3d_type)                         :: dist_3d, dist_vir
     227             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
     228          50 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
     229             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
     230             :       TYPE(libint_potential_type)                        :: identity_pot
     231          50 :       TYPE(mp_cart_type)                                 :: mp_comm_t3c, mp_comm_vir
     232             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     233             :       TYPE(neighbor_list_3c_type)                        :: nl_3c
     234             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
     235          50 :          POINTER                                         :: nl_2c
     236          50 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     237          50 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     238             :       TYPE(qs_rho_type), POINTER                         :: rho
     239             :       TYPE(section_vals_type), POINTER                   :: qs_section
     240             :       TYPE(virial_type), POINTER                         :: virial
     241             : 
     242          50 :       NULLIFY (dft_control, para_env, particle_set, qs_kind_set, dist_2d, nl_2c, blacs_env, matrix_s, &
     243          50 :                rho, rho_ao, cell, qs_section, orb_basis, ri_basis, virial)
     244             : 
     245          50 :       CALL cite_reference(Bussy2023)
     246             : 
     247          50 :       CALL timeset(routineN, handle)
     248             : 
     249             :       CALL get_qs_env(qs_env, natom=natom, nkind=nkind, dft_control=dft_control, para_env=para_env, &
     250          50 :                       particle_set=particle_set, qs_kind_set=qs_kind_set, cell=cell, virial=virial)
     251          50 :       IF (dft_control%qs_control%gapw) THEN
     252           0 :          CPABORT("Low-scaling RPA/SOS-MP2 forces only available with GPW")
     253             :       END IF
     254             : 
     255          50 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
     256             : 
     257          50 :       do_periodic = .FALSE.
     258         128 :       IF (ANY(cell%perd == 1)) do_periodic = .TRUE.
     259          50 :       force_data%do_periodic = do_periodic
     260             : 
     261             :       !Dealing with the 3-center derivatives
     262          50 :       pdims_t3c = 0
     263          50 :       CALL dbt_pgrid_create(para_env, pdims_t3c, pgrid_t3c)
     264             : 
     265             :       !Make sure we use the proper QS EPS_PGF_ORB values
     266          50 :       qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
     267          50 :       CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
     268          50 :       IF (n_rep /= 0) THEN
     269           0 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
     270             :       ELSE
     271          50 :          CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
     272          50 :          eps_pgf_orb = SQRT(eps_pgf_orb)
     273             :       END IF
     274          50 :       eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
     275             : 
     276         200 :       ALLOCATE (sizes_RI(natom), sizes_AO(natom))
     277         400 :       ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
     278          50 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
     279          50 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_RI, basis=basis_set_ri_aux)
     280          50 :       CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
     281          50 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_AO, basis=basis_set_ao)
     282             : 
     283         150 :       DO ibasis = 1, SIZE(basis_set_ao)
     284         100 :          orb_basis => basis_set_ao(ibasis)%gto_basis_set
     285         100 :          CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
     286         100 :          ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     287         150 :          CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
     288             :       END DO
     289             : 
     290             :       CALL create_3c_tensor(t_3c_template, dist_RI, dist_AO_1, dist_AO_2, pgrid_t3c, &
     291          50 :                             sizes_RI, sizes_AO, sizes_AO, map1=[1], map2=[2, 3], name="der (RI AO | AO)")
     292             : 
     293        1550 :       ALLOCATE (t_3c_der_RI_prv(1, 1, 3), t_3c_der_AO_prv(1, 1, 3))
     294         200 :       DO i_xyz = 1, 3
     295         150 :          CALL dbt_create(t_3c_template, t_3c_der_RI_prv(1, 1, i_xyz))
     296         200 :          CALL dbt_create(t_3c_template, t_3c_der_AO_prv(1, 1, i_xyz))
     297             :       END DO
     298             : 
     299          50 :       IF (use_virial) THEN
     300          52 :          ALLOCATE (force_data%t_3c_virial, force_data%t_3c_virial_split)
     301           4 :          CALL dbt_create(t_3c_template, force_data%t_3c_virial)
     302           4 :          CALL dbt_create(t_3c_M, force_data%t_3c_virial_split)
     303             :       END IF
     304          50 :       CALL dbt_destroy(t_3c_template)
     305             : 
     306          50 :       CALL dbt_mp_environ_pgrid(pgrid_t3c, pdims, pcoord)
     307          50 :       CALL mp_comm_t3c%create(pgrid_t3c%mp_comm_2d, 3, pdims)
     308             :       CALL distribution_3d_create(dist_3d, dist_RI, dist_AO_1, dist_AO_2, &
     309          50 :                                   nkind, particle_set, mp_comm_t3c, own_comm=.TRUE.)
     310             : 
     311             :       !In case of virial, we need to store the 3c_nl
     312          50 :       IF (use_virial) THEN
     313           4 :          ALLOCATE (force_data%nl_3c)
     314           4 :          CALL mp_comm_vir%create(pgrid_t3c%mp_comm_2d, 3, pdims)
     315             :          CALL distribution_3d_create(dist_vir, dist_RI, dist_AO_1, dist_AO_2, &
     316           4 :                                      nkind, particle_set, mp_comm_vir, own_comm=.TRUE.)
     317             :          CALL build_3c_neighbor_lists(force_data%nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, &
     318             :                                       dist_vir, mp2_env%ri_metric, "RPA_3c_nl", qs_env, op_pos=1, &
     319           4 :                                       sym_jk=.FALSE., own_dist=.TRUE.)
     320             :       END IF
     321             : 
     322             :       CALL build_3c_neighbor_lists(nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, dist_3d, &
     323             :                                    mp2_env%ri_metric, "RPA_3c_nl", qs_env, op_pos=1, sym_jk=.TRUE., &
     324          50 :                                    own_dist=.TRUE.)
     325          50 :       DEALLOCATE (dist_RI, dist_AO_1, dist_AO_2)
     326             : 
     327             :       !Prepare the resulting 3c tensors in the format of t_3c_M for compatible traces: (RI|AO AO), split blocks
     328          50 :       CALL dbt_get_info(t_3c_M, nblks_total=nblks_total)
     329         250 :       ALLOCATE (force_data%bsizes_RI_split(nblks_total(1)), force_data%bsizes_AO_split(nblks_total(2)))
     330          50 :       CALL dbt_get_info(t_3c_M, blk_size_1=force_data%bsizes_RI_split, blk_size_2=force_data%bsizes_AO_split)
     331         200 :       DO i_xyz = 1, 3
     332         150 :          CALL dbt_create(t_3c_M, force_data%t_3c_der_RI(i_xyz))
     333         200 :          CALL dbt_create(t_3c_M, force_data%t_3c_der_AO(i_xyz))
     334             :       END DO
     335             : 
     336             :       !Keep track of atom index corresponding to split blocks
     337         100 :       ALLOCATE (force_data%idx_to_at_RI(nblks_total(1)))
     338          50 :       CALL get_idx_to_atom(force_data%idx_to_at_RI, force_data%bsizes_RI_split, sizes_RI)
     339             : 
     340         100 :       ALLOCATE (force_data%idx_to_at_AO(nblks_total(2)))
     341          50 :       CALL get_idx_to_atom(force_data%idx_to_at_AO, force_data%bsizes_AO_split, sizes_AO)
     342             : 
     343          50 :       n_mem = mp2_env%ri_rpa_im_time%cut_memory
     344          50 :       CALL create_tensor_batches(sizes_RI, n_mem, dummy_start, dummy_end, start_blocks, end_blocks)
     345          50 :       DEALLOCATE (dummy_start, dummy_end)
     346             : 
     347      212300 :       ALLOCATE (force_data%t_3c_der_AO_comp(n_mem, 3), force_data%t_3c_der_RI_comp(n_mem, 3))
     348        1100 :       ALLOCATE (force_data%t_3c_der_AO_ind(n_mem, 3), force_data%t_3c_der_RI_ind(n_mem, 3))
     349             : 
     350          50 :       memory = 0.0_dp
     351          50 :       nze_tot = 0
     352         150 :       DO i_mem = 1, n_mem
     353             :          CALL build_3c_derivatives(t_3c_der_RI_prv, t_3c_der_AO_prv, mp2_env%ri_rpa_im_time%eps_filter, &
     354             :                                    qs_env, nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, &
     355             :                                    mp2_env%ri_metric, der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1, &
     356         300 :                                    bounds_i=[start_blocks(i_mem), end_blocks(i_mem)])
     357             : 
     358         450 :          DO i_xyz = 1, 3
     359         300 :             CALL dbt_copy(t_3c_der_RI_prv(1, 1, i_xyz), force_data%t_3c_der_RI(i_xyz), move_data=.TRUE.)
     360         300 :             CALL dbt_filter(force_data%t_3c_der_RI(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     361         300 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
     362         300 :             nze_tot = nze_tot + nze
     363             : 
     364         300 :             CALL alloc_containers(force_data%t_3c_der_RI_comp(i_mem, i_xyz), 1)
     365             :             CALL compress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
     366         300 :                                  force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress, memory)
     367         300 :             CALL dbt_clear(force_data%t_3c_der_RI(i_xyz))
     368             : 
     369         300 :             CALL dbt_copy(t_3c_der_AO_prv(1, 1, i_xyz), force_data%t_3c_der_AO(i_xyz), move_data=.TRUE.)
     370         300 :             CALL dbt_filter(force_data%t_3c_der_AO(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     371         300 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
     372         300 :             nze_tot = nze_tot + nze
     373             : 
     374         300 :             CALL alloc_containers(force_data%t_3c_der_AO_comp(i_mem, i_xyz), 1)
     375             :             CALL compress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
     376         300 :                                  force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress, memory)
     377        1000 :             CALL dbt_clear(force_data%t_3c_der_AO(i_xyz))
     378             :          END DO
     379             :       END DO
     380          50 :       CALL neighbor_list_3c_destroy(nl_3c)
     381         200 :       DO i_xyz = 1, 3
     382         150 :          CALL dbt_destroy(t_3c_der_RI_prv(1, 1, i_xyz))
     383         200 :          CALL dbt_destroy(t_3c_der_AO_prv(1, 1, i_xyz))
     384             :       END DO
     385             : 
     386          50 :       CALL para_env%sum(memory)
     387          50 :       compression_factor = REAL(nze_tot, dp)*1.0E-06*8.0_dp/memory
     388          50 :       IF (unit_nr > 0) THEN
     389             :          WRITE (UNIT=unit_nr, FMT="((T3,A,T66,F11.2,A4))") &
     390          25 :             "MEMORY_INFO| Memory for 3-center derivatives (compressed):", memory, ' MiB'
     391             : 
     392             :          WRITE (UNIT=unit_nr, FMT="((T3,A,T60,F21.2))") &
     393          25 :             "MEMORY_INFO| Compression factor:                  ", compression_factor
     394             :       END IF
     395             : 
     396             :       !Dealing with the 2-center derivatives
     397          50 :       CALL get_qs_env(qs_env, distribution_2d=dist_2d, blacs_env=blacs_env, matrix_s=matrix_s)
     398          50 :       CALL cp_dbcsr_dist2d_to_dist(dist_2d, dbcsr_dist)
     399         150 :       ALLOCATE (row_bsize(SIZE(sizes_RI)))
     400         100 :       ALLOCATE (col_bsize(SIZE(sizes_RI)))
     401         212 :       row_bsize(:) = sizes_RI(:)
     402         212 :       col_bsize(:) = sizes_RI(:)
     403             : 
     404          50 :       pdims_t2c = 0
     405          50 :       CALL dbt_pgrid_create(para_env, pdims_t2c, pgrid_t2c)
     406             :       CALL create_2c_tensor(t_2c_template, dist1, dist2, pgrid_t2c, force_data%bsizes_RI_split, &
     407          50 :                             force_data%bsizes_RI_split, name='(RI| RI)')
     408          50 :       DEALLOCATE (dist1, dist2)
     409             : 
     410          50 :       CALL dbcsr_create(t_2c_int_tmp(1), "(P|Q) RPA", dbcsr_dist, dbcsr_type_symmetric, row_bsize, col_bsize)
     411         200 :       DO i_xyz = 1, 3
     412             :          CALL dbcsr_create(t_2c_der_tmp(1, i_xyz), "(P|Q) RPA der", dbcsr_dist, &
     413         200 :                            dbcsr_type_antisymmetric, row_bsize, col_bsize)
     414             :       END DO
     415             : 
     416          50 :       IF (use_virial) THEN
     417           4 :          ALLOCATE (force_data%RI_virial_pot, force_data%RI_virial_met)
     418             :          CALL dbcsr_create(force_data%RI_virial_pot, "RI_virial", dbcsr_dist, &
     419           4 :                            dbcsr_type_no_symmetry, row_bsize, col_bsize)
     420             :          CALL dbcsr_create(force_data%RI_virial_met, "RI_virial", dbcsr_dist, &
     421           4 :                            dbcsr_type_no_symmetry, row_bsize, col_bsize)
     422             :       END IF
     423             : 
     424             :       ! Main (P|Q) integrals and derivatives
     425             :       ! Integrals are passed as a full matrix => convert to DBCSR
     426          50 :       CALL dbcsr_create(dbcsr_work, template=t_2c_int_tmp(1))
     427          50 :       CALL copy_fm_to_dbcsr(fm_matrix_PQ, dbcsr_work)
     428             : 
     429             :       ! We need the  +/- square root of (P|Q)
     430          50 :       CALL dbcsr_create(dbcsr_work2, template=t_2c_int_tmp(1))
     431          50 :       CALL dbcsr_create(dbcsr_work3, template=t_2c_int_tmp(1))
     432          50 :       CALL dbcsr_copy(dbcsr_work2, dbcsr_work)
     433          50 :       CALL cp_dbcsr_power(dbcsr_work, -0.5_dp, 1.0E-7_dp, n_dependent, para_env, blacs_env) !1.0E-7 ev qunenching thresh
     434             : 
     435             :       ! Transfer to tensor format with split blocks
     436          50 :       CALL dbt_create(dbcsr_work, t_2c_tmp)
     437          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work, t_2c_tmp)
     438          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_pot_msqrt)
     439          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_pot_msqrt, move_data=.TRUE.)
     440          50 :       CALL dbt_filter(force_data%t_2c_pot_msqrt, mp2_env%ri_rpa_im_time%eps_filter)
     441             : 
     442          50 :       CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work2, dbcsr_work, 0.0_dp, dbcsr_work3)
     443          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work3, t_2c_tmp)
     444          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_pot_psqrt)
     445          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_pot_psqrt, move_data=.TRUE.)
     446          50 :       CALL dbt_filter(force_data%t_2c_pot_psqrt, mp2_env%ri_rpa_im_time%eps_filter)
     447          50 :       CALL dbt_destroy(t_2c_tmp)
     448          50 :       CALL dbcsr_release(dbcsr_work2)
     449          50 :       CALL dbcsr_release(dbcsr_work3)
     450          50 :       CALL dbcsr_clear(dbcsr_work)
     451             : 
     452             :       ! Deal with the 2c potential derivatives. Only precompute if not in PBCs
     453          50 :       IF (.NOT. do_periodic) THEN
     454             :          CALL build_2c_neighbor_lists(nl_2c, basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter, &
     455          26 :                                       "RPA_2c_nl_pot", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     456             :          CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     457          26 :                                    basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
     458          26 :          CALL release_neighbor_list_sets(nl_2c)
     459             : 
     460         104 :          DO i_xyz = 1, 3
     461          78 :             CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     462          78 :             CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     463          78 :             CALL dbt_create(t_2c_template, force_data%t_2c_der_pot(i_xyz))
     464          78 :             CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_pot(i_xyz), move_data=.TRUE.)
     465          78 :             CALL dbt_filter(force_data%t_2c_der_pot(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     466          78 :             CALL dbt_destroy(t_2c_tmp)
     467         104 :             CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     468             :          END DO
     469             : 
     470          26 :          IF (use_virial) THEN
     471             :             CALL build_2c_neighbor_lists(force_data%nl_2c_pot, basis_set_ri_aux, basis_set_ri_aux, &
     472             :                                          mp2_env%potential_parameter, "RPA_2c_nl_pot", qs_env, &
     473           0 :                                          sym_ij=.FALSE., dist_2d=dist_2d)
     474             :          END IF
     475             :       END IF
     476             :       ! Create a G_PQ matrix to collect the terms for the force trace in the periodic case
     477          50 :       CALL dbcsr_create(force_data%G_PQ, "G_PQ", dbcsr_dist, dbcsr_type_no_symmetry, row_bsize, col_bsize)
     478             : 
     479             :       ! we need the RI metric derivatives and the inverse of the integrals
     480             :       CALL build_2c_neighbor_lists(nl_2c, basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric, &
     481          50 :                                    "RPA_2c_nl_metric", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     482             :       CALL build_2c_integrals(t_2c_int_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     483          50 :                               basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
     484             :       CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     485          50 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
     486          50 :       CALL release_neighbor_list_sets(nl_2c)
     487             : 
     488          50 :       IF (use_virial) THEN
     489             :          CALL build_2c_neighbor_lists(force_data%nl_2c_met, basis_set_ri_aux, basis_set_ri_aux, &
     490             :                                       mp2_env%ri_metric, "RPA_2c_nl_metric", qs_env, sym_ij=.FALSE., &
     491           4 :                                       dist_2d=dist_2d)
     492             :       END IF
     493             : 
     494          50 :       CALL dbcsr_copy(dbcsr_work, t_2c_int_tmp(1))
     495          50 :       CALL cp_dbcsr_cholesky_decompose(dbcsr_work, para_env=para_env, blacs_env=blacs_env)
     496          50 :       CALL cp_dbcsr_cholesky_invert(dbcsr_work, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
     497             : 
     498          50 :       CALL dbt_create(dbcsr_work, t_2c_tmp)
     499          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work, t_2c_tmp)
     500          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_inv_metric)
     501          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_inv_metric, move_data=.TRUE.)
     502          50 :       CALL dbt_filter(force_data%t_2c_inv_metric, mp2_env%ri_rpa_im_time%eps_filter)
     503          50 :       CALL dbt_destroy(t_2c_tmp)
     504          50 :       CALL dbcsr_clear(dbcsr_work)
     505          50 :       CALL dbcsr_clear(t_2c_int_tmp(1))
     506             : 
     507         200 :       DO i_xyz = 1, 3
     508         150 :          CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     509         150 :          CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     510         150 :          CALL dbt_create(t_2c_template, force_data%t_2c_der_metric(i_xyz))
     511         150 :          CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_metric(i_xyz), move_data=.TRUE.)
     512         150 :          CALL dbt_filter(force_data%t_2c_der_metric(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     513         150 :          CALL dbt_destroy(t_2c_tmp)
     514         200 :          CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     515             :       END DO
     516             : 
     517             :       !Pre-calculate matrix K = metric^-1 * V^0.5
     518          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_K)
     519             :       CALL dbt_contract(1.0_dp, force_data%t_2c_inv_metric, force_data%t_2c_pot_psqrt, &
     520             :                         0.0_dp, force_data%t_2c_K, &
     521             :                         contract_1=[2], notcontract_1=[1], &
     522             :                         contract_2=[1], notcontract_2=[2], &
     523          50 :                         map_1=[1], map_2=[2], filter_eps=mp2_env%ri_rpa_im_time%eps_filter)
     524             : 
     525             :       ! Finally, we need the overlap matrix derivative and the inverse of the integrals
     526          50 :       CALL dbt_destroy(t_2c_template)
     527          50 :       CALL dbcsr_release(dbcsr_work)
     528          50 :       CALL dbcsr_release(t_2c_int_tmp(1))
     529         200 :       DO i_xyz = 1, 3
     530         200 :          CALL dbcsr_release(t_2c_der_tmp(1, i_xyz))
     531             :       END DO
     532             : 
     533          50 :       DEALLOCATE (row_bsize, col_bsize)
     534         150 :       ALLOCATE (row_bsize(SIZE(sizes_AO)))
     535         100 :       ALLOCATE (col_bsize(SIZE(sizes_AO)))
     536         212 :       row_bsize(:) = sizes_AO(:)
     537         212 :       col_bsize(:) = sizes_AO(:)
     538             : 
     539             :       CALL create_2c_tensor(t_2c_template, dist1, dist2, pgrid_t2c, force_data%bsizes_AO_split, &
     540             :                             force_data%bsizes_AO_split, name='(AO| AO)')
     541          50 :       DEALLOCATE (dist1, dist2)
     542             : 
     543         200 :       DO i_xyz = 1, 3
     544             :          CALL dbcsr_create(t_2c_der_tmp(1, i_xyz), "(P|Q) RPA der", dbcsr_dist, &
     545         200 :                            dbcsr_type_antisymmetric, row_bsize, col_bsize)
     546             :       END DO
     547             : 
     548          50 :       identity_pot%potential_type = do_potential_id
     549             :       CALL build_2c_neighbor_lists(nl_2c, basis_set_ao, basis_set_ao, identity_pot, &
     550          50 :                                    "RPA_2c_nl_metric", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     551             :       CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     552          50 :                                 basis_set_ao, basis_set_ao, identity_pot)
     553          50 :       CALL release_neighbor_list_sets(nl_2c)
     554             : 
     555          50 :       IF (use_virial) THEN
     556             :          CALL build_2c_neighbor_lists(force_data%nl_2c_ovlp, basis_set_ao, basis_set_ao, identity_pot, &
     557           4 :                                       "RPA_2c_nl_metric", qs_env, sym_ij=.FALSE., dist_2d=dist_2d)
     558             :       END IF
     559             : 
     560          50 :       CALL dbcsr_create(force_data%inv_ovlp, template=matrix_s(1)%matrix)
     561          50 :       CALL dbcsr_copy(force_data%inv_ovlp, matrix_s(1)%matrix)
     562          50 :       CALL cp_dbcsr_cholesky_decompose(force_data%inv_ovlp, para_env=para_env, blacs_env=blacs_env)
     563          50 :       CALL cp_dbcsr_cholesky_invert(force_data%inv_ovlp, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
     564             : 
     565         200 :       DO i_xyz = 1, 3
     566         150 :          CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     567         150 :          CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     568         150 :          CALL dbt_create(t_2c_template, force_data%t_2c_der_ovlp(i_xyz))
     569         150 :          CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_ovlp(i_xyz), move_data=.TRUE.)
     570         150 :          CALL dbt_filter(force_data%t_2c_der_ovlp(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     571         150 :          CALL dbt_destroy(t_2c_tmp)
     572         200 :          CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     573             :       END DO
     574             : 
     575             :       !Create the rest of the 2-center AO tensors
     576          50 :       nspins = dft_control%nspins
     577         324 :       ALLOCATE (force_data%P_virt(nspins), force_data%P_occ(nspins))
     578         274 :       ALLOCATE (force_data%sum_YP_tau(nspins), force_data%sum_O_tau(nspins))
     579         112 :       DO ispin = 1, nspins
     580          62 :          ALLOCATE (force_data%P_virt(ispin)%matrix, force_data%P_occ(ispin)%matrix)
     581          62 :          ALLOCATE (force_data%sum_YP_tau(ispin)%matrix, force_data%sum_O_tau(ispin)%matrix)
     582          62 :          CALL dbcsr_create(force_data%P_virt(ispin)%matrix, template=matrix_s(1)%matrix)
     583          62 :          CALL dbcsr_create(force_data%P_occ(ispin)%matrix, template=matrix_s(1)%matrix)
     584          62 :          CALL dbcsr_create(force_data%sum_O_tau(ispin)%matrix, template=matrix_s(1)%matrix)
     585          62 :          CALL dbcsr_create(force_data%sum_YP_tau(ispin)%matrix, template=matrix_s(1)%matrix)
     586             : 
     587          62 :          CALL dbcsr_copy(force_data%sum_O_tau(ispin)%matrix, matrix_s(1)%matrix)
     588          62 :          CALL dbcsr_copy(force_data%sum_YP_tau(ispin)%matrix, matrix_s(1)%matrix)
     589             : 
     590          62 :          CALL dbcsr_set(force_data%sum_O_tau(ispin)%matrix, 0.0_dp)
     591         112 :          CALL dbcsr_set(force_data%sum_YP_tau(ispin)%matrix, 0.0_dp)
     592             :       END DO
     593             : 
     594             :       !Populate the density matrices: 1 = P_virt*S +P_occ*S ==> P_virt = S^-1 - P_occ
     595          50 :       CALL get_qs_env(qs_env, rho=rho)
     596          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
     597          50 :       CALL dbcsr_copy(force_data%P_occ(1)%matrix, rho_ao(1)%matrix)
     598          50 :       IF (nspins == 1) THEN
     599          38 :          CALL dbcsr_scale(force_data%P_occ(1)%matrix, 0.5_dp) !because double occupency
     600             :       ELSE
     601          12 :          CALL dbcsr_copy(force_data%P_occ(2)%matrix, rho_ao(2)%matrix)
     602             :       END IF
     603         112 :       DO ispin = 1, nspins
     604          62 :          CALL dbcsr_copy(force_data%P_virt(ispin)%matrix, force_data%inv_ovlp)
     605         112 :          CALL dbcsr_add(force_data%P_virt(ispin)%matrix, force_data%P_occ(ispin)%matrix, 1.0_dp, -1.0_dp)
     606             :       END DO
     607             : 
     608         150 :       DO ibasis = 1, SIZE(basis_set_ao)
     609         100 :          orb_basis => basis_set_ao(ibasis)%gto_basis_set
     610         100 :          CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
     611         100 :          ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     612         150 :          CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
     613             :       END DO
     614             : 
     615          50 :       CALL dbt_destroy(t_2c_template)
     616          50 :       CALL dbcsr_release(dbcsr_work)
     617         200 :       DO i_xyz = 1, 3
     618         200 :          CALL dbcsr_release(t_2c_der_tmp(1, i_xyz))
     619             :       END DO
     620          50 :       DEALLOCATE (row_bsize, col_bsize)
     621          50 :       CALL dbt_pgrid_destroy(pgrid_t3c)
     622          50 :       CALL dbt_pgrid_destroy(pgrid_t2c)
     623          50 :       CALL dbcsr_distribution_release(dbcsr_dist)
     624          50 :       CALL timestop(handle)
     625             : 
     626         750 :    END SUBROUTINE init_im_time_forces
     627             : 
     628             : ! **************************************************************************************************
     629             : !> \brief Updates the cubic-scaling SOS-Laplace-MP2 contribution to the forces at each quadrature point
     630             : !> \param force_data ...
     631             : !> \param mat_P_omega ...
     632             : !> \param t_3c_M ...
     633             : !> \param t_3c_O ...
     634             : !> \param t_3c_O_compressed ...
     635             : !> \param t_3c_O_ind ...
     636             : !> \param fm_scaled_dm_occ_tau ...
     637             : !> \param fm_scaled_dm_virt_tau ...
     638             : !> \param fm_mo_coeff_occ ...
     639             : !> \param fm_mo_coeff_virt ...
     640             : !> \param fm_mo_coeff_occ_scaled ...
     641             : !> \param fm_mo_coeff_virt_scaled ...
     642             : !> \param starts_array_mc ...
     643             : !> \param ends_array_mc ...
     644             : !> \param starts_array_mc_block ...
     645             : !> \param ends_array_mc_block ...
     646             : !> \param num_integ_points ...
     647             : !> \param nmo ...
     648             : !> \param Eigenval ...
     649             : !> \param tau_tj ...
     650             : !> \param tau_wj ...
     651             : !> \param cut_memory ...
     652             : !> \param Pspin ...
     653             : !> \param Qspin ...
     654             : !> \param open_shell ...
     655             : !> \param unit_nr ...
     656             : !> \param dbcsr_time ...
     657             : !> \param dbcsr_nflop ...
     658             : !> \param mp2_env ...
     659             : !> \param qs_env ...
     660             : !> \note In open-shell, we need to take Q from one spin, and everything from the other
     661             : ! **************************************************************************************************
     662         130 :    SUBROUTINE calc_laplace_loop_forces(force_data, mat_P_omega, t_3c_M, t_3c_O, t_3c_O_compressed, &
     663          26 :                                        t_3c_O_ind, fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, &
     664          26 :                                        fm_mo_coeff_occ, fm_mo_coeff_virt, fm_mo_coeff_occ_scaled, &
     665          26 :                                        fm_mo_coeff_virt_scaled, starts_array_mc, ends_array_mc, &
     666          26 :                                        starts_array_mc_block, ends_array_mc_block, num_integ_points, &
     667          52 :                                        nmo, Eigenval, tau_tj, tau_wj, cut_memory, Pspin, Qspin, &
     668             :                                        open_shell, unit_nr, dbcsr_time, dbcsr_nflop, mp2_env, qs_env)
     669             : 
     670             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
     671             :       TYPE(dbcsr_p_type), DIMENSION(:, :), INTENT(INOUT) :: mat_P_omega
     672             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M, t_3c_O
     673             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
     674             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
     675             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_scaled_dm_occ_tau, &
     676             :                                                             fm_scaled_dm_virt_tau
     677             :       TYPE(cp_fm_type), DIMENSION(:), INTENT(IN)         :: fm_mo_coeff_occ, fm_mo_coeff_virt
     678             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_mo_coeff_occ_scaled, &
     679             :                                                             fm_mo_coeff_virt_scaled
     680             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
     681             :                                                             starts_array_mc_block, &
     682             :                                                             ends_array_mc_block
     683             :       INTEGER, INTENT(IN)                                :: num_integ_points, nmo
     684             :       REAL(KIND=dp), DIMENSION(:, :), INTENT(IN)         :: Eigenval
     685             :       REAL(KIND=dp), DIMENSION(num_integ_points), &
     686             :          INTENT(IN)                                      :: tau_tj
     687             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
     688             :          INTENT(IN)                                      :: tau_wj
     689             :       INTEGER, INTENT(IN)                                :: cut_memory, Pspin, Qspin
     690             :       LOGICAL, INTENT(IN)                                :: open_shell
     691             :       INTEGER, INTENT(IN)                                :: unit_nr
     692             :       REAL(dp), INTENT(INOUT)                            :: dbcsr_time
     693             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
     694             :       TYPE(mp2_type)                                     :: mp2_env
     695             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     696             : 
     697             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_laplace_loop_forces'
     698             : 
     699             :       INTEGER :: dummy_int, handle, handle2, i_mem, i_xyz, ibasis, ispin, j_xyz, jquad, k_xyz, &
     700             :          n_mem_RI, n_rep, natom, nkind, nspins, unit_nr_dbcsr
     701             :       INTEGER(int_8)                                     :: flop, nze, nze_ddint, nze_der_AO, &
     702             :                                                             nze_der_RI, nze_KQK
     703          26 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, batch_blk_end, &
     704          26 :                                                             batch_blk_start, batch_end_RI, &
     705          26 :                                                             batch_start_RI, kind_of, mc_ranges, &
     706          26 :                                                             mc_ranges_RI
     707          26 :       INTEGER, DIMENSION(:, :), POINTER                  :: dummy_ptr
     708             :       LOGICAL                                            :: memory_info, use_virial
     709             :       REAL(dp)                                           :: eps_filter, eps_pgf_orb, &
     710             :                                                             eps_pgf_orb_old, fac, occ, occ_ddint, &
     711             :                                                             occ_der_AO, occ_der_RI, occ_KQK, &
     712             :                                                             omega, pref, t1, t2, tau
     713             :       REAL(dp), DIMENSION(3, 3)                          :: work_virial, work_virial_ovlp
     714          26 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     715             :       TYPE(cell_type), POINTER                           :: cell
     716          26 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks, matrix_s
     717          26 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: mat_dm_occ, mat_dm_virt
     718             :       TYPE(dbcsr_type)                                   :: dbcsr_work1, dbcsr_work2, dbcsr_work3, &
     719             :                                                             exp_occ, exp_virt, R_occ, R_virt, &
     720             :                                                             virial_ovlp, Y_1, Y_2
     721        1274 :       TYPE(dbt_type) :: t_2c_AO, t_2c_RI, t_2c_RI_2, t_2c_tmp, t_3c_0, t_3c_1, t_3c_3, t_3c_4, &
     722        1274 :          t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_help_1, t_3c_help_2, t_3c_ints, t_3c_sparse, &
     723        1456 :          t_3c_work, t_dm_occ, t_dm_virt, t_KQKT, t_M_occ, t_M_virt, t_Q, t_R_occ, t_R_virt
     724          26 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:)          :: t_P
     725             :       TYPE(dft_control_type), POINTER                    :: dft_control
     726             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
     727          26 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
     728             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
     729             :       TYPE(libint_potential_type)                        :: identity_pot
     730             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     731          26 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     732          26 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
     733          26 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     734             :       TYPE(section_vals_type), POINTER                   :: qs_section
     735             :       TYPE(virial_type), POINTER                         :: virial
     736             : 
     737          26 :       NULLIFY (matrix_s, dummy_ptr, atomic_kind_set, force, matrix_s, matrix_ks, mat_dm_occ, mat_dm_virt)
     738          26 :       NULLIFY (dft_control, virial, particle_set, cell, para_env, orb_basis, ri_basis, qs_section)
     739          26 :       NULLIFY (qs_kind_set)
     740             : 
     741          26 :       CALL timeset(routineN, handle)
     742             : 
     743             :       CALL get_qs_env(qs_env, matrix_s=matrix_s, natom=natom, atomic_kind_set=atomic_kind_set, &
     744             :                       force=force, matrix_ks=matrix_ks, dft_control=dft_control, virial=virial, &
     745             :                       particle_set=particle_set, cell=cell, para_env=para_env, nkind=nkind, &
     746          26 :                       qs_kind_set=qs_kind_set)
     747          26 :       eps_filter = mp2_env%ri_rpa_im_time%eps_filter
     748          26 :       nspins = dft_control%nspins
     749             : 
     750          26 :       memory_info = mp2_env%ri_rpa_im_time%memory_info
     751          26 :       IF (memory_info) THEN
     752           0 :          unit_nr_dbcsr = unit_nr
     753             :       ELSE
     754          26 :          unit_nr_dbcsr = 0
     755             :       END IF
     756             : 
     757          26 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
     758             : 
     759          26 :       IF (use_virial) virial%pv_calculate = .TRUE.
     760             : 
     761          26 :       IF (use_virial) THEN
     762           2 :          qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
     763           2 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
     764           2 :          IF (n_rep /= 0) THEN
     765           0 :             CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
     766             :          ELSE
     767           2 :             CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
     768           2 :             eps_pgf_orb = SQRT(eps_pgf_orb)
     769             :          END IF
     770           2 :          eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
     771             : 
     772          16 :          ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
     773           2 :          CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
     774           2 :          CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
     775             : 
     776           8 :          DO ibasis = 1, SIZE(basis_set_ao)
     777           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
     778           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
     779           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     780           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
     781             :          END DO
     782             :       END IF
     783             : 
     784             :       !We follow the general logic of the compute_mat_P_omega routine
     785         268 :       ALLOCATE (t_P(nspins))
     786          26 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI)
     787          26 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI_2)
     788          26 :       CALL dbt_create(force_data%t_2c_der_ovlp(1), t_2c_AO)
     789             : 
     790          26 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
     791             : 
     792             :       ! Always do the batching of the MO on mu and sigma, such that it is consistent between
     793             :       ! the occupied and the virtual quantities
     794          78 :       ALLOCATE (mc_ranges(cut_memory + 1))
     795          78 :       mc_ranges(:cut_memory) = starts_array_mc_block(:)
     796          26 :       mc_ranges(cut_memory + 1) = ends_array_mc_block(cut_memory) + 1
     797             : 
     798             :       ! Also need some batching on the RI, because it loses sparsity at some point
     799          26 :       n_mem_RI = cut_memory
     800             :       CALL create_tensor_batches(force_data%bsizes_RI_split, n_mem_RI, batch_start_RI, batch_end_RI, &
     801          26 :                                  batch_blk_start, batch_blk_end)
     802          78 :       ALLOCATE (mc_ranges_RI(n_mem_RI + 1))
     803          78 :       mc_ranges_RI(1:n_mem_RI) = batch_blk_start(1:n_mem_RI)
     804          26 :       mc_ranges_RI(n_mem_RI + 1) = batch_blk_end(n_mem_RI) + 1
     805          26 :       DEALLOCATE (batch_blk_start, batch_blk_end)
     806             : 
     807             :       !Pre-allocate all required tensors and matrices
     808          60 :       DO ispin = 1, nspins
     809          60 :          CALL dbt_create(t_2c_RI, t_P(ispin))
     810             :       END DO
     811          26 :       CALL dbt_create(t_2c_RI, t_Q)
     812          26 :       CALL dbt_create(t_2c_RI, t_KQKT)
     813          26 :       CALL dbt_create(t_2c_AO, t_dm_occ)
     814          26 :       CALL dbt_create(t_2c_AO, t_dm_virt)
     815             : 
     816             :       !note: t_3c_O and t_3c_M have different mappings (map_1d, map_2d)
     817          26 :       CALL dbt_create(t_3c_O, t_M_occ)
     818          26 :       CALL dbt_create(t_3c_O, t_M_virt)
     819          26 :       CALL dbt_create(t_3c_O, t_3c_0)
     820             : 
     821          26 :       CALL dbt_create(t_3c_O, t_3c_1)
     822          26 :       CALL dbt_create(t_3c_O, t_3c_3)
     823          26 :       CALL dbt_create(t_3c_O, t_3c_4)
     824          26 :       CALL dbt_create(t_3c_O, t_3c_5)
     825          26 :       CALL dbt_create(t_3c_M, t_3c_6)
     826          26 :       CALL dbt_create(t_3c_M, t_3c_7)
     827          26 :       CALL dbt_create(t_3c_M, t_3c_8)
     828          26 :       CALL dbt_create(t_3c_M, t_3c_sparse)
     829          26 :       CALL dbt_create(t_3c_O, t_3c_help_1)
     830          26 :       CALL dbt_create(t_3c_O, t_3c_help_2)
     831          26 :       CALL dbt_create(t_2c_AO, t_R_occ)
     832          26 :       CALL dbt_create(t_2c_AO, t_R_virt)
     833          26 :       CALL dbt_create(t_3c_M, t_3c_ints)
     834          26 :       CALL dbt_create(t_3c_M, t_3c_work)
     835             : 
     836             :       !Pre-define the sparsity of t_3c_4 as a function of the derivatives
     837          26 :       occ_der_AO = 0; nze_der_AO = 0
     838          26 :       occ_der_RI = 0; nze_der_RI = 0
     839         104 :       DO i_xyz = 1, 3
     840         260 :          DO i_mem = 1, cut_memory
     841             :             CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
     842         156 :                                    force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
     843         156 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
     844         156 :             occ_der_RI = occ_der_RI + occ
     845         156 :             nze_der_RI = nze_der_RI + nze
     846         156 :             CALL dbt_copy(force_data%t_3c_der_RI(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
     847             : 
     848             :             CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
     849         156 :                                    force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
     850         156 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
     851         156 :             occ_der_AO = occ_der_AO + occ
     852         156 :             nze_der_AO = nze_der_AO + nze
     853         156 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, order=[1, 3, 2], summation=.TRUE.)
     854         546 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
     855             :          END DO
     856             :       END DO
     857          26 :       occ_der_RI = occ_der_RI/3.0_dp
     858          26 :       occ_der_AO = occ_der_AO/3.0_dp
     859          26 :       nze_der_RI = nze_der_RI/3
     860          26 :       nze_der_AO = nze_der_AO/3
     861             : 
     862          26 :       CALL dbcsr_create(R_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     863          26 :       CALL dbcsr_create(R_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     864          26 :       CALL dbcsr_create(dbcsr_work1, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     865          26 :       CALL dbcsr_create(dbcsr_work2, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     866          26 :       CALL dbcsr_create(dbcsr_work3, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     867          26 :       CALL dbcsr_create(exp_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     868          26 :       CALL dbcsr_create(exp_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     869          26 :       IF (use_virial) CALL dbcsr_create(virial_ovlp, template=dbcsr_work1)
     870             : 
     871          26 :       CALL dbt_batched_contract_init(t_3c_0, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
     872          26 :       CALL dbt_batched_contract_init(t_3c_1, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
     873          26 :       CALL dbt_batched_contract_init(t_3c_3, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     874          26 :       CALL dbt_batched_contract_init(t_M_occ, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     875          26 :       CALL dbt_batched_contract_init(t_M_virt, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     876             : 
     877          26 :       CALL dbt_batched_contract_init(t_3c_ints, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     878          26 :       CALL dbt_batched_contract_init(t_3c_work, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     879             : 
     880             :       CALL dbt_batched_contract_init(t_3c_4, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     881          26 :                                      batch_range_3=mc_ranges)
     882             :       CALL dbt_batched_contract_init(t_3c_5, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     883          26 :                                      batch_range_3=mc_ranges)
     884             :       CALL dbt_batched_contract_init(t_3c_6, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     885          26 :                                      batch_range_3=mc_ranges)
     886             :       CALL dbt_batched_contract_init(t_3c_7, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     887          26 :                                      batch_range_3=mc_ranges)
     888             :       CALL dbt_batched_contract_init(t_3c_8, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     889          26 :                                      batch_range_3=mc_ranges)
     890             :       CALL dbt_batched_contract_init(t_3c_sparse, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     891          26 :                                      batch_range_3=mc_ranges)
     892             : 
     893          26 :       work_virial = 0.0_dp
     894          26 :       work_virial_ovlp = 0.0_dp
     895         104 :       DO jquad = 1, num_integ_points
     896          78 :          tau = tau_tj(jquad)
     897          78 :          omega = tau_wj(jquad)
     898          78 :          fac = -2.0_dp*omega*mp2_env%scale_S
     899          78 :          IF (open_shell) fac = 0.5_dp*fac
     900          78 :          occ_ddint = 0; nze_ddint = 0
     901             : 
     902          78 :          CALL para_env%sync()
     903          78 :          t1 = m_walltime()
     904             : 
     905             :          !Deal with the force contributions where there is no explicit 3-center quantities, i.e. the
     906             :          !forces due to the metric and potential derivatives
     907         180 :          DO ispin = 1, nspins
     908         102 :             CALL dbt_create(mat_P_omega(jquad, ispin)%matrix, t_2c_tmp)
     909         102 :             CALL dbt_copy_matrix_to_tensor(mat_P_omega(jquad, ispin)%matrix, t_2c_tmp)
     910         102 :             CALL dbt_copy(t_2c_tmp, t_P(ispin), move_data=.TRUE.)
     911         102 :             CALL dbt_filter(t_P(ispin), eps_filter)
     912         180 :             CALL dbt_destroy(t_2c_tmp)
     913             :          END DO
     914             : 
     915             :          !Q = K^T*P*K, open-shell: Q is from one spin, everything else from the other
     916             :          CALL dbt_contract(1.0_dp, t_P(Qspin), force_data%t_2c_K, 0.0_dp, t_2c_RI, &
     917             :                            contract_1=[2], notcontract_1=[1], &
     918             :                            contract_2=[1], notcontract_2=[2], &
     919             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
     920          78 :                            flop=flop, unit_nr=unit_nr_dbcsr)
     921          78 :          dbcsr_nflop = dbcsr_nflop + flop
     922             :          CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_2c_RI, 0.0_dp, t_Q, &
     923             :                            contract_1=[1], notcontract_1=[2], &
     924             :                            contract_2=[1], notcontract_2=[2], &
     925             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
     926          78 :                            flop=flop, unit_nr=unit_nr_dbcsr)
     927          78 :          dbcsr_nflop = dbcsr_nflop + flop
     928          78 :          CALL dbt_clear(t_2c_RI)
     929             : 
     930             :          CALL perform_2c_ops(force, t_KQKT, force_data, fac, t_Q, t_P(Pspin), t_2c_RI, t_2c_RI_2, &
     931          78 :                              use_virial, atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
     932          78 :          CALL get_tensor_occupancy(t_KQKT, nze_KQK, occ_KQK)
     933             : 
     934             :          !Calculate the pseudo-density matrix in tensor form. There are a few useless arguments for SOS-MP2
     935             :          CALL compute_mat_dm_global(fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, tau_tj, num_integ_points, &
     936             :                                     nmo, fm_mo_coeff_occ(Pspin), fm_mo_coeff_virt(Pspin), &
     937             :                                     fm_mo_coeff_occ_scaled, fm_mo_coeff_virt_scaled, mat_dm_occ, mat_dm_virt, &
     938             :                                     matrix_s, Pspin, Eigenval(:, Pspin), 0.0_dp, eps_filter, &
     939             :                                     mp2_env%ri_rpa_im_time%memory_info, unit_nr, &
     940          78 :                                     jquad, .FALSE., .FALSE., qs_env, dummy_int, dummy_ptr, para_env)
     941             : 
     942          78 :          CALL dbt_create(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
     943          78 :          CALL dbt_copy_matrix_to_tensor(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
     944          78 :          CALL dbt_copy(t_2c_tmp, t_dm_occ, move_data=.TRUE.)
     945          78 :          CALL dbt_filter(t_dm_occ, eps_filter)
     946          78 :          CALL dbt_destroy(t_2c_tmp)
     947             : 
     948          78 :          CALL dbt_create(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
     949          78 :          CALL dbt_copy_matrix_to_tensor(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
     950          78 :          CALL dbt_copy(t_2c_tmp, t_dm_virt, move_data=.TRUE.)
     951          78 :          CALL dbt_filter(t_dm_virt, eps_filter)
     952          78 :          CALL dbt_destroy(t_2c_tmp)
     953             : 
     954             :          !Deal with the 3-center quantities.
     955             :          CALL perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
     956             :                              t_KQKT, t_dm_occ, t_dm_virt, t_3c_O, t_3c_M, t_M_occ, t_M_virt, t_3c_0, t_3c_1, &
     957             :                              t_3c_3, t_3c_4, t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_sparse, t_3c_help_1, t_3c_help_2, &
     958             :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
     959             :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
     960             :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
     961          78 :                              unit_nr_dbcsr, mp2_env)
     962             : 
     963          78 :          CALL timeset(routineN//"_dbcsr", handle2)
     964             :          !We go back to DBCSR matrices from now on
     965             :          !Note: R matrices are in fact symmetric, but use a normal type for convenience
     966          78 :          CALL dbt_create(matrix_s(1)%matrix, t_2c_tmp)
     967          78 :          CALL dbt_copy(t_R_occ, t_2c_tmp, move_data=.TRUE.)
     968          78 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_occ)
     969             : 
     970          78 :          CALL dbt_copy(t_R_virt, t_2c_tmp, move_data=.TRUE.)
     971          78 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_virt)
     972             : 
     973             :          !Iteratively calculate the Y1 and Y2 matrices
     974             :          CALL dbcsr_multiply('N', 'N', tau, force_data%P_occ(Pspin)%matrix, &
     975          78 :                              matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     976          78 :          CALL build_Y_matrix(Y_1, dbcsr_work1, force_data%P_occ(Pspin)%matrix, R_virt, eps_filter)
     977          78 :          CALL matrix_exponential(exp_occ, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
     978             : 
     979             :          CALL dbcsr_multiply('N', 'N', -tau, force_data%P_virt(Pspin)%matrix, &
     980          78 :                              matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     981          78 :          CALL build_Y_matrix(Y_2, dbcsr_work1, force_data%P_virt(Pspin)%matrix, R_occ, eps_filter)
     982          78 :          CALL matrix_exponential(exp_virt, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
     983             : 
     984             :          !The force contribution coming from [-S^-1*(e^-tau*P_virt*F)^T*R_occ*S^-1
     985             :          !                                    +tau*S^-1*Y_2^T*F*S^-1] * der_S
     986          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, R_occ, force_data%inv_ovlp, 0.0_dp, dbcsr_work1)
     987          78 :          CALL dbcsr_multiply('T', 'N', 1.0_dp, exp_virt, dbcsr_work1, 0.0_dp, dbcsr_work3)
     988          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, force_data%inv_ovlp, dbcsr_work3, 0.0_dp, dbcsr_work2)
     989             : 
     990          78 :          CALL dbcsr_multiply('N', 'T', tau, force_data%inv_ovlp, Y_2, 0.0_dp, dbcsr_work3)
     991          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work3, matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     992          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work1, force_data%inv_ovlp, 0.0_dp, dbcsr_work3)
     993             : 
     994          78 :          CALL dbcsr_add(dbcsr_work2, dbcsr_work3, 1.0_dp, -1.0_dp)
     995             : 
     996          78 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work2, t_2c_tmp)
     997          78 :          CALL dbt_copy(t_2c_tmp, t_2c_AO, move_data=.TRUE.)
     998             : 
     999          78 :          pref = -1.0_dp*fac
    1000             :          CALL get_2c_der_force(force, t_2c_AO, force_data%t_2c_der_ovlp, atom_of_kind, &
    1001          78 :                                kind_of, force_data%idx_to_at_AO, pref, do_ovlp=.TRUE.)
    1002             : 
    1003          78 :          IF (use_virial) CALL dbcsr_add(virial_ovlp, dbcsr_work2, 1.0_dp, pref)
    1004             : 
    1005             :          !The final contribution from Tr[(tau*Y_1*P_occ - tau*Y_2*P_virt) * der_F]
    1006             :          CALL dbcsr_multiply('N', 'N', tau*fac, Y_1, force_data%P_occ(Pspin)%matrix, 1.0_dp, &
    1007          78 :                              force_data%sum_YP_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1008             :          CALL dbcsr_multiply('N', 'N', -tau*fac, Y_2, force_data%P_virt(Pspin)%matrix, 1.0_dp, &
    1009          78 :                              force_data%sum_YP_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1010             : 
    1011             :          !Build-up the RHS of the response equation.
    1012          78 :          pref = -omega*mp2_env%scale_S
    1013             :          CALL dbcsr_multiply('N', 'N', pref, R_virt, exp_occ, 1.0_dp, &
    1014          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1015             :          CALL dbcsr_multiply('N', 'N', -pref, R_occ, exp_virt, 1.0_dp, &
    1016          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1017             :          CALL dbcsr_multiply('N', 'N', pref*tau, matrix_ks(Pspin)%matrix, Y_1, 1.0_dp, &
    1018          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1019             :          CALL dbcsr_multiply('N', 'N', pref*tau, matrix_ks(Pspin)%matrix, Y_2, 1.0_dp, &
    1020          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1021             : 
    1022          78 :          CALL timestop(handle2)
    1023             : 
    1024             :          !Print some info
    1025          78 :          CALL para_env%sync()
    1026          78 :          t2 = m_walltime()
    1027          78 :          dbcsr_time = dbcsr_time + t2 - t1
    1028             : 
    1029          78 :          IF (unit_nr > 0) THEN
    1030             :             WRITE (unit_nr, '(/T3,A,1X,I3,A)') &
    1031          39 :                'RPA_LOW_SCALING_INFO| Info for time point', jquad, '    (gradients)'
    1032             :             WRITE (unit_nr, '(T6,A,T56,F25.6)') &
    1033          39 :                'Execution time (s):', t2 - t1
    1034             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1035          39 :                'Occupancy of 3c AO derivs:', REAL(nze_der_AO, dp), '/', occ_der_AO*100, '%'
    1036             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1037          39 :                'Occupancy of 3c RI derivs:', REAL(nze_der_RI, dp), '/', occ_der_RI*100, '%'
    1038             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1039          39 :                'Occupancy of the Docc * Dvirt * 3c-int tensor', REAL(nze_ddint, dp), '/', occ_ddint*100, '%'
    1040             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1041          39 :                'Occupancy of KQK^T 2c-tensor:', REAL(nze_KQK, dp), '/', occ_KQK*100, '%'
    1042          39 :             CALL m_flush(unit_nr)
    1043             :          END IF
    1044             : 
    1045             :          !intermediate clean-up
    1046          78 :          CALL dbcsr_release(Y_1)
    1047          78 :          CALL dbcsr_release(Y_2)
    1048         416 :          CALL dbt_destroy(t_2c_tmp)
    1049             :       END DO !jquad
    1050             : 
    1051          26 :       CALL dbt_batched_contract_finalize(t_3c_0)
    1052          26 :       CALL dbt_batched_contract_finalize(t_3c_1)
    1053          26 :       CALL dbt_batched_contract_finalize(t_3c_3)
    1054          26 :       CALL dbt_batched_contract_finalize(t_M_occ)
    1055          26 :       CALL dbt_batched_contract_finalize(t_M_virt)
    1056             : 
    1057          26 :       CALL dbt_batched_contract_finalize(t_3c_ints)
    1058          26 :       CALL dbt_batched_contract_finalize(t_3c_work)
    1059             : 
    1060          26 :       CALL dbt_batched_contract_finalize(t_3c_4)
    1061          26 :       CALL dbt_batched_contract_finalize(t_3c_5)
    1062          26 :       CALL dbt_batched_contract_finalize(t_3c_6)
    1063          26 :       CALL dbt_batched_contract_finalize(t_3c_7)
    1064          26 :       CALL dbt_batched_contract_finalize(t_3c_8)
    1065          26 :       CALL dbt_batched_contract_finalize(t_3c_sparse)
    1066             : 
    1067             :       !Calculate the 2c and 3c contributions to the virial
    1068          26 :       IF (use_virial) THEN
    1069           2 :          CALL dbt_copy(force_data%t_3c_virial_split, force_data%t_3c_virial, move_data=.TRUE.)
    1070             :          CALL calc_3c_virial(work_virial, force_data%t_3c_virial, 1.0_dp, qs_env, force_data%nl_3c, &
    1071             :                              basis_set_ri_aux, basis_set_ao, basis_set_ao, mp2_env%ri_metric, &
    1072           2 :                              der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1)
    1073             : 
    1074             :          CALL calc_2c_virial(work_virial, force_data%RI_virial_met, 1.0_dp, qs_env, force_data%nl_2c_met, &
    1075           2 :                              basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
    1076           2 :          CALL dbcsr_clear(force_data%RI_virial_met)
    1077             : 
    1078           2 :          IF (.NOT. force_data%do_periodic) THEN
    1079             :             CALL calc_2c_virial(work_virial, force_data%RI_virial_pot, 1.0_dp, qs_env, force_data%nl_2c_pot, &
    1080           0 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
    1081           0 :             CALL dbcsr_clear(force_data%RI_virial_pot)
    1082             :          END IF
    1083             : 
    1084           2 :          identity_pot%potential_type = do_potential_id
    1085             :          CALL calc_2c_virial(work_virial_ovlp, virial_ovlp, 1.0_dp, qs_env, force_data%nl_2c_ovlp, &
    1086           2 :                              basis_set_ao, basis_set_ao, identity_pot)
    1087           2 :          CALL dbcsr_release(virial_ovlp)
    1088             : 
    1089           8 :          DO k_xyz = 1, 3
    1090          26 :             DO j_xyz = 1, 3
    1091          78 :                DO i_xyz = 1, 3
    1092             :                   virial%pv_mp2(i_xyz, j_xyz) = virial%pv_mp2(i_xyz, j_xyz) &
    1093          54 :                                                 - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1094             :                   virial%pv_overlap(i_xyz, j_xyz) = virial%pv_overlap(i_xyz, j_xyz) &
    1095          54 :                                                     - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1096             :                   virial%pv_virial(i_xyz, j_xyz) = virial%pv_virial(i_xyz, j_xyz) &
    1097             :                                                    - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz) &
    1098          72 :                                                    - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1099             :                END DO
    1100             :             END DO
    1101             :          END DO
    1102             :       END IF
    1103             : 
    1104             :       !Calculate the periodic contributions of (P|Q) to the force and the virial
    1105          26 :       work_virial = 0.0_dp
    1106          26 :       IF (force_data%do_periodic) THEN
    1107          10 :          IF (mp2_env%eri_method == do_eri_gpw) THEN
    1108           6 :             CALL get_2c_gpw_forces(force_data%G_PQ, force, work_virial, use_virial, mp2_env, qs_env)
    1109           4 :          ELSE IF (mp2_env%eri_method == do_eri_mme) THEN
    1110           4 :             CALL get_2c_mme_forces(force_data%G_PQ, force, mp2_env, qs_env)
    1111           4 :             IF (use_virial) CPABORT("Stress tensor not available with MME intrgrals")
    1112             :          ELSE
    1113           0 :             CPABORT("Periodic case not possible with OS integrals")
    1114             :          END IF
    1115          10 :          CALL dbcsr_clear(force_data%G_PQ)
    1116             :       END IF
    1117             : 
    1118          26 :       IF (use_virial) THEN
    1119          26 :          virial%pv_mp2 = virial%pv_mp2 + work_virial
    1120          26 :          virial%pv_virial = virial%pv_virial + work_virial
    1121           2 :          virial%pv_calculate = .FALSE.
    1122             : 
    1123           6 :          DO ibasis = 1, SIZE(basis_set_ao)
    1124           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1125           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
    1126           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1127           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
    1128             :          END DO
    1129             :       END IF
    1130             : 
    1131             :       !clean-up
    1132          26 :       IF (ASSOCIATED(dummy_ptr)) DEALLOCATE (dummy_ptr)
    1133          60 :       DO ispin = 1, nspins
    1134          60 :          CALL dbt_destroy(t_P(ispin))
    1135             :       END DO
    1136          26 :       CALL dbt_destroy(t_3c_0)
    1137          26 :       CALL dbt_destroy(t_3c_1)
    1138          26 :       CALL dbt_destroy(t_3c_3)
    1139          26 :       CALL dbt_destroy(t_3c_4)
    1140          26 :       CALL dbt_destroy(t_3c_5)
    1141          26 :       CALL dbt_destroy(t_3c_6)
    1142          26 :       CALL dbt_destroy(t_3c_7)
    1143          26 :       CALL dbt_destroy(t_3c_8)
    1144          26 :       CALL dbt_destroy(t_3c_sparse)
    1145          26 :       CALL dbt_destroy(t_3c_help_1)
    1146          26 :       CALL dbt_destroy(t_3c_help_2)
    1147          26 :       CALL dbt_destroy(t_3c_ints)
    1148          26 :       CALL dbt_destroy(t_3c_work)
    1149          26 :       CALL dbt_destroy(t_R_occ)
    1150          26 :       CALL dbt_destroy(t_R_virt)
    1151          26 :       CALL dbt_destroy(t_dm_occ)
    1152          26 :       CALL dbt_destroy(t_dm_virt)
    1153          26 :       CALL dbt_destroy(t_Q)
    1154          26 :       CALL dbt_destroy(t_KQKT)
    1155          26 :       CALL dbt_destroy(t_M_occ)
    1156          26 :       CALL dbt_destroy(t_M_virt)
    1157          26 :       CALL dbcsr_release(R_occ)
    1158          26 :       CALL dbcsr_release(R_virt)
    1159          26 :       CALL dbcsr_release(dbcsr_work1)
    1160          26 :       CALL dbcsr_release(dbcsr_work2)
    1161          26 :       CALL dbcsr_release(dbcsr_work3)
    1162          26 :       CALL dbcsr_release(exp_occ)
    1163          26 :       CALL dbcsr_release(exp_virt)
    1164             : 
    1165          26 :       CALL dbt_destroy(t_2c_RI)
    1166          26 :       CALL dbt_destroy(t_2c_RI_2)
    1167          26 :       CALL dbt_destroy(t_2c_AO)
    1168          26 :       CALL dbcsr_deallocate_matrix_set(mat_dm_occ)
    1169          26 :       CALL dbcsr_deallocate_matrix_set(mat_dm_virt)
    1170             : 
    1171          26 :       CALL timestop(handle)
    1172             : 
    1173         138 :    END SUBROUTINE calc_laplace_loop_forces
    1174             : 
    1175             : ! **************************************************************************************************
    1176             : !> \brief Updates the cubic-scaling RPA contribution to the forces at each quadrature point. This
    1177             : !>        routine is adapted from the corresponding Laplace SOS-MP2 loop force one.
    1178             : !> \param force_data ...
    1179             : !> \param mat_P_omega ...
    1180             : !> \param t_3c_M ...
    1181             : !> \param t_3c_O ...
    1182             : !> \param t_3c_O_compressed ...
    1183             : !> \param t_3c_O_ind ...
    1184             : !> \param fm_scaled_dm_occ_tau ...
    1185             : !> \param fm_scaled_dm_virt_tau ...
    1186             : !> \param fm_mo_coeff_occ ...
    1187             : !> \param fm_mo_coeff_virt ...
    1188             : !> \param fm_mo_coeff_occ_scaled ...
    1189             : !> \param fm_mo_coeff_virt_scaled ...
    1190             : !> \param starts_array_mc ...
    1191             : !> \param ends_array_mc ...
    1192             : !> \param starts_array_mc_block ...
    1193             : !> \param ends_array_mc_block ...
    1194             : !> \param num_integ_points ...
    1195             : !> \param nmo ...
    1196             : !> \param Eigenval ...
    1197             : !> \param e_fermi ...
    1198             : !> \param weights_cos_tf_t_to_w ...
    1199             : !> \param weights_cos_tf_w_to_t ...
    1200             : !> \param tj ...
    1201             : !> \param wj ...
    1202             : !> \param tau_tj ...
    1203             : !> \param cut_memory ...
    1204             : !> \param ispin ...
    1205             : !> \param open_shell ...
    1206             : !> \param unit_nr ...
    1207             : !> \param dbcsr_time ...
    1208             : !> \param dbcsr_nflop ...
    1209             : !> \param mp2_env ...
    1210             : !> \param qs_env ...
    1211             : ! **************************************************************************************************
    1212         180 :    SUBROUTINE calc_rpa_loop_forces(force_data, mat_P_omega, t_3c_M, t_3c_O, t_3c_O_compressed, &
    1213          36 :                                    t_3c_O_ind, fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, &
    1214          36 :                                    fm_mo_coeff_occ, fm_mo_coeff_virt, fm_mo_coeff_occ_scaled, &
    1215          36 :                                    fm_mo_coeff_virt_scaled, starts_array_mc, ends_array_mc, &
    1216          36 :                                    starts_array_mc_block, ends_array_mc_block, num_integ_points, &
    1217          36 :                                    nmo, Eigenval, e_fermi, weights_cos_tf_t_to_w, weights_cos_tf_w_to_t, &
    1218          36 :                                    tj, wj, tau_tj, cut_memory, ispin, open_shell, unit_nr, dbcsr_time, &
    1219             :                                    dbcsr_nflop, mp2_env, qs_env)
    1220             : 
    1221             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1222             :       TYPE(dbcsr_p_type), DIMENSION(:, :), INTENT(INOUT) :: mat_P_omega
    1223             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M, t_3c_O
    1224             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
    1225             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
    1226             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_scaled_dm_occ_tau, &
    1227             :                                                             fm_scaled_dm_virt_tau
    1228             :       TYPE(cp_fm_type), DIMENSION(:), INTENT(IN)         :: fm_mo_coeff_occ, fm_mo_coeff_virt
    1229             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_mo_coeff_occ_scaled, &
    1230             :                                                             fm_mo_coeff_virt_scaled
    1231             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
    1232             :                                                             starts_array_mc_block, &
    1233             :                                                             ends_array_mc_block
    1234             :       INTEGER, INTENT(IN)                                :: num_integ_points, nmo
    1235             :       REAL(KIND=dp), DIMENSION(:, :), INTENT(IN)         :: Eigenval
    1236             :       REAL(KIND=dp), INTENT(IN)                          :: e_fermi
    1237             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
    1238             :          INTENT(IN)                                      :: weights_cos_tf_t_to_w, &
    1239             :                                                             weights_cos_tf_w_to_t
    1240             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
    1241             :          INTENT(IN)                                      :: tj, wj
    1242             :       REAL(KIND=dp), DIMENSION(num_integ_points), &
    1243             :          INTENT(IN)                                      :: tau_tj
    1244             :       INTEGER, INTENT(IN)                                :: cut_memory, ispin
    1245             :       LOGICAL, INTENT(IN)                                :: open_shell
    1246             :       INTEGER, INTENT(IN)                                :: unit_nr
    1247             :       REAL(dp), INTENT(INOUT)                            :: dbcsr_time
    1248             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
    1249             :       TYPE(mp2_type)                                     :: mp2_env
    1250             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1251             : 
    1252             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_rpa_loop_forces'
    1253             : 
    1254             :       INTEGER :: dummy_int, handle, handle2, i_mem, i_xyz, ibasis, iquad, j_xyz, jquad, k_xyz, &
    1255             :          n_mem_RI, n_rep, natom, nkind, nspins, unit_nr_dbcsr
    1256             :       INTEGER(int_8)                                     :: flop, nze, nze_ddint, nze_der_AO, &
    1257             :                                                             nze_der_RI, nze_KBK
    1258          36 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, batch_blk_end, &
    1259          36 :                                                             batch_blk_start, batch_end_RI, &
    1260          36 :                                                             batch_start_RI, kind_of, mc_ranges, &
    1261          36 :                                                             mc_ranges_RI
    1262          36 :       INTEGER, DIMENSION(:, :), POINTER                  :: dummy_ptr
    1263             :       LOGICAL                                            :: memory_info, use_virial
    1264             :       REAL(dp) :: eps_filter, eps_pgf_orb, eps_pgf_orb_old, fac, occ, occ_ddint, occ_der_AO, &
    1265             :          occ_der_RI, occ_KBK, omega, pref, spin_fac, t1, t2, tau, weight
    1266             :       REAL(dp), DIMENSION(3, 3)                          :: work_virial, work_virial_ovlp
    1267          36 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    1268             :       TYPE(cell_type), POINTER                           :: cell
    1269             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
    1270          36 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: mat_P_tau, matrix_ks, matrix_s
    1271          36 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: mat_dm_occ, mat_dm_virt
    1272             :       TYPE(dbcsr_type)                                   :: dbcsr_work1, dbcsr_work2, dbcsr_work3, &
    1273             :                                                             dbcsr_work_symm, exp_occ, exp_virt, &
    1274             :                                                             R_occ, R_virt, virial_ovlp, Y_1, Y_2
    1275        1764 :       TYPE(dbt_type) :: t_2c_AO, t_2c_RI, t_2c_RI_2, t_2c_tmp, t_3c_0, t_3c_1, t_3c_3, t_3c_4, &
    1276        1764 :          t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_help_1, t_3c_help_2, t_3c_ints, t_3c_sparse, &
    1277        2016 :          t_3c_work, t_dm_occ, t_dm_virt, t_KBKT, t_M_occ, t_M_virt, t_P, t_R_occ, t_R_virt
    1278          36 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:)          :: t_B
    1279             :       TYPE(dft_control_type), POINTER                    :: dft_control
    1280             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    1281          36 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
    1282             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
    1283             :       TYPE(libint_potential_type)                        :: identity_pot
    1284             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1285          36 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    1286          36 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1287          36 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    1288             :       TYPE(section_vals_type), POINTER                   :: qs_section
    1289             :       TYPE(virial_type), POINTER                         :: virial
    1290             : 
    1291          36 :       NULLIFY (matrix_s, dummy_ptr, atomic_kind_set, force, matrix_s, matrix_ks, mat_dm_occ, mat_dm_virt)
    1292          36 :       NULLIFY (dft_control, virial, particle_set, cell, blacs_env, para_env, orb_basis, ri_basis)
    1293          36 :       NULLIFY (qs_kind_set)
    1294             : 
    1295          36 :       CALL timeset(routineN, handle)
    1296             : 
    1297             :       CALL get_qs_env(qs_env, matrix_s=matrix_s, natom=natom, atomic_kind_set=atomic_kind_set, &
    1298             :                       force=force, matrix_ks=matrix_ks, dft_control=dft_control, virial=virial, &
    1299             :                       particle_set=particle_set, cell=cell, blacs_env=blacs_env, para_env=para_env, &
    1300          36 :                       qs_kind_set=qs_kind_set, nkind=nkind)
    1301          36 :       eps_filter = mp2_env%ri_rpa_im_time%eps_filter
    1302          36 :       nspins = dft_control%nspins
    1303             : 
    1304          36 :       memory_info = mp2_env%ri_rpa_im_time%memory_info
    1305          36 :       IF (memory_info) THEN
    1306           0 :          unit_nr_dbcsr = unit_nr
    1307             :       ELSE
    1308          36 :          unit_nr_dbcsr = 0
    1309             :       END IF
    1310             : 
    1311          36 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
    1312             : 
    1313          36 :       IF (use_virial) virial%pv_calculate = .TRUE.
    1314             : 
    1315          36 :       IF (use_virial) THEN
    1316           2 :          qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
    1317           2 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
    1318           2 :          IF (n_rep /= 0) THEN
    1319           0 :             CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
    1320             :          ELSE
    1321           2 :             CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
    1322           2 :             eps_pgf_orb = SQRT(eps_pgf_orb)
    1323             :          END IF
    1324           2 :          eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
    1325             : 
    1326          16 :          ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
    1327           2 :          CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    1328           2 :          CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
    1329             : 
    1330           8 :          DO ibasis = 1, SIZE(basis_set_ao)
    1331           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1332           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
    1333           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1334           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
    1335             :          END DO
    1336             :       END IF
    1337             : 
    1338             :       !We follow the general logic of the compute_mat_P_omega routine
    1339          36 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI)
    1340          36 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI_2)
    1341          36 :       CALL dbt_create(force_data%t_2c_der_ovlp(1), t_2c_AO)
    1342             : 
    1343          36 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    1344             : 
    1345             :       ! Always do the batching of the MO on mu and sigma, such that it is consistent between
    1346             :       ! the occupied and the virtual quantities
    1347         108 :       ALLOCATE (mc_ranges(cut_memory + 1))
    1348         108 :       mc_ranges(:cut_memory) = starts_array_mc_block(:)
    1349          36 :       mc_ranges(cut_memory + 1) = ends_array_mc_block(cut_memory) + 1
    1350             : 
    1351             :       ! Also need some batching on the RI, because it loses sparsity at some point
    1352          36 :       n_mem_RI = cut_memory
    1353             :       CALL create_tensor_batches(force_data%bsizes_RI_split, n_mem_RI, batch_start_RI, batch_end_RI, &
    1354          36 :                                  batch_blk_start, batch_blk_end)
    1355         108 :       ALLOCATE (mc_ranges_RI(n_mem_RI + 1))
    1356         108 :       mc_ranges_RI(1:n_mem_RI) = batch_blk_start(1:n_mem_RI)
    1357          36 :       mc_ranges_RI(n_mem_RI + 1) = batch_blk_end(n_mem_RI) + 1
    1358          36 :       DEALLOCATE (batch_blk_start, batch_blk_end)
    1359             : 
    1360             :       !Pre-allocate all required tensors and matrices
    1361          36 :       CALL dbt_create(t_2c_RI, t_P)
    1362          36 :       CALL dbt_create(t_2c_RI, t_KBKT)
    1363          36 :       CALL dbt_create(t_2c_AO, t_dm_occ)
    1364          36 :       CALL dbt_create(t_2c_AO, t_dm_virt)
    1365             : 
    1366             :       !note: t_3c_O and t_3c_M have different mappings (map_1d, map_2d)
    1367          36 :       CALL dbt_create(t_3c_O, t_M_occ)
    1368          36 :       CALL dbt_create(t_3c_O, t_M_virt)
    1369          36 :       CALL dbt_create(t_3c_O, t_3c_0)
    1370             : 
    1371          36 :       CALL dbt_create(t_3c_O, t_3c_1)
    1372          36 :       CALL dbt_create(t_3c_O, t_3c_3)
    1373          36 :       CALL dbt_create(t_3c_O, t_3c_4)
    1374          36 :       CALL dbt_create(t_3c_O, t_3c_5)
    1375          36 :       CALL dbt_create(t_3c_M, t_3c_6)
    1376          36 :       CALL dbt_create(t_3c_M, t_3c_7)
    1377          36 :       CALL dbt_create(t_3c_M, t_3c_8)
    1378          36 :       CALL dbt_create(t_3c_M, t_3c_sparse)
    1379          36 :       CALL dbt_create(t_3c_O, t_3c_help_1)
    1380          36 :       CALL dbt_create(t_3c_O, t_3c_help_2)
    1381          36 :       CALL dbt_create(t_2c_AO, t_R_occ)
    1382          36 :       CALL dbt_create(t_2c_AO, t_R_virt)
    1383          36 :       CALL dbt_create(t_3c_M, t_3c_ints)
    1384          36 :       CALL dbt_create(t_3c_M, t_3c_work)
    1385             : 
    1386             :       !Before entring the loop, need to compute the 2c tensors B = (1 + Q(w))^-1 - 1, for each
    1387             :       !frequency grid point, before doing the transformation to the time grid
    1388         416 :       ALLOCATE (t_B(num_integ_points))
    1389         128 :       DO jquad = 1, num_integ_points
    1390         128 :          CALL dbt_create(t_2c_RI, t_B(jquad))
    1391             :       END DO
    1392             : 
    1393         200 :       ALLOCATE (mat_P_tau(num_integ_points))
    1394         128 :       DO jquad = 1, num_integ_points
    1395          92 :          ALLOCATE (mat_P_tau(jquad)%matrix)
    1396         128 :          CALL dbcsr_create(mat_P_tau(jquad)%matrix, template=mat_P_omega(jquad, ispin)%matrix)
    1397             :       END DO
    1398             : 
    1399          36 :       CALL dbcsr_create(dbcsr_work_symm, template=force_data%G_PQ, matrix_type=dbcsr_type_symmetric)
    1400          36 :       CALL dbt_create(dbcsr_work_symm, t_2c_tmp)
    1401             : 
    1402             :       !loop over freqeuncies
    1403         128 :       DO iquad = 1, num_integ_points
    1404          92 :          omega = tj(iquad)
    1405             : 
    1406             :          !calculate (1 + Q(w))^-1 - 1 for the given freq.
    1407             :          !Always take spin alpha (get 2*alpha in closed shell, and alpha+beta in open-shell)
    1408          92 :          CALL dbcsr_copy(dbcsr_work_symm, mat_P_omega(iquad, 1)%matrix)
    1409          92 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work_symm, t_2c_tmp)
    1410          92 :          CALL dbt_copy(t_2c_tmp, t_2c_RI, move_data=.TRUE.)
    1411             : 
    1412             :          CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_2c_RI_2, &
    1413             :                            contract_1=[2], notcontract_1=[1], &
    1414             :                            contract_2=[1], notcontract_2=[2], &
    1415             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1416          92 :                            flop=flop, unit_nr=unit_nr_dbcsr)
    1417          92 :          dbcsr_nflop = dbcsr_nflop + flop
    1418             :          CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_2c_RI_2, 0.0_dp, t_2c_RI, &
    1419             :                            contract_1=[1], notcontract_1=[2], &
    1420             :                            contract_2=[1], notcontract_2=[2], &
    1421             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1422          92 :                            flop=flop, unit_nr=unit_nr_dbcsr)
    1423          92 :          CALL dbt_copy(t_2c_RI, t_2c_tmp, move_data=.TRUE.)
    1424          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, dbcsr_work_symm)
    1425          92 :          CALL dbcsr_add_on_diag(dbcsr_work_symm, 1.0_dp)
    1426             : 
    1427          92 :          CALL cp_dbcsr_cholesky_decompose(dbcsr_work_symm, para_env=para_env, blacs_env=blacs_env)
    1428          92 :          CALL cp_dbcsr_cholesky_invert(dbcsr_work_symm, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
    1429             : 
    1430          92 :          CALL dbcsr_add_on_diag(dbcsr_work_symm, -1.0_dp)
    1431             : 
    1432         372 :          DO jquad = 1, num_integ_points
    1433         244 :             tau = tau_tj(jquad)
    1434             : 
    1435             :             !the P matrix to time.
    1436         244 :             weight = weights_cos_tf_w_to_t(jquad, iquad)*COS(tau*omega)
    1437         244 :             IF (open_shell) THEN
    1438          64 :                IF (ispin == 1) THEN
    1439             :                   !mat_P_omega contains the sum of alpha and beta spin => we only want alpha
    1440          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 1)%matrix, 1.0_dp, weight)
    1441          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 2)%matrix, 1.0_dp, -weight)
    1442             :                ELSE
    1443          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 2)%matrix, 1.0_dp, weight)
    1444             :                END IF
    1445             :             ELSE
    1446             :                !factor 0.5 because originam matrix Q is scaled by 2 in RPA (spin)
    1447         180 :                weight = 0.5_dp*weight
    1448         180 :                CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 1)%matrix, 1.0_dp, weight)
    1449             :             END IF
    1450             : 
    1451             :             !convert B matrix to time
    1452         244 :             weight = weights_cos_tf_t_to_w(iquad, jquad)*COS(tau*omega)*wj(iquad)
    1453         244 :             CALL dbt_copy_matrix_to_tensor(dbcsr_work_symm, t_2c_tmp)
    1454         244 :             CALL dbt_scale(t_2c_tmp, weight)
    1455         336 :             CALL dbt_copy(t_2c_tmp, t_B(jquad), summation=.TRUE., move_data=.TRUE.)
    1456             :          END DO
    1457             :       END DO
    1458          36 :       CALL dbt_destroy(t_2c_tmp)
    1459          36 :       CALL dbcsr_release(dbcsr_work_symm)
    1460          36 :       CALL dbt_clear(t_2c_RI)
    1461          36 :       CALL dbt_clear(t_2c_RI_2)
    1462             : 
    1463             :       !Pre-define the sparsity of t_3c_4 as a function of the derivatives
    1464          36 :       occ_der_AO = 0; nze_der_AO = 0
    1465          36 :       occ_der_RI = 0; nze_der_RI = 0
    1466         144 :       DO i_xyz = 1, 3
    1467         360 :          DO i_mem = 1, cut_memory
    1468             :             CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
    1469         216 :                                    force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    1470         216 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
    1471         216 :             occ_der_RI = occ_der_RI + occ
    1472         216 :             nze_der_RI = nze_der_RI + nze
    1473         216 :             CALL dbt_copy(force_data%t_3c_der_RI(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
    1474             : 
    1475             :             CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
    1476         216 :                                    force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    1477         216 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
    1478         216 :             occ_der_AO = occ_der_AO + occ
    1479         216 :             nze_der_AO = nze_der_AO + nze
    1480         216 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, order=[1, 3, 2], summation=.TRUE.)
    1481         756 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
    1482             :          END DO
    1483             :       END DO
    1484          36 :       occ_der_RI = occ_der_RI/3.0_dp
    1485          36 :       occ_der_AO = occ_der_AO/3.0_dp
    1486          36 :       nze_der_RI = nze_der_RI/3
    1487          36 :       nze_der_AO = nze_der_AO/3
    1488             : 
    1489          36 :       CALL dbcsr_create(R_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1490          36 :       CALL dbcsr_create(R_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1491          36 :       CALL dbcsr_create(dbcsr_work_symm, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_symmetric)
    1492          36 :       CALL dbcsr_create(dbcsr_work1, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1493          36 :       CALL dbcsr_create(dbcsr_work2, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1494          36 :       CALL dbcsr_create(dbcsr_work3, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1495          36 :       CALL dbcsr_create(exp_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1496          36 :       CALL dbcsr_create(exp_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1497          36 :       IF (use_virial) CALL dbcsr_create(virial_ovlp, template=dbcsr_work1)
    1498             : 
    1499          36 :       CALL dbt_batched_contract_init(t_3c_0, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
    1500          36 :       CALL dbt_batched_contract_init(t_3c_1, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
    1501          36 :       CALL dbt_batched_contract_init(t_3c_3, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1502          36 :       CALL dbt_batched_contract_init(t_M_occ, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1503          36 :       CALL dbt_batched_contract_init(t_M_virt, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1504             : 
    1505          36 :       CALL dbt_batched_contract_init(t_3c_ints, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1506          36 :       CALL dbt_batched_contract_init(t_3c_work, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1507             : 
    1508             :       CALL dbt_batched_contract_init(t_3c_4, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1509          36 :                                      batch_range_3=mc_ranges)
    1510             :       CALL dbt_batched_contract_init(t_3c_5, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1511          36 :                                      batch_range_3=mc_ranges)
    1512             :       CALL dbt_batched_contract_init(t_3c_6, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1513          36 :                                      batch_range_3=mc_ranges)
    1514             :       CALL dbt_batched_contract_init(t_3c_7, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1515          36 :                                      batch_range_3=mc_ranges)
    1516             :       CALL dbt_batched_contract_init(t_3c_8, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1517          36 :                                      batch_range_3=mc_ranges)
    1518             :       CALL dbt_batched_contract_init(t_3c_sparse, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1519          36 :                                      batch_range_3=mc_ranges)
    1520             : 
    1521          36 :       fac = 1.0_dp/fourpi*mp2_env%ri_rpa%scale_rpa
    1522          36 :       IF (open_shell) fac = 0.5_dp*fac
    1523             : 
    1524          36 :       work_virial = 0.0_dp
    1525          36 :       work_virial_ovlp = 0.0_dp
    1526         128 :       DO jquad = 1, num_integ_points
    1527          92 :          tau = tau_tj(jquad)
    1528          92 :          occ_ddint = 0; nze_ddint = 0
    1529             : 
    1530          92 :          CALL para_env%sync()
    1531          92 :          t1 = m_walltime()
    1532             : 
    1533             :          !Deal with the force contributions where there is no explicit 3-center quantities, i.e. the
    1534             :          !forces due to the metric and potential derivatives
    1535          92 :          CALL dbt_create(mat_P_tau(jquad)%matrix, t_2c_tmp)
    1536          92 :          CALL dbt_copy_matrix_to_tensor(mat_P_tau(jquad)%matrix, t_2c_tmp)
    1537          92 :          CALL dbt_copy(t_2c_tmp, t_P, move_data=.TRUE.)
    1538          92 :          CALL dbt_filter(t_P, eps_filter)
    1539          92 :          CALL dbt_destroy(t_2c_tmp)
    1540             : 
    1541             :          CALL perform_2c_ops(force, t_KBKT, force_data, fac, t_B(jquad), t_P, t_2c_RI, t_2c_RI_2, &
    1542          92 :                              use_virial, atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
    1543          92 :          CALL get_tensor_occupancy(t_KBKT, nze_KBK, occ_KBK)
    1544             : 
    1545             :          !Calculate the pseudo-density matrix in tensor form. There are a few useless arguments for SOS-MP2
    1546             :          CALL compute_mat_dm_global(fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, tau_tj, num_integ_points, &
    1547             :                                     nmo, fm_mo_coeff_occ(ispin), fm_mo_coeff_virt(ispin), &
    1548             :                                     fm_mo_coeff_occ_scaled, fm_mo_coeff_virt_scaled, mat_dm_occ, mat_dm_virt, &
    1549             :                                     matrix_s, ispin, Eigenval(:, ispin), e_fermi, eps_filter, &
    1550             :                                     mp2_env%ri_rpa_im_time%memory_info, unit_nr, &
    1551          92 :                                     jquad, .FALSE., .FALSE., qs_env, dummy_int, dummy_ptr, para_env)
    1552             : 
    1553          92 :          CALL dbt_create(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
    1554          92 :          CALL dbt_copy_matrix_to_tensor(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
    1555          92 :          CALL dbt_copy(t_2c_tmp, t_dm_occ, move_data=.TRUE.)
    1556          92 :          CALL dbt_filter(t_dm_occ, eps_filter)
    1557          92 :          CALL dbt_destroy(t_2c_tmp)
    1558             : 
    1559          92 :          CALL dbt_create(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
    1560          92 :          CALL dbt_copy_matrix_to_tensor(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
    1561          92 :          CALL dbt_copy(t_2c_tmp, t_dm_virt, move_data=.TRUE.)
    1562          92 :          CALL dbt_filter(t_dm_virt, eps_filter)
    1563          92 :          CALL dbt_destroy(t_2c_tmp)
    1564             : 
    1565             :          !Deal with the 3-center quantities.
    1566             :          CALL perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
    1567             :                              t_KBKT, t_dm_occ, t_dm_virt, t_3c_O, t_3c_M, t_M_occ, t_M_virt, t_3c_0, t_3c_1, &
    1568             :                              t_3c_3, t_3c_4, t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_sparse, t_3c_help_1, t_3c_help_2, &
    1569             :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
    1570             :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
    1571             :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
    1572          92 :                              unit_nr_dbcsr, mp2_env)
    1573             : 
    1574          92 :          CALL timeset(routineN//"_dbcsr", handle2)
    1575             :          !We go back to DBCSR matrices from now on
    1576             :          !Note: R matrices are in fact symmetric, but use a normal type for convenience
    1577          92 :          CALL dbt_create(matrix_s(1)%matrix, t_2c_tmp)
    1578          92 :          CALL dbt_copy(t_R_occ, t_2c_tmp, move_data=.TRUE.)
    1579          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_occ)
    1580             : 
    1581          92 :          CALL dbt_copy(t_R_virt, t_2c_tmp, move_data=.TRUE.)
    1582          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_virt)
    1583             : 
    1584             :          !Iteratively calculate the Y1 and Y2 matrices
    1585          92 :          CALL dbcsr_copy(dbcsr_work_symm, matrix_ks(ispin)%matrix)
    1586          92 :          CALL dbcsr_add(dbcsr_work_symm, matrix_s(1)%matrix, 1.0_dp, -e_fermi)
    1587             :          CALL dbcsr_multiply('N', 'N', tau, force_data%P_occ(ispin)%matrix, &
    1588          92 :                              dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1589          92 :          CALL build_Y_matrix(Y_1, dbcsr_work1, force_data%P_occ(ispin)%matrix, R_virt, eps_filter)
    1590          92 :          CALL matrix_exponential(exp_occ, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
    1591             : 
    1592             :          CALL dbcsr_multiply('N', 'N', -tau, force_data%P_virt(ispin)%matrix, &
    1593          92 :                              dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1594          92 :          CALL build_Y_matrix(Y_2, dbcsr_work1, force_data%P_virt(ispin)%matrix, R_occ, eps_filter)
    1595          92 :          CALL matrix_exponential(exp_virt, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
    1596             : 
    1597             :          !The force contribution coming from [-S^-1*(e^-tau*P_virt*F)^T*R_occ*S^-1
    1598             :          !                                    +tau*S^-1*Y_2^T*F*S^-1] * der_S
    1599             :          !as well as -tau*e_fermi*Y_1*P^occ + tau*e_fermi*Y_2*P^virt
    1600          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, R_occ, force_data%inv_ovlp, 0.0_dp, dbcsr_work1)
    1601          92 :          CALL dbcsr_multiply('T', 'N', 1.0_dp, exp_virt, dbcsr_work1, 0.0_dp, dbcsr_work3)
    1602          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, force_data%inv_ovlp, dbcsr_work3, 0.0_dp, dbcsr_work2)
    1603             : 
    1604          92 :          CALL dbcsr_multiply('N', 'T', tau, force_data%inv_ovlp, Y_2, 0.0_dp, dbcsr_work3)
    1605          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work3, dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1606          92 :          CALL dbcsr_multiply('N', 'N', -1.0_dp, dbcsr_work1, force_data%inv_ovlp, 1.0_dp, dbcsr_work2)
    1607             : 
    1608          92 :          CALL dbcsr_multiply('N', 'T', tau*e_fermi, force_data%P_occ(ispin)%matrix, Y_1, 1.0_dp, dbcsr_work2)
    1609          92 :          CALL dbcsr_multiply('N', 'T', -tau*e_fermi, force_data%P_virt(ispin)%matrix, Y_2, 1.0_dp, dbcsr_work2)
    1610             : 
    1611          92 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work2, t_2c_tmp)
    1612          92 :          CALL dbt_copy(t_2c_tmp, t_2c_AO, move_data=.TRUE.)
    1613             : 
    1614          92 :          pref = -1.0_dp*fac
    1615             :          CALL get_2c_der_force(force, t_2c_AO, force_data%t_2c_der_ovlp, atom_of_kind, &
    1616          92 :                                kind_of, force_data%idx_to_at_AO, pref, do_ovlp=.TRUE.)
    1617             : 
    1618          92 :          IF (use_virial) CALL dbcsr_add(virial_ovlp, dbcsr_work2, 1.0_dp, pref)
    1619             : 
    1620             :          !The final contribution from Tr[(tau*Y_1*P_occ - tau*Y_2*P_virt) * der_F]
    1621             :          CALL dbcsr_multiply('N', 'N', fac*tau, Y_1, force_data%P_occ(ispin)%matrix, 1.0_dp, &
    1622          92 :                              force_data%sum_YP_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1623             :          CALL dbcsr_multiply('N', 'N', -fac*tau, Y_2, force_data%P_virt(ispin)%matrix, 1.0_dp, &
    1624          92 :                              force_data%sum_YP_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1625             : 
    1626          92 :          spin_fac = 0.5_dp*fac
    1627          92 :          IF (open_shell) spin_fac = 2.0_dp*spin_fac
    1628             :          !Build-up the RHS of the response equation.
    1629             :          CALL dbcsr_multiply('N', 'N', 1.0_dp*spin_fac, R_virt, exp_occ, 1.0_dp, &
    1630          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1631             :          CALL dbcsr_multiply('N', 'N', -1.0_dp*spin_fac, R_occ, exp_virt, 1.0_dp, &
    1632          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1633             :          CALL dbcsr_multiply('N', 'N', tau*spin_fac, dbcsr_work_symm, Y_1, 1.0_dp, &
    1634          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1635             :          CALL dbcsr_multiply('N', 'N', tau*spin_fac, dbcsr_work_symm, Y_2, 1.0_dp, &
    1636          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1637             : 
    1638          92 :          CALL timestop(handle2)
    1639             : 
    1640             :          !Print some info
    1641          92 :          CALL para_env%sync()
    1642          92 :          t2 = m_walltime()
    1643          92 :          dbcsr_time = dbcsr_time + t2 - t1
    1644             : 
    1645          92 :          IF (unit_nr > 0) THEN
    1646             :             WRITE (unit_nr, '(/T3,A,1X,I3,A)') &
    1647          46 :                'RPA_LOW_SCALING_INFO| Info for time point', jquad, '    (gradients)'
    1648             :             WRITE (unit_nr, '(T6,A,T56,F25.6)') &
    1649          46 :                'Time:', t2 - t1
    1650             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1651          46 :                'Occupancy of 3c AO derivs:', REAL(nze_der_AO, dp), '/', occ_der_AO*100, '%'
    1652             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1653          46 :                'Occupancy of 3c RI derivs:', REAL(nze_der_RI, dp), '/', occ_der_RI*100, '%'
    1654             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1655          46 :                'Occupancy of the Docc * Dvirt * 3c-int tensor', REAL(nze_ddint, dp), '/', occ_ddint*100, '%'
    1656             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1657          46 :                'Occupancy of KBK^T 2c-tensor:', REAL(nze_KBK, dp), '/', occ_KBK*100, '%'
    1658          46 :             CALL m_flush(unit_nr)
    1659             :          END IF
    1660             : 
    1661             :          !intermediate clean-up
    1662          92 :          CALL dbcsr_release(Y_1)
    1663          92 :          CALL dbcsr_release(Y_2)
    1664         496 :          CALL dbt_destroy(t_2c_tmp)
    1665             : 
    1666             :       END DO !jquad
    1667             : 
    1668          36 :       CALL dbt_batched_contract_finalize(t_3c_0)
    1669          36 :       CALL dbt_batched_contract_finalize(t_3c_1)
    1670          36 :       CALL dbt_batched_contract_finalize(t_3c_3)
    1671          36 :       CALL dbt_batched_contract_finalize(t_M_occ)
    1672          36 :       CALL dbt_batched_contract_finalize(t_M_virt)
    1673             : 
    1674          36 :       CALL dbt_batched_contract_finalize(t_3c_ints)
    1675          36 :       CALL dbt_batched_contract_finalize(t_3c_work)
    1676             : 
    1677          36 :       CALL dbt_batched_contract_finalize(t_3c_4)
    1678          36 :       CALL dbt_batched_contract_finalize(t_3c_5)
    1679          36 :       CALL dbt_batched_contract_finalize(t_3c_6)
    1680          36 :       CALL dbt_batched_contract_finalize(t_3c_7)
    1681          36 :       CALL dbt_batched_contract_finalize(t_3c_8)
    1682          36 :       CALL dbt_batched_contract_finalize(t_3c_sparse)
    1683             : 
    1684             :       !Calculate the 2c and 3c contributions to the virial
    1685          36 :       IF (use_virial) THEN
    1686           2 :          CALL dbt_copy(force_data%t_3c_virial_split, force_data%t_3c_virial, move_data=.TRUE.)
    1687             :          CALL calc_3c_virial(work_virial, force_data%t_3c_virial, 1.0_dp, qs_env, force_data%nl_3c, &
    1688             :                              basis_set_ri_aux, basis_set_ao, basis_set_ao, mp2_env%ri_metric, &
    1689           2 :                              der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1)
    1690             : 
    1691             :          CALL calc_2c_virial(work_virial, force_data%RI_virial_met, 1.0_dp, qs_env, force_data%nl_2c_met, &
    1692           2 :                              basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
    1693           2 :          CALL dbcsr_clear(force_data%RI_virial_met)
    1694             : 
    1695           2 :          IF (.NOT. force_data%do_periodic) THEN
    1696             :             CALL calc_2c_virial(work_virial, force_data%RI_virial_pot, 1.0_dp, qs_env, force_data%nl_2c_pot, &
    1697           0 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
    1698           0 :             CALL dbcsr_clear(force_data%RI_virial_pot)
    1699             :          END IF
    1700             : 
    1701           2 :          identity_pot%potential_type = do_potential_id
    1702             :          CALL calc_2c_virial(work_virial_ovlp, virial_ovlp, 1.0_dp, qs_env, force_data%nl_2c_ovlp, &
    1703           2 :                              basis_set_ao, basis_set_ao, identity_pot)
    1704           2 :          CALL dbcsr_release(virial_ovlp)
    1705             : 
    1706           8 :          DO k_xyz = 1, 3
    1707          26 :             DO j_xyz = 1, 3
    1708          78 :                DO i_xyz = 1, 3
    1709             :                   virial%pv_mp2(i_xyz, j_xyz) = virial%pv_mp2(i_xyz, j_xyz) &
    1710          54 :                                                 - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1711             :                   virial%pv_overlap(i_xyz, j_xyz) = virial%pv_overlap(i_xyz, j_xyz) &
    1712          54 :                                                     - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1713             :                   virial%pv_virial(i_xyz, j_xyz) = virial%pv_virial(i_xyz, j_xyz) &
    1714             :                                                    - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz) &
    1715          72 :                                                    - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1716             :                END DO
    1717             :             END DO
    1718             :          END DO
    1719             :       END IF
    1720             : 
    1721             :       !Calculate the periodic contributions of (P|Q) to the force and the virial
    1722          36 :       work_virial = 0.0_dp
    1723          36 :       IF (force_data%do_periodic) THEN
    1724          18 :          IF (mp2_env%eri_method == do_eri_gpw) THEN
    1725           6 :             CALL get_2c_gpw_forces(force_data%G_PQ, force, work_virial, use_virial, mp2_env, qs_env)
    1726          12 :          ELSE IF (mp2_env%eri_method == do_eri_mme) THEN
    1727          12 :             CALL get_2c_mme_forces(force_data%G_PQ, force, mp2_env, qs_env)
    1728          12 :             IF (use_virial) CPABORT("Stress tensor not available with MME intrgrals")
    1729             :          ELSE
    1730           0 :             CPABORT("Periodic case not possible with OS integrals")
    1731             :          END IF
    1732          18 :          CALL dbcsr_clear(force_data%G_PQ)
    1733             :       END IF
    1734             : 
    1735          36 :       IF (use_virial) THEN
    1736          26 :          virial%pv_mp2 = virial%pv_mp2 + work_virial
    1737          26 :          virial%pv_virial = virial%pv_virial + work_virial
    1738           2 :          virial%pv_calculate = .FALSE.
    1739             : 
    1740           6 :          DO ibasis = 1, SIZE(basis_set_ao)
    1741           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1742           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
    1743           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1744           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
    1745             :          END DO
    1746             :       END IF
    1747             : 
    1748             :       !clean-up
    1749          36 :       IF (ASSOCIATED(dummy_ptr)) DEALLOCATE (dummy_ptr)
    1750         128 :       DO jquad = 1, num_integ_points
    1751         128 :          CALL dbt_destroy(t_B(jquad))
    1752             :       END DO
    1753          36 :       CALL dbt_destroy(t_P)
    1754          36 :       CALL dbt_destroy(t_3c_0)
    1755          36 :       CALL dbt_destroy(t_3c_1)
    1756          36 :       CALL dbt_destroy(t_3c_3)
    1757          36 :       CALL dbt_destroy(t_3c_4)
    1758          36 :       CALL dbt_destroy(t_3c_5)
    1759          36 :       CALL dbt_destroy(t_3c_6)
    1760          36 :       CALL dbt_destroy(t_3c_7)
    1761          36 :       CALL dbt_destroy(t_3c_8)
    1762          36 :       CALL dbt_destroy(t_3c_sparse)
    1763          36 :       CALL dbt_destroy(t_3c_help_1)
    1764          36 :       CALL dbt_destroy(t_3c_help_2)
    1765          36 :       CALL dbt_destroy(t_3c_ints)
    1766          36 :       CALL dbt_destroy(t_3c_work)
    1767          36 :       CALL dbt_destroy(t_R_occ)
    1768          36 :       CALL dbt_destroy(t_R_virt)
    1769          36 :       CALL dbt_destroy(t_dm_occ)
    1770          36 :       CALL dbt_destroy(t_dm_virt)
    1771          36 :       CALL dbt_destroy(t_KBKT)
    1772          36 :       CALL dbt_destroy(t_M_occ)
    1773          36 :       CALL dbt_destroy(t_M_virt)
    1774          36 :       CALL dbcsr_release(R_occ)
    1775          36 :       CALL dbcsr_release(R_virt)
    1776          36 :       CALL dbcsr_release(dbcsr_work_symm)
    1777          36 :       CALL dbcsr_release(dbcsr_work1)
    1778          36 :       CALL dbcsr_release(dbcsr_work2)
    1779          36 :       CALL dbcsr_release(dbcsr_work3)
    1780          36 :       CALL dbcsr_release(exp_occ)
    1781          36 :       CALL dbcsr_release(exp_virt)
    1782             : 
    1783          36 :       CALL dbt_destroy(t_2c_RI)
    1784          36 :       CALL dbt_destroy(t_2c_RI_2)
    1785          36 :       CALL dbt_destroy(t_2c_AO)
    1786          36 :       CALL dbcsr_deallocate_matrix_set(mat_dm_occ)
    1787          36 :       CALL dbcsr_deallocate_matrix_set(mat_dm_virt)
    1788          36 :       CALL dbcsr_deallocate_matrix_set(mat_P_tau)
    1789             : 
    1790          36 :       CALL timestop(handle)
    1791             : 
    1792         236 :    END SUBROUTINE calc_rpa_loop_forces
    1793             : 
    1794             : ! **************************************************************************************************
    1795             : !> \brief This subroutines performs the 2c tensor operations that are common accros low-scaling RPA
    1796             : !>        and SOS-MP2, including forces and virial
    1797             : !> \param force ...
    1798             : !> \param t_KBKT returns the 2c tensor product of K*B*K^T
    1799             : !> \param force_data ...
    1800             : !> \param fac ...
    1801             : !> \param t_B depending on RPA or SOS-MP2, t_B contains (1 + Q)^-1 - 1 or simply Q, respectively
    1802             : !> \param t_P ...
    1803             : !> \param t_2c_RI ...
    1804             : !> \param t_2c_RI_2 ...
    1805             : !> \param use_virial ...
    1806             : !> \param atom_of_kind ...
    1807             : !> \param kind_of ...
    1808             : !> \param eps_filter ...
    1809             : !> \param dbcsr_nflop ...
    1810             : !> \param unit_nr_dbcsr ...
    1811             : ! **************************************************************************************************
    1812         170 :    SUBROUTINE perform_2c_ops(force, t_KBKT, force_data, fac, t_B, t_P, t_2c_RI, t_2c_RI_2, use_virial, &
    1813         170 :                              atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
    1814             : 
    1815             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1816             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_KBKT
    1817             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1818             :       REAL(dp), INTENT(IN)                               :: fac
    1819             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_B, t_P, t_2c_RI, t_2c_RI_2
    1820             :       LOGICAL, INTENT(IN)                                :: use_virial
    1821             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: atom_of_kind, kind_of
    1822             :       REAL(dp), INTENT(IN)                               :: eps_filter
    1823             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
    1824             :       INTEGER, INTENT(IN)                                :: unit_nr_dbcsr
    1825             : 
    1826             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'perform_2c_ops'
    1827             : 
    1828             :       INTEGER                                            :: handle
    1829             :       INTEGER(int_8)                                     :: flop
    1830             :       REAL(dp)                                           :: pref
    1831        2890 :       TYPE(dbt_type)                                     :: t_2c_tmp, t_2c_virial
    1832             : 
    1833         170 :       CALL timeset(routineN, handle)
    1834             : 
    1835         170 :       IF (use_virial) CALL dbt_create(force_data%RI_virial_pot, t_2c_virial)
    1836             : 
    1837             :       !P^T*K*B + P*K*B^T (note we calculate and save K*B*K^T for later, and P=P^T)
    1838             :       CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_B, 0.0_dp, t_2c_RI, &
    1839             :                         contract_1=[2], notcontract_1=[1], &
    1840             :                         contract_2=[1], notcontract_2=[2], &
    1841             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1842         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1843         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1844             : 
    1845             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_KBKT, &
    1846             :                         contract_1=[2], notcontract_1=[1], &
    1847             :                         contract_2=[2], notcontract_2=[1], &
    1848             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1849         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1850         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1851             : 
    1852             :       CALL dbt_contract(2.0_dp, t_P, t_2c_RI, 0.0_dp, t_2c_RI_2, & !t_2c_RI_2 holds P^T*K*B
    1853             :                         contract_1=[2], notcontract_1=[1], &
    1854             :                         contract_2=[1], notcontract_2=[2], &
    1855             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1856         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1857         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1858         170 :       CALL dbt_clear(t_2c_RI)
    1859             :       !t_2c_RI_2 currently holds 2*P^T*K*B = P^T*K*B + P*K*B^T (because of symmetry)
    1860             : 
    1861             :       !For the metric contribution, we need S^-1*(P^T*K*B + P*K*B^T)*K^T
    1862             :       CALL dbt_contract(1.0_dp, force_data%t_2c_inv_metric, t_2c_RI_2, 0.0_dp, t_2c_RI, &
    1863             :                         contract_1=[2], notcontract_1=[1], &
    1864             :                         contract_2=[1], notcontract_2=[2], &
    1865             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1866         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1867         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1868             : 
    1869             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_2c_RI_2, &
    1870             :                         contract_1=[2], notcontract_1=[1], &
    1871             :                         contract_2=[2], notcontract_2=[1], &
    1872             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1873         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1874         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1875             : 
    1876             :       !Here we do the trace for the force
    1877         170 :       pref = -1.0_dp*fac
    1878             :       CALL get_2c_der_force(force, t_2c_RI_2, force_data%t_2c_der_metric, atom_of_kind, &
    1879         170 :                             kind_of, force_data%idx_to_at_RI, pref, do_mp2=.TRUE.)
    1880         170 :       IF (use_virial) THEN
    1881          12 :          CALL dbt_copy(t_2c_RI_2, t_2c_virial)
    1882          12 :          CALL dbt_scale(t_2c_virial, pref)
    1883          12 :          CALL dbt_copy_tensor_to_matrix(t_2c_virial, force_data%RI_virial_met, summation=.TRUE.)
    1884          12 :          CALL dbt_clear(t_2c_virial)
    1885             :       END IF
    1886             : 
    1887             :       !For the potential contribution, we need S^-1*(P^T*K*B + P*K*B^T)*V^-0.5
    1888             :       !some of it is still in t_2c_RI: ( S^-1*(P^T*K*B + P*K*B^T) )
    1889             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_pot_msqrt, 0.0_dp, t_2c_RI_2, &
    1890             :                         contract_1=[2], notcontract_1=[1], &
    1891             :                         contract_2=[1], notcontract_2=[2], &
    1892             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1893         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1894         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1895             : 
    1896             :       !Here we do the trace for the force. In the periodic case, we store the matrix in G_PQ for later
    1897         170 :       pref = 0.5_dp*fac
    1898         170 :       IF (force_data%do_periodic) THEN
    1899          76 :          CALL dbt_scale(t_2c_RI_2, pref)
    1900          76 :          CALL dbt_create(force_data%G_PQ, t_2c_tmp)
    1901          76 :          CALL dbt_copy(t_2c_RI_2, t_2c_tmp, move_data=.TRUE.)
    1902          76 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, force_data%G_PQ, summation=.TRUE.)
    1903          76 :          CALL dbt_destroy(t_2c_tmp)
    1904             :       ELSE
    1905             :          CALL get_2c_der_force(force, t_2c_RI_2, force_data%t_2c_der_pot, atom_of_kind, &
    1906          94 :                                kind_of, force_data%idx_to_at_RI, pref, do_mp2=.TRUE.)
    1907             : 
    1908          94 :          IF (use_virial) THEN
    1909           0 :             CALL dbt_copy(t_2c_RI_2, t_2c_virial)
    1910           0 :             CALL dbt_scale(t_2c_virial, pref)
    1911           0 :             CALL dbt_copy_tensor_to_matrix(t_2c_virial, force_data%RI_virial_pot, summation=.TRUE.)
    1912           0 :             CALL dbt_clear(t_2c_virial)
    1913             :          END IF
    1914             :       END IF
    1915             : 
    1916         170 :       CALL dbt_clear(t_2c_RI)
    1917         170 :       CALL dbt_clear(t_2c_RI_2)
    1918             : 
    1919         170 :       IF (use_virial) CALL dbt_destroy(t_2c_virial)
    1920             : 
    1921         170 :       CALL timestop(handle)
    1922             : 
    1923         170 :    END SUBROUTINE perform_2c_ops
    1924             : 
    1925             : ! **************************************************************************************************
    1926             : !> \brief This subroutines performs the 3c tensor operations that are common accros low-scaling RPA
    1927             : !>        and SOS-MP2, including forces and virial
    1928             : !> \param force ...
    1929             : !> \param t_R_occ ...
    1930             : !> \param t_R_virt ...
    1931             : !> \param force_data ...
    1932             : !> \param fac ...
    1933             : !> \param cut_memory ...
    1934             : !> \param n_mem_RI ...
    1935             : !> \param t_KBKT ...
    1936             : !> \param t_dm_occ ...
    1937             : !> \param t_dm_virt ...
    1938             : !> \param t_3c_O ...
    1939             : !> \param t_3c_M ...
    1940             : !> \param t_M_occ ...
    1941             : !> \param t_M_virt ...
    1942             : !> \param t_3c_0 ...
    1943             : !> \param t_3c_1 ...
    1944             : !> \param t_3c_3 ...
    1945             : !> \param t_3c_4 ...
    1946             : !> \param t_3c_5 ...
    1947             : !> \param t_3c_6 ...
    1948             : !> \param t_3c_7 ...
    1949             : !> \param t_3c_8 ...
    1950             : !> \param t_3c_sparse ...
    1951             : !> \param t_3c_help_1 ...
    1952             : !> \param t_3c_help_2 ...
    1953             : !> \param t_3c_ints ...
    1954             : !> \param t_3c_work ...
    1955             : !> \param starts_array_mc ...
    1956             : !> \param ends_array_mc ...
    1957             : !> \param batch_start_RI ...
    1958             : !> \param batch_end_RI ...
    1959             : !> \param t_3c_O_compressed ...
    1960             : !> \param t_3c_O_ind ...
    1961             : !> \param use_virial ...
    1962             : !> \param atom_of_kind ...
    1963             : !> \param kind_of ...
    1964             : !> \param eps_filter ...
    1965             : !> \param occ_ddint ...
    1966             : !> \param nze_ddint ...
    1967             : !> \param dbcsr_nflop ...
    1968             : !> \param unit_nr_dbcsr ...
    1969             : !> \param mp2_env ...
    1970             : ! **************************************************************************************************
    1971         170 :    SUBROUTINE perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
    1972             :                              t_KBKT, t_dm_occ, t_dm_virt, t_3c_O, t_3c_M, t_M_occ, t_M_virt, t_3c_0, t_3c_1, &
    1973             :                              t_3c_3, t_3c_4, t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_sparse, t_3c_help_1, t_3c_help_2, &
    1974         170 :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
    1975         170 :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
    1976         170 :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
    1977             :                              unit_nr_dbcsr, mp2_env)
    1978             : 
    1979             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1980             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_R_occ, t_R_virt
    1981             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1982             :       REAL(dp), INTENT(IN)                               :: fac
    1983             :       INTEGER, INTENT(IN)                                :: cut_memory, n_mem_RI
    1984             :       TYPE(dbt_type), INTENT(INOUT) :: t_KBKT, t_dm_occ, t_dm_virt, t_3c_O, t_3c_M, t_M_occ, &
    1985             :          t_M_virt, t_3c_0, t_3c_1, t_3c_3, t_3c_4, t_3c_5, t_3c_6, t_3c_7, t_3c_8, t_3c_sparse, &
    1986             :          t_3c_help_1, t_3c_help_2, t_3c_ints, t_3c_work
    1987             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
    1988             :                                                             batch_start_RI, batch_end_RI
    1989             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
    1990             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
    1991             :       LOGICAL, INTENT(IN)                                :: use_virial
    1992             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: atom_of_kind, kind_of
    1993             :       REAL(dp), INTENT(IN)                               :: eps_filter
    1994             :       REAL(dp), INTENT(INOUT)                            :: occ_ddint
    1995             :       INTEGER(int_8), INTENT(INOUT)                      :: nze_ddint, dbcsr_nflop
    1996             :       INTEGER, INTENT(IN)                                :: unit_nr_dbcsr
    1997             :       TYPE(mp2_type)                                     :: mp2_env
    1998             : 
    1999             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'perform_3c_ops'
    2000             : 
    2001             :       INTEGER                                            :: dummy_int, handle, handle2, i_mem, &
    2002             :                                                             i_xyz, j_mem, k_mem
    2003             :       INTEGER(int_8)                                     :: flop, nze
    2004             :       INTEGER, DIMENSION(2, 1)                           :: ibounds, jbounds, kbounds
    2005             :       INTEGER, DIMENSION(2, 2)                           :: bounds_2c
    2006             :       INTEGER, DIMENSION(2, 3)                           :: bounds_cpy
    2007             :       INTEGER, DIMENSION(3)                              :: bounds_3c
    2008             :       REAL(dp)                                           :: memory, occ, pref
    2009         170 :       TYPE(block_ind_type), ALLOCATABLE, DIMENSION(:, :) :: blk_indices
    2010             :       TYPE(hfx_compression_type), ALLOCATABLE, &
    2011         170 :          DIMENSION(:, :)                                 :: store_3c
    2012             : 
    2013         170 :       CALL timeset(routineN, handle)
    2014             : 
    2015         170 :       CALL dbt_get_info(t_3c_M, nfull_total=bounds_3c)
    2016             : 
    2017             :       !Pre-compute and compress KBK^T * (pq|R)
    2018      360910 :       ALLOCATE (store_3c(n_mem_RI, cut_memory))
    2019        1700 :       ALLOCATE (blk_indices(n_mem_RI, cut_memory))
    2020         170 :       memory = 0.0_dp
    2021         170 :       CALL timeset(routineN//"_pre_3c", handle2)
    2022             :       !temporarily build the full int 3c tensor
    2023         170 :       CALL dbt_copy(t_3c_O, t_3c_0)
    2024         510 :       DO i_mem = 1, cut_memory
    2025             :          CALL decompress_tensor(t_3c_O, t_3c_O_ind(i_mem)%ind, t_3c_O_compressed(i_mem), &
    2026         340 :                                 mp2_env%ri_rpa_im_time%eps_compress)
    2027         340 :          CALL dbt_copy(t_3c_O, t_3c_ints)
    2028         340 :          CALL dbt_copy(t_3c_O, t_3c_0, move_data=.TRUE., summation=.TRUE.)
    2029             : 
    2030        1190 :          DO k_mem = 1, n_mem_RI
    2031        2040 :             kbounds(:, 1) = [batch_start_RI(k_mem), batch_end_RI(k_mem)]
    2032             : 
    2033         680 :             CALL alloc_containers(store_3c(k_mem, i_mem), 1)
    2034             : 
    2035             :             !contract witht KBK^T over the RI index and store
    2036         680 :             CALL dbt_batched_contract_init(t_KBKT)
    2037             :             CALL dbt_contract(1.0_dp, t_KBKT, t_3c_ints, 0.0_dp, t_3c_work, &
    2038             :                               contract_1=[2], notcontract_1=[1], &
    2039             :                               contract_2=[1], notcontract_2=[2, 3], &
    2040             :                               map_1=[1], map_2=[2, 3], filter_eps=eps_filter, &
    2041         680 :                               bounds_2=kbounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2042         680 :             CALL dbt_batched_contract_finalize(t_KBKT)
    2043         680 :             dbcsr_nflop = dbcsr_nflop + flop
    2044             : 
    2045         680 :             CALL dbt_copy(t_3c_work, t_3c_M, move_data=.TRUE.)
    2046             :             CALL compress_tensor(t_3c_M, blk_indices(k_mem, i_mem)%ind, store_3c(k_mem, i_mem), &
    2047        1020 :                                  mp2_env%ri_rpa_im_time%eps_compress, memory)
    2048             :          END DO
    2049             :       END DO !i_mem
    2050         170 :       CALL dbt_clear(t_3c_M)
    2051         170 :       CALL dbt_copy(t_3c_M, t_3c_ints)
    2052         170 :       CALL timestop(handle2)
    2053             : 
    2054         170 :       CALL dbt_batched_contract_init(t_R_occ)
    2055         170 :       CALL dbt_batched_contract_init(t_R_virt)
    2056         510 :       DO i_mem = 1, cut_memory
    2057        1020 :          ibounds(:, 1) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2058             : 
    2059             :          !Compute the matrices M (integrals in t_3c_0)
    2060         340 :          CALL timeset(routineN//"_3c_M", handle2)
    2061         340 :          CALL dbt_batched_contract_init(t_dm_occ)
    2062             :          CALL dbt_contract(1.0_dp, t_3c_0, t_dm_occ, 0.0_dp, t_3c_1, &
    2063             :                            contract_1=[3], notcontract_1=[1, 2], &
    2064             :                            contract_2=[1], notcontract_2=[2], &
    2065             :                            map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2066         340 :                            bounds_3=ibounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2067         340 :          dbcsr_nflop = dbcsr_nflop + flop
    2068         340 :          CALL dbt_batched_contract_finalize(t_dm_occ)
    2069         340 :          CALL dbt_copy(t_3c_1, t_M_occ, order=[1, 3, 2], move_data=.TRUE.)
    2070             : 
    2071         340 :          CALL dbt_batched_contract_init(t_dm_virt)
    2072             :          CALL dbt_contract(1.0_dp, t_3c_0, t_dm_virt, 0.0_dp, t_3c_1, &
    2073             :                            contract_1=[3], notcontract_1=[1, 2], &
    2074             :                            contract_2=[1], notcontract_2=[2], &
    2075             :                            map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2076         340 :                            bounds_3=ibounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2077         340 :          dbcsr_nflop = dbcsr_nflop + flop
    2078         340 :          CALL dbt_batched_contract_finalize(t_dm_virt)
    2079         340 :          CALL dbt_copy(t_3c_1, t_M_virt, order=[1, 3, 2], move_data=.TRUE.)
    2080         340 :          CALL timestop(handle2)
    2081             : 
    2082             :          !Compute the R matrices
    2083         340 :          CALL timeset(routineN//"_3c_R", handle2)
    2084        1020 :          DO k_mem = 1, n_mem_RI
    2085             :             CALL decompress_tensor(t_3c_M, blk_indices(k_mem, i_mem)%ind, store_3c(k_mem, i_mem), &
    2086         680 :                                    mp2_env%ri_rpa_im_time%eps_compress)
    2087         680 :             CALL dbt_copy(t_3c_M, t_3c_3, move_data=.TRUE.)
    2088             : 
    2089             :             CALL dbt_contract(1.0_dp, t_M_occ, t_3c_3, 1.0_dp, t_R_occ, &
    2090             :                               contract_1=[1, 2], notcontract_1=[3], &
    2091             :                               contract_2=[1, 2], notcontract_2=[3], &
    2092             :                               map_1=[1], map_2=[2], filter_eps=eps_filter, &
    2093         680 :                               flop=flop, unit_nr=unit_nr_dbcsr)
    2094         680 :             dbcsr_nflop = dbcsr_nflop + flop
    2095             : 
    2096             :             CALL dbt_contract(1.0_dp, t_M_virt, t_3c_3, 1.0_dp, t_R_virt, &
    2097             :                               contract_1=[1, 2], notcontract_1=[3], &
    2098             :                               contract_2=[1, 2], notcontract_2=[3], &
    2099             :                               map_1=[1], map_2=[2], filter_eps=eps_filter, &
    2100         680 :                               flop=flop, unit_nr=unit_nr_dbcsr)
    2101        1020 :             dbcsr_nflop = dbcsr_nflop + flop
    2102             :          END DO
    2103         340 :          CALL dbt_copy(t_3c_M, t_3c_3)
    2104         340 :          CALL dbt_copy(t_3c_M, t_M_virt)
    2105         340 :          CALL timestop(handle2)
    2106             : 
    2107         340 :          CALL dbt_copy(t_M_occ, t_3c_4, move_data=.TRUE.)
    2108             : 
    2109        1020 :          DO j_mem = 1, cut_memory
    2110        2040 :             jbounds(:, 1) = [starts_array_mc(j_mem), ends_array_mc(j_mem)]
    2111             : 
    2112        2040 :             bounds_cpy(:, 1) = [1, bounds_3c(1)]
    2113        2040 :             bounds_cpy(:, 2) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2114        2040 :             bounds_cpy(:, 3) = [starts_array_mc(j_mem), ends_array_mc(j_mem)]
    2115         680 :             CALL dbt_copy(t_3c_sparse, t_3c_7, bounds=bounds_cpy)
    2116             : 
    2117         680 :             CALL dbt_batched_contract_init(t_dm_virt)
    2118        2040 :             DO k_mem = 1, n_mem_RI
    2119        4080 :                bounds_2c(:, 1) = [batch_start_RI(k_mem), batch_end_RI(k_mem)]
    2120        4080 :                bounds_2c(:, 2) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2121             : 
    2122        1360 :                CALL timeset(routineN//"_3c_dm", handle2)
    2123             : 
    2124             :                !Calculate (mu nu| P) * D_occ * D_virt
    2125             :                !Note: technically need M_occ*D_virt + M_virt*D_occ, but it is equivalent to 2*M_occ*D_virt
    2126             :                CALL dbt_contract(2.0_dp, t_3c_4, t_dm_virt, 0.0_dp, t_3c_5, &
    2127             :                                  contract_1=[3], notcontract_1=[1, 2], &
    2128             :                                  contract_2=[1], notcontract_2=[2], &
    2129             :                                  map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2130        1360 :                                  bounds_2=bounds_2c, bounds_3=jbounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2131        1360 :                dbcsr_nflop = dbcsr_nflop + flop
    2132             : 
    2133        1360 :                CALL get_tensor_occupancy(t_3c_5, nze, occ)
    2134        1360 :                nze_ddint = nze_ddint + nze
    2135        1360 :                occ_ddint = occ_ddint + occ
    2136             : 
    2137        1360 :                CALL dbt_copy(t_3c_5, t_3c_6, move_data=.TRUE.)
    2138        1360 :                CALL timestop(handle2)
    2139             : 
    2140             :                !Calculate the contraction of the above with K*B*K^T
    2141        1360 :                CALL timeset(routineN//"_3c_KBK", handle2)
    2142        1360 :                CALL dbt_batched_contract_init(t_KBKT)
    2143             :                CALL dbt_contract(1.0_dp, t_KBKT, t_3c_6, 0.0_dp, t_3c_7, &
    2144             :                                  contract_1=[2], notcontract_1=[1], &
    2145             :                                  contract_2=[1], notcontract_2=[2, 3], &
    2146             :                                  map_1=[1], map_2=[2, 3], &
    2147        1360 :                                  retain_sparsity=.TRUE., flop=flop, unit_nr=unit_nr_dbcsr)
    2148        1360 :                dbcsr_nflop = dbcsr_nflop + flop
    2149        1360 :                CALL dbt_batched_contract_finalize(t_KBKT)
    2150        1360 :                CALL timestop(handle2)
    2151        6120 :                CALL dbt_copy(t_3c_7, t_3c_8, summation=.TRUE.)
    2152             : 
    2153             :             END DO !k_mem
    2154        1020 :             CALL dbt_batched_contract_finalize(t_dm_virt)
    2155             :          END DO !j_mem
    2156             : 
    2157         340 :          CALL dbt_copy(t_3c_8, t_3c_help_1, move_data=.TRUE.)
    2158             : 
    2159         340 :          pref = 1.0_dp*fac
    2160        1020 :          DO k_mem = 1, cut_memory
    2161        2720 :             DO i_xyz = 1, 3
    2162        2040 :                CALL dbt_clear(force_data%t_3c_der_RI(i_xyz))
    2163             :                CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(k_mem, i_xyz)%ind, &
    2164        2720 :                                       force_data%t_3c_der_RI_comp(k_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    2165             :             END DO
    2166             :             CALL get_force_from_3c_trace(force, t_3c_help_1, force_data%t_3c_der_RI, atom_of_kind, kind_of, &
    2167        1020 :                                          force_data%idx_to_at_RI, pref, do_mp2=.TRUE., deriv_dim=1)
    2168             :          END DO
    2169             : 
    2170         340 :          IF (use_virial) THEN
    2171          24 :             CALL dbt_copy(t_3c_help_1, t_3c_help_2)
    2172          24 :             CALL dbt_scale(t_3c_help_2, pref)
    2173          24 :             CALL dbt_copy(t_3c_help_2, force_data%t_3c_virial_split, summation=.TRUE., move_data=.TRUE.)
    2174             :          END IF
    2175             : 
    2176         340 :          CALL dbt_copy(t_3c_help_1, t_3c_help_2)
    2177         340 :          CALL dbt_copy(t_3c_help_1, t_3c_help_2, order=[1, 3, 2], move_data=.TRUE., summation=.TRUE.)
    2178        1020 :          DO k_mem = 1, cut_memory
    2179        2720 :             DO i_xyz = 1, 3
    2180        2040 :                CALL dbt_clear(force_data%t_3c_der_AO(i_xyz))
    2181             :                CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(k_mem, i_xyz)%ind, &
    2182        2720 :                                       force_data%t_3c_der_AO_comp(k_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    2183             :             END DO
    2184             :             CALL get_force_from_3c_trace(force, t_3c_help_2, force_data%t_3c_der_AO, atom_of_kind, kind_of, &
    2185        1020 :                                          force_data%idx_to_at_AO, pref, do_mp2=.TRUE., deriv_dim=3)
    2186             :          END DO
    2187             : 
    2188        1190 :          CALL dbt_clear(t_3c_help_2)
    2189             :       END DO !i_mem
    2190         170 :       CALL dbt_batched_contract_finalize(t_R_occ)
    2191         170 :       CALL dbt_batched_contract_finalize(t_R_virt)
    2192             : 
    2193         510 :       DO k_mem = 1, n_mem_RI
    2194        1190 :          DO i_mem = 1, cut_memory
    2195        1020 :             CALL dealloc_containers(store_3c(k_mem, i_mem), dummy_int)
    2196             :          END DO
    2197             :       END DO
    2198         850 :       DEALLOCATE (store_3c, blk_indices)
    2199             : 
    2200         170 :       CALL timestop(handle)
    2201             : 
    2202         340 :    END SUBROUTINE perform_3c_ops
    2203             : 
    2204             : ! **************************************************************************************************
    2205             : !> \brief All the forces that can be calculated after the loop on the Laplace quaradture, using
    2206             : !>        terms collected during the said loop. This inludes the z-vector equation and its reponse
    2207             : !>        forces, as well as the force coming from the trace with the derivative of the KS matrix
    2208             : !> \param force_data ...
    2209             : !> \param unit_nr ...
    2210             : !> \param qs_env ...
    2211             : ! **************************************************************************************************
    2212          50 :    SUBROUTINE calc_post_loop_forces(force_data, unit_nr, qs_env)
    2213             : 
    2214             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    2215             :       INTEGER, INTENT(IN)                                :: unit_nr
    2216             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2217             : 
    2218             :       CHARACTER(len=*), PARAMETER :: routineN = 'calc_post_loop_forces'
    2219             : 
    2220             :       INTEGER                                            :: handle, ispin, nao, nao_aux, nocc, nspins
    2221             :       LOGICAL                                            :: do_exx
    2222             :       REAL(dp)                                           :: focc
    2223             :       TYPE(admm_type), POINTER                           :: admm_env
    2224             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    2225          50 :       TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:)        :: cpmos, mo_occ
    2226             :       TYPE(cp_fm_type), POINTER                          :: mo_coeff
    2227          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: dbcsr_p_work, matrix_p_mp2, &
    2228          50 :                                                             matrix_p_mp2_admm, matrix_s, &
    2229          50 :                                                             matrix_s_aux, work_admm, YP_admm
    2230             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2231             :       TYPE(linres_control_type), POINTER                 :: linres_control
    2232          50 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    2233             :       TYPE(qs_p_env_type), POINTER                       :: p_env
    2234             :       TYPE(section_vals_type), POINTER                   :: hfx_section, lr_section
    2235             : 
    2236          50 :       NULLIFY (linres_control, p_env, dft_control, matrix_s, mos, mo_coeff, fm_struct, lr_section, &
    2237          50 :                dbcsr_p_work, YP_admm, matrix_p_mp2, admm_env, work_admm, matrix_s_aux, matrix_p_mp2_admm)
    2238             : 
    2239          50 :       CALL timeset(routineN, handle)
    2240             : 
    2241          50 :       CALL get_qs_env(qs_env, dft_control=dft_control, matrix_s=matrix_s, mos=mos)
    2242          50 :       nspins = dft_control%nspins
    2243             : 
    2244             :       ! Setting up for the z-vector equation
    2245             : 
    2246             :       ! Initialize linres_control
    2247          50 :       lr_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%LOW_SCALING%CPHF")
    2248             : 
    2249          50 :       ALLOCATE (linres_control)
    2250          50 :       CALL section_vals_val_get(lr_section, "MAX_ITER", i_val=linres_control%max_iter)
    2251          50 :       CALL section_vals_val_get(lr_section, "EPS_CONV", r_val=linres_control%eps)
    2252          50 :       CALL section_vals_val_get(lr_section, "PRECONDITIONER", i_val=linres_control%preconditioner_type)
    2253          50 :       CALL section_vals_val_get(lr_section, "ENERGY_GAP", r_val=linres_control%energy_gap)
    2254             : 
    2255          50 :       linres_control%do_kernel = .TRUE.
    2256          50 :       linres_control%lr_triplet = .FALSE.
    2257          50 :       linres_control%converged = .FALSE.
    2258          50 :       linres_control%eps_filter = qs_env%mp2_env%ri_rpa_im_time%eps_filter
    2259             : 
    2260          50 :       CALL set_qs_env(qs_env, linres_control=linres_control)
    2261             : 
    2262          50 :       IF (unit_nr > 0) THEN
    2263          25 :          WRITE (unit_nr, *)
    2264          25 :          WRITE (unit_nr, '(T3,A)') 'MP2_CPHF| Iterative solution of Z-Vector equations'
    2265          25 :          WRITE (unit_nr, '(T3,A,T45,ES8.1)') 'MP2_CPHF| Convergence threshold:', linres_control%eps
    2266          25 :          WRITE (unit_nr, '(T3,A,T45,I8)') 'MP2_CPHF| Maximum number of iterations: ', linres_control%max_iter
    2267             :       END IF
    2268             : 
    2269         350 :       ALLOCATE (p_env)
    2270          50 :       CALL p_env_create(p_env, qs_env, orthogonal_orbitals=.TRUE., linres_control=linres_control)
    2271          50 :       CALL p_env_psi0_changed(p_env, qs_env)
    2272             : 
    2273             :       ! Matrix allocation
    2274          50 :       CALL dbcsr_allocate_matrix_set(p_env%p1, nspins)
    2275          50 :       CALL dbcsr_allocate_matrix_set(p_env%w1, nspins)
    2276          50 :       CALL dbcsr_allocate_matrix_set(dbcsr_p_work, nspins)
    2277         112 :       DO ispin = 1, nspins
    2278          62 :          ALLOCATE (p_env%p1(ispin)%matrix, p_env%w1(ispin)%matrix, dbcsr_p_work(ispin)%matrix)
    2279          62 :          CALL dbcsr_create(matrix=p_env%p1(ispin)%matrix, template=matrix_s(1)%matrix)
    2280          62 :          CALL dbcsr_create(matrix=p_env%w1(ispin)%matrix, template=matrix_s(1)%matrix)
    2281          62 :          CALL dbcsr_create(matrix=dbcsr_p_work(ispin)%matrix, template=matrix_s(1)%matrix)
    2282          62 :          CALL dbcsr_copy(p_env%p1(ispin)%matrix, matrix_s(1)%matrix)
    2283          62 :          CALL dbcsr_copy(p_env%w1(ispin)%matrix, matrix_s(1)%matrix)
    2284          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, matrix_s(1)%matrix)
    2285          62 :          CALL dbcsr_set(p_env%p1(ispin)%matrix, 0.0_dp)
    2286          62 :          CALL dbcsr_set(p_env%w1(ispin)%matrix, 0.0_dp)
    2287         112 :          CALL dbcsr_set(dbcsr_p_work(ispin)%matrix, 0.0_dp)
    2288             :       END DO
    2289             : 
    2290          50 :       IF (dft_control%do_admm) THEN
    2291          16 :          CALL get_admm_env(qs_env%admm_env, matrix_s_aux_fit=matrix_s_aux)
    2292          16 :          CALL dbcsr_allocate_matrix_set(p_env%p1_admm, nspins)
    2293          16 :          CALL dbcsr_allocate_matrix_set(work_admm, nspins)
    2294          36 :          DO ispin = 1, nspins
    2295          20 :             ALLOCATE (p_env%p1_admm(ispin)%matrix, work_admm(ispin)%matrix)
    2296          20 :             CALL dbcsr_create(p_env%p1_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2297          20 :             CALL dbcsr_copy(p_env%p1_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2298          20 :             CALL dbcsr_set(p_env%p1_admm(ispin)%matrix, 0.0_dp)
    2299          20 :             CALL dbcsr_create(work_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2300          20 :             CALL dbcsr_copy(work_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2301          36 :             CALL dbcsr_set(work_admm(ispin)%matrix, 0.0_dp)
    2302             :          END DO
    2303             :       END IF
    2304             : 
    2305             :       ! Preparing the RHS of the z-vector equation
    2306          50 :       CALL prepare_for_response(force_data, qs_env)
    2307         374 :       ALLOCATE (cpmos(nspins), mo_occ(nspins))
    2308         112 :       DO ispin = 1, nspins
    2309          62 :          CALL get_mo_set(mo_set=mos(ispin), mo_coeff=mo_coeff, nao=nao, homo=nocc)
    2310          62 :          NULLIFY (fm_struct)
    2311             :          CALL cp_fm_struct_create(fm_struct, ncol_global=nocc, &
    2312          62 :                                   template_fmstruct=mo_coeff%matrix_struct)
    2313          62 :          CALL cp_fm_create(cpmos(ispin), fm_struct)
    2314          62 :          CALL cp_fm_set_all(cpmos(ispin), 0.0_dp)
    2315          62 :          CALL cp_fm_create(mo_occ(ispin), fm_struct)
    2316          62 :          CALL cp_fm_to_fm(mo_coeff, mo_occ(ispin), nocc)
    2317         174 :          CALL cp_fm_struct_release(fm_struct)
    2318             :       END DO
    2319             : 
    2320             :       ! in case of EXX, need to add the HF Hamiltonian to the RHS of the Z-vector equation
    2321             :       ! Strategy: we take the ks_matrix, remove the current xc contribution, and then add the RPA HF one
    2322          50 :       do_exx = .FALSE.
    2323          50 :       IF (qs_env%mp2_env%method == ri_rpa_method_gpw) THEN
    2324          28 :          hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%RI_RPA%HF")
    2325          28 :          CALL section_vals_get(hfx_section, explicit=do_exx)
    2326             :       END IF
    2327             : 
    2328          50 :       IF (do_exx) THEN
    2329             :          CALL add_exx_to_rhs(rhs=force_data%sum_O_tau, &
    2330             :                              qs_env=qs_env, &
    2331             :                              ext_hfx_section=hfx_section, &
    2332             :                              x_data=qs_env%mp2_env%ri_rpa%x_data, &
    2333             :                              recalc_integrals=.FALSE., &
    2334             :                              do_admm=qs_env%mp2_env%ri_rpa%do_admm, &
    2335             :                              do_exx=do_exx, &
    2336          18 :                              reuse_hfx=qs_env%mp2_env%ri_rpa%reuse_hfx)
    2337             :       END IF
    2338             : 
    2339          50 :       focc = 2.0_dp
    2340          50 :       IF (nspins == 1) focc = 4.0_dp
    2341         112 :       DO ispin = 1, nspins
    2342          62 :          CALL get_mo_set(mo_set=mos(ispin), mo_coeff=mo_coeff, homo=nocc)
    2343             :          CALL cp_dbcsr_sm_fm_multiply(force_data%sum_O_tau(ispin)%matrix, mo_occ(ispin), &
    2344             :                                       cpmos(ispin), nocc, &
    2345         112 :                                       alpha=focc, beta=0.0_dp)
    2346             :       END DO
    2347             : 
    2348             :       ! The z-vector equation and associated forces
    2349          50 :       CALL response_equation_new(qs_env, p_env, cpmos, unit_nr)
    2350             : 
    2351             :       ! Save the mp2 density matrix
    2352          50 :       CALL get_qs_env(qs_env, matrix_p_mp2=matrix_p_mp2)
    2353          50 :       IF (ASSOCIATED(matrix_p_mp2)) CALL dbcsr_deallocate_matrix_set(matrix_p_mp2)
    2354         112 :       DO ispin = 1, nspins
    2355          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, p_env%p1(ispin)%matrix)
    2356         112 :          CALL dbcsr_add(dbcsr_p_work(ispin)%matrix, force_data%sum_YP_tau(ispin)%matrix, 1.0_dp, 1.0_dp)
    2357             :       END DO
    2358          50 :       CALL set_ks_env(qs_env%ks_env, matrix_p_mp2=dbcsr_p_work)
    2359             : 
    2360          50 :       IF (dft_control%do_admm) THEN
    2361          16 :          CALL dbcsr_allocate_matrix_set(YP_admm, nspins)
    2362          16 :          CALL get_qs_env(qs_env, matrix_p_mp2_admm=matrix_p_mp2_admm, admm_env=admm_env)
    2363          16 :          nao = admm_env%nao_orb
    2364          16 :          nao_aux = admm_env%nao_aux_fit
    2365          16 :          IF (ASSOCIATED(matrix_p_mp2_admm)) CALL dbcsr_deallocate_matrix_set(matrix_p_mp2_admm)
    2366          36 :          DO ispin = 1, nspins
    2367             : 
    2368             :             !sum_YP_tau in the auxiliary basis
    2369          20 :             CALL copy_dbcsr_to_fm(force_data%sum_YP_tau(ispin)%matrix, admm_env%work_orb_orb)
    2370             :             CALL parallel_gemm('N', 'N', nao_aux, nao, nao, 1.0_dp, admm_env%A, admm_env%work_orb_orb, &
    2371          20 :                                0.0_dp, admm_env%work_aux_orb)
    2372             :             CALL parallel_gemm('N', 'T', nao_aux, nao_aux, nao, 1.0_dp, admm_env%work_aux_orb, admm_env%A, &
    2373          20 :                                0.0_dp, admm_env%work_aux_aux)
    2374          20 :             CALL copy_fm_to_dbcsr(admm_env%work_aux_aux, work_admm(ispin)%matrix, keep_sparsity=.TRUE.)
    2375             : 
    2376             :             !save the admm representation od sum_YP_tau
    2377          20 :             ALLOCATE (YP_admm(ispin)%matrix)
    2378          20 :             CALL dbcsr_create(YP_admm(ispin)%matrix, template=work_admm(ispin)%matrix)
    2379          20 :             CALL dbcsr_copy(YP_admm(ispin)%matrix, work_admm(ispin)%matrix)
    2380             : 
    2381          36 :             CALL dbcsr_add(work_admm(ispin)%matrix, p_env%p1_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    2382             : 
    2383             :          END DO
    2384          16 :          CALL set_ks_env(qs_env%ks_env, matrix_p_mp2_admm=work_admm)
    2385             :       END IF
    2386             : 
    2387             :       !Calculate the response force and the force from the trace with F
    2388          50 :       CALL update_im_time_forces(p_env, force_data%sum_O_tau, force_data%sum_YP_tau, YP_admm, qs_env)
    2389             : 
    2390             :       !clean-up
    2391          50 :       IF (dft_control%do_admm) CALL dbcsr_deallocate_matrix_set(YP_admm)
    2392             : 
    2393          50 :       CALL cp_fm_release(cpmos)
    2394          50 :       CALL cp_fm_release(mo_occ)
    2395          50 :       CALL p_env_release(p_env)
    2396          50 :       DEALLOCATE (p_env)
    2397             : 
    2398          50 :       CALL timestop(handle)
    2399             : 
    2400         100 :    END SUBROUTINE calc_post_loop_forces
    2401             : 
    2402             : ! **************************************************************************************************
    2403             : !> \brief Prepares the RHS of the z-vector equation. Apply the xc and HFX kernel on the previously
    2404             : !>        stored sum_YP_tau density, and add it to the final force_data%sum_O_tau quantity
    2405             : !> \param force_data ...
    2406             : !> \param qs_env ...
    2407             : ! **************************************************************************************************
    2408          50 :    SUBROUTINE prepare_for_response(force_data, qs_env)
    2409             : 
    2410             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    2411             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2412             : 
    2413             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'prepare_for_response'
    2414             : 
    2415             :       INTEGER                                            :: handle, ispin, nao, nao_aux, nspins
    2416             :       LOGICAL                                            :: do_hfx, do_tau, do_tau_admm
    2417             :       REAL(dp)                                           :: ehartree
    2418             :       TYPE(admm_type), POINTER                           :: admm_env
    2419          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: dbcsr_p_work, ker_tau_admm, matrix_s, &
    2420          50 :                                                             matrix_s_aux, work_admm
    2421             :       TYPE(dbcsr_type)                                   :: dbcsr_work
    2422             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2423             :       TYPE(pw_c1d_gs_type)                               :: rhoz_tot_gspace, zv_hartree_gspace
    2424          50 :       TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER        :: rhoz_g
    2425             :       TYPE(pw_env_type), POINTER                         :: pw_env
    2426             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    2427             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2428             :       TYPE(pw_r3d_rs_type)                               :: zv_hartree_rspace
    2429          50 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rhoz_r, tauz_r, v_xc, v_xc_tau
    2430             :       TYPE(qs_rho_type), POINTER                         :: rho, rho_aux_fit
    2431             :       TYPE(section_vals_type), POINTER                   :: hfx_section, xc_section
    2432             :       TYPE(task_list_type), POINTER                      :: task_list_aux_fit
    2433             : 
    2434          50 :       NULLIFY (pw_env, rhoz_r, rhoz_g, tauz_r, v_xc, v_xc_tau, &
    2435          50 :                poisson_env, auxbas_pw_pool, dft_control, admm_env, xc_section, rho, rho_aux_fit, &
    2436          50 :                task_list_aux_fit, ker_tau_admm, work_admm, dbcsr_p_work, matrix_s, hfx_section)
    2437             : 
    2438          50 :       CALL timeset(routineN, handle)
    2439             : 
    2440          50 :       CALL get_qs_env(qs_env, dft_control=dft_control, pw_env=pw_env, rho=rho, matrix_s=matrix_s)
    2441          50 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool, poisson_env=poisson_env)
    2442          50 :       nspins = dft_control%nspins
    2443             : 
    2444          50 :       CALL dbcsr_allocate_matrix_set(dbcsr_p_work, nspins)
    2445         112 :       DO ispin = 1, nspins
    2446          62 :          ALLOCATE (dbcsr_p_work(ispin)%matrix)
    2447          62 :          CALL dbcsr_create(matrix=dbcsr_p_work(ispin)%matrix, template=matrix_s(1)%matrix)
    2448          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, matrix_s(1)%matrix)
    2449         112 :          CALL dbcsr_set(dbcsr_p_work(ispin)%matrix, 0.0_dp)
    2450             :       END DO
    2451             : 
    2452             :       !Apply the kernel on the density saved in force_data%sum_YP_tau
    2453         374 :       ALLOCATE (rhoz_r(nspins), rhoz_g(nspins))
    2454         112 :       DO ispin = 1, nspins
    2455          62 :          CALL auxbas_pw_pool%create_pw(rhoz_r(ispin))
    2456         112 :          CALL auxbas_pw_pool%create_pw(rhoz_g(ispin))
    2457             :       END DO
    2458          50 :       CALL auxbas_pw_pool%create_pw(rhoz_tot_gspace)
    2459          50 :       CALL auxbas_pw_pool%create_pw(zv_hartree_rspace)
    2460          50 :       CALL auxbas_pw_pool%create_pw(zv_hartree_gspace)
    2461             : 
    2462          50 :       CALL pw_zero(rhoz_tot_gspace)
    2463         112 :       DO ispin = 1, nspins
    2464             :          CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=force_data%sum_YP_tau(ispin)%matrix, &
    2465          62 :                                  rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin))
    2466         112 :          CALL pw_axpy(rhoz_g(ispin), rhoz_tot_gspace)
    2467             :       END DO
    2468             : 
    2469             :       CALL pw_poisson_solve(poisson_env, rhoz_tot_gspace, ehartree, &
    2470          50 :                             zv_hartree_gspace)
    2471             : 
    2472          50 :       CALL pw_transfer(zv_hartree_gspace, zv_hartree_rspace)
    2473          50 :       CALL pw_scale(zv_hartree_rspace, zv_hartree_rspace%pw_grid%dvol)
    2474             : 
    2475          50 :       CALL qs_rho_get(rho, tau_r_valid=do_tau)
    2476          50 :       IF (do_tau) THEN
    2477             :          BLOCK
    2478             :             TYPE(pw_c1d_gs_type) :: tauz_g
    2479          24 :             ALLOCATE (tauz_r(nspins))
    2480           8 :             CALL auxbas_pw_pool%create_pw(tauz_g)
    2481          16 :             DO ispin = 1, nspins
    2482           8 :                CALL auxbas_pw_pool%create_pw(tauz_r(ispin))
    2483             : 
    2484             :                CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=force_data%sum_YP_tau(ispin)%matrix, &
    2485          16 :                                        rho=tauz_r(ispin), rho_gspace=tauz_g, compute_tau=.TRUE.)
    2486             :             END DO
    2487          16 :             CALL auxbas_pw_pool%give_back_pw(tauz_g)
    2488             :          END BLOCK
    2489             :       END IF
    2490             : 
    2491          50 :       IF (dft_control%do_admm) THEN
    2492          16 :          CALL get_qs_env(qs_env, admm_env=admm_env)
    2493          16 :          xc_section => admm_env%xc_section_primary
    2494             :       ELSE
    2495          34 :          xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    2496             :       END IF
    2497             : 
    2498             :       !Primary XC kernel
    2499          50 :       CALL create_kernel(qs_env, v_xc, v_xc_tau, rho, rhoz_r, rhoz_g, tauz_r, xc_section)
    2500             : 
    2501         112 :       DO ispin = 1, nspins
    2502          62 :          CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    2503          62 :          CALL pw_axpy(zv_hartree_rspace, v_xc(ispin))
    2504             :          CALL integrate_v_rspace(qs_env=qs_env, &
    2505             :                                  v_rspace=v_xc(ispin), &
    2506             :                                  hmat=dbcsr_p_work(ispin), &
    2507          62 :                                  calculate_forces=.FALSE.)
    2508             : 
    2509         112 :          CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    2510             :       END DO
    2511          50 :       CALL auxbas_pw_pool%give_back_pw(rhoz_tot_gspace)
    2512          50 :       CALL auxbas_pw_pool%give_back_pw(zv_hartree_rspace)
    2513          50 :       CALL auxbas_pw_pool%give_back_pw(zv_hartree_gspace)
    2514          50 :       DEALLOCATE (v_xc)
    2515             : 
    2516          50 :       IF (do_tau) THEN
    2517          16 :          DO ispin = 1, nspins
    2518           8 :             CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    2519             :             CALL integrate_v_rspace(qs_env=qs_env, &
    2520             :                                     v_rspace=v_xc_tau(ispin), &
    2521             :                                     hmat=dbcsr_p_work(ispin), &
    2522             :                                     compute_tau=.TRUE., &
    2523           8 :                                     calculate_forces=.FALSE.)
    2524          16 :             CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    2525             :          END DO
    2526           8 :          DEALLOCATE (v_xc_tau)
    2527             :       END IF
    2528             : 
    2529             :       !Auxiliary xc kernel (admm)
    2530          50 :       IF (dft_control%do_admm) THEN
    2531          16 :          CALL get_qs_env(qs_env, admm_env=admm_env)
    2532             :          CALL get_admm_env(admm_env, matrix_s_aux_fit=matrix_s_aux, &
    2533          16 :                            task_list_aux_fit=task_list_aux_fit, rho_aux_fit=rho_aux_fit)
    2534             : 
    2535          16 :          CALL qs_rho_get(rho_aux_fit, tau_r_valid=do_tau_admm)
    2536             : 
    2537          16 :          CALL dbcsr_allocate_matrix_set(work_admm, nspins)
    2538          16 :          CALL dbcsr_allocate_matrix_set(ker_tau_admm, nspins)
    2539          36 :          DO ispin = 1, nspins
    2540          20 :             ALLOCATE (work_admm(ispin)%matrix, ker_tau_admm(ispin)%matrix)
    2541          20 :             CALL dbcsr_create(work_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2542          20 :             CALL dbcsr_copy(work_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2543          20 :             CALL dbcsr_set(work_admm(ispin)%matrix, 0.0_dp)
    2544          20 :             CALL dbcsr_create(ker_tau_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2545          20 :             CALL dbcsr_copy(ker_tau_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2546          36 :             CALL dbcsr_set(ker_tau_admm(ispin)%matrix, 0.0_dp)
    2547             :          END DO
    2548             : 
    2549             :          !get the density in the auxuliary density
    2550          16 :          CPASSERT(ASSOCIATED(admm_env%work_orb_orb))
    2551          16 :          CPASSERT(ASSOCIATED(admm_env%work_aux_orb))
    2552          16 :          CPASSERT(ASSOCIATED(admm_env%work_aux_aux))
    2553          16 :          nao = admm_env%nao_orb
    2554          16 :          nao_aux = admm_env%nao_aux_fit
    2555          36 :          DO ispin = 1, nspins
    2556          20 :             CALL copy_dbcsr_to_fm(force_data%sum_YP_tau(ispin)%matrix, admm_env%work_orb_orb)
    2557             :             CALL parallel_gemm('N', 'N', nao_aux, nao, nao, 1.0_dp, admm_env%A, admm_env%work_orb_orb, &
    2558          20 :                                0.0_dp, admm_env%work_aux_orb)
    2559             :             CALL parallel_gemm('N', 'T', nao_aux, nao_aux, nao, 1.0_dp, admm_env%work_aux_orb, admm_env%A, &
    2560          20 :                                0.0_dp, admm_env%work_aux_aux)
    2561          36 :             CALL copy_fm_to_dbcsr(admm_env%work_aux_aux, ker_tau_admm(ispin)%matrix, keep_sparsity=.TRUE.)
    2562             :          END DO
    2563             : 
    2564          16 :          IF (.NOT. qs_env%admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    2565          36 :             DO ispin = 1, nspins
    2566          20 :                CALL pw_zero(rhoz_r(ispin))
    2567          20 :                CALL pw_zero(rhoz_g(ispin))
    2568             :                CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=ker_tau_admm(ispin)%matrix, &
    2569             :                                        rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin), &
    2570          36 :                                        basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    2571             :             END DO
    2572             : 
    2573          16 :             IF (do_tau_admm) THEN
    2574             :                BLOCK
    2575             :                   TYPE(pw_c1d_gs_type) :: tauz_g
    2576           0 :                   CALL auxbas_pw_pool%create_pw(tauz_g)
    2577           0 :                   DO ispin = 1, nspins
    2578           0 :                      CALL pw_zero(tauz_r(ispin))
    2579             :                      CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=ker_tau_admm(ispin)%matrix, &
    2580             :                                              rho=tauz_r(ispin), rho_gspace=tauz_g, &
    2581             :                                              basis_type="AUX_FIT", task_list_external=task_list_aux_fit, &
    2582           0 :                                              compute_tau=.TRUE.)
    2583             :                   END DO
    2584           0 :                   CALL auxbas_pw_pool%give_back_pw(tauz_g)
    2585             :                END BLOCK
    2586             :             END IF
    2587             : 
    2588          16 :             xc_section => admm_env%xc_section_aux
    2589          16 :             CALL create_kernel(qs_env, v_xc, v_xc_tau, rho_aux_fit, rhoz_r, rhoz_g, tauz_r, xc_section)
    2590             : 
    2591          36 :             DO ispin = 1, nspins
    2592          20 :                CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    2593             :                CALL integrate_v_rspace(qs_env=qs_env, &
    2594             :                                        v_rspace=v_xc(ispin), &
    2595             :                                        hmat=work_admm(ispin), &
    2596             :                                        calculate_forces=.FALSE., &
    2597             :                                        basis_type="AUX_FIT", &
    2598          20 :                                        task_list_external=task_list_aux_fit)
    2599          36 :                CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    2600             :             END DO
    2601          16 :             DEALLOCATE (v_xc)
    2602             : 
    2603          16 :             IF (do_tau_admm) THEN
    2604           0 :                DO ispin = 1, nspins
    2605           0 :                   CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    2606             :                   CALL integrate_v_rspace(qs_env=qs_env, &
    2607             :                                           v_rspace=v_xc_tau(ispin), &
    2608             :                                           hmat=work_admm(ispin), &
    2609             :                                           calculate_forces=.FALSE., &
    2610             :                                           basis_type="AUX_FIT", &
    2611             :                                           task_list_external=task_list_aux_fit, &
    2612           0 :                                           compute_tau=.TRUE.)
    2613           0 :                   CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    2614             :                END DO
    2615           0 :                DEALLOCATE (v_xc_tau)
    2616             :             END IF
    2617             :          END IF !admm
    2618             :       END IF
    2619             : 
    2620         112 :       DO ispin = 1, nspins
    2621          62 :          CALL auxbas_pw_pool%give_back_pw(rhoz_r(ispin))
    2622         112 :          CALL auxbas_pw_pool%give_back_pw(rhoz_g(ispin))
    2623             :       END DO
    2624          50 :       DEALLOCATE (rhoz_r, rhoz_g)
    2625             : 
    2626          50 :       IF (do_tau) THEN
    2627          16 :          DO ispin = 1, nspins
    2628          16 :             CALL auxbas_pw_pool%give_back_pw(tauz_r(ispin))
    2629             :          END DO
    2630           8 :          DEALLOCATE (tauz_r)
    2631             :       END IF
    2632             : 
    2633             :       !HFX kernel
    2634          50 :       hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%HF")
    2635          50 :       CALL section_vals_get(hfx_section, explicit=do_hfx)
    2636          50 :       IF (do_hfx) THEN
    2637          32 :          IF (dft_control%do_admm) THEN
    2638          16 :             CALL tddft_hfx_matrix(work_admm, ker_tau_admm, qs_env, .FALSE., .FALSE.)
    2639             : 
    2640             :             !Going back to primary basis
    2641          16 :             CALL dbcsr_create(dbcsr_work, template=dbcsr_p_work(1)%matrix)
    2642          16 :             CALL dbcsr_copy(dbcsr_work, dbcsr_p_work(1)%matrix)
    2643          16 :             CALL dbcsr_set(dbcsr_work, 0.0_dp)
    2644          36 :             DO ispin = 1, nspins
    2645          20 :                CALL copy_dbcsr_to_fm(work_admm(ispin)%matrix, admm_env%work_aux_aux)
    2646             :                CALL parallel_gemm('N', 'N', nao_aux, nao, nao_aux, 1.0_dp, admm_env%work_aux_aux, admm_env%A, &
    2647          20 :                                   0.0_dp, admm_env%work_aux_orb)
    2648             :                CALL parallel_gemm('T', 'N', nao, nao, nao_aux, 1.0_dp, admm_env%A, admm_env%work_aux_orb, &
    2649          20 :                                   0.0_dp, admm_env%work_orb_orb)
    2650          20 :                CALL copy_fm_to_dbcsr(admm_env%work_orb_orb, dbcsr_work, keep_sparsity=.TRUE.)
    2651          36 :                CALL dbcsr_add(dbcsr_p_work(ispin)%matrix, dbcsr_work, 1.0_dp, 1.0_dp)
    2652             :             END DO
    2653          16 :             CALL dbcsr_release(dbcsr_work)
    2654          16 :             CALL dbcsr_deallocate_matrix_set(ker_tau_admm)
    2655             :          ELSE
    2656          16 :             CALL tddft_hfx_matrix(dbcsr_p_work, force_data%sum_YP_tau, qs_env, .FALSE., .FALSE.)
    2657             :          END IF
    2658             :       END IF
    2659             : 
    2660         112 :       DO ispin = 1, nspins
    2661         112 :          CALL dbcsr_add(force_data%sum_O_tau(ispin)%matrix, dbcsr_p_work(ispin)%matrix, 1.0_dp, 1.0_dp)
    2662             :       END DO
    2663             : 
    2664          50 :       CALL dbcsr_deallocate_matrix_set(dbcsr_p_work)
    2665          50 :       CALL dbcsr_deallocate_matrix_set(work_admm)
    2666             : 
    2667          50 :       CALL timestop(handle)
    2668             : 
    2669         200 :    END SUBROUTINE prepare_for_response
    2670             : 
    2671             : ! **************************************************************************************************
    2672             : !> \brief Calculate the force and virial due to the (P|Q) GPW integral derivatives
    2673             : !> \param G_PQ ...
    2674             : !> \param force ...
    2675             : !> \param h_stress ...
    2676             : !> \param use_virial ...
    2677             : !> \param mp2_env ...
    2678             : !> \param qs_env ...
    2679             : ! **************************************************************************************************
    2680          12 :    SUBROUTINE get_2c_gpw_forces(G_PQ, force, h_stress, use_virial, mp2_env, qs_env)
    2681             : 
    2682             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: G_PQ
    2683             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    2684             :       REAL(dp), DIMENSION(3, 3), INTENT(INOUT)           :: h_stress
    2685             :       LOGICAL, INTENT(IN)                                :: use_virial
    2686             :       TYPE(mp2_type), INTENT(INOUT)                      :: mp2_env
    2687             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2688             : 
    2689             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'get_2c_gpw_forces'
    2690             : 
    2691             :       INTEGER :: atom_a, color, handle, i, i_RI, i_xyz, iatom, igrid_level, ikind, ipgf, iset, j, &
    2692             :          j_RI, jatom, lb_RI, n_RI, natom, ncoa, ncoms, nkind, nproc, nseta, o1, offset, pdims(2), &
    2693             :          sgfa, ub_RI
    2694          24 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, iproc_map, kind_of, &
    2695          12 :                                                             sizes_RI
    2696          24 :       INTEGER, DIMENSION(:), POINTER                     :: col_dist, la_max, la_min, npgfa, nsgfa, &
    2697          12 :                                                             row_dist
    2698          12 :       INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, pgrid
    2699             :       LOGICAL                                            :: found, one_proc_group
    2700             :       REAL(dp)                                           :: cutoff_old, radius, relative_cutoff_old
    2701          12 :       REAL(dp), ALLOCATABLE, DIMENSION(:)                :: e_cutoff_old, wf_vector
    2702             :       REAL(dp), DIMENSION(3)                             :: force_a, force_b, ra
    2703             :       REAL(dp), DIMENSION(3, 3)                          :: my_virial_a, my_virial_b
    2704          12 :       REAL(KIND=dp), DIMENSION(:, :), POINTER            :: h_tmp, I_ab, pab, pblock, sphi_a, zeta
    2705          12 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    2706             :       TYPE(cell_type), POINTER                           :: cell
    2707             :       TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
    2708             :       TYPE(dbcsr_type)                                   :: tmp_G_PQ
    2709             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2710             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    2711          12 :          DIMENSION(:), TARGET                            :: basis_set_ri_aux
    2712             :       TYPE(gto_basis_set_type), POINTER                  :: basis_set_a
    2713          12 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    2714             :       TYPE(mp_para_env_type), POINTER                    :: para_env, para_env_ext
    2715             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
    2716          12 :          POINTER                                         :: sab_orb
    2717          12 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    2718          48 :       TYPE(pw_c1d_gs_type)                               :: dvg(3), pot_g, rho_g, rho_g_copy
    2719             :       TYPE(pw_env_type), POINTER                         :: pw_env_ext
    2720             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    2721             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2722             :       TYPE(pw_r3d_rs_type)                               :: psi_L, rho_r
    2723          12 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    2724          12 :       TYPE(realspace_grid_type), DIMENSION(:), POINTER   :: rs_v
    2725             :       TYPE(task_list_type), POINTER                      :: task_list_ext
    2726             : 
    2727          12 :       NULLIFY (sab_orb, task_list_ext, particle_set, qs_kind_set, dft_control, pw_env_ext, auxbas_pw_pool, &
    2728          12 :                poisson_env, atomic_kind_set, para_env, cell, rs_v, mos, basis_set_a)
    2729             : 
    2730          12 :       CALL timeset(routineN, handle)
    2731             : 
    2732             :       CALL get_qs_env(qs_env, dft_control=dft_control, para_env=para_env, sab_orb=sab_orb, &
    2733             :                       natom=natom, nkind=nkind, qs_kind_set=qs_kind_set, particle_set=particle_set, &
    2734          12 :                       mos=mos, cell=cell, atomic_kind_set=atomic_kind_set)
    2735             : 
    2736             :       !The idea is to use GPW to compute the integrals and derivatives. Because the potential needs
    2737             :       !to be calculated for each phi_j (column) of all AO pairs, and because that is expensive, we want
    2738             :       !to minimize the amount of time we do that. Therefore, we work with a special distribution, where
    2739             :       !each column of the resulting DBCSR matrix is mapped to a sub-communicator.
    2740             : 
    2741             :       !Try to get the optimal pdims (we want a grid that is flat: many cols, few rows)
    2742          12 :       IF (para_env%num_pe <= natom) THEN
    2743             :          pdims(1) = 1
    2744             :          pdims(2) = para_env%num_pe
    2745             :       ELSE
    2746           0 :          DO i = natom, 1, -1
    2747           0 :             IF (MODULO(para_env%num_pe, i) == 0) THEN
    2748           0 :                pdims(1) = para_env%num_pe/i
    2749           0 :                pdims(2) = i
    2750           0 :                EXIT
    2751             :             END IF
    2752             :          END DO
    2753             :       END IF
    2754             : 
    2755          48 :       ALLOCATE (row_dist(natom), col_dist(natom))
    2756          48 :       DO iatom = 1, natom
    2757          48 :          row_dist(iatom) = MODULO(iatom, pdims(1))
    2758             :       END DO
    2759          48 :       DO jatom = 1, natom
    2760          48 :          col_dist(jatom) = MODULO(jatom, pdims(2))
    2761             :       END DO
    2762             : 
    2763          48 :       ALLOCATE (pgrid(0:pdims(1) - 1, 0:pdims(2) - 1))
    2764          12 :       nproc = 0
    2765          24 :       DO i = 0, pdims(1) - 1
    2766          48 :          DO j = 0, pdims(2) - 1
    2767          24 :             pgrid(i, j) = nproc
    2768          36 :             nproc = nproc + 1
    2769             :          END DO
    2770             :       END DO
    2771             : 
    2772          12 :       CALL dbcsr_distribution_new(dbcsr_dist, group=para_env%get_handle(), pgrid=pgrid, row_dist=row_dist, col_dist=col_dist)
    2773             : 
    2774             :       !The temporary DBCSR integrals and derivatives matrices in this flat distribution
    2775          12 :       CALL dbcsr_create(tmp_G_PQ, template=G_PQ, matrix_type=dbcsr_type_no_symmetry, dist=dbcsr_dist)
    2776          12 :       CALL dbcsr_complete_redistribute(G_PQ, tmp_G_PQ)
    2777             : 
    2778          84 :       ALLOCATE (basis_set_ri_aux(nkind), sizes_RI(natom))
    2779          12 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    2780          12 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_RI, basis=basis_set_ri_aux)
    2781          48 :       n_RI = SUM(sizes_RI)
    2782             : 
    2783          12 :       one_proc_group = mp2_env%mp2_num_proc == 1
    2784          12 :       ALLOCATE (para_env_ext)
    2785          12 :       IF (one_proc_group) THEN
    2786             :          !one subgroup per proc
    2787           4 :          CALL para_env_ext%from_split(para_env, para_env%mepos)
    2788             :       ELSE
    2789             :          !Split the communicator accross the columns of the matrix
    2790           8 :          ncoms = MIN(pdims(2), para_env%num_pe/mp2_env%mp2_num_proc)
    2791          16 :          DO i = 0, pdims(1) - 1
    2792          32 :             DO j = 0, pdims(2) - 1
    2793          24 :                IF (pgrid(i, j) == para_env%mepos) color = MODULO(j + 1, ncoms)
    2794             :             END DO
    2795             :          END DO
    2796           8 :          CALL para_env_ext%from_split(para_env, color)
    2797             :       END IF
    2798             : 
    2799             :       !sab_orb and task_list_ext are essentially dummies
    2800             :       CALL prepare_gpw(qs_env, dft_control, e_cutoff_old, cutoff_old, relative_cutoff_old, para_env_ext, pw_env_ext, &
    2801          12 :                        auxbas_pw_pool, poisson_env, task_list_ext, rho_r, rho_g, pot_g, psi_L, sab_orb)
    2802             : 
    2803          12 :       IF (use_virial) THEN
    2804           4 :          CALL auxbas_pw_pool%create_pw(rho_g_copy)
    2805          16 :          DO i_xyz = 1, 3
    2806          16 :             CALL auxbas_pw_pool%create_pw(dvg(i_xyz))
    2807             :          END DO
    2808             :       END IF
    2809             : 
    2810          36 :       ALLOCATE (wf_vector(n_RI))
    2811             : 
    2812          12 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    2813             : 
    2814          36 :       ALLOCATE (iproc_map(natom))
    2815             : 
    2816             :       !Loop over the atomic blocks
    2817          48 :       DO jatom = 1, natom
    2818             : 
    2819             :          !Only calculate if on the correct sub-communicator/proc
    2820          36 :          IF (one_proc_group) THEN
    2821          48 :             iproc_map = 0
    2822          48 :             DO iatom = 1, natom
    2823          48 :                IF (pgrid(row_dist(iatom), col_dist(jatom)) == para_env%mepos) iproc_map(iatom) = 1
    2824             :             END DO
    2825          30 :             IF (.NOT. ANY(iproc_map == 1)) CYCLE
    2826             :          ELSE
    2827          24 :             IF (.NOT. MODULO(col_dist(jatom) + 1, ncoms) == color) CYCLE
    2828             :          END IF
    2829             : 
    2830          60 :          lb_RI = SUM(sizes_RI(1:jatom - 1))
    2831          30 :          ub_RI = lb_RI + sizes_RI(jatom)
    2832         872 :          DO j_RI = lb_RI + 1, ub_RI
    2833             : 
    2834       69720 :             wf_vector = 0.0_dp
    2835         830 :             wf_vector(j_RI) = 1.0_dp
    2836             : 
    2837             :             CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, qs_kind_set, cell, &
    2838             :                                     particle_set, pw_env_ext, dft_control%qs_control%eps_rho_rspace, &
    2839         830 :                                     basis_type="RI_AUX")
    2840             : 
    2841         830 :             IF (use_virial) THEN
    2842         166 :                CALL calc_potential_gpw(rho_r, rho_g, poisson_env, pot_g, mp2_env%potential_parameter, dvg)
    2843             : 
    2844       13944 :                wf_vector = 0.0_dp
    2845         664 :                DO iatom = 1, natom
    2846             :                   !only compute if i,j atom pair on correct proc
    2847         498 :                   IF (one_proc_group) THEN
    2848         498 :                      IF (.NOT. iproc_map(iatom) == 1) CYCLE
    2849             :                   END IF
    2850             : 
    2851         498 :                   CALL dbcsr_get_block_p(tmp_G_PQ, iatom, jatom, pblock, found)
    2852         498 :                   IF (.NOT. found) CYCLE
    2853             : 
    2854         996 :                   i_RI = SUM(sizes_RI(1:iatom - 1))
    2855       14940 :                   wf_vector(i_RI + 1:i_RI + sizes_RI(iatom)) = pblock(:, j_RI - lb_RI)
    2856             :                END DO
    2857             : 
    2858         166 :                CALL pw_copy(rho_g, rho_g_copy)
    2859             :                CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, qs_kind_set, cell, &
    2860             :                                        particle_set, pw_env_ext, dft_control%qs_control%eps_rho_rspace, &
    2861         166 :                                        basis_type="RI_AUX")
    2862             : 
    2863             :                CALL calc_potential_gpw(psi_L, rho_g, poisson_env, pot_g, mp2_env%potential_parameter, &
    2864         166 :                                        no_transfer=.TRUE.)
    2865             :                CALL virial_gpw_potential(rho_g_copy, pot_g, rho_g, dvg, h_stress, &
    2866         166 :                                          mp2_env%potential_parameter, para_env_ext)
    2867             :             ELSE
    2868         664 :                CALL calc_potential_gpw(rho_r, rho_g, poisson_env, pot_g, mp2_env%potential_parameter)
    2869             :             END IF
    2870             : 
    2871         830 :             NULLIFY (rs_v)
    2872         830 :             CALL pw_env_get(pw_env_ext, rs_grids=rs_v)
    2873         830 :             CALL potential_pw2rs(rs_v, rho_r, pw_env_ext)
    2874             : 
    2875        3356 :             DO iatom = 1, natom
    2876             : 
    2877             :                !only compute if i,j atom pair on correct proc
    2878        2490 :                IF (one_proc_group) THEN
    2879         498 :                   IF (.NOT. iproc_map(iatom) == 1) CYCLE
    2880             :                END IF
    2881             : 
    2882        2490 :                force_a(:) = 0.0_dp
    2883        2490 :                force_b(:) = 0.0_dp
    2884        2490 :                IF (use_virial) THEN
    2885         498 :                   my_virial_a = 0.0_dp
    2886         498 :                   my_virial_b = 0.0_dp
    2887             :                END IF
    2888             : 
    2889        2490 :                ikind = kind_of(iatom)
    2890        2490 :                atom_a = atom_of_kind(iatom)
    2891             : 
    2892        2490 :                basis_set_a => basis_set_ri_aux(ikind)%gto_basis_set
    2893        2490 :                first_sgfa => basis_set_a%first_sgf
    2894        2490 :                la_max => basis_set_a%lmax
    2895        2490 :                la_min => basis_set_a%lmin
    2896        2490 :                nseta = basis_set_a%nset
    2897        2490 :                nsgfa => basis_set_a%nsgf_set
    2898        2490 :                sphi_a => basis_set_a%sphi
    2899        2490 :                zeta => basis_set_a%zet
    2900        2490 :                npgfa => basis_set_a%npgf
    2901             : 
    2902        2490 :                ra(:) = pbc(particle_set(iatom)%r, cell)
    2903             : 
    2904        2490 :                CALL dbcsr_get_block_p(tmp_G_PQ, iatom, jatom, pblock, found)
    2905        2490 :                IF (.NOT. found) CYCLE
    2906             : 
    2907             :                offset = 0
    2908       15936 :                DO iset = 1, nseta
    2909       14442 :                   ncoa = npgfa(iset)*ncoset(la_max(iset))
    2910       14442 :                   sgfa = first_sgfa(1, iset)
    2911             : 
    2912      131472 :                   ALLOCATE (h_tmp(ncoa, 1)); h_tmp = 0.0_dp
    2913       99102 :                   ALLOCATE (I_ab(nsgfa(iset), 1)); I_ab = 0.0_dp
    2914      117030 :                   ALLOCATE (pab(ncoa, 1)); pab = 0.0_dp
    2915             : 
    2916       97110 :                   I_ab(1:nsgfa(iset), 1) = 2.0_dp*pblock(offset + 1:offset + nsgfa(iset), j_RI - lb_RI)
    2917             :                   CALL dgemm("N", "N", ncoa, 1, nsgfa(iset), 1.0_dp, sphi_a(1, sgfa), SIZE(sphi_a, 1), &
    2918       14442 :                              I_ab(1, 1), nsgfa(iset), 0.0_dp, pab(1, 1), ncoa)
    2919             : 
    2920       43326 :                   igrid_level = gaussian_gridlevel(pw_env_ext%gridlevel_info, MINVAL(zeta(:, iset)))
    2921             : 
    2922             :                   ! The last three parameters are used to check whether a given function is within the own range.
    2923             :                   ! Here, it is always the case, so let's enforce it because mod(0, 1)==0
    2924       14442 :                   IF (map_gaussian_here(rs_v(igrid_level), cell%h_inv, ra, 0, 1, 0)) THEN
    2925       28884 :                      DO ipgf = 1, npgfa(iset)
    2926       14442 :                         o1 = (ipgf - 1)*ncoset(la_max(iset))
    2927       14442 :                         igrid_level = gaussian_gridlevel(pw_env_ext%gridlevel_info, zeta(ipgf, iset))
    2928             : 
    2929             :                         radius = exp_radius_very_extended(la_min=la_min(iset), la_max=la_max(iset), &
    2930             :                                                           lb_min=0, lb_max=0, ra=ra, rb=ra, rp=ra, &
    2931             :                                                           zetp=zeta(ipgf, iset), &
    2932             :                                                           eps=dft_control%qs_control%eps_gvg_rspace, &
    2933       14442 :                                                           prefactor=1.0_dp, cutoff=1.0_dp)
    2934             : 
    2935             :                         CALL integrate_pgf_product( &
    2936             :                            la_max=la_max(iset), zeta=zeta(ipgf, iset), la_min=la_min(iset), &
    2937             :                            lb_max=0, zetb=0.0_dp, lb_min=0, &
    2938             :                            ra=ra, rab=(/0.0_dp, 0.0_dp, 0.0_dp/), &
    2939             :                            rsgrid=rs_v(igrid_level), &
    2940             :                            hab=h_tmp, pab=pab, &
    2941             :                            o1=o1, &
    2942             :                            o2=0, &
    2943             :                            radius=radius, &
    2944             :                            calculate_forces=.TRUE., &
    2945             :                            force_a=force_a, force_b=force_b, &
    2946       28884 :                            use_virial=use_virial, my_virial_a=my_virial_a, my_virial_b=my_virial_b)
    2947             : 
    2948             :                      END DO
    2949             : 
    2950             :                   END IF
    2951             : 
    2952       14442 :                   offset = offset + nsgfa(iset)
    2953       15936 :                   DEALLOCATE (pab, h_tmp, I_ab)
    2954             :                END DO !iset
    2955             : 
    2956        5976 :                force(ikind)%mp2_non_sep(:, atom_a) = force(ikind)%mp2_non_sep(:, atom_a) + force_a + force_b
    2957       10790 :                IF (use_virial) h_stress = h_stress + my_virial_a + my_virial_b
    2958             : 
    2959             :             END DO !iatom
    2960             :          END DO !j_RI
    2961             :       END DO !jatom
    2962             : 
    2963          12 :       IF (use_virial) THEN
    2964           4 :          CALL auxbas_pw_pool%give_back_pw(rho_g_copy)
    2965          16 :          DO i_xyz = 1, 3
    2966          16 :             CALL auxbas_pw_pool%give_back_pw(dvg(i_xyz))
    2967             :          END DO
    2968             :       END IF
    2969             : 
    2970             :       CALL cleanup_gpw(qs_env, e_cutoff_old, cutoff_old, relative_cutoff_old, para_env_ext, pw_env_ext, &
    2971          12 :                        task_list_ext, auxbas_pw_pool, rho_r, rho_g, pot_g, psi_L)
    2972             : 
    2973          12 :       CALL dbcsr_release(tmp_G_PQ)
    2974          12 :       CALL dbcsr_distribution_release(dbcsr_dist)
    2975          12 :       DEALLOCATE (col_dist, row_dist, pgrid)
    2976             : 
    2977          12 :       CALL mp_para_env_release(para_env_ext)
    2978             : 
    2979          12 :       CALL timestop(handle)
    2980             : 
    2981          48 :    END SUBROUTINE get_2c_gpw_forces
    2982             : 
    2983             : ! **************************************************************************************************
    2984             : !> \brief Calculate the forces due to the (P|Q) MME integral derivatives
    2985             : !> \param G_PQ ...
    2986             : !> \param force ...
    2987             : !> \param mp2_env ...
    2988             : !> \param qs_env ...
    2989             : ! **************************************************************************************************
    2990          16 :    SUBROUTINE get_2c_mme_forces(G_PQ, force, mp2_env, qs_env)
    2991             : 
    2992             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: G_PQ
    2993             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    2994             :       TYPE(mp2_type), INTENT(INOUT)                      :: mp2_env
    2995             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2996             : 
    2997             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'get_2c_mme_forces'
    2998             : 
    2999             :       INTEGER :: atom_a, atom_b, G_count, handle, i_xyz, iatom, ikind, iset, jatom, jkind, jset, &
    3000             :          natom, nkind, nseta, nsetb, offset_hab_a, offset_hab_b, R_count, sgfa, sgfb
    3001          16 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, kind_of
    3002          16 :       INTEGER, DIMENSION(:), POINTER                     :: la_max, la_min, lb_max, lb_min, npgfa, &
    3003          16 :                                                             npgfb, nsgfa, nsgfb
    3004          16 :       INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, first_sgfb
    3005             :       LOGICAL                                            :: found
    3006             :       REAL(dp)                                           :: new_force, pref
    3007          16 :       REAL(dp), ALLOCATABLE, DIMENSION(:, :)             :: hab
    3008          16 :       REAL(dp), ALLOCATABLE, DIMENSION(:, :, :)          :: hdab
    3009          16 :       REAL(dp), DIMENSION(:, :), POINTER                 :: pblock
    3010             :       REAL(KIND=dp), DIMENSION(3)                        :: ra, rb
    3011          16 :       REAL(KIND=dp), DIMENSION(:, :), POINTER            :: sphi_a, sphi_b, zeta, zetb
    3012          16 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    3013             :       TYPE(cell_type), POINTER                           :: cell
    3014             :       TYPE(dbcsr_iterator_type)                          :: iter
    3015             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    3016          16 :          DIMENSION(:), TARGET                            :: basis_set_ri_aux
    3017             :       TYPE(gto_basis_set_type), POINTER                  :: basis_set_a, basis_set_b
    3018             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    3019          16 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    3020          16 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    3021             : 
    3022          16 :       NULLIFY (qs_kind_set, basis_set_a, basis_set_b, pblock, particle_set, &
    3023          16 :                cell, la_max, la_min, lb_min, npgfa, lb_max, npgfb, nsgfa, &
    3024          16 :                nsgfb, first_sgfa, first_sgfb, sphi_a, sphi_b, zeta, zetb, &
    3025          16 :                atomic_kind_set, para_env)
    3026             : 
    3027          16 :       CALL timeset(routineN, handle)
    3028             : 
    3029             :       CALL get_qs_env(qs_env, qs_kind_set=qs_kind_set, nkind=nkind, particle_set=particle_set, &
    3030          16 :                       cell=cell, atomic_kind_set=atomic_kind_set, natom=natom, para_env=para_env)
    3031             : 
    3032          16 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    3033             : 
    3034          80 :       ALLOCATE (basis_set_ri_aux(nkind))
    3035          16 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    3036             : 
    3037          16 :       G_count = 0; R_count = 0
    3038             : 
    3039          16 :       CALL dbcsr_iterator_start(iter, G_PQ)
    3040         116 :       DO WHILE (dbcsr_iterator_blocks_left(iter))
    3041             : 
    3042         100 :          CALL dbcsr_iterator_next_block(iter, row=iatom, column=jatom)
    3043         100 :          CALL dbcsr_get_block_p(G_PQ, iatom, jatom, pblock, found)
    3044         100 :          IF (.NOT. found) CYCLE
    3045         100 :          IF (iatom > jatom) CYCLE
    3046          64 :          pref = 2.0_dp
    3047          64 :          IF (iatom == jatom) pref = 1.0_dp
    3048             : 
    3049          64 :          ikind = kind_of(iatom)
    3050          64 :          jkind = kind_of(jatom)
    3051             : 
    3052          64 :          atom_a = atom_of_kind(iatom)
    3053          64 :          atom_b = atom_of_kind(jatom)
    3054             : 
    3055          64 :          basis_set_a => basis_set_ri_aux(ikind)%gto_basis_set
    3056          64 :          first_sgfa => basis_set_a%first_sgf
    3057          64 :          la_max => basis_set_a%lmax
    3058          64 :          la_min => basis_set_a%lmin
    3059          64 :          nseta = basis_set_a%nset
    3060          64 :          nsgfa => basis_set_a%nsgf_set
    3061          64 :          sphi_a => basis_set_a%sphi
    3062          64 :          zeta => basis_set_a%zet
    3063          64 :          npgfa => basis_set_a%npgf
    3064             : 
    3065          64 :          basis_set_b => basis_set_ri_aux(jkind)%gto_basis_set
    3066          64 :          first_sgfb => basis_set_b%first_sgf
    3067          64 :          lb_max => basis_set_b%lmax
    3068          64 :          lb_min => basis_set_b%lmin
    3069          64 :          nsetb = basis_set_b%nset
    3070          64 :          nsgfb => basis_set_b%nsgf_set
    3071          64 :          sphi_b => basis_set_b%sphi
    3072          64 :          zetb => basis_set_b%zet
    3073          64 :          npgfb => basis_set_b%npgf
    3074             : 
    3075          64 :          ra(:) = pbc(particle_set(iatom)%r, cell)
    3076          64 :          rb(:) = pbc(particle_set(jatom)%r, cell)
    3077             : 
    3078         256 :          ALLOCATE (hab(basis_set_a%nsgf, basis_set_b%nsgf))
    3079         256 :          ALLOCATE (hdab(3, basis_set_a%nsgf, basis_set_b%nsgf))
    3080       47944 :          hab(:, :) = 0.0_dp
    3081      187912 :          hdab(:, :, :) = 0.0_dp
    3082             : 
    3083          64 :          offset_hab_a = 0
    3084         756 :          DO iset = 1, nseta
    3085         692 :             sgfa = first_sgfa(1, iset)
    3086             : 
    3087         692 :             offset_hab_b = 0
    3088        6340 :             DO jset = 1, nsetb
    3089        5648 :                sgfb = first_sgfb(1, jset)
    3090             : 
    3091             :                CALL integrate_set_2c(mp2_env%eri_mme_param%par, mp2_env%potential_parameter, la_min(iset), &
    3092             :                                      la_max(iset), lb_min(jset), lb_max(jset), npgfa(iset), npgfb(jset), &
    3093             :                                      zeta(:, iset), zetb(:, jset), ra, rb, hab, nsgfa(iset), nsgfb(jset), &
    3094             :                                      offset_hab_a, offset_hab_b, 0, 0, sphi_a, sphi_b, sgfa, sgfb, &
    3095             :                                      nsgfa(iset), nsgfb(jset), do_eri_mme, hdab=hdab, &
    3096        5648 :                                      G_count=G_count, R_count=R_count)
    3097             : 
    3098        6340 :                offset_hab_b = offset_hab_b + nsgfb(jset)
    3099             :             END DO
    3100         756 :             offset_hab_a = offset_hab_a + nsgfa(iset)
    3101             :          END DO
    3102             : 
    3103         256 :          DO i_xyz = 1, 3
    3104      143832 :             new_force = pref*SUM(pblock(:, :)*hdab(i_xyz, :, :))
    3105         192 :             force(ikind)%mp2_non_sep(i_xyz, atom_a) = force(ikind)%mp2_non_sep(i_xyz, atom_a) + new_force
    3106         256 :             force(jkind)%mp2_non_sep(i_xyz, atom_b) = force(jkind)%mp2_non_sep(i_xyz, atom_b) - new_force
    3107             :          END DO
    3108             : 
    3109         216 :          DEALLOCATE (hab, hdab)
    3110             :       END DO
    3111          16 :       CALL dbcsr_iterator_stop(iter)
    3112             : 
    3113          16 :       CALL cp_eri_mme_update_local_counts(mp2_env%eri_mme_param, para_env, G_count_2c=G_count, R_count_2c=R_count)
    3114             : 
    3115          16 :       CALL timestop(handle)
    3116             : 
    3117          48 :    END SUBROUTINE get_2c_mme_forces
    3118             : 
    3119             : ! **************************************************************************************************
    3120             : !> \brief This routines gather all the force updates due to the response density and the trace with F
    3121             : !>        Also update the forces due to the SCF density for XC and exact exchange
    3122             : !> \param p_env the p_env coming from the response calculation
    3123             : !> \param matrix_hz the matrix going into the RHS of the response equation
    3124             : !> \param matrix_p_F the density matrix with which we evaluate Trace[P*F]
    3125             : !> \param matrix_p_F_admm ...
    3126             : !> \param qs_env ...
    3127             : !> \note very much inspired from the response_force routine in response_solver.F, especially for virial
    3128             : ! **************************************************************************************************
    3129          50 :    SUBROUTINE update_im_time_forces(p_env, matrix_hz, matrix_p_F, matrix_p_F_admm, qs_env)
    3130             : 
    3131             :       TYPE(qs_p_env_type), POINTER                       :: p_env
    3132             :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_hz, matrix_p_F, matrix_p_F_admm
    3133             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3134             : 
    3135             :       CHARACTER(len=*), PARAMETER :: routineN = 'update_im_time_forces'
    3136             : 
    3137             :       INTEGER                                            :: handle, i, idens, ispin, n_rep_hf, nao, &
    3138             :                                                             nao_aux, nder, nimages, nocc, nspins
    3139          50 :       INTEGER, DIMENSION(:, :, :), POINTER               :: cell_to_index
    3140             :       LOGICAL                                            :: do_exx, do_hfx, do_tau, do_tau_admm, &
    3141             :                                                             use_virial
    3142             :       REAL(dp)                                           :: dummy_real1, dummy_real2, ehartree, &
    3143             :                                                             eps_ppnl, exc, focc
    3144             :       REAL(dp), DIMENSION(3, 3)                          :: h_stress, pv_loc
    3145             :       TYPE(admm_type), POINTER                           :: admm_env
    3146          50 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    3147          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: current_density, current_density_admm, &
    3148          50 :          current_mat_h, matrix_p_mp2, matrix_p_mp2_admm, matrix_s, matrix_s_aux_fit, matrix_w, &
    3149          50 :          rho_ao, rho_ao_aux, scrm, scrm_admm
    3150          50 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: dbcsr_work_h, dbcsr_work_p
    3151             :       TYPE(dbcsr_type)                                   :: dbcsr_work
    3152             :       TYPE(dft_control_type), POINTER                    :: dft_control
    3153          50 :       TYPE(hfx_type), DIMENSION(:, :), POINTER           :: x_data
    3154          50 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    3155             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    3156             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
    3157          50 :          POINTER                                         :: sab_orb, sac_ae, sac_ppl, sap_ppnl
    3158          50 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    3159             :       TYPE(pw_c1d_gs_type)                               :: rho_tot_gspace, rhoz_tot_gspace, &
    3160             :                                                             zv_hartree_gspace
    3161          50 :       TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER        :: rhoz_g
    3162             :       TYPE(pw_env_type), POINTER                         :: pw_env
    3163             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    3164             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    3165             :       TYPE(pw_r3d_rs_type)                               :: vh_rspace, vhxc_rspace, zv_hartree_rspace
    3166          50 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rhoz_r, tauz_r, v_xc, v_xc_tau, &
    3167          50 :                                                             vadmm_rspace, vtau_rspace, vxc_rspace
    3168          50 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    3169          50 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    3170             :       TYPE(qs_rho_type), POINTER                         :: rho, rho_aux_fit
    3171             :       TYPE(section_vals_type), POINTER                   :: hfx_section, xc_section
    3172             :       TYPE(task_list_type), POINTER                      :: task_list_aux_fit
    3173             :       TYPE(virial_type), POINTER                         :: virial
    3174             : 
    3175          50 :       NULLIFY (scrm, rho, dft_control, matrix_p_mp2, matrix_s, matrix_p_mp2_admm, admm_env, sab_orb, &
    3176          50 :                cell_to_index, dbcsr_work_p, dbcsr_work_h, sac_ae, sac_ppl, sap_ppnl, force, virial, &
    3177          50 :                qs_kind_set, atomic_kind_set, particle_set, pw_env, poisson_env, auxbas_pw_pool, &
    3178          50 :                task_list_aux_fit, matrix_s_aux_fit, scrm_admm, rho_aux_fit, rho_ao_aux, x_data, &
    3179          50 :                hfx_section, xc_section, para_env, rhoz_g, rhoz_r, tauz_r, v_xc, v_xc_tau, &
    3180          50 :                vxc_rspace, vtau_rspace, vadmm_rspace, rho_ao, matrix_w)
    3181             : 
    3182          50 :       CALL timeset(routineN, handle)
    3183             : 
    3184             :       CALL get_qs_env(qs_env, rho=rho, dft_control=dft_control, matrix_s=matrix_s, admm_env=admm_env, &
    3185             :                       sab_orb=sab_orb, sac_ae=sac_ae, sac_ppl=sac_ppl, sap_ppnl=sap_ppnl, force=force, &
    3186             :                       virial=virial, particle_set=particle_set, qs_kind_set=qs_kind_set, &
    3187          50 :                       atomic_kind_set=atomic_kind_set, x_data=x_data, para_env=para_env)
    3188          50 :       nspins = dft_control%nspins
    3189             : 
    3190          50 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
    3191          50 :       IF (use_virial) virial%pv_calculate = .TRUE.
    3192             : 
    3193             :       !Whether we replace the force/energy of SCF XC with HF in RPA
    3194          50 :       do_exx = .FALSE.
    3195          50 :       IF (qs_env%mp2_env%method == ri_rpa_method_gpw) THEN
    3196          28 :          hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%RI_RPA%HF")
    3197          28 :          CALL section_vals_get(hfx_section, explicit=do_exx)
    3198             :       END IF
    3199             : 
    3200             :       !Get the mp2 density matrix which is p_env%p1 + matrix_p_F
    3201          50 :       CALL get_qs_env(qs_env, matrix_p_mp2=matrix_p_mp2, matrix_p_mp2_admm=matrix_p_mp2_admm)
    3202             : 
    3203             :       !The kinetic term (only response density)
    3204          50 :       NULLIFY (scrm)
    3205          50 :       IF (nspins == 2) CALL dbcsr_add(matrix_p_mp2(1)%matrix, matrix_p_mp2(2)%matrix, 1.0_dp, 1.0_dp)
    3206             :       CALL build_kinetic_matrix(qs_env%ks_env, matrix_t=scrm, &
    3207             :                                 matrix_name="KINETIC ENERGY MATRIX", &
    3208             :                                 basis_type="ORB", &
    3209             :                                 sab_nl=sab_orb, calculate_forces=.TRUE., &
    3210          50 :                                 matrix_p=matrix_p_mp2(1)%matrix)
    3211          50 :       IF (nspins == 2) CALL dbcsr_add(matrix_p_mp2(1)%matrix, matrix_p_mp2(2)%matrix, 1.0_dp, -1.0_dp)
    3212          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3213             : 
    3214             :       !The pseudo-potential terms (only reponse density)
    3215          50 :       CALL dbcsr_allocate_matrix_set(scrm, nspins)
    3216         112 :       DO ispin = 1, nspins
    3217          62 :          ALLOCATE (scrm(ispin)%matrix)
    3218          62 :          CALL dbcsr_create(scrm(ispin)%matrix, template=matrix_s(1)%matrix)
    3219          62 :          CALL dbcsr_copy(scrm(ispin)%matrix, matrix_s(1)%matrix)
    3220         112 :          CALL dbcsr_set(scrm(ispin)%matrix, 0.0_dp)
    3221             :       END DO
    3222             : 
    3223          50 :       nder = 1
    3224          50 :       nimages = 1
    3225          50 :       NULLIFY (cell_to_index)
    3226         424 :       ALLOCATE (dbcsr_work_p(nspins, 1), dbcsr_work_h(nspins, 1))
    3227         112 :       DO ispin = 1, nspins
    3228          62 :          dbcsr_work_p(ispin, 1)%matrix => matrix_p_mp2(ispin)%matrix
    3229         112 :          dbcsr_work_h(ispin, 1)%matrix => scrm(ispin)%matrix
    3230             :       END DO
    3231             : 
    3232          50 :       IF (ASSOCIATED(sac_ae)) THEN
    3233             :          CALL build_core_ae(dbcsr_work_h, dbcsr_work_p, force, &
    3234             :                             virial, .TRUE., use_virial, nder, &
    3235             :                             qs_kind_set, atomic_kind_set, particle_set, &
    3236           0 :                             sab_orb, sac_ae, nimages, cell_to_index)
    3237             :       END IF
    3238             : 
    3239          50 :       IF (ASSOCIATED(sac_ppl)) THEN
    3240             :          CALL build_core_ppl(dbcsr_work_h, dbcsr_work_p, force, &
    3241             :                              virial, .TRUE., use_virial, nder, &
    3242             :                              qs_kind_set, atomic_kind_set, particle_set, &
    3243          50 :                              sab_orb, sac_ppl, nimages, cell_to_index, "ORB")
    3244             :       END IF
    3245             : 
    3246          50 :       IF (ASSOCIATED(sap_ppnl)) THEN
    3247          50 :          eps_ppnl = dft_control%qs_control%eps_ppnl
    3248             :          CALL build_core_ppnl(dbcsr_work_h, dbcsr_work_p, force, &
    3249             :                               virial, .TRUE., use_virial, nder, &
    3250             :                               qs_kind_set, atomic_kind_set, particle_set, &
    3251          50 :                               sab_orb, sap_ppnl, eps_ppnl, nimages, cell_to_index, "ORB")
    3252             :       END IF
    3253          50 :       DEALLOCATE (dbcsr_work_p, dbcsr_work_h)
    3254             : 
    3255          50 :       IF (use_virial) THEN
    3256           4 :          h_stress = 0.0_dp
    3257          52 :          virial%pv_xc = 0.0_dp
    3258           4 :          NULLIFY (vxc_rspace, vtau_rspace, vadmm_rspace)
    3259             :          CALL ks_ref_potential(qs_env, vh_rspace, vxc_rspace, vtau_rspace, vadmm_rspace, &
    3260           4 :                                dummy_real1, dummy_real2, h_stress)
    3261          52 :          virial%pv_ehartree = virial%pv_ehartree + h_stress/REAL(para_env%num_pe, dp)
    3262          52 :          virial%pv_virial = virial%pv_virial + h_stress/REAL(para_env%num_pe, dp)
    3263           4 :          IF (.NOT. do_exx) THEN
    3264             :             !if RPA EXX, then do not consider XC virial (replaced by RPA%HF virial)
    3265          52 :             virial%pv_exc = virial%pv_exc - virial%pv_xc
    3266          52 :             virial%pv_virial = virial%pv_virial - virial%pv_xc
    3267             :          END IF
    3268             :       ELSE
    3269          46 :          CALL ks_ref_potential(qs_env, vh_rspace, vxc_rspace, vtau_rspace, vadmm_rspace, dummy_real1, dummy_real2)
    3270             :       END IF
    3271          50 :       do_tau = ASSOCIATED(vtau_rspace)
    3272             : 
    3273             :       !Core forces from the SCF
    3274          50 :       CALL integrate_v_core_rspace(vh_rspace, qs_env)
    3275             : 
    3276             :       !The Hartree-xc potential term, P*dVHxc (mp2 + SCF density x deriv of the SCF potential)
    3277             :       !Get the total density
    3278          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
    3279         112 :       DO ispin = 1, nspins
    3280         112 :          CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, 1.0_dp)
    3281             :       END DO
    3282             : 
    3283          50 :       CALL get_qs_env(qs_env, pw_env=pw_env)
    3284             :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool, &
    3285          50 :                       poisson_env=poisson_env)
    3286          50 :       CALL auxbas_pw_pool%create_pw(vhxc_rspace)
    3287             : 
    3288          98 :       IF (use_virial) pv_loc = virial%pv_virial
    3289             : 
    3290          50 :       IF (do_exx) THEN
    3291             :          !Only want response XC contribution, but SCF+response Hartree contribution
    3292          44 :          DO ispin = 1, nspins
    3293             :             !Hartree
    3294          26 :             CALL pw_transfer(vh_rspace, vhxc_rspace)
    3295             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3296             :                                     hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3297          26 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3298             :             !XC
    3299          26 :             CALL pw_transfer(vxc_rspace(ispin), vhxc_rspace)
    3300             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3301             :                                     hmat=scrm(ispin), pmat=matrix_p_mp2(ispin), &
    3302          26 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3303          44 :             IF (do_tau) THEN
    3304             :                CALL integrate_v_rspace(v_rspace=vtau_rspace(ispin), &
    3305             :                                        hmat=scrm(ispin), pmat=matrix_p_mp2(ispin), &
    3306           0 :                                        qs_env=qs_env, calculate_forces=.TRUE., compute_tau=.TRUE.)
    3307             :             END IF
    3308             :          END DO
    3309             :       ELSE
    3310          68 :          DO ispin = 1, nspins
    3311          36 :             CALL pw_transfer(vh_rspace, vhxc_rspace)
    3312          36 :             CALL pw_axpy(vxc_rspace(ispin), vhxc_rspace)
    3313             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3314             :                                     hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3315          36 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3316          68 :             IF (do_tau) THEN
    3317             :                CALL integrate_v_rspace(v_rspace=vtau_rspace(ispin), &
    3318             :                                        hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3319           8 :                                        qs_env=qs_env, calculate_forces=.TRUE., compute_tau=.TRUE.)
    3320             :             END IF
    3321             :          END DO
    3322             :       END IF
    3323          50 :       CALL auxbas_pw_pool%give_back_pw(vhxc_rspace)
    3324             : 
    3325          98 :       IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3326             : 
    3327             :       !The admm projection contribution (mp2 + SCF densities). If EXX, then only mp2 density
    3328          50 :       IF (dft_control%do_admm) THEN
    3329             :          CALL get_admm_env(admm_env, task_list_aux_fit=task_list_aux_fit, rho_aux_fit=rho_aux_fit, &
    3330          16 :                            matrix_s_aux_fit=matrix_s_aux_fit)
    3331          16 :          CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux)
    3332          16 :          CALL dbcsr_allocate_matrix_set(scrm_admm, nspins)
    3333          36 :          DO ispin = 1, nspins
    3334          20 :             ALLOCATE (scrm_admm(ispin)%matrix)
    3335          20 :             CALL dbcsr_create(scrm_admm(ispin)%matrix, template=matrix_s_aux_fit(1)%matrix)
    3336          20 :             CALL dbcsr_copy(scrm_admm(ispin)%matrix, matrix_s_aux_fit(1)%matrix)
    3337          36 :             CALL dbcsr_set(scrm_admm(ispin)%matrix, 0.0_dp)
    3338             :          END DO
    3339             : 
    3340          64 :          IF (use_virial) pv_loc = virial%pv_virial
    3341          16 :          IF (.NOT. qs_env%admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    3342          36 :             DO ispin = 1, nspins
    3343          36 :                IF (do_exx) THEN
    3344             :                   CALL integrate_v_rspace(v_rspace=vadmm_rspace(ispin), &
    3345             :                                           hmat=scrm_admm(ispin), pmat=matrix_p_mp2_admm(ispin), &
    3346             :                                           qs_env=qs_env, calculate_forces=.TRUE., &
    3347           8 :                                           basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3348             :                ELSE
    3349          12 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    3350             :                   CALL integrate_v_rspace(v_rspace=vadmm_rspace(ispin), &
    3351             :                                           hmat=scrm_admm(ispin), pmat=rho_ao_aux(ispin), &
    3352             :                                           qs_env=qs_env, calculate_forces=.TRUE., &
    3353          12 :                                           basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3354          12 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, -1.0_dp)
    3355             :                END IF
    3356             :             END DO
    3357             :          END IF
    3358          64 :          IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3359             : 
    3360          16 :          CALL tddft_hfx_matrix(scrm_admm, rho_ao_aux, qs_env, .FALSE., .FALSE.)
    3361             : 
    3362          16 :          IF (do_exx) THEN
    3363           4 :             CALL admm_projection_derivative(qs_env, scrm_admm, matrix_p_mp2)
    3364             :          ELSE
    3365          12 :             CALL admm_projection_derivative(qs_env, scrm_admm, rho_ao)
    3366             :          END IF
    3367             :       END IF
    3368             : 
    3369             :       !The exact-exchange term (mp2 + SCF densities)
    3370          50 :       xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    3371          50 :       hfx_section => section_vals_get_subs_vals(xc_section, "HF")
    3372          50 :       CALL section_vals_get(hfx_section, explicit=do_hfx)
    3373             : 
    3374          50 :       IF (do_hfx) THEN
    3375          32 :          CALL section_vals_get(hfx_section, n_repetition=n_rep_hf)
    3376          32 :          CPASSERT(n_rep_hf == 1)
    3377          80 :          IF (use_virial) virial%pv_fock_4c = 0.0_dp
    3378             : 
    3379             :          !In case of EXX, only want to response HFX forces, as the SCF will change according to RI_RPA%HF
    3380          32 :          IF (do_exx) THEN
    3381           8 :             IF (dft_control%do_admm) THEN
    3382           4 :                CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3383           4 :                CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux, rho_ao_kp=dbcsr_work_p)
    3384           4 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3385             : 
    3386             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3387             :                                             x_data(1, 1)%general_parameter%fraction, &
    3388             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2_admm, &
    3389           0 :                                             use_virial=use_virial, resp_only=.TRUE.)
    3390             :                ELSE
    3391             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2_admm, hfx_section, para_env, &
    3392           4 :                                                1, use_virial, resp_only=.TRUE.)
    3393             :                END IF
    3394             :             ELSE
    3395           8 :                DO ispin = 1, nspins
    3396           8 :                   CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, -1.0_dp)
    3397             :                END DO
    3398           4 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3399           4 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3400             : 
    3401             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3402             :                                             x_data(1, 1)%general_parameter%fraction, &
    3403             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2, &
    3404           0 :                                             use_virial=use_virial, resp_only=.TRUE.)
    3405             :                ELSE
    3406             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2, hfx_section, para_env, &
    3407           4 :                                                1, use_virial, resp_only=.TRUE.)
    3408             :                END IF
    3409           8 :                DO ispin = 1, nspins
    3410           8 :                   CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, 1.0_dp)
    3411             :                END DO
    3412             :             END IF !admm
    3413             : 
    3414             :          ELSE !No Exx
    3415          24 :             IF (dft_control%do_admm) THEN
    3416          12 :                CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3417          12 :                CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux, rho_ao_kp=dbcsr_work_p)
    3418          24 :                DO ispin = 1, nspins
    3419          24 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    3420             :                END DO
    3421          12 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3422             : 
    3423             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3424             :                                             x_data(1, 1)%general_parameter%fraction, &
    3425             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2_admm, &
    3426           0 :                                             use_virial=use_virial, resp_only=.FALSE.)
    3427             :                ELSE
    3428             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2_admm, hfx_section, para_env, &
    3429          12 :                                                1, use_virial, resp_only=.FALSE.)
    3430             :                END IF
    3431          24 :                DO ispin = 1, nspins
    3432          24 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, -1.0_dp)
    3433             :                END DO
    3434             :             ELSE
    3435          12 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3436          12 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3437             : 
    3438             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3439             :                                             x_data(1, 1)%general_parameter%fraction, &
    3440             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2, &
    3441           0 :                                             use_virial=use_virial, resp_only=.FALSE.)
    3442             :                ELSE
    3443             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2, hfx_section, para_env, &
    3444          12 :                                                1, use_virial, resp_only=.FALSE.)
    3445             :                END IF
    3446             :             END IF
    3447             :          END IF !do_exx
    3448             : 
    3449          32 :          IF (use_virial) THEN
    3450          52 :             virial%pv_exx = virial%pv_exx - virial%pv_fock_4c
    3451          52 :             virial%pv_virial = virial%pv_virial - virial%pv_fock_4c
    3452             :          END IF
    3453             :       END IF
    3454             : 
    3455             :       !retrieve the SCF density
    3456          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
    3457         112 :       DO ispin = 1, nspins
    3458         112 :          CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, -1.0_dp)
    3459             :       END DO
    3460             : 
    3461             :       !From here, we need to do everything twice. Once for the response density, and once for the
    3462             :       !density that is used for the trace Tr[P*F]. The reason is that the former is needed for the
    3463             :       !eventual overlap contribution from matrix_wz
    3464             :       !Only with the mp2 density
    3465             : 
    3466         436 :       ALLOCATE (current_density(nspins), current_mat_h(nspins), current_density_admm(nspins))
    3467         150 :       DO idens = 1, 2
    3468         224 :          DO ispin = 1, nspins
    3469         224 :             IF (idens == 1) THEN
    3470          62 :                current_density(ispin)%matrix => matrix_p_F(ispin)%matrix
    3471          62 :                current_mat_h(ispin)%matrix => scrm(ispin)%matrix
    3472          62 :                IF (dft_control%do_admm) current_density_admm(ispin)%matrix => matrix_p_F_admm(ispin)%matrix
    3473             :             ELSE
    3474          62 :                current_density(ispin)%matrix => p_env%p1(ispin)%matrix
    3475          62 :                current_mat_h(ispin)%matrix => matrix_hz(ispin)%matrix
    3476          62 :                IF (dft_control%do_admm) current_density_admm(ispin)%matrix => p_env%p1_admm(ispin)%matrix
    3477             :             END IF
    3478             :          END DO
    3479             : 
    3480             :          !The core-denstiy derivative
    3481         748 :          ALLOCATE (rhoz_r(nspins), rhoz_g(nspins))
    3482         224 :          DO ispin = 1, nspins
    3483         124 :             CALL auxbas_pw_pool%create_pw(rhoz_r(ispin))
    3484         224 :             CALL auxbas_pw_pool%create_pw(rhoz_g(ispin))
    3485             :          END DO
    3486         100 :          CALL auxbas_pw_pool%create_pw(rhoz_tot_gspace)
    3487         100 :          CALL auxbas_pw_pool%create_pw(zv_hartree_rspace)
    3488         100 :          CALL auxbas_pw_pool%create_pw(zv_hartree_gspace)
    3489             : 
    3490         100 :          CALL pw_zero(rhoz_tot_gspace)
    3491         224 :          DO ispin = 1, nspins
    3492             :             CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3493         124 :                                     rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin))
    3494         224 :             CALL pw_axpy(rhoz_g(ispin), rhoz_tot_gspace)
    3495             :          END DO
    3496             : 
    3497         100 :          IF (use_virial) THEN
    3498             : 
    3499           8 :             CALL get_qs_env(qs_env, rho=rho)
    3500           8 :             CALL auxbas_pw_pool%create_pw(rho_tot_gspace)
    3501             : 
    3502           8 :             CALL calc_rho_tot_gspace(rho_tot_gspace, qs_env, rho)
    3503             : 
    3504           8 :             h_stress(:, :) = 0.0_dp
    3505             :             CALL pw_poisson_solve(poisson_env, &
    3506             :                                   density=rhoz_tot_gspace, &
    3507             :                                   ehartree=ehartree, &
    3508             :                                   vhartree=zv_hartree_gspace, &
    3509             :                                   h_stress=h_stress, &
    3510           8 :                                   aux_density=rho_tot_gspace)
    3511             : 
    3512           8 :             CALL auxbas_pw_pool%give_back_pw(rho_tot_gspace)
    3513             : 
    3514             :             !Green contribution
    3515         104 :             virial%pv_ehartree = virial%pv_ehartree + 2.0_dp*h_stress/REAL(para_env%num_pe, dp)
    3516         104 :             virial%pv_virial = virial%pv_virial + 2.0_dp*h_stress/REAL(para_env%num_pe, dp)
    3517             : 
    3518             :          ELSE
    3519             :             CALL pw_poisson_solve(poisson_env, rhoz_tot_gspace, ehartree, &
    3520          92 :                                   zv_hartree_gspace)
    3521             :          END IF
    3522             : 
    3523         100 :          CALL pw_transfer(zv_hartree_gspace, zv_hartree_rspace)
    3524         100 :          CALL pw_scale(zv_hartree_rspace, zv_hartree_rspace%pw_grid%dvol)
    3525         100 :          CALL integrate_v_core_rspace(zv_hartree_rspace, qs_env)
    3526             : 
    3527         100 :          IF (do_tau) THEN
    3528             :             BLOCK
    3529             :                TYPE(pw_c1d_gs_type) :: tauz_g
    3530          16 :                CALL auxbas_pw_pool%create_pw(tauz_g)
    3531          48 :                ALLOCATE (tauz_r(nspins))
    3532          32 :                DO ispin = 1, nspins
    3533          16 :                   CALL auxbas_pw_pool%create_pw(tauz_r(ispin))
    3534             : 
    3535             :                   CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3536          32 :                                           rho=tauz_r(ispin), rho_gspace=tauz_g, compute_tau=.TRUE.)
    3537             :                END DO
    3538          16 :                CALL auxbas_pw_pool%give_back_pw(tauz_g)
    3539             :             END BLOCK
    3540             :          END IF
    3541             : 
    3542             :          !Volume contribution to the virial
    3543         100 :          IF (use_virial) THEN
    3544             :             !Volume contribution
    3545             :             exc = 0.0_dp
    3546          16 :             DO ispin = 1, nspins
    3547             :                exc = exc + pw_integral_ab(rhoz_r(ispin), vxc_rspace(ispin))/ &
    3548          16 :                      vxc_rspace(ispin)%pw_grid%dvol
    3549             :             END DO
    3550           8 :             IF (ASSOCIATED(vtau_rspace)) THEN
    3551           0 :                DO ispin = 1, nspins
    3552             :                   exc = exc + pw_integral_ab(tauz_r(ispin), vtau_rspace(ispin))/ &
    3553           0 :                         vtau_rspace(ispin)%pw_grid%dvol
    3554             :                END DO
    3555             :             END IF
    3556          32 :             DO i = 1, 3
    3557          24 :                virial%pv_ehartree(i, i) = virial%pv_ehartree(i, i) - 4.0_dp*ehartree/REAL(para_env%num_pe, dp)
    3558          24 :                virial%pv_exc(i, i) = virial%pv_exc(i, i) - exc/REAL(para_env%num_pe, dp)
    3559             :                virial%pv_virial(i, i) = virial%pv_virial(i, i) - 4.0_dp*ehartree/REAL(para_env%num_pe, dp) &
    3560          32 :                                         - exc/REAL(para_env%num_pe, dp)
    3561             :             END DO
    3562             :          END IF
    3563             : 
    3564             :          !The xc-kernel term.
    3565         100 :          IF (dft_control%do_admm) THEN
    3566          32 :             CALL get_qs_env(qs_env, admm_env=admm_env)
    3567          32 :             xc_section => admm_env%xc_section_primary
    3568             :          ELSE
    3569          68 :             xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    3570             :          END IF
    3571             : 
    3572         196 :          IF (use_virial) virial%pv_xc = 0.0_dp
    3573             : 
    3574             :          CALL create_kernel(qs_env, &
    3575             :                             vxc=v_xc, &
    3576             :                             vxc_tau=v_xc_tau, &
    3577             :                             rho=rho, &
    3578             :                             rho1_r=rhoz_r, &
    3579             :                             rho1_g=rhoz_g, &
    3580             :                             tau1_r=tauz_r, &
    3581             :                             xc_section=xc_section, &
    3582             :                             compute_virial=use_virial, &
    3583         100 :                             virial_xc=virial%pv_xc)
    3584             : 
    3585         100 :          IF (use_virial) THEN
    3586         104 :             virial%pv_exc = virial%pv_exc + virial%pv_xc
    3587         104 :             virial%pv_virial = virial%pv_virial + virial%pv_xc
    3588             : 
    3589         104 :             pv_loc = virial%pv_virial
    3590             :          END IF
    3591             : 
    3592         100 :          CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3593         224 :          DO ispin = 1, nspins
    3594         124 :             CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    3595         124 :             CALL pw_axpy(zv_hartree_rspace, v_xc(ispin))
    3596             :             CALL integrate_v_rspace(qs_env=qs_env, &
    3597             :                                     v_rspace=v_xc(ispin), &
    3598             :                                     hmat=current_mat_h(ispin), &
    3599             :                                     pmat=dbcsr_work_p(ispin, 1), &
    3600         124 :                                     calculate_forces=.TRUE.)
    3601         224 :             CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    3602             :          END DO
    3603         100 :          CALL auxbas_pw_pool%give_back_pw(rhoz_tot_gspace)
    3604         100 :          CALL auxbas_pw_pool%give_back_pw(zv_hartree_rspace)
    3605         100 :          CALL auxbas_pw_pool%give_back_pw(zv_hartree_gspace)
    3606         100 :          DEALLOCATE (v_xc)
    3607             : 
    3608         100 :          IF (do_tau) THEN
    3609          32 :             DO ispin = 1, nspins
    3610          16 :                CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    3611             :                CALL integrate_v_rspace(qs_env=qs_env, &
    3612             :                                        v_rspace=v_xc_tau(ispin), &
    3613             :                                        hmat=current_mat_h(ispin), &
    3614             :                                        pmat=dbcsr_work_p(ispin, 1), &
    3615             :                                        compute_tau=.TRUE., &
    3616          16 :                                        calculate_forces=.TRUE.)
    3617          32 :                CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    3618             :             END DO
    3619          16 :             DEALLOCATE (v_xc_tau)
    3620             :          END IF
    3621             : 
    3622         196 :          IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3623             : 
    3624         100 :          IF (do_hfx) THEN
    3625          64 :             IF (dft_control%do_admm) THEN
    3626          72 :                DO ispin = 1, nspins
    3627          72 :                   CALL dbcsr_set(scrm_admm(ispin)%matrix, 0.0_dp)
    3628             :                END DO
    3629          32 :                CALL qs_rho_get(rho_aux_fit, tau_r_valid=do_tau_admm)
    3630             : 
    3631          32 :                IF (.NOT. admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    3632          32 :                   CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3633          72 :                   DO ispin = 1, nspins
    3634          40 :                      CALL pw_zero(rhoz_r(ispin))
    3635          40 :                      CALL pw_zero(rhoz_g(ispin))
    3636             :                      CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density_admm(ispin)%matrix, &
    3637             :                                              rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin), &
    3638          72 :                                              basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3639             :                   END DO
    3640             : 
    3641          32 :                   IF (do_tau_admm) THEN
    3642             :                      BLOCK
    3643             :                         TYPE(pw_c1d_gs_type) :: tauz_g
    3644           0 :                         CALL auxbas_pw_pool%create_pw(tauz_g)
    3645           0 :                         DO ispin = 1, nspins
    3646           0 :                            CALL pw_zero(tauz_r(ispin))
    3647             :                            CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3648             :                                                    rho=tauz_r(ispin), rho_gspace=tauz_g, &
    3649             :                                                    basis_type="AUX_FIT", task_list_external=task_list_aux_fit, &
    3650           0 :                                                    compute_tau=.TRUE.)
    3651             :                         END DO
    3652           0 :                         CALL auxbas_pw_pool%give_back_pw(tauz_g)
    3653             :                      END BLOCK
    3654             :                   END IF
    3655             : 
    3656             :                   !Volume contribution to the virial
    3657          32 :                   IF (use_virial) THEN
    3658             :                      exc = 0.0_dp
    3659          16 :                      DO ispin = 1, nspins
    3660             :                         exc = exc + pw_integral_ab(rhoz_r(ispin), vadmm_rspace(ispin))/ &
    3661          16 :                               vadmm_rspace(ispin)%pw_grid%dvol
    3662             :                      END DO
    3663          32 :                      DO i = 1, 3
    3664          24 :                         virial%pv_exc(i, i) = virial%pv_exc(i, i) - exc/REAL(para_env%num_pe, dp)
    3665          32 :                         virial%pv_virial(i, i) = virial%pv_virial(i, i) - exc/REAL(para_env%num_pe, dp)
    3666             :                      END DO
    3667             : 
    3668         104 :                      virial%pv_xc = 0.0_dp
    3669             :                   END IF
    3670             : 
    3671          32 :                   xc_section => admm_env%xc_section_aux
    3672             :                   CALL create_kernel(qs_env, v_xc, v_xc_tau, rho_aux_fit, rhoz_r, rhoz_g, tauz_r, xc_section, &
    3673          32 :                                      compute_virial=use_virial, virial_xc=virial%pv_xc)
    3674             : 
    3675          32 :                   IF (use_virial) THEN
    3676         104 :                      virial%pv_exc = virial%pv_exc + virial%pv_xc
    3677         104 :                      virial%pv_virial = virial%pv_virial + virial%pv_xc
    3678             : 
    3679         104 :                      pv_loc = virial%pv_virial
    3680             :                   END IF
    3681             : 
    3682          32 :                   CALL qs_rho_get(rho_aux_fit, rho_ao_kp=dbcsr_work_p)
    3683          72 :                   DO ispin = 1, nspins
    3684          40 :                      CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    3685             :                      CALL integrate_v_rspace(qs_env=qs_env, &
    3686             :                                              v_rspace=v_xc(ispin), &
    3687             :                                              hmat=scrm_admm(ispin), &
    3688             :                                              pmat=dbcsr_work_p(ispin, 1), &
    3689             :                                              calculate_forces=.TRUE., &
    3690             :                                              basis_type="AUX_FIT", &
    3691          40 :                                              task_list_external=task_list_aux_fit)
    3692          72 :                      CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    3693             :                   END DO
    3694          32 :                   DEALLOCATE (v_xc)
    3695             : 
    3696          32 :                   IF (do_tau_admm) THEN
    3697           0 :                      DO ispin = 1, nspins
    3698           0 :                         CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    3699             :                         CALL integrate_v_rspace(qs_env=qs_env, &
    3700             :                                                 v_rspace=v_xc_tau(ispin), &
    3701             :                                                 hmat=scrm_admm(ispin), &
    3702             :                                                 pmat=dbcsr_work_p(ispin, 1), &
    3703             :                                                 calculate_forces=.TRUE., &
    3704             :                                                 basis_type="AUX_FIT", &
    3705             :                                                 task_list_external=task_list_aux_fit, &
    3706           0 :                                                 compute_tau=.TRUE.)
    3707           0 :                         CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    3708             :                      END DO
    3709           0 :                      DEALLOCATE (v_xc_tau)
    3710             :                   END IF
    3711             : 
    3712         128 :                   IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3713             :                END IF
    3714             : 
    3715          32 :                CALL tddft_hfx_matrix(scrm_admm, current_density_admm, qs_env, .FALSE., .FALSE.)
    3716             : 
    3717          32 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3718          32 :                CALL admm_projection_derivative(qs_env, scrm_admm, dbcsr_work_p(:, 1))
    3719             : 
    3720             :                !If response density, need to get matrix_hz contribution
    3721          32 :                CALL dbcsr_create(dbcsr_work, template=matrix_s(1)%matrix)
    3722          32 :                IF (idens == 2) THEN
    3723          16 :                   nao = admm_env%nao_orb
    3724          16 :                   nao_aux = admm_env%nao_aux_fit
    3725          36 :                   DO ispin = 1, nspins
    3726          20 :                      CALL dbcsr_copy(dbcsr_work, matrix_hz(ispin)%matrix)
    3727          20 :                      CALL dbcsr_set(dbcsr_work, 0.0_dp)
    3728             : 
    3729             :                      CALL cp_dbcsr_sm_fm_multiply(scrm_admm(ispin)%matrix, admm_env%A, &
    3730          20 :                                                   admm_env%work_aux_orb, nao)
    3731             :                      CALL parallel_gemm('T', 'N', nao, nao, nao_aux, &
    3732             :                                         1.0_dp, admm_env%A, admm_env%work_aux_orb, 0.0_dp, &
    3733          20 :                                         admm_env%work_orb_orb)
    3734          20 :                      CALL copy_fm_to_dbcsr(admm_env%work_orb_orb, dbcsr_work, keep_sparsity=.TRUE.)
    3735          36 :                      CALL dbcsr_add(matrix_hz(ispin)%matrix, dbcsr_work, 1.0_dp, 1.0_dp)
    3736             :                   END DO
    3737             :                END IF
    3738             : 
    3739          32 :                CALL dbcsr_release(dbcsr_work)
    3740             :             ELSE !no admm
    3741             : 
    3742             :                !Need the contribution to matrix_hz as well
    3743          32 :                IF (idens == 2) THEN
    3744          16 :                   CALL tddft_hfx_matrix(matrix_hz, current_density, qs_env, .FALSE., .FALSE.)
    3745             :                END IF
    3746             :             END IF !admm
    3747             :          END IF !do_hfx
    3748             : 
    3749         224 :          DO ispin = 1, nspins
    3750         124 :             CALL auxbas_pw_pool%give_back_pw(rhoz_r(ispin))
    3751         224 :             CALL auxbas_pw_pool%give_back_pw(rhoz_g(ispin))
    3752             :          END DO
    3753         100 :          DEALLOCATE (rhoz_r, rhoz_g)
    3754             : 
    3755         150 :          IF (do_tau) THEN
    3756          32 :             DO ispin = 1, nspins
    3757          32 :                CALL auxbas_pw_pool%give_back_pw(tauz_r(ispin))
    3758             :             END DO
    3759          16 :             DEALLOCATE (tauz_r)
    3760             :          END IF
    3761             :       END DO !idens
    3762          50 :       CALL dbcsr_deallocate_matrix_set(scrm_admm)
    3763             : 
    3764          50 :       DEALLOCATE (current_density, current_mat_h, current_density_admm)
    3765          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3766             : 
    3767             :       !The energy weighted and overlap term. ONLY with the response density
    3768          50 :       focc = 2.0_dp
    3769          50 :       IF (nspins == 2) focc = 1.0_dp
    3770          50 :       CALL get_qs_env(qs_env, mos=mos)
    3771         112 :       DO ispin = 1, nspins
    3772          62 :          CALL get_mo_set(mo_set=mos(ispin), homo=nocc)
    3773             :          CALL calculate_whz_matrix(mos(ispin)%mo_coeff, matrix_hz(ispin)%matrix, &
    3774         112 :                                    p_env%w1(ispin)%matrix, focc, nocc)
    3775             :       END DO
    3776          50 :       IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, p_env%w1(2)%matrix, 1.0_dp, 1.0_dp)
    3777             : 
    3778             :       !Add to it the SCF W matrix, except if EXX (because taken care of by HF response)
    3779          50 :       IF (.NOT. do_exx) THEN
    3780          32 :          CALL compute_matrix_w(qs_env, calc_forces=.TRUE.)
    3781          32 :          CALL get_qs_env(qs_env, matrix_w=matrix_w)
    3782          32 :          CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(1)%matrix, 1.0_dp, 1.0_dp)
    3783          32 :          IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(2)%matrix, 1.0_dp, 1.0_dp)
    3784             :       END IF
    3785             : 
    3786          50 :       NULLIFY (scrm)
    3787             :       CALL build_overlap_matrix(qs_env%ks_env, matrix_s=scrm, &
    3788             :                                 matrix_name="OVERLAP MATRIX", &
    3789             :                                 basis_type_a="ORB", basis_type_b="ORB", &
    3790             :                                 sab_nl=sab_orb, calculate_forces=.TRUE., &
    3791          50 :                                 matrix_p=p_env%w1(1)%matrix)
    3792             : 
    3793          50 :       IF (.NOT. do_exx) THEN
    3794          32 :          CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(1)%matrix, 1.0_dp, -1.0_dp)
    3795          32 :          IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(2)%matrix, 1.0_dp, -1.0_dp)
    3796          68 :          DO ispin = 1, nspins
    3797          68 :             CALL dbcsr_set(matrix_w(ispin)%matrix, 0.0_dp)
    3798             :          END DO
    3799             :       END IF
    3800             : 
    3801          50 :       IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, p_env%w1(2)%matrix, 1.0_dp, -1.0_dp)
    3802          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3803             : 
    3804          50 :       IF (use_virial) virial%pv_calculate = .FALSE.
    3805             : 
    3806             :       !clean-up
    3807          50 :       CALL auxbas_pw_pool%give_back_pw(vh_rspace)
    3808             : 
    3809         112 :       DO ispin = 1, nspins
    3810          62 :          CALL auxbas_pw_pool%give_back_pw(vxc_rspace(ispin))
    3811          62 :          IF (ASSOCIATED(vtau_rspace)) THEN
    3812           8 :             CALL auxbas_pw_pool%give_back_pw(vtau_rspace(ispin))
    3813             :          END IF
    3814         112 :          IF (ASSOCIATED(vadmm_rspace)) THEN
    3815          20 :             CALL auxbas_pw_pool%give_back_pw(vadmm_rspace(ispin))
    3816             :          END IF
    3817             :       END DO
    3818          50 :       DEALLOCATE (vxc_rspace)
    3819          50 :       IF (ASSOCIATED(vtau_rspace)) DEALLOCATE (vtau_rspace)
    3820          50 :       IF (ASSOCIATED(vadmm_rspace)) DEALLOCATE (vadmm_rspace)
    3821             : 
    3822          50 :       CALL timestop(handle)
    3823             : 
    3824         100 :    END SUBROUTINE update_im_time_forces
    3825             : 
    3826             : ! **************************************************************************************************
    3827             : !> \brief Iteratively builds the matrix Y = sum_k Y_k until convergence, where
    3828             : !>        Y_k = 1/k*2^n (A/2^n) Y_k-1 + 1/k!*2^n * PR(n) * (A/2^n)^(k-1)
    3829             : !>        n is chosen such that the norm of A is < 1 (and e^A converges fast)
    3830             : !>        PR(n) =  e^(A/2^n)*PR(n-1) + PR(n-1)*e^(A/2^n), PR(0) = P*R^T
    3831             : !> \param Y ...
    3832             : !> \param A ...
    3833             : !> \param P ...
    3834             : !> \param R ...
    3835             : !> \param filter_eps ...
    3836             : ! **************************************************************************************************
    3837         340 :    SUBROUTINE build_Y_matrix(Y, A, P, R, filter_eps)
    3838             : 
    3839             :       TYPE(dbcsr_type), INTENT(OUT)                      :: Y
    3840             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: A, P, R
    3841             :       REAL(dp), INTENT(IN)                               :: filter_eps
    3842             : 
    3843             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'build_Y_matrix'
    3844             : 
    3845             :       INTEGER                                            :: handle, k, n
    3846             :       REAL(dp)                                           :: norm_scalar, threshold
    3847             :       TYPE(dbcsr_type)                                   :: A2n, exp_A2n, PRn, work, work2, Yk
    3848             : 
    3849         340 :       CALL timeset(routineN, handle)
    3850             : 
    3851         340 :       threshold = 1.0E-16_dp
    3852             : 
    3853             :       !Find n such that norm(A) < 1 and we insure convergence of the exponential
    3854         340 :       norm_scalar = dbcsr_frobenius_norm(A)
    3855             : 
    3856             :       !checked: result invariant with value of n
    3857         340 :       n = 1
    3858         466 :       DO
    3859         806 :          IF ((norm_scalar/2.0_dp**n) < 1.0_dp) EXIT
    3860         466 :          n = n + 1
    3861             :       END DO
    3862             : 
    3863             :       !Calculate PR(n) recursively
    3864         340 :       CALL dbcsr_create(PRn, template=A, matrix_type=dbcsr_type_no_symmetry)
    3865         340 :       CALL dbcsr_create(work, template=A, matrix_type=dbcsr_type_no_symmetry)
    3866         340 :       CALL dbcsr_multiply('N', 'N', 1.0_dp, P, R, 0.0_dp, work, filter_eps=filter_eps)
    3867         340 :       CALL dbcsr_create(exp_A2n, template=A, matrix_type=dbcsr_type_no_symmetry)
    3868             : 
    3869        1146 :       DO k = 1, n
    3870         806 :          CALL matrix_exponential(exp_A2n, A, 1.0_dp, 0.5_dp**k, threshold)
    3871         806 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, exp_A2n, work, 0.0_dp, PRn, filter_eps=filter_eps)
    3872         806 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, work, exp_A2n, 1.0_dp, PRn, filter_eps=filter_eps)
    3873        1146 :          CALL dbcsr_copy(work, PRn)
    3874             :       END DO
    3875         340 :       CALL dbcsr_release(exp_A2n)
    3876             : 
    3877             :       !Calculate Y iteratively, until convergence
    3878         340 :       CALL dbcsr_create(A2n, template=A, matrix_type=dbcsr_type_no_symmetry)
    3879         340 :       CALL dbcsr_copy(A2n, A)
    3880         340 :       CALL dbcsr_scale(A2n, 0.5_dp**n)
    3881         340 :       CALL dbcsr_create(Y, template=A, matrix_type=dbcsr_type_no_symmetry)
    3882         340 :       CALL dbcsr_create(Yk, template=A, matrix_type=dbcsr_type_no_symmetry)
    3883         340 :       CALL dbcsr_create(work2, template=A, matrix_type=dbcsr_type_no_symmetry)
    3884             : 
    3885             :       !k=1
    3886         340 :       CALL dbcsr_scale(PRn, 0.5_dp**n)
    3887         340 :       CALL dbcsr_copy(work, PRn)
    3888         340 :       CALL dbcsr_copy(work2, PRn)
    3889         340 :       CALL dbcsr_add(Y, PRn, 1.0_dp, 1.0_dp)
    3890             : 
    3891         340 :       k = 1
    3892        1908 :       DO
    3893        2248 :          k = k + 1
    3894        2248 :          CALL dbcsr_multiply('N', 'N', 1.0_dp/REAL(k, dp), A2n, work, 0.0_dp, Yk, filter_eps=filter_eps)
    3895        2248 :          CALL dbcsr_multiply('N', 'N', 1.0_dp/REAL(k, dp), work2, A2n, 0.0_dp, PRn, filter_eps=filter_eps)
    3896             : 
    3897        2248 :          CALL dbcsr_add(Yk, PRn, 1.0_dp, 1.0_dp)
    3898        2248 :          CALL dbcsr_add(Y, Yk, 1.0_dp, 1.0_dp)
    3899             : 
    3900        2248 :          IF (dbcsr_frobenius_norm(Yk) < threshold) EXIT
    3901        1908 :          CALL dbcsr_copy(work, Yk)
    3902        1908 :          CALL dbcsr_copy(work2, PRn)
    3903             :       END DO
    3904             : 
    3905         340 :       CALL dbcsr_release(work)
    3906         340 :       CALL dbcsr_release(work2)
    3907         340 :       CALL dbcsr_release(PRn)
    3908         340 :       CALL dbcsr_release(A2n)
    3909         340 :       CALL dbcsr_release(Yk)
    3910             : 
    3911         340 :       CALL timestop(handle)
    3912             : 
    3913         340 :    END SUBROUTINE build_Y_matrix
    3914             : 
    3915             : ! **************************************************************************************************
    3916             : !> \brief Overwrites the "optimal" Laplace quadrature with that of the first step
    3917             : !> \param tj ...
    3918             : !> \param wj ...
    3919             : !> \param tau_tj ...
    3920             : !> \param tau_wj ...
    3921             : !> \param weights_cos_tf_t_to_w ...
    3922             : !> \param weights_cos_tf_w_to_t ...
    3923             : !> \param do_laplace ...
    3924             : !> \param do_im_time ...
    3925             : !> \param num_integ_points ...
    3926             : !> \param unit_nr ...
    3927             : !> \param qs_env ...
    3928             : ! **************************************************************************************************
    3929         200 :    SUBROUTINE keep_initial_quad(tj, wj, tau_tj, tau_wj, weights_cos_tf_t_to_w, weights_cos_tf_w_to_t, &
    3930             :                                 do_laplace, do_im_time, num_integ_points, unit_nr, qs_env)
    3931             : 
    3932             :       REAL(dp), ALLOCATABLE, DIMENSION(:), INTENT(INOUT) :: tj, wj, tau_tj, tau_wj
    3933             :       REAL(dp), ALLOCATABLE, DIMENSION(:, :), &
    3934             :          INTENT(INOUT)                                   :: weights_cos_tf_t_to_w, &
    3935             :                                                             weights_cos_tf_w_to_t
    3936             :       LOGICAL, INTENT(IN)                                :: do_laplace, do_im_time
    3937             :       INTEGER, INTENT(IN)                                :: num_integ_points, unit_nr
    3938             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3939             : 
    3940             :       INTEGER                                            :: jquad
    3941             : 
    3942         200 :       IF (do_laplace .OR. do_im_time) THEN
    3943         162 :          IF (.NOT. ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tau_tj)) THEN
    3944         378 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tau_tj(num_integ_points))
    3945         378 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tau_wj(num_integ_points))
    3946        1074 :             qs_env%mp2_env%ri_rpa_im_time%tau_tj(:) = tau_tj(:)
    3947        1074 :             qs_env%mp2_env%ri_rpa_im_time%tau_wj(:) = tau_wj(:)
    3948             :          ELSE
    3949             :             !If weights already stored, we overwrite the new ones
    3950         152 :             tau_tj(:) = qs_env%mp2_env%ri_rpa_im_time%tau_tj(:)
    3951         152 :             tau_wj(:) = qs_env%mp2_env%ri_rpa_im_time%tau_wj(:)
    3952             :          END IF
    3953             :       END IF
    3954         200 :       IF (.NOT. do_laplace) THEN
    3955         142 :          IF (.NOT. ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tj)) THEN
    3956         348 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tj(num_integ_points))
    3957         348 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%wj(num_integ_points))
    3958        1066 :             qs_env%mp2_env%ri_rpa_im_time%tj(:) = tj(:)
    3959        1066 :             qs_env%mp2_env%ri_rpa_im_time%wj(:) = wj(:)
    3960         116 :             IF (do_im_time) THEN
    3961         352 :                ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(num_integ_points, num_integ_points))
    3962         352 :                ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(num_integ_points, num_integ_points))
    3963       13812 :                qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(:, :) = weights_cos_tf_t_to_w(:, :)
    3964       13812 :                qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(:, :) = weights_cos_tf_w_to_t(:, :)
    3965             :             END IF
    3966             :          ELSE
    3967         110 :             tj(:) = qs_env%mp2_env%ri_rpa_im_time%tj(:)
    3968         110 :             wj(:) = qs_env%mp2_env%ri_rpa_im_time%wj(:)
    3969          26 :             IF (do_im_time) THEN
    3970         184 :                weights_cos_tf_t_to_w(:, :) = qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(:, :)
    3971         184 :                weights_cos_tf_w_to_t(:, :) = qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(:, :)
    3972             :             END IF
    3973             :          END IF
    3974             :       END IF
    3975         200 :       IF (unit_nr > 0) THEN
    3976             :          !Printing order same as in mp2_grids.F for consistency
    3977         100 :          IF (ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tj) .AND. (.NOT. do_laplace)) THEN
    3978             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") &
    3979          71 :                "MINIMAX_INFO| Number of integration points:", num_integ_points
    3980             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T54,A,T72,A)") &
    3981          71 :                "MINIMAX_INFO| Minimax params (freq grid, scaled):", "Weights", "Abscissas"
    3982         588 :             DO jquad = 1, num_integ_points
    3983         588 :                WRITE (UNIT=unit_nr, FMT="(T41,F20.10,F20.10)") wj(jquad), tj(jquad)
    3984             :             END DO
    3985          71 :             CALL m_flush(unit_nr)
    3986             :          END IF
    3987         100 :          IF (ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tau_tj)) THEN
    3988             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") &
    3989          81 :                "MINIMAX_INFO| Number of integration points:", num_integ_points
    3990             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T54,A,T72,A)") &
    3991          81 :                "MINIMAX_INFO| Minimax params (time grid, scaled):", "Weights", "Abscissas"
    3992         613 :             DO jquad = 1, num_integ_points
    3993         613 :                WRITE (UNIT=unit_nr, FMT="(T41,F20.10,F20.10)") tau_wj(jquad), tau_tj(jquad)
    3994             :             END DO
    3995          81 :             CALL m_flush(unit_nr)
    3996             :          END IF
    3997             :       END IF
    3998             : 
    3999         200 :    END SUBROUTINE keep_initial_quad
    4000             : 
    4001             : END MODULE rpa_im_time_force_methods

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