LCOV - code coverage report
Current view: top level - src - rpa_im_time_force_methods.F (source / functions) Hit Total Coverage
Test: CP2K Regtests (git:15a58fb) Lines: 1885 1935 97.4 %
Date: 2025-02-18 08:24:35 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_add_on_diag, dbcsr_clear, dbcsr_complete_redistribute, dbcsr_copy, &
      32             :         dbcsr_create, 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_frobenius_norm
      40             :    USE cp_dbcsr_diag,                   ONLY: cp_dbcsr_power
      41             :    USE cp_dbcsr_operations,             ONLY: copy_dbcsr_to_fm,&
      42             :                                               copy_fm_to_dbcsr,&
      43             :                                               cp_dbcsr_dist2d_to_dist,&
      44             :                                               cp_dbcsr_sm_fm_multiply,&
      45             :                                               dbcsr_allocate_matrix_set,&
      46             :                                               dbcsr_deallocate_matrix_set
      47             :    USE cp_eri_mme_interface,            ONLY: cp_eri_mme_update_local_counts
      48             :    USE cp_fm_struct,                    ONLY: cp_fm_struct_create,&
      49             :                                               cp_fm_struct_release,&
      50             :                                               cp_fm_struct_type
      51             :    USE cp_fm_types,                     ONLY: cp_fm_create,&
      52             :                                               cp_fm_release,&
      53             :                                               cp_fm_set_all,&
      54             :                                               cp_fm_to_fm,&
      55             :                                               cp_fm_type
      56             :    USE dbt_api,                         ONLY: &
      57             :         dbt_batched_contract_finalize, dbt_batched_contract_init, dbt_clear, dbt_contract, &
      58             :         dbt_copy, dbt_copy_matrix_to_tensor, dbt_copy_tensor_to_matrix, dbt_create, dbt_destroy, &
      59             :         dbt_filter, dbt_get_info, dbt_mp_environ_pgrid, dbt_pgrid_create, dbt_pgrid_destroy, &
      60             :         dbt_pgrid_type, dbt_scale, dbt_type
      61             :    USE distribution_2d_types,           ONLY: distribution_2d_type
      62             :    USE ec_methods,                      ONLY: create_kernel
      63             :    USE gaussian_gridlevels,             ONLY: gaussian_gridlevel
      64             :    USE hfx_admm_utils,                  ONLY: tddft_hfx_matrix
      65             :    USE hfx_derivatives,                 ONLY: derivatives_four_center
      66             :    USE hfx_exx,                         ONLY: add_exx_to_rhs
      67             :    USE hfx_ri,                          ONLY: get_2c_der_force,&
      68             :                                               get_force_from_3c_trace,&
      69             :                                               get_idx_to_atom,&
      70             :                                               hfx_ri_update_forces
      71             :    USE hfx_types,                       ONLY: alloc_containers,&
      72             :                                               block_ind_type,&
      73             :                                               dealloc_containers,&
      74             :                                               hfx_compression_type,&
      75             :                                               hfx_type
      76             :    USE input_constants,                 ONLY: do_admm_aux_exch_func_none,&
      77             :                                               do_eri_gpw,&
      78             :                                               do_eri_mme,&
      79             :                                               do_potential_id,&
      80             :                                               ri_rpa_method_gpw
      81             :    USE input_section_types,             ONLY: section_vals_get,&
      82             :                                               section_vals_get_subs_vals,&
      83             :                                               section_vals_type,&
      84             :                                               section_vals_val_get
      85             :    USE iterate_matrix,                  ONLY: matrix_exponential
      86             :    USE kinds,                           ONLY: dp,&
      87             :                                               int_8
      88             :    USE libint_2c_3c,                    ONLY: libint_potential_type
      89             :    USE machine,                         ONLY: m_flush,&
      90             :                                               m_walltime
      91             :    USE mathconstants,                   ONLY: fourpi
      92             :    USE message_passing,                 ONLY: mp_cart_type,&
      93             :                                               mp_para_env_release,&
      94             :                                               mp_para_env_type
      95             :    USE mp2_eri,                         ONLY: integrate_set_2c
      96             :    USE mp2_eri_gpw,                     ONLY: calc_potential_gpw,&
      97             :                                               cleanup_gpw,&
      98             :                                               prepare_gpw,&
      99             :                                               virial_gpw_potential
     100             :    USE mp2_types,                       ONLY: mp2_type
     101             :    USE orbital_pointers,                ONLY: ncoset
     102             :    USE parallel_gemm_api,               ONLY: parallel_gemm
     103             :    USE particle_methods,                ONLY: get_particle_set
     104             :    USE particle_types,                  ONLY: particle_type
     105             :    USE pw_env_types,                    ONLY: pw_env_get,&
     106             :                                               pw_env_type
     107             :    USE pw_methods,                      ONLY: pw_axpy,&
     108             :                                               pw_copy,&
     109             :                                               pw_integral_ab,&
     110             :                                               pw_scale,&
     111             :                                               pw_transfer,&
     112             :                                               pw_zero
     113             :    USE pw_poisson_methods,              ONLY: pw_poisson_solve
     114             :    USE pw_poisson_types,                ONLY: pw_poisson_type
     115             :    USE pw_pool_types,                   ONLY: pw_pool_type
     116             :    USE pw_types,                        ONLY: pw_c1d_gs_type,&
     117             :                                               pw_r3d_rs_type
     118             :    USE qs_collocate_density,            ONLY: calculate_rho_elec,&
     119             :                                               collocate_function
     120             :    USE qs_density_matrices,             ONLY: calculate_whz_matrix
     121             :    USE qs_environment_types,            ONLY: get_qs_env,&
     122             :                                               qs_environment_type,&
     123             :                                               set_qs_env
     124             :    USE qs_force_types,                  ONLY: qs_force_type
     125             :    USE qs_integral_utils,               ONLY: basis_set_list_setup
     126             :    USE qs_integrate_potential,          ONLY: integrate_pgf_product,&
     127             :                                               integrate_v_core_rspace,&
     128             :                                               integrate_v_rspace
     129             :    USE qs_interactions,                 ONLY: init_interaction_radii_orb_basis
     130             :    USE qs_kind_types,                   ONLY: qs_kind_type
     131             :    USE qs_kinetic,                      ONLY: build_kinetic_matrix
     132             :    USE qs_ks_methods,                   ONLY: calc_rho_tot_gspace
     133             :    USE qs_ks_reference,                 ONLY: ks_ref_potential
     134             :    USE qs_ks_types,                     ONLY: set_ks_env
     135             :    USE qs_linres_types,                 ONLY: linres_control_type
     136             :    USE qs_matrix_w,                     ONLY: compute_matrix_w
     137             :    USE qs_mo_types,                     ONLY: get_mo_set,&
     138             :                                               mo_set_type
     139             :    USE qs_neighbor_list_types,          ONLY: neighbor_list_set_p_type,&
     140             :                                               release_neighbor_list_sets
     141             :    USE qs_overlap,                      ONLY: build_overlap_matrix
     142             :    USE qs_p_env_methods,                ONLY: p_env_create,&
     143             :                                               p_env_psi0_changed
     144             :    USE qs_p_env_types,                  ONLY: p_env_release,&
     145             :                                               qs_p_env_type
     146             :    USE qs_rho_types,                    ONLY: qs_rho_get,&
     147             :                                               qs_rho_type
     148             :    USE qs_tensors,                      ONLY: &
     149             :         build_2c_derivatives, build_2c_integrals, build_2c_neighbor_lists, build_3c_derivatives, &
     150             :         build_3c_neighbor_lists, calc_2c_virial, calc_3c_virial, compress_tensor, &
     151             :         decompress_tensor, get_tensor_occupancy, neighbor_list_3c_destroy
     152             :    USE qs_tensors_types,                ONLY: create_2c_tensor,&
     153             :                                               create_3c_tensor,&
     154             :                                               create_tensor_batches,&
     155             :                                               distribution_3d_create,&
     156             :                                               distribution_3d_type,&
     157             :                                               neighbor_list_3c_type
     158             :    USE realspace_grid_types,            ONLY: map_gaussian_here,&
     159             :                                               realspace_grid_type
     160             :    USE response_solver,                 ONLY: response_equation_new
     161             :    USE rpa_im_time,                     ONLY: compute_mat_dm_global
     162             :    USE rpa_im_time_force_types,         ONLY: im_time_force_type
     163             :    USE rs_pw_interface,                 ONLY: potential_pw2rs
     164             :    USE task_list_types,                 ONLY: task_list_type
     165             :    USE virial_types,                    ONLY: virial_type
     166             : #include "./base/base_uses.f90"
     167             : 
     168             :    IMPLICIT NONE
     169             : 
     170             :    PRIVATE
     171             : 
     172             :    CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'rpa_im_time_force_methods'
     173             : 
     174             :    PUBLIC :: init_im_time_forces, calc_laplace_loop_forces, calc_post_loop_forces, &
     175             :              keep_initial_quad, calc_rpa_loop_forces
     176             : 
     177             : CONTAINS
     178             : 
     179             : ! **************************************************************************************************
     180             : !> \brief Initializes and pre-calculates all needed tensors for the forces
     181             : !> \param force_data ...
     182             : !> \param fm_matrix_PQ ...
     183             : !> \param t_3c_M the 3-center M tensor to be used as a template
     184             : !> \param unit_nr ...
     185             : !> \param mp2_env ...
     186             : !> \param qs_env ...
     187             : ! **************************************************************************************************
     188          50 :    SUBROUTINE init_im_time_forces(force_data, fm_matrix_PQ, t_3c_M, unit_nr, mp2_env, qs_env)
     189             : 
     190             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
     191             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_PQ
     192             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M
     193             :       INTEGER, INTENT(IN)                                :: unit_nr
     194             :       TYPE(mp2_type)                                     :: mp2_env
     195             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     196             : 
     197             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'init_im_time_forces'
     198             : 
     199             :       INTEGER                                            :: handle, i_mem, i_xyz, ibasis, ispin, &
     200             :                                                             n_dependent, n_mem, n_rep, natom, &
     201             :                                                             nkind, nspins
     202             :       INTEGER(int_8)                                     :: nze, nze_tot
     203          50 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: dist1, dist2, dist_AO_1, dist_AO_2, &
     204          50 :                                                             dist_RI, dummy_end, dummy_start, &
     205         100 :                                                             end_blocks, sizes_AO, sizes_RI, &
     206          50 :                                                             start_blocks
     207             :       INTEGER, DIMENSION(2)                              :: pdims_t2c
     208             :       INTEGER, DIMENSION(3)                              :: nblks_total, pcoord, pdims, pdims_t3c
     209         100 :       INTEGER, DIMENSION(:), POINTER                     :: col_bsize, row_bsize
     210             :       LOGICAL                                            :: do_periodic, use_virial
     211             :       REAL(dp)                                           :: compression_factor, eps_pgf_orb, &
     212             :                                                             eps_pgf_orb_old, memory, occ
     213             :       TYPE(cell_type), POINTER                           :: cell
     214             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
     215             :       TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
     216         100 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_s, rho_ao
     217             :       TYPE(dbcsr_type)                                   :: dbcsr_work, dbcsr_work2, dbcsr_work3
     218         100 :       TYPE(dbcsr_type), DIMENSION(1)                     :: t_2c_int_tmp
     219         350 :       TYPE(dbcsr_type), DIMENSION(1, 3)                  :: t_2c_der_tmp
     220         250 :       TYPE(dbt_pgrid_type)                               :: pgrid_t2c, pgrid_t3c
     221        1000 :       TYPE(dbt_type)                                     :: t_2c_template, t_2c_tmp, t_3c_template
     222          50 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:, :, :)    :: t_3c_der_AO_prv, t_3c_der_RI_prv
     223             :       TYPE(dft_control_type), POINTER                    :: dft_control
     224             :       TYPE(distribution_2d_type), POINTER                :: dist_2d
     225             :       TYPE(distribution_3d_type)                         :: dist_3d, dist_vir
     226             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
     227          50 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
     228             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
     229             :       TYPE(libint_potential_type)                        :: identity_pot
     230          50 :       TYPE(mp_cart_type)                                 :: mp_comm_t3c, mp_comm_vir
     231             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     232             :       TYPE(neighbor_list_3c_type)                        :: nl_3c
     233             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
     234          50 :          POINTER                                         :: nl_2c
     235          50 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     236          50 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     237             :       TYPE(qs_rho_type), POINTER                         :: rho
     238             :       TYPE(section_vals_type), POINTER                   :: qs_section
     239             :       TYPE(virial_type), POINTER                         :: virial
     240             : 
     241          50 :       NULLIFY (dft_control, para_env, particle_set, qs_kind_set, dist_2d, nl_2c, blacs_env, matrix_s, &
     242          50 :                rho, rho_ao, cell, qs_section, orb_basis, ri_basis, virial)
     243             : 
     244          50 :       CALL cite_reference(Bussy2023)
     245             : 
     246          50 :       CALL timeset(routineN, handle)
     247             : 
     248             :       CALL get_qs_env(qs_env, natom=natom, nkind=nkind, dft_control=dft_control, para_env=para_env, &
     249          50 :                       particle_set=particle_set, qs_kind_set=qs_kind_set, cell=cell, virial=virial)
     250          50 :       IF (dft_control%qs_control%gapw) THEN
     251           0 :          CPABORT("Low-scaling RPA/SOS-MP2 forces only available with GPW")
     252             :       END IF
     253             : 
     254          50 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
     255             : 
     256          50 :       do_periodic = .FALSE.
     257         128 :       IF (ANY(cell%perd == 1)) do_periodic = .TRUE.
     258          50 :       force_data%do_periodic = do_periodic
     259             : 
     260             :       !Dealing with the 3-center derivatives
     261          50 :       pdims_t3c = 0
     262          50 :       CALL dbt_pgrid_create(para_env, pdims_t3c, pgrid_t3c)
     263             : 
     264             :       !Make sure we use the proper QS EPS_PGF_ORB values
     265          50 :       qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
     266          50 :       CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
     267          50 :       IF (n_rep /= 0) THEN
     268           0 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
     269             :       ELSE
     270          50 :          CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
     271          50 :          eps_pgf_orb = SQRT(eps_pgf_orb)
     272             :       END IF
     273          50 :       eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
     274             : 
     275         200 :       ALLOCATE (sizes_RI(natom), sizes_AO(natom))
     276         400 :       ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
     277          50 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
     278          50 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_RI, basis=basis_set_ri_aux)
     279          50 :       CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
     280          50 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_AO, basis=basis_set_ao)
     281             : 
     282         150 :       DO ibasis = 1, SIZE(basis_set_ao)
     283         100 :          orb_basis => basis_set_ao(ibasis)%gto_basis_set
     284         100 :          CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
     285         100 :          ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     286         150 :          CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
     287             :       END DO
     288             : 
     289             :       CALL create_3c_tensor(t_3c_template, dist_RI, dist_AO_1, dist_AO_2, pgrid_t3c, &
     290          50 :                             sizes_RI, sizes_AO, sizes_AO, map1=[1], map2=[2, 3], name="der (RI AO | AO)")
     291             : 
     292        1550 :       ALLOCATE (t_3c_der_RI_prv(1, 1, 3), t_3c_der_AO_prv(1, 1, 3))
     293         200 :       DO i_xyz = 1, 3
     294         150 :          CALL dbt_create(t_3c_template, t_3c_der_RI_prv(1, 1, i_xyz))
     295         200 :          CALL dbt_create(t_3c_template, t_3c_der_AO_prv(1, 1, i_xyz))
     296             :       END DO
     297             : 
     298          50 :       IF (use_virial) THEN
     299          52 :          ALLOCATE (force_data%t_3c_virial, force_data%t_3c_virial_split)
     300           4 :          CALL dbt_create(t_3c_template, force_data%t_3c_virial)
     301           4 :          CALL dbt_create(t_3c_M, force_data%t_3c_virial_split)
     302             :       END IF
     303          50 :       CALL dbt_destroy(t_3c_template)
     304             : 
     305          50 :       CALL dbt_mp_environ_pgrid(pgrid_t3c, pdims, pcoord)
     306          50 :       CALL mp_comm_t3c%create(pgrid_t3c%mp_comm_2d, 3, pdims)
     307             :       CALL distribution_3d_create(dist_3d, dist_RI, dist_AO_1, dist_AO_2, &
     308          50 :                                   nkind, particle_set, mp_comm_t3c, own_comm=.TRUE.)
     309             : 
     310             :       !In case of virial, we need to store the 3c_nl
     311          50 :       IF (use_virial) THEN
     312           4 :          ALLOCATE (force_data%nl_3c)
     313           4 :          CALL mp_comm_vir%create(pgrid_t3c%mp_comm_2d, 3, pdims)
     314             :          CALL distribution_3d_create(dist_vir, dist_RI, dist_AO_1, dist_AO_2, &
     315           4 :                                      nkind, particle_set, mp_comm_vir, own_comm=.TRUE.)
     316             :          CALL build_3c_neighbor_lists(force_data%nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, &
     317             :                                       dist_vir, mp2_env%ri_metric, "RPA_3c_nl", qs_env, op_pos=1, &
     318           4 :                                       sym_jk=.FALSE., own_dist=.TRUE.)
     319             :       END IF
     320             : 
     321             :       CALL build_3c_neighbor_lists(nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, dist_3d, &
     322             :                                    mp2_env%ri_metric, "RPA_3c_nl", qs_env, op_pos=1, sym_jk=.TRUE., &
     323          50 :                                    own_dist=.TRUE.)
     324          50 :       DEALLOCATE (dist_RI, dist_AO_1, dist_AO_2)
     325             : 
     326             :       !Prepare the resulting 3c tensors in the format of t_3c_M for compatible traces: (RI|AO AO), split blocks
     327          50 :       CALL dbt_get_info(t_3c_M, nblks_total=nblks_total)
     328         250 :       ALLOCATE (force_data%bsizes_RI_split(nblks_total(1)), force_data%bsizes_AO_split(nblks_total(2)))
     329          50 :       CALL dbt_get_info(t_3c_M, blk_size_1=force_data%bsizes_RI_split, blk_size_2=force_data%bsizes_AO_split)
     330         200 :       DO i_xyz = 1, 3
     331         150 :          CALL dbt_create(t_3c_M, force_data%t_3c_der_RI(i_xyz))
     332         200 :          CALL dbt_create(t_3c_M, force_data%t_3c_der_AO(i_xyz))
     333             :       END DO
     334             : 
     335             :       !Keep track of atom index corresponding to split blocks
     336         100 :       ALLOCATE (force_data%idx_to_at_RI(nblks_total(1)))
     337          50 :       CALL get_idx_to_atom(force_data%idx_to_at_RI, force_data%bsizes_RI_split, sizes_RI)
     338             : 
     339         100 :       ALLOCATE (force_data%idx_to_at_AO(nblks_total(2)))
     340          50 :       CALL get_idx_to_atom(force_data%idx_to_at_AO, force_data%bsizes_AO_split, sizes_AO)
     341             : 
     342          50 :       n_mem = mp2_env%ri_rpa_im_time%cut_memory
     343          50 :       CALL create_tensor_batches(sizes_RI, n_mem, dummy_start, dummy_end, start_blocks, end_blocks)
     344          50 :       DEALLOCATE (dummy_start, dummy_end)
     345             : 
     346      212300 :       ALLOCATE (force_data%t_3c_der_AO_comp(n_mem, 3), force_data%t_3c_der_RI_comp(n_mem, 3))
     347        1100 :       ALLOCATE (force_data%t_3c_der_AO_ind(n_mem, 3), force_data%t_3c_der_RI_ind(n_mem, 3))
     348             : 
     349          50 :       memory = 0.0_dp
     350          50 :       nze_tot = 0
     351         150 :       DO i_mem = 1, n_mem
     352             :          CALL build_3c_derivatives(t_3c_der_RI_prv, t_3c_der_AO_prv, mp2_env%ri_rpa_im_time%eps_filter, &
     353             :                                    qs_env, nl_3c, basis_set_ri_aux, basis_set_ao, basis_set_ao, &
     354             :                                    mp2_env%ri_metric, der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1, &
     355         300 :                                    bounds_i=[start_blocks(i_mem), end_blocks(i_mem)])
     356             : 
     357         450 :          DO i_xyz = 1, 3
     358         300 :             CALL dbt_copy(t_3c_der_RI_prv(1, 1, i_xyz), force_data%t_3c_der_RI(i_xyz), move_data=.TRUE.)
     359         300 :             CALL dbt_filter(force_data%t_3c_der_RI(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     360         300 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
     361         300 :             nze_tot = nze_tot + nze
     362             : 
     363         300 :             CALL alloc_containers(force_data%t_3c_der_RI_comp(i_mem, i_xyz), 1)
     364             :             CALL compress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
     365         300 :                                  force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress, memory)
     366         300 :             CALL dbt_clear(force_data%t_3c_der_RI(i_xyz))
     367             : 
     368         300 :             CALL dbt_copy(t_3c_der_AO_prv(1, 1, i_xyz), force_data%t_3c_der_AO(i_xyz), move_data=.TRUE.)
     369         300 :             CALL dbt_filter(force_data%t_3c_der_AO(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     370         300 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
     371         300 :             nze_tot = nze_tot + nze
     372             : 
     373         300 :             CALL alloc_containers(force_data%t_3c_der_AO_comp(i_mem, i_xyz), 1)
     374             :             CALL compress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
     375         300 :                                  force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress, memory)
     376        1000 :             CALL dbt_clear(force_data%t_3c_der_AO(i_xyz))
     377             :          END DO
     378             :       END DO
     379          50 :       CALL neighbor_list_3c_destroy(nl_3c)
     380         200 :       DO i_xyz = 1, 3
     381         150 :          CALL dbt_destroy(t_3c_der_RI_prv(1, 1, i_xyz))
     382         200 :          CALL dbt_destroy(t_3c_der_AO_prv(1, 1, i_xyz))
     383             :       END DO
     384             : 
     385          50 :       CALL para_env%sum(memory)
     386          50 :       compression_factor = REAL(nze_tot, dp)*1.0E-06*8.0_dp/memory
     387          50 :       IF (unit_nr > 0) THEN
     388             :          WRITE (UNIT=unit_nr, FMT="((T3,A,T66,F11.2,A4))") &
     389          25 :             "MEMORY_INFO| Memory for 3-center derivatives (compressed):", memory, ' MiB'
     390             : 
     391             :          WRITE (UNIT=unit_nr, FMT="((T3,A,T60,F21.2))") &
     392          25 :             "MEMORY_INFO| Compression factor:                  ", compression_factor
     393             :       END IF
     394             : 
     395             :       !Dealing with the 2-center derivatives
     396          50 :       CALL get_qs_env(qs_env, distribution_2d=dist_2d, blacs_env=blacs_env, matrix_s=matrix_s)
     397          50 :       CALL cp_dbcsr_dist2d_to_dist(dist_2d, dbcsr_dist)
     398         150 :       ALLOCATE (row_bsize(SIZE(sizes_RI)))
     399         100 :       ALLOCATE (col_bsize(SIZE(sizes_RI)))
     400         212 :       row_bsize(:) = sizes_RI(:)
     401         212 :       col_bsize(:) = sizes_RI(:)
     402             : 
     403          50 :       pdims_t2c = 0
     404          50 :       CALL dbt_pgrid_create(para_env, pdims_t2c, pgrid_t2c)
     405             :       CALL create_2c_tensor(t_2c_template, dist1, dist2, pgrid_t2c, force_data%bsizes_RI_split, &
     406          50 :                             force_data%bsizes_RI_split, name='(RI| RI)')
     407          50 :       DEALLOCATE (dist1, dist2)
     408             : 
     409          50 :       CALL dbcsr_create(t_2c_int_tmp(1), "(P|Q) RPA", dbcsr_dist, dbcsr_type_symmetric, row_bsize, col_bsize)
     410         200 :       DO i_xyz = 1, 3
     411             :          CALL dbcsr_create(t_2c_der_tmp(1, i_xyz), "(P|Q) RPA der", dbcsr_dist, &
     412         200 :                            dbcsr_type_antisymmetric, row_bsize, col_bsize)
     413             :       END DO
     414             : 
     415          50 :       IF (use_virial) THEN
     416           4 :          ALLOCATE (force_data%RI_virial_pot, force_data%RI_virial_met)
     417             :          CALL dbcsr_create(force_data%RI_virial_pot, "RI_virial", dbcsr_dist, &
     418           4 :                            dbcsr_type_no_symmetry, row_bsize, col_bsize)
     419             :          CALL dbcsr_create(force_data%RI_virial_met, "RI_virial", dbcsr_dist, &
     420           4 :                            dbcsr_type_no_symmetry, row_bsize, col_bsize)
     421             :       END IF
     422             : 
     423             :       ! Main (P|Q) integrals and derivatives
     424             :       ! Integrals are passed as a full matrix => convert to DBCSR
     425          50 :       CALL dbcsr_create(dbcsr_work, template=t_2c_int_tmp(1))
     426          50 :       CALL copy_fm_to_dbcsr(fm_matrix_PQ, dbcsr_work)
     427             : 
     428             :       ! We need the  +/- square root of (P|Q)
     429          50 :       CALL dbcsr_create(dbcsr_work2, template=t_2c_int_tmp(1))
     430          50 :       CALL dbcsr_create(dbcsr_work3, template=t_2c_int_tmp(1))
     431          50 :       CALL dbcsr_copy(dbcsr_work2, dbcsr_work)
     432          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
     433             : 
     434             :       ! Transfer to tensor format with split blocks
     435          50 :       CALL dbt_create(dbcsr_work, t_2c_tmp)
     436          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work, t_2c_tmp)
     437          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_pot_msqrt)
     438          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_pot_msqrt, move_data=.TRUE.)
     439          50 :       CALL dbt_filter(force_data%t_2c_pot_msqrt, mp2_env%ri_rpa_im_time%eps_filter)
     440             : 
     441          50 :       CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work2, dbcsr_work, 0.0_dp, dbcsr_work3)
     442          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work3, t_2c_tmp)
     443          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_pot_psqrt)
     444          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_pot_psqrt, move_data=.TRUE.)
     445          50 :       CALL dbt_filter(force_data%t_2c_pot_psqrt, mp2_env%ri_rpa_im_time%eps_filter)
     446          50 :       CALL dbt_destroy(t_2c_tmp)
     447          50 :       CALL dbcsr_release(dbcsr_work2)
     448          50 :       CALL dbcsr_release(dbcsr_work3)
     449          50 :       CALL dbcsr_clear(dbcsr_work)
     450             : 
     451             :       ! Deal with the 2c potential derivatives. Only precompute if not in PBCs
     452          50 :       IF (.NOT. do_periodic) THEN
     453             :          CALL build_2c_neighbor_lists(nl_2c, basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter, &
     454          26 :                                       "RPA_2c_nl_pot", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     455             :          CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     456          26 :                                    basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
     457          26 :          CALL release_neighbor_list_sets(nl_2c)
     458             : 
     459         104 :          DO i_xyz = 1, 3
     460          78 :             CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     461          78 :             CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     462          78 :             CALL dbt_create(t_2c_template, force_data%t_2c_der_pot(i_xyz))
     463          78 :             CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_pot(i_xyz), move_data=.TRUE.)
     464          78 :             CALL dbt_filter(force_data%t_2c_der_pot(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     465          78 :             CALL dbt_destroy(t_2c_tmp)
     466         104 :             CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     467             :          END DO
     468             : 
     469          26 :          IF (use_virial) THEN
     470             :             CALL build_2c_neighbor_lists(force_data%nl_2c_pot, basis_set_ri_aux, basis_set_ri_aux, &
     471             :                                          mp2_env%potential_parameter, "RPA_2c_nl_pot", qs_env, &
     472           0 :                                          sym_ij=.FALSE., dist_2d=dist_2d)
     473             :          END IF
     474             :       END IF
     475             :       ! Create a G_PQ matrix to collect the terms for the force trace in the periodic case
     476          50 :       CALL dbcsr_create(force_data%G_PQ, "G_PQ", dbcsr_dist, dbcsr_type_no_symmetry, row_bsize, col_bsize)
     477             : 
     478             :       ! we need the RI metric derivatives and the inverse of the integrals
     479             :       CALL build_2c_neighbor_lists(nl_2c, basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric, &
     480          50 :                                    "RPA_2c_nl_metric", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     481             :       CALL build_2c_integrals(t_2c_int_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     482          50 :                               basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
     483             :       CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     484          50 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
     485          50 :       CALL release_neighbor_list_sets(nl_2c)
     486             : 
     487          50 :       IF (use_virial) THEN
     488             :          CALL build_2c_neighbor_lists(force_data%nl_2c_met, basis_set_ri_aux, basis_set_ri_aux, &
     489             :                                       mp2_env%ri_metric, "RPA_2c_nl_metric", qs_env, sym_ij=.FALSE., &
     490           4 :                                       dist_2d=dist_2d)
     491             :       END IF
     492             : 
     493          50 :       CALL dbcsr_copy(dbcsr_work, t_2c_int_tmp(1))
     494          50 :       CALL cp_dbcsr_cholesky_decompose(dbcsr_work, para_env=para_env, blacs_env=blacs_env)
     495          50 :       CALL cp_dbcsr_cholesky_invert(dbcsr_work, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
     496             : 
     497          50 :       CALL dbt_create(dbcsr_work, t_2c_tmp)
     498          50 :       CALL dbt_copy_matrix_to_tensor(dbcsr_work, t_2c_tmp)
     499          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_inv_metric)
     500          50 :       CALL dbt_copy(t_2c_tmp, force_data%t_2c_inv_metric, move_data=.TRUE.)
     501          50 :       CALL dbt_filter(force_data%t_2c_inv_metric, mp2_env%ri_rpa_im_time%eps_filter)
     502          50 :       CALL dbt_destroy(t_2c_tmp)
     503          50 :       CALL dbcsr_clear(dbcsr_work)
     504          50 :       CALL dbcsr_clear(t_2c_int_tmp(1))
     505             : 
     506         200 :       DO i_xyz = 1, 3
     507         150 :          CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     508         150 :          CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     509         150 :          CALL dbt_create(t_2c_template, force_data%t_2c_der_metric(i_xyz))
     510         150 :          CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_metric(i_xyz), move_data=.TRUE.)
     511         150 :          CALL dbt_filter(force_data%t_2c_der_metric(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     512         150 :          CALL dbt_destroy(t_2c_tmp)
     513         200 :          CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     514             :       END DO
     515             : 
     516             :       !Pre-calculate matrix K = metric^-1 * V^0.5
     517          50 :       CALL dbt_create(t_2c_template, force_data%t_2c_K)
     518             :       CALL dbt_contract(1.0_dp, force_data%t_2c_inv_metric, force_data%t_2c_pot_psqrt, &
     519             :                         0.0_dp, force_data%t_2c_K, &
     520             :                         contract_1=[2], notcontract_1=[1], &
     521             :                         contract_2=[1], notcontract_2=[2], &
     522          50 :                         map_1=[1], map_2=[2], filter_eps=mp2_env%ri_rpa_im_time%eps_filter)
     523             : 
     524             :       ! Finally, we need the overlap matrix derivative and the inverse of the integrals
     525          50 :       CALL dbt_destroy(t_2c_template)
     526          50 :       CALL dbcsr_release(dbcsr_work)
     527          50 :       CALL dbcsr_release(t_2c_int_tmp(1))
     528         200 :       DO i_xyz = 1, 3
     529         200 :          CALL dbcsr_release(t_2c_der_tmp(1, i_xyz))
     530             :       END DO
     531             : 
     532          50 :       DEALLOCATE (row_bsize, col_bsize)
     533         150 :       ALLOCATE (row_bsize(SIZE(sizes_AO)))
     534         100 :       ALLOCATE (col_bsize(SIZE(sizes_AO)))
     535         212 :       row_bsize(:) = sizes_AO(:)
     536         212 :       col_bsize(:) = sizes_AO(:)
     537             : 
     538             :       CALL create_2c_tensor(t_2c_template, dist1, dist2, pgrid_t2c, force_data%bsizes_AO_split, &
     539             :                             force_data%bsizes_AO_split, name='(AO| AO)')
     540          50 :       DEALLOCATE (dist1, dist2)
     541             : 
     542         200 :       DO i_xyz = 1, 3
     543             :          CALL dbcsr_create(t_2c_der_tmp(1, i_xyz), "(P|Q) RPA der", dbcsr_dist, &
     544         200 :                            dbcsr_type_antisymmetric, row_bsize, col_bsize)
     545             :       END DO
     546             : 
     547          50 :       identity_pot%potential_type = do_potential_id
     548             :       CALL build_2c_neighbor_lists(nl_2c, basis_set_ao, basis_set_ao, identity_pot, &
     549          50 :                                    "RPA_2c_nl_metric", qs_env, sym_ij=.TRUE., dist_2d=dist_2d)
     550             :       CALL build_2c_derivatives(t_2c_der_tmp, mp2_env%ri_rpa_im_time%eps_filter, qs_env, nl_2c, &
     551          50 :                                 basis_set_ao, basis_set_ao, identity_pot)
     552          50 :       CALL release_neighbor_list_sets(nl_2c)
     553             : 
     554          50 :       IF (use_virial) THEN
     555             :          CALL build_2c_neighbor_lists(force_data%nl_2c_ovlp, basis_set_ao, basis_set_ao, identity_pot, &
     556           4 :                                       "RPA_2c_nl_metric", qs_env, sym_ij=.FALSE., dist_2d=dist_2d)
     557             :       END IF
     558             : 
     559          50 :       CALL dbcsr_create(force_data%inv_ovlp, template=matrix_s(1)%matrix)
     560          50 :       CALL dbcsr_copy(force_data%inv_ovlp, matrix_s(1)%matrix)
     561          50 :       CALL cp_dbcsr_cholesky_decompose(force_data%inv_ovlp, para_env=para_env, blacs_env=blacs_env)
     562          50 :       CALL cp_dbcsr_cholesky_invert(force_data%inv_ovlp, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
     563             : 
     564         200 :       DO i_xyz = 1, 3
     565         150 :          CALL dbt_create(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     566         150 :          CALL dbt_copy_matrix_to_tensor(t_2c_der_tmp(1, i_xyz), t_2c_tmp)
     567         150 :          CALL dbt_create(t_2c_template, force_data%t_2c_der_ovlp(i_xyz))
     568         150 :          CALL dbt_copy(t_2c_tmp, force_data%t_2c_der_ovlp(i_xyz), move_data=.TRUE.)
     569         150 :          CALL dbt_filter(force_data%t_2c_der_ovlp(i_xyz), mp2_env%ri_rpa_im_time%eps_filter)
     570         150 :          CALL dbt_destroy(t_2c_tmp)
     571         200 :          CALL dbcsr_clear(t_2c_der_tmp(1, i_xyz))
     572             :       END DO
     573             : 
     574             :       !Create the rest of the 2-center AO tensors
     575          50 :       nspins = dft_control%nspins
     576         324 :       ALLOCATE (force_data%P_virt(nspins), force_data%P_occ(nspins))
     577         274 :       ALLOCATE (force_data%sum_YP_tau(nspins), force_data%sum_O_tau(nspins))
     578         112 :       DO ispin = 1, nspins
     579          62 :          ALLOCATE (force_data%P_virt(ispin)%matrix, force_data%P_occ(ispin)%matrix)
     580          62 :          ALLOCATE (force_data%sum_YP_tau(ispin)%matrix, force_data%sum_O_tau(ispin)%matrix)
     581          62 :          CALL dbcsr_create(force_data%P_virt(ispin)%matrix, template=matrix_s(1)%matrix)
     582          62 :          CALL dbcsr_create(force_data%P_occ(ispin)%matrix, template=matrix_s(1)%matrix)
     583          62 :          CALL dbcsr_create(force_data%sum_O_tau(ispin)%matrix, template=matrix_s(1)%matrix)
     584          62 :          CALL dbcsr_create(force_data%sum_YP_tau(ispin)%matrix, template=matrix_s(1)%matrix)
     585             : 
     586          62 :          CALL dbcsr_copy(force_data%sum_O_tau(ispin)%matrix, matrix_s(1)%matrix)
     587          62 :          CALL dbcsr_copy(force_data%sum_YP_tau(ispin)%matrix, matrix_s(1)%matrix)
     588             : 
     589          62 :          CALL dbcsr_set(force_data%sum_O_tau(ispin)%matrix, 0.0_dp)
     590         112 :          CALL dbcsr_set(force_data%sum_YP_tau(ispin)%matrix, 0.0_dp)
     591             :       END DO
     592             : 
     593             :       !Populate the density matrices: 1 = P_virt*S +P_occ*S ==> P_virt = S^-1 - P_occ
     594          50 :       CALL get_qs_env(qs_env, rho=rho)
     595          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
     596          50 :       CALL dbcsr_copy(force_data%P_occ(1)%matrix, rho_ao(1)%matrix)
     597          50 :       IF (nspins == 1) THEN
     598          38 :          CALL dbcsr_scale(force_data%P_occ(1)%matrix, 0.5_dp) !because double occupency
     599             :       ELSE
     600          12 :          CALL dbcsr_copy(force_data%P_occ(2)%matrix, rho_ao(2)%matrix)
     601             :       END IF
     602         112 :       DO ispin = 1, nspins
     603          62 :          CALL dbcsr_copy(force_data%P_virt(ispin)%matrix, force_data%inv_ovlp)
     604         112 :          CALL dbcsr_add(force_data%P_virt(ispin)%matrix, force_data%P_occ(ispin)%matrix, 1.0_dp, -1.0_dp)
     605             :       END DO
     606             : 
     607         150 :       DO ibasis = 1, SIZE(basis_set_ao)
     608         100 :          orb_basis => basis_set_ao(ibasis)%gto_basis_set
     609         100 :          CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
     610         100 :          ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     611         150 :          CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
     612             :       END DO
     613             : 
     614          50 :       CALL dbt_destroy(t_2c_template)
     615          50 :       CALL dbcsr_release(dbcsr_work)
     616         200 :       DO i_xyz = 1, 3
     617         200 :          CALL dbcsr_release(t_2c_der_tmp(1, i_xyz))
     618             :       END DO
     619          50 :       DEALLOCATE (row_bsize, col_bsize)
     620          50 :       CALL dbt_pgrid_destroy(pgrid_t3c)
     621          50 :       CALL dbt_pgrid_destroy(pgrid_t2c)
     622          50 :       CALL dbcsr_distribution_release(dbcsr_dist)
     623          50 :       CALL timestop(handle)
     624             : 
     625         750 :    END SUBROUTINE init_im_time_forces
     626             : 
     627             : ! **************************************************************************************************
     628             : !> \brief Updates the cubic-scaling SOS-Laplace-MP2 contribution to the forces at each quadrature point
     629             : !> \param force_data ...
     630             : !> \param mat_P_omega ...
     631             : !> \param t_3c_M ...
     632             : !> \param t_3c_O ...
     633             : !> \param t_3c_O_compressed ...
     634             : !> \param t_3c_O_ind ...
     635             : !> \param fm_scaled_dm_occ_tau ...
     636             : !> \param fm_scaled_dm_virt_tau ...
     637             : !> \param fm_mo_coeff_occ ...
     638             : !> \param fm_mo_coeff_virt ...
     639             : !> \param fm_mo_coeff_occ_scaled ...
     640             : !> \param fm_mo_coeff_virt_scaled ...
     641             : !> \param starts_array_mc ...
     642             : !> \param ends_array_mc ...
     643             : !> \param starts_array_mc_block ...
     644             : !> \param ends_array_mc_block ...
     645             : !> \param num_integ_points ...
     646             : !> \param nmo ...
     647             : !> \param Eigenval ...
     648             : !> \param tau_tj ...
     649             : !> \param tau_wj ...
     650             : !> \param cut_memory ...
     651             : !> \param Pspin ...
     652             : !> \param Qspin ...
     653             : !> \param open_shell ...
     654             : !> \param unit_nr ...
     655             : !> \param dbcsr_time ...
     656             : !> \param dbcsr_nflop ...
     657             : !> \param mp2_env ...
     658             : !> \param qs_env ...
     659             : !> \note In open-shell, we need to take Q from one spin, and everything from the other
     660             : ! **************************************************************************************************
     661         130 :    SUBROUTINE calc_laplace_loop_forces(force_data, mat_P_omega, t_3c_M, t_3c_O, t_3c_O_compressed, &
     662          26 :                                        t_3c_O_ind, fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, &
     663          26 :                                        fm_mo_coeff_occ, fm_mo_coeff_virt, fm_mo_coeff_occ_scaled, &
     664          26 :                                        fm_mo_coeff_virt_scaled, starts_array_mc, ends_array_mc, &
     665          26 :                                        starts_array_mc_block, ends_array_mc_block, num_integ_points, &
     666          52 :                                        nmo, Eigenval, tau_tj, tau_wj, cut_memory, Pspin, Qspin, &
     667             :                                        open_shell, unit_nr, dbcsr_time, dbcsr_nflop, mp2_env, qs_env)
     668             : 
     669             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
     670             :       TYPE(dbcsr_p_type), DIMENSION(:, :), INTENT(INOUT) :: mat_P_omega
     671             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M, t_3c_O
     672             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
     673             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
     674             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_scaled_dm_occ_tau, &
     675             :                                                             fm_scaled_dm_virt_tau
     676             :       TYPE(cp_fm_type), DIMENSION(:), INTENT(IN)         :: fm_mo_coeff_occ, fm_mo_coeff_virt
     677             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_mo_coeff_occ_scaled, &
     678             :                                                             fm_mo_coeff_virt_scaled
     679             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
     680             :                                                             starts_array_mc_block, &
     681             :                                                             ends_array_mc_block
     682             :       INTEGER, INTENT(IN)                                :: num_integ_points, nmo
     683             :       REAL(KIND=dp), DIMENSION(:, :), INTENT(IN)         :: Eigenval
     684             :       REAL(KIND=dp), DIMENSION(0:num_integ_points), &
     685             :          INTENT(IN)                                      :: tau_tj
     686             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
     687             :          INTENT(IN)                                      :: tau_wj
     688             :       INTEGER, INTENT(IN)                                :: cut_memory, Pspin, Qspin
     689             :       LOGICAL, INTENT(IN)                                :: open_shell
     690             :       INTEGER, INTENT(IN)                                :: unit_nr
     691             :       REAL(dp), INTENT(INOUT)                            :: dbcsr_time
     692             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
     693             :       TYPE(mp2_type)                                     :: mp2_env
     694             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     695             : 
     696             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_laplace_loop_forces'
     697             : 
     698             :       INTEGER :: dummy_int, handle, handle2, i_mem, i_xyz, ibasis, ispin, j_xyz, jquad, k_xyz, &
     699             :          n_mem_RI, n_rep, natom, nkind, nspins, unit_nr_dbcsr
     700             :       INTEGER(int_8)                                     :: flop, nze, nze_ddint, nze_der_AO, &
     701             :                                                             nze_der_RI, nze_KQK
     702          26 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, batch_blk_end, &
     703          26 :                                                             batch_blk_start, batch_end_RI, &
     704          26 :                                                             batch_start_RI, kind_of, mc_ranges, &
     705          26 :                                                             mc_ranges_RI
     706          26 :       INTEGER, DIMENSION(:, :), POINTER                  :: dummy_ptr
     707             :       LOGICAL                                            :: memory_info, use_virial
     708             :       REAL(dp)                                           :: eps_filter, eps_pgf_orb, &
     709             :                                                             eps_pgf_orb_old, fac, occ, occ_ddint, &
     710             :                                                             occ_der_AO, occ_der_RI, occ_KQK, &
     711             :                                                             omega, pref, t1, t2, tau
     712             :       REAL(dp), DIMENSION(3, 3)                          :: work_virial, work_virial_ovlp
     713          26 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     714             :       TYPE(cell_type), POINTER                           :: cell
     715          26 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks, matrix_s
     716          26 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: mat_dm_occ, mat_dm_virt
     717             :       TYPE(dbcsr_type)                                   :: dbcsr_work1, dbcsr_work2, dbcsr_work3, &
     718             :                                                             exp_occ, exp_virt, R_occ, R_virt, &
     719             :                                                             virial_ovlp, Y_1, Y_2
     720        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, &
     721        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, &
     722        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
     723          26 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:)          :: t_P
     724             :       TYPE(dft_control_type), POINTER                    :: dft_control
     725             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
     726          26 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
     727             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
     728             :       TYPE(libint_potential_type)                        :: identity_pot
     729             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     730          26 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     731          26 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
     732          26 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     733             :       TYPE(section_vals_type), POINTER                   :: qs_section
     734             :       TYPE(virial_type), POINTER                         :: virial
     735             : 
     736          26 :       NULLIFY (matrix_s, dummy_ptr, atomic_kind_set, force, matrix_s, matrix_ks, mat_dm_occ, mat_dm_virt)
     737          26 :       NULLIFY (dft_control, virial, particle_set, cell, para_env, orb_basis, ri_basis, qs_section)
     738          26 :       NULLIFY (qs_kind_set)
     739             : 
     740          26 :       CALL timeset(routineN, handle)
     741             : 
     742             :       CALL get_qs_env(qs_env, matrix_s=matrix_s, natom=natom, atomic_kind_set=atomic_kind_set, &
     743             :                       force=force, matrix_ks=matrix_ks, dft_control=dft_control, virial=virial, &
     744             :                       particle_set=particle_set, cell=cell, para_env=para_env, nkind=nkind, &
     745          26 :                       qs_kind_set=qs_kind_set)
     746          26 :       eps_filter = mp2_env%ri_rpa_im_time%eps_filter
     747          26 :       nspins = dft_control%nspins
     748             : 
     749          26 :       memory_info = mp2_env%ri_rpa_im_time%memory_info
     750          26 :       IF (memory_info) THEN
     751           0 :          unit_nr_dbcsr = unit_nr
     752             :       ELSE
     753          26 :          unit_nr_dbcsr = 0
     754             :       END IF
     755             : 
     756          26 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
     757             : 
     758          26 :       IF (use_virial) virial%pv_calculate = .TRUE.
     759             : 
     760          26 :       IF (use_virial) THEN
     761           2 :          qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
     762           2 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
     763           2 :          IF (n_rep /= 0) THEN
     764           0 :             CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
     765             :          ELSE
     766           2 :             CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
     767           2 :             eps_pgf_orb = SQRT(eps_pgf_orb)
     768             :          END IF
     769           2 :          eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
     770             : 
     771          16 :          ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
     772           2 :          CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
     773           2 :          CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
     774             : 
     775           8 :          DO ibasis = 1, SIZE(basis_set_ao)
     776           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
     777           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
     778           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
     779           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
     780             :          END DO
     781             :       END IF
     782             : 
     783             :       !We follow the general logic of the compute_mat_P_omega routine
     784         268 :       ALLOCATE (t_P(nspins))
     785          26 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI)
     786          26 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI_2)
     787          26 :       CALL dbt_create(force_data%t_2c_der_ovlp(1), t_2c_AO)
     788             : 
     789          26 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
     790             : 
     791             :       ! Always do the batching of the MO on mu and sigma, such that it is consistent between
     792             :       ! the occupied and the virtual quantities
     793          78 :       ALLOCATE (mc_ranges(cut_memory + 1))
     794          78 :       mc_ranges(:cut_memory) = starts_array_mc_block(:)
     795          26 :       mc_ranges(cut_memory + 1) = ends_array_mc_block(cut_memory) + 1
     796             : 
     797             :       ! Also need some batching on the RI, because it loses sparsity at some point
     798          26 :       n_mem_RI = cut_memory
     799             :       CALL create_tensor_batches(force_data%bsizes_RI_split, n_mem_RI, batch_start_RI, batch_end_RI, &
     800          26 :                                  batch_blk_start, batch_blk_end)
     801          78 :       ALLOCATE (mc_ranges_RI(n_mem_RI + 1))
     802          78 :       mc_ranges_RI(1:n_mem_RI) = batch_blk_start(1:n_mem_RI)
     803          26 :       mc_ranges_RI(n_mem_RI + 1) = batch_blk_end(n_mem_RI) + 1
     804          26 :       DEALLOCATE (batch_blk_start, batch_blk_end)
     805             : 
     806             :       !Pre-allocate all required tensors and matrices
     807          60 :       DO ispin = 1, nspins
     808          60 :          CALL dbt_create(t_2c_RI, t_P(ispin))
     809             :       END DO
     810          26 :       CALL dbt_create(t_2c_RI, t_Q)
     811          26 :       CALL dbt_create(t_2c_RI, t_KQKT)
     812          26 :       CALL dbt_create(t_2c_AO, t_dm_occ)
     813          26 :       CALL dbt_create(t_2c_AO, t_dm_virt)
     814             : 
     815             :       !note: t_3c_O and t_3c_M have different mappings (map_1d, map_2d)
     816          26 :       CALL dbt_create(t_3c_O, t_M_occ)
     817          26 :       CALL dbt_create(t_3c_O, t_M_virt)
     818          26 :       CALL dbt_create(t_3c_O, t_3c_0)
     819             : 
     820          26 :       CALL dbt_create(t_3c_O, t_3c_1)
     821          26 :       CALL dbt_create(t_3c_O, t_3c_3)
     822          26 :       CALL dbt_create(t_3c_O, t_3c_4)
     823          26 :       CALL dbt_create(t_3c_O, t_3c_5)
     824          26 :       CALL dbt_create(t_3c_M, t_3c_6)
     825          26 :       CALL dbt_create(t_3c_M, t_3c_7)
     826          26 :       CALL dbt_create(t_3c_M, t_3c_8)
     827          26 :       CALL dbt_create(t_3c_M, t_3c_sparse)
     828          26 :       CALL dbt_create(t_3c_O, t_3c_help_1)
     829          26 :       CALL dbt_create(t_3c_O, t_3c_help_2)
     830          26 :       CALL dbt_create(t_2c_AO, t_R_occ)
     831          26 :       CALL dbt_create(t_2c_AO, t_R_virt)
     832          26 :       CALL dbt_create(t_3c_M, t_3c_ints)
     833          26 :       CALL dbt_create(t_3c_M, t_3c_work)
     834             : 
     835             :       !Pre-define the sparsity of t_3c_4 as a function of the derivatives
     836          26 :       occ_der_AO = 0; nze_der_AO = 0
     837          26 :       occ_der_RI = 0; nze_der_RI = 0
     838         104 :       DO i_xyz = 1, 3
     839         260 :          DO i_mem = 1, cut_memory
     840             :             CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
     841         156 :                                    force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
     842         156 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
     843         156 :             occ_der_RI = occ_der_RI + occ
     844         156 :             nze_der_RI = nze_der_RI + nze
     845         156 :             CALL dbt_copy(force_data%t_3c_der_RI(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
     846             : 
     847             :             CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
     848         156 :                                    force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
     849         156 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
     850         156 :             occ_der_AO = occ_der_AO + occ
     851         156 :             nze_der_AO = nze_der_AO + nze
     852         156 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, order=[1, 3, 2], summation=.TRUE.)
     853         546 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
     854             :          END DO
     855             :       END DO
     856          26 :       occ_der_RI = occ_der_RI/3.0_dp
     857          26 :       occ_der_AO = occ_der_AO/3.0_dp
     858          26 :       nze_der_RI = nze_der_RI/3
     859          26 :       nze_der_AO = nze_der_AO/3
     860             : 
     861          26 :       CALL dbcsr_create(R_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     862          26 :       CALL dbcsr_create(R_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     863          26 :       CALL dbcsr_create(dbcsr_work1, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     864          26 :       CALL dbcsr_create(dbcsr_work2, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     865          26 :       CALL dbcsr_create(dbcsr_work3, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     866          26 :       CALL dbcsr_create(exp_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     867          26 :       CALL dbcsr_create(exp_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
     868          26 :       IF (use_virial) CALL dbcsr_create(virial_ovlp, template=dbcsr_work1)
     869             : 
     870          26 :       CALL dbt_batched_contract_init(t_3c_0, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
     871          26 :       CALL dbt_batched_contract_init(t_3c_1, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
     872          26 :       CALL dbt_batched_contract_init(t_3c_3, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     873          26 :       CALL dbt_batched_contract_init(t_M_occ, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     874          26 :       CALL dbt_batched_contract_init(t_M_virt, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     875             : 
     876          26 :       CALL dbt_batched_contract_init(t_3c_ints, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     877          26 :       CALL dbt_batched_contract_init(t_3c_work, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
     878             : 
     879             :       CALL dbt_batched_contract_init(t_3c_4, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     880          26 :                                      batch_range_3=mc_ranges)
     881             :       CALL dbt_batched_contract_init(t_3c_5, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     882          26 :                                      batch_range_3=mc_ranges)
     883             :       CALL dbt_batched_contract_init(t_3c_6, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     884          26 :                                      batch_range_3=mc_ranges)
     885             :       CALL dbt_batched_contract_init(t_3c_7, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     886          26 :                                      batch_range_3=mc_ranges)
     887             :       CALL dbt_batched_contract_init(t_3c_8, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     888          26 :                                      batch_range_3=mc_ranges)
     889             :       CALL dbt_batched_contract_init(t_3c_sparse, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
     890          26 :                                      batch_range_3=mc_ranges)
     891             : 
     892          26 :       work_virial = 0.0_dp
     893          26 :       work_virial_ovlp = 0.0_dp
     894         104 :       DO jquad = 1, num_integ_points
     895          78 :          tau = tau_tj(jquad)
     896          78 :          omega = tau_wj(jquad)
     897          78 :          fac = -2.0_dp*omega*mp2_env%scale_S
     898          78 :          IF (open_shell) fac = 0.5_dp*fac
     899          78 :          occ_ddint = 0; nze_ddint = 0
     900             : 
     901          78 :          CALL para_env%sync()
     902          78 :          t1 = m_walltime()
     903             : 
     904             :          !Deal with the force contributions where there is no explicit 3-center quantities, i.e. the
     905             :          !forces due to the metric and potential derivatives
     906         180 :          DO ispin = 1, nspins
     907         102 :             CALL dbt_create(mat_P_omega(jquad, ispin)%matrix, t_2c_tmp)
     908         102 :             CALL dbt_copy_matrix_to_tensor(mat_P_omega(jquad, ispin)%matrix, t_2c_tmp)
     909         102 :             CALL dbt_copy(t_2c_tmp, t_P(ispin), move_data=.TRUE.)
     910         102 :             CALL dbt_filter(t_P(ispin), eps_filter)
     911         180 :             CALL dbt_destroy(t_2c_tmp)
     912             :          END DO
     913             : 
     914             :          !Q = K^T*P*K, open-shell: Q is from one spin, everything else from the other
     915             :          CALL dbt_contract(1.0_dp, t_P(Qspin), force_data%t_2c_K, 0.0_dp, t_2c_RI, &
     916             :                            contract_1=[2], notcontract_1=[1], &
     917             :                            contract_2=[1], notcontract_2=[2], &
     918             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
     919          78 :                            flop=flop, unit_nr=unit_nr_dbcsr)
     920          78 :          dbcsr_nflop = dbcsr_nflop + flop
     921             :          CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_2c_RI, 0.0_dp, t_Q, &
     922             :                            contract_1=[1], notcontract_1=[2], &
     923             :                            contract_2=[1], notcontract_2=[2], &
     924             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
     925          78 :                            flop=flop, unit_nr=unit_nr_dbcsr)
     926          78 :          dbcsr_nflop = dbcsr_nflop + flop
     927          78 :          CALL dbt_clear(t_2c_RI)
     928             : 
     929             :          CALL perform_2c_ops(force, t_KQKT, force_data, fac, t_Q, t_P(Pspin), t_2c_RI, t_2c_RI_2, &
     930          78 :                              use_virial, atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
     931          78 :          CALL get_tensor_occupancy(t_KQKT, nze_KQK, occ_KQK)
     932             : 
     933             :          !Calculate the pseudo-density matrix in tensor form. There are a few useless arguments for SOS-MP2
     934             :          CALL compute_mat_dm_global(fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, tau_tj, num_integ_points, &
     935             :                                     nmo, fm_mo_coeff_occ(Pspin), fm_mo_coeff_virt(Pspin), &
     936             :                                     fm_mo_coeff_occ_scaled, fm_mo_coeff_virt_scaled, mat_dm_occ, mat_dm_virt, &
     937             :                                     matrix_s, Pspin, Eigenval(:, Pspin), 0.0_dp, eps_filter, &
     938             :                                     mp2_env%ri_rpa_im_time%memory_info, unit_nr, &
     939          78 :                                     jquad, .FALSE., .FALSE., qs_env, dummy_int, dummy_ptr, para_env)
     940             : 
     941          78 :          CALL dbt_create(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
     942          78 :          CALL dbt_copy_matrix_to_tensor(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
     943          78 :          CALL dbt_copy(t_2c_tmp, t_dm_occ, move_data=.TRUE.)
     944          78 :          CALL dbt_filter(t_dm_occ, eps_filter)
     945          78 :          CALL dbt_destroy(t_2c_tmp)
     946             : 
     947          78 :          CALL dbt_create(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
     948          78 :          CALL dbt_copy_matrix_to_tensor(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
     949          78 :          CALL dbt_copy(t_2c_tmp, t_dm_virt, move_data=.TRUE.)
     950          78 :          CALL dbt_filter(t_dm_virt, eps_filter)
     951          78 :          CALL dbt_destroy(t_2c_tmp)
     952             : 
     953             :          !Deal with the 3-center quantities.
     954             :          CALL perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
     955             :                              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, &
     956             :                              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, &
     957             :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
     958             :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
     959             :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
     960          78 :                              unit_nr_dbcsr, mp2_env)
     961             : 
     962          78 :          CALL timeset(routineN//"_dbcsr", handle2)
     963             :          !We go back to DBCSR matrices from now on
     964             :          !Note: R matrices are in fact symmetric, but use a normal type for convenience
     965          78 :          CALL dbt_create(matrix_s(1)%matrix, t_2c_tmp)
     966          78 :          CALL dbt_copy(t_R_occ, t_2c_tmp, move_data=.TRUE.)
     967          78 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_occ)
     968             : 
     969          78 :          CALL dbt_copy(t_R_virt, t_2c_tmp, move_data=.TRUE.)
     970          78 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_virt)
     971             : 
     972             :          !Iteratively calculate the Y1 and Y2 matrices
     973             :          CALL dbcsr_multiply('N', 'N', tau, force_data%P_occ(Pspin)%matrix, &
     974          78 :                              matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     975          78 :          CALL build_Y_matrix(Y_1, dbcsr_work1, force_data%P_occ(Pspin)%matrix, R_virt, eps_filter)
     976          78 :          CALL matrix_exponential(exp_occ, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
     977             : 
     978             :          CALL dbcsr_multiply('N', 'N', -tau, force_data%P_virt(Pspin)%matrix, &
     979          78 :                              matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     980          78 :          CALL build_Y_matrix(Y_2, dbcsr_work1, force_data%P_virt(Pspin)%matrix, R_occ, eps_filter)
     981          78 :          CALL matrix_exponential(exp_virt, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
     982             : 
     983             :          !The force contribution coming from [-S^-1*(e^-tau*P_virt*F)^T*R_occ*S^-1
     984             :          !                                    +tau*S^-1*Y_2^T*F*S^-1] * der_S
     985          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, R_occ, force_data%inv_ovlp, 0.0_dp, dbcsr_work1)
     986          78 :          CALL dbcsr_multiply('T', 'N', 1.0_dp, exp_virt, dbcsr_work1, 0.0_dp, dbcsr_work3)
     987          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, force_data%inv_ovlp, dbcsr_work3, 0.0_dp, dbcsr_work2)
     988             : 
     989          78 :          CALL dbcsr_multiply('N', 'T', tau, force_data%inv_ovlp, Y_2, 0.0_dp, dbcsr_work3)
     990          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work3, matrix_ks(Pspin)%matrix, 0.0_dp, dbcsr_work1)
     991          78 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work1, force_data%inv_ovlp, 0.0_dp, dbcsr_work3)
     992             : 
     993          78 :          CALL dbcsr_add(dbcsr_work2, dbcsr_work3, 1.0_dp, -1.0_dp)
     994             : 
     995          78 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work2, t_2c_tmp)
     996          78 :          CALL dbt_copy(t_2c_tmp, t_2c_AO, move_data=.TRUE.)
     997             : 
     998          78 :          pref = -1.0_dp*fac
     999             :          CALL get_2c_der_force(force, t_2c_AO, force_data%t_2c_der_ovlp, atom_of_kind, &
    1000          78 :                                kind_of, force_data%idx_to_at_AO, pref, do_ovlp=.TRUE.)
    1001             : 
    1002          78 :          IF (use_virial) CALL dbcsr_add(virial_ovlp, dbcsr_work2, 1.0_dp, pref)
    1003             : 
    1004             :          !The final contribution from Tr[(tau*Y_1*P_occ - tau*Y_2*P_virt) * der_F]
    1005             :          CALL dbcsr_multiply('N', 'N', tau*fac, Y_1, force_data%P_occ(Pspin)%matrix, 1.0_dp, &
    1006          78 :                              force_data%sum_YP_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1007             :          CALL dbcsr_multiply('N', 'N', -tau*fac, Y_2, force_data%P_virt(Pspin)%matrix, 1.0_dp, &
    1008          78 :                              force_data%sum_YP_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1009             : 
    1010             :          !Build-up the RHS of the response equation.
    1011          78 :          pref = -omega*mp2_env%scale_S
    1012             :          CALL dbcsr_multiply('N', 'N', pref, R_virt, exp_occ, 1.0_dp, &
    1013          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1014             :          CALL dbcsr_multiply('N', 'N', -pref, R_occ, exp_virt, 1.0_dp, &
    1015          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1016             :          CALL dbcsr_multiply('N', 'N', pref*tau, matrix_ks(Pspin)%matrix, Y_1, 1.0_dp, &
    1017          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1018             :          CALL dbcsr_multiply('N', 'N', pref*tau, matrix_ks(Pspin)%matrix, Y_2, 1.0_dp, &
    1019          78 :                              force_data%sum_O_tau(Pspin)%matrix, retain_sparsity=.TRUE.)
    1020             : 
    1021          78 :          CALL timestop(handle2)
    1022             : 
    1023             :          !Print some info
    1024          78 :          CALL para_env%sync()
    1025          78 :          t2 = m_walltime()
    1026          78 :          dbcsr_time = dbcsr_time + t2 - t1
    1027             : 
    1028          78 :          IF (unit_nr > 0) THEN
    1029             :             WRITE (unit_nr, '(/T3,A,1X,I3,A)') &
    1030          39 :                'RPA_LOW_SCALING_INFO| Info for time point', jquad, '    (gradients)'
    1031             :             WRITE (unit_nr, '(T6,A,T56,F25.6)') &
    1032          39 :                'Execution time (s):', t2 - t1
    1033             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1034          39 :                'Occupancy of 3c AO derivs:', REAL(nze_der_AO, dp), '/', occ_der_AO*100, '%'
    1035             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1036          39 :                'Occupancy of 3c RI derivs:', REAL(nze_der_RI, dp), '/', occ_der_RI*100, '%'
    1037             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1038          39 :                'Occupancy of the Docc * Dvirt * 3c-int tensor', REAL(nze_ddint, dp), '/', occ_ddint*100, '%'
    1039             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1040          39 :                'Occupancy of KQK^T 2c-tensor:', REAL(nze_KQK, dp), '/', occ_KQK*100, '%'
    1041          39 :             CALL m_flush(unit_nr)
    1042             :          END IF
    1043             : 
    1044             :          !intermediate clean-up
    1045          78 :          CALL dbcsr_release(Y_1)
    1046          78 :          CALL dbcsr_release(Y_2)
    1047         416 :          CALL dbt_destroy(t_2c_tmp)
    1048             :       END DO !jquad
    1049             : 
    1050          26 :       CALL dbt_batched_contract_finalize(t_3c_0)
    1051          26 :       CALL dbt_batched_contract_finalize(t_3c_1)
    1052          26 :       CALL dbt_batched_contract_finalize(t_3c_3)
    1053          26 :       CALL dbt_batched_contract_finalize(t_M_occ)
    1054          26 :       CALL dbt_batched_contract_finalize(t_M_virt)
    1055             : 
    1056          26 :       CALL dbt_batched_contract_finalize(t_3c_ints)
    1057          26 :       CALL dbt_batched_contract_finalize(t_3c_work)
    1058             : 
    1059          26 :       CALL dbt_batched_contract_finalize(t_3c_4)
    1060          26 :       CALL dbt_batched_contract_finalize(t_3c_5)
    1061          26 :       CALL dbt_batched_contract_finalize(t_3c_6)
    1062          26 :       CALL dbt_batched_contract_finalize(t_3c_7)
    1063          26 :       CALL dbt_batched_contract_finalize(t_3c_8)
    1064          26 :       CALL dbt_batched_contract_finalize(t_3c_sparse)
    1065             : 
    1066             :       !Calculate the 2c and 3c contributions to the virial
    1067          26 :       IF (use_virial) THEN
    1068           2 :          CALL dbt_copy(force_data%t_3c_virial_split, force_data%t_3c_virial, move_data=.TRUE.)
    1069             :          CALL calc_3c_virial(work_virial, force_data%t_3c_virial, 1.0_dp, qs_env, force_data%nl_3c, &
    1070             :                              basis_set_ri_aux, basis_set_ao, basis_set_ao, mp2_env%ri_metric, &
    1071           2 :                              der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1)
    1072             : 
    1073             :          CALL calc_2c_virial(work_virial, force_data%RI_virial_met, 1.0_dp, qs_env, force_data%nl_2c_met, &
    1074           2 :                              basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
    1075           2 :          CALL dbcsr_clear(force_data%RI_virial_met)
    1076             : 
    1077           2 :          IF (.NOT. force_data%do_periodic) THEN
    1078             :             CALL calc_2c_virial(work_virial, force_data%RI_virial_pot, 1.0_dp, qs_env, force_data%nl_2c_pot, &
    1079           0 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
    1080           0 :             CALL dbcsr_clear(force_data%RI_virial_pot)
    1081             :          END IF
    1082             : 
    1083           2 :          identity_pot%potential_type = do_potential_id
    1084             :          CALL calc_2c_virial(work_virial_ovlp, virial_ovlp, 1.0_dp, qs_env, force_data%nl_2c_ovlp, &
    1085           2 :                              basis_set_ao, basis_set_ao, identity_pot)
    1086           2 :          CALL dbcsr_release(virial_ovlp)
    1087             : 
    1088           8 :          DO k_xyz = 1, 3
    1089          26 :             DO j_xyz = 1, 3
    1090          78 :                DO i_xyz = 1, 3
    1091             :                   virial%pv_mp2(i_xyz, j_xyz) = virial%pv_mp2(i_xyz, j_xyz) &
    1092          54 :                                                 - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1093             :                   virial%pv_overlap(i_xyz, j_xyz) = virial%pv_overlap(i_xyz, j_xyz) &
    1094          54 :                                                     - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1095             :                   virial%pv_virial(i_xyz, j_xyz) = virial%pv_virial(i_xyz, j_xyz) &
    1096             :                                                    - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz) &
    1097          72 :                                                    - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1098             :                END DO
    1099             :             END DO
    1100             :          END DO
    1101             :       END IF
    1102             : 
    1103             :       !Calculate the periodic contributions of (P|Q) to the force and the virial
    1104          26 :       work_virial = 0.0_dp
    1105          26 :       IF (force_data%do_periodic) THEN
    1106          10 :          IF (mp2_env%eri_method == do_eri_gpw) THEN
    1107           6 :             CALL get_2c_gpw_forces(force_data%G_PQ, force, work_virial, use_virial, mp2_env, qs_env)
    1108           4 :          ELSE IF (mp2_env%eri_method == do_eri_mme) THEN
    1109           4 :             CALL get_2c_mme_forces(force_data%G_PQ, force, mp2_env, qs_env)
    1110           4 :             IF (use_virial) CPABORT("Stress tensor not available with MME intrgrals")
    1111             :          ELSE
    1112           0 :             CPABORT("Periodic case not possible with OS integrals")
    1113             :          END IF
    1114          10 :          CALL dbcsr_clear(force_data%G_PQ)
    1115             :       END IF
    1116             : 
    1117          26 :       IF (use_virial) THEN
    1118          26 :          virial%pv_mp2 = virial%pv_mp2 + work_virial
    1119          26 :          virial%pv_virial = virial%pv_virial + work_virial
    1120           2 :          virial%pv_calculate = .FALSE.
    1121             : 
    1122           6 :          DO ibasis = 1, SIZE(basis_set_ao)
    1123           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1124           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
    1125           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1126           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
    1127             :          END DO
    1128             :       END IF
    1129             : 
    1130             :       !clean-up
    1131          26 :       IF (ASSOCIATED(dummy_ptr)) DEALLOCATE (dummy_ptr)
    1132          60 :       DO ispin = 1, nspins
    1133          60 :          CALL dbt_destroy(t_P(ispin))
    1134             :       END DO
    1135          26 :       CALL dbt_destroy(t_3c_0)
    1136          26 :       CALL dbt_destroy(t_3c_1)
    1137          26 :       CALL dbt_destroy(t_3c_3)
    1138          26 :       CALL dbt_destroy(t_3c_4)
    1139          26 :       CALL dbt_destroy(t_3c_5)
    1140          26 :       CALL dbt_destroy(t_3c_6)
    1141          26 :       CALL dbt_destroy(t_3c_7)
    1142          26 :       CALL dbt_destroy(t_3c_8)
    1143          26 :       CALL dbt_destroy(t_3c_sparse)
    1144          26 :       CALL dbt_destroy(t_3c_help_1)
    1145          26 :       CALL dbt_destroy(t_3c_help_2)
    1146          26 :       CALL dbt_destroy(t_3c_ints)
    1147          26 :       CALL dbt_destroy(t_3c_work)
    1148          26 :       CALL dbt_destroy(t_R_occ)
    1149          26 :       CALL dbt_destroy(t_R_virt)
    1150          26 :       CALL dbt_destroy(t_dm_occ)
    1151          26 :       CALL dbt_destroy(t_dm_virt)
    1152          26 :       CALL dbt_destroy(t_Q)
    1153          26 :       CALL dbt_destroy(t_KQKT)
    1154          26 :       CALL dbt_destroy(t_M_occ)
    1155          26 :       CALL dbt_destroy(t_M_virt)
    1156          26 :       CALL dbcsr_release(R_occ)
    1157          26 :       CALL dbcsr_release(R_virt)
    1158          26 :       CALL dbcsr_release(dbcsr_work1)
    1159          26 :       CALL dbcsr_release(dbcsr_work2)
    1160          26 :       CALL dbcsr_release(dbcsr_work3)
    1161          26 :       CALL dbcsr_release(exp_occ)
    1162          26 :       CALL dbcsr_release(exp_virt)
    1163             : 
    1164          26 :       CALL dbt_destroy(t_2c_RI)
    1165          26 :       CALL dbt_destroy(t_2c_RI_2)
    1166          26 :       CALL dbt_destroy(t_2c_AO)
    1167          26 :       CALL dbcsr_deallocate_matrix_set(mat_dm_occ)
    1168          26 :       CALL dbcsr_deallocate_matrix_set(mat_dm_virt)
    1169             : 
    1170          26 :       CALL timestop(handle)
    1171             : 
    1172         138 :    END SUBROUTINE calc_laplace_loop_forces
    1173             : 
    1174             : ! **************************************************************************************************
    1175             : !> \brief Updates the cubic-scaling RPA contribution to the forces at each quadrature point. This
    1176             : !>        routine is adapted from the corresponding Laplace SOS-MP2 loop force one.
    1177             : !> \param force_data ...
    1178             : !> \param mat_P_omega ...
    1179             : !> \param t_3c_M ...
    1180             : !> \param t_3c_O ...
    1181             : !> \param t_3c_O_compressed ...
    1182             : !> \param t_3c_O_ind ...
    1183             : !> \param fm_scaled_dm_occ_tau ...
    1184             : !> \param fm_scaled_dm_virt_tau ...
    1185             : !> \param fm_mo_coeff_occ ...
    1186             : !> \param fm_mo_coeff_virt ...
    1187             : !> \param fm_mo_coeff_occ_scaled ...
    1188             : !> \param fm_mo_coeff_virt_scaled ...
    1189             : !> \param starts_array_mc ...
    1190             : !> \param ends_array_mc ...
    1191             : !> \param starts_array_mc_block ...
    1192             : !> \param ends_array_mc_block ...
    1193             : !> \param num_integ_points ...
    1194             : !> \param nmo ...
    1195             : !> \param Eigenval ...
    1196             : !> \param e_fermi ...
    1197             : !> \param weights_cos_tf_t_to_w ...
    1198             : !> \param weights_cos_tf_w_to_t ...
    1199             : !> \param tj ...
    1200             : !> \param wj ...
    1201             : !> \param tau_tj ...
    1202             : !> \param cut_memory ...
    1203             : !> \param ispin ...
    1204             : !> \param open_shell ...
    1205             : !> \param unit_nr ...
    1206             : !> \param dbcsr_time ...
    1207             : !> \param dbcsr_nflop ...
    1208             : !> \param mp2_env ...
    1209             : !> \param qs_env ...
    1210             : ! **************************************************************************************************
    1211         180 :    SUBROUTINE calc_rpa_loop_forces(force_data, mat_P_omega, t_3c_M, t_3c_O, t_3c_O_compressed, &
    1212          36 :                                    t_3c_O_ind, fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, &
    1213          36 :                                    fm_mo_coeff_occ, fm_mo_coeff_virt, fm_mo_coeff_occ_scaled, &
    1214          36 :                                    fm_mo_coeff_virt_scaled, starts_array_mc, ends_array_mc, &
    1215          36 :                                    starts_array_mc_block, ends_array_mc_block, num_integ_points, &
    1216          36 :                                    nmo, Eigenval, e_fermi, weights_cos_tf_t_to_w, weights_cos_tf_w_to_t, &
    1217          36 :                                    tj, wj, tau_tj, cut_memory, ispin, open_shell, unit_nr, dbcsr_time, &
    1218             :                                    dbcsr_nflop, mp2_env, qs_env)
    1219             : 
    1220             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1221             :       TYPE(dbcsr_p_type), DIMENSION(:, :), INTENT(INOUT) :: mat_P_omega
    1222             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_3c_M, t_3c_O
    1223             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
    1224             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
    1225             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_scaled_dm_occ_tau, &
    1226             :                                                             fm_scaled_dm_virt_tau
    1227             :       TYPE(cp_fm_type), DIMENSION(:), INTENT(IN)         :: fm_mo_coeff_occ, fm_mo_coeff_virt
    1228             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_mo_coeff_occ_scaled, &
    1229             :                                                             fm_mo_coeff_virt_scaled
    1230             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
    1231             :                                                             starts_array_mc_block, &
    1232             :                                                             ends_array_mc_block
    1233             :       INTEGER, INTENT(IN)                                :: num_integ_points, nmo
    1234             :       REAL(KIND=dp), DIMENSION(:, :), INTENT(IN)         :: Eigenval
    1235             :       REAL(KIND=dp), INTENT(IN)                          :: e_fermi
    1236             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
    1237             :          INTENT(IN)                                      :: weights_cos_tf_t_to_w, &
    1238             :                                                             weights_cos_tf_w_to_t
    1239             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
    1240             :          INTENT(IN)                                      :: tj, wj
    1241             :       REAL(KIND=dp), DIMENSION(0:num_integ_points), &
    1242             :          INTENT(IN)                                      :: tau_tj
    1243             :       INTEGER, INTENT(IN)                                :: cut_memory, ispin
    1244             :       LOGICAL, INTENT(IN)                                :: open_shell
    1245             :       INTEGER, INTENT(IN)                                :: unit_nr
    1246             :       REAL(dp), INTENT(INOUT)                            :: dbcsr_time
    1247             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
    1248             :       TYPE(mp2_type)                                     :: mp2_env
    1249             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1250             : 
    1251             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'calc_rpa_loop_forces'
    1252             : 
    1253             :       INTEGER :: dummy_int, handle, handle2, i_mem, i_xyz, ibasis, iquad, j_xyz, jquad, k_xyz, &
    1254             :          n_mem_RI, n_rep, natom, nkind, nspins, unit_nr_dbcsr
    1255             :       INTEGER(int_8)                                     :: flop, nze, nze_ddint, nze_der_AO, &
    1256             :                                                             nze_der_RI, nze_KBK
    1257          36 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, batch_blk_end, &
    1258          36 :                                                             batch_blk_start, batch_end_RI, &
    1259          36 :                                                             batch_start_RI, kind_of, mc_ranges, &
    1260          36 :                                                             mc_ranges_RI
    1261          36 :       INTEGER, DIMENSION(:, :), POINTER                  :: dummy_ptr
    1262             :       LOGICAL                                            :: memory_info, use_virial
    1263             :       REAL(dp) :: eps_filter, eps_pgf_orb, eps_pgf_orb_old, fac, occ, occ_ddint, occ_der_AO, &
    1264             :          occ_der_RI, occ_KBK, omega, pref, spin_fac, t1, t2, tau, weight
    1265             :       REAL(dp), DIMENSION(3, 3)                          :: work_virial, work_virial_ovlp
    1266          36 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    1267             :       TYPE(cell_type), POINTER                           :: cell
    1268             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
    1269          36 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: mat_P_tau, matrix_ks, matrix_s
    1270          36 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: mat_dm_occ, mat_dm_virt
    1271             :       TYPE(dbcsr_type)                                   :: dbcsr_work1, dbcsr_work2, dbcsr_work3, &
    1272             :                                                             dbcsr_work_symm, exp_occ, exp_virt, &
    1273             :                                                             R_occ, R_virt, virial_ovlp, Y_1, Y_2
    1274        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, &
    1275        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, &
    1276        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
    1277          36 :       TYPE(dbt_type), ALLOCATABLE, DIMENSION(:)          :: t_B
    1278             :       TYPE(dft_control_type), POINTER                    :: dft_control
    1279             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    1280          36 :          DIMENSION(:), TARGET                            :: basis_set_ao, basis_set_ri_aux
    1281             :       TYPE(gto_basis_set_type), POINTER                  :: orb_basis, ri_basis
    1282             :       TYPE(libint_potential_type)                        :: identity_pot
    1283             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1284          36 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    1285          36 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1286          36 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    1287             :       TYPE(section_vals_type), POINTER                   :: qs_section
    1288             :       TYPE(virial_type), POINTER                         :: virial
    1289             : 
    1290          36 :       NULLIFY (matrix_s, dummy_ptr, atomic_kind_set, force, matrix_s, matrix_ks, mat_dm_occ, mat_dm_virt)
    1291          36 :       NULLIFY (dft_control, virial, particle_set, cell, blacs_env, para_env, orb_basis, ri_basis)
    1292          36 :       NULLIFY (qs_kind_set)
    1293             : 
    1294          36 :       CALL timeset(routineN, handle)
    1295             : 
    1296             :       CALL get_qs_env(qs_env, matrix_s=matrix_s, natom=natom, atomic_kind_set=atomic_kind_set, &
    1297             :                       force=force, matrix_ks=matrix_ks, dft_control=dft_control, virial=virial, &
    1298             :                       particle_set=particle_set, cell=cell, blacs_env=blacs_env, para_env=para_env, &
    1299          36 :                       qs_kind_set=qs_kind_set, nkind=nkind)
    1300          36 :       eps_filter = mp2_env%ri_rpa_im_time%eps_filter
    1301          36 :       nspins = dft_control%nspins
    1302             : 
    1303          36 :       memory_info = mp2_env%ri_rpa_im_time%memory_info
    1304          36 :       IF (memory_info) THEN
    1305           0 :          unit_nr_dbcsr = unit_nr
    1306             :       ELSE
    1307          36 :          unit_nr_dbcsr = 0
    1308             :       END IF
    1309             : 
    1310          36 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
    1311             : 
    1312          36 :       IF (use_virial) virial%pv_calculate = .TRUE.
    1313             : 
    1314          36 :       IF (use_virial) THEN
    1315           2 :          qs_section => section_vals_get_subs_vals(qs_env%input, "DFT%QS")
    1316           2 :          CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", n_rep_val=n_rep)
    1317           2 :          IF (n_rep /= 0) THEN
    1318           0 :             CALL section_vals_val_get(qs_section, "EPS_PGF_ORB", r_val=eps_pgf_orb)
    1319             :          ELSE
    1320           2 :             CALL section_vals_val_get(qs_section, "EPS_DEFAULT", r_val=eps_pgf_orb)
    1321           2 :             eps_pgf_orb = SQRT(eps_pgf_orb)
    1322             :          END IF
    1323           2 :          eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
    1324             : 
    1325          16 :          ALLOCATE (basis_set_ri_aux(nkind), basis_set_ao(nkind))
    1326           2 :          CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    1327           2 :          CALL basis_set_list_setup(basis_set_ao, "ORB", qs_kind_set)
    1328             : 
    1329           8 :          DO ibasis = 1, SIZE(basis_set_ao)
    1330           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1331           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb)
    1332           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1333           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb)
    1334             :          END DO
    1335             :       END IF
    1336             : 
    1337             :       !We follow the general logic of the compute_mat_P_omega routine
    1338          36 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI)
    1339          36 :       CALL dbt_create(force_data%t_2c_K, t_2c_RI_2)
    1340          36 :       CALL dbt_create(force_data%t_2c_der_ovlp(1), t_2c_AO)
    1341             : 
    1342          36 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    1343             : 
    1344             :       ! Always do the batching of the MO on mu and sigma, such that it is consistent between
    1345             :       ! the occupied and the virtual quantities
    1346         108 :       ALLOCATE (mc_ranges(cut_memory + 1))
    1347         108 :       mc_ranges(:cut_memory) = starts_array_mc_block(:)
    1348          36 :       mc_ranges(cut_memory + 1) = ends_array_mc_block(cut_memory) + 1
    1349             : 
    1350             :       ! Also need some batching on the RI, because it loses sparsity at some point
    1351          36 :       n_mem_RI = cut_memory
    1352             :       CALL create_tensor_batches(force_data%bsizes_RI_split, n_mem_RI, batch_start_RI, batch_end_RI, &
    1353          36 :                                  batch_blk_start, batch_blk_end)
    1354         108 :       ALLOCATE (mc_ranges_RI(n_mem_RI + 1))
    1355         108 :       mc_ranges_RI(1:n_mem_RI) = batch_blk_start(1:n_mem_RI)
    1356          36 :       mc_ranges_RI(n_mem_RI + 1) = batch_blk_end(n_mem_RI) + 1
    1357          36 :       DEALLOCATE (batch_blk_start, batch_blk_end)
    1358             : 
    1359             :       !Pre-allocate all required tensors and matrices
    1360          36 :       CALL dbt_create(t_2c_RI, t_P)
    1361          36 :       CALL dbt_create(t_2c_RI, t_KBKT)
    1362          36 :       CALL dbt_create(t_2c_AO, t_dm_occ)
    1363          36 :       CALL dbt_create(t_2c_AO, t_dm_virt)
    1364             : 
    1365             :       !note: t_3c_O and t_3c_M have different mappings (map_1d, map_2d)
    1366          36 :       CALL dbt_create(t_3c_O, t_M_occ)
    1367          36 :       CALL dbt_create(t_3c_O, t_M_virt)
    1368          36 :       CALL dbt_create(t_3c_O, t_3c_0)
    1369             : 
    1370          36 :       CALL dbt_create(t_3c_O, t_3c_1)
    1371          36 :       CALL dbt_create(t_3c_O, t_3c_3)
    1372          36 :       CALL dbt_create(t_3c_O, t_3c_4)
    1373          36 :       CALL dbt_create(t_3c_O, t_3c_5)
    1374          36 :       CALL dbt_create(t_3c_M, t_3c_6)
    1375          36 :       CALL dbt_create(t_3c_M, t_3c_7)
    1376          36 :       CALL dbt_create(t_3c_M, t_3c_8)
    1377          36 :       CALL dbt_create(t_3c_M, t_3c_sparse)
    1378          36 :       CALL dbt_create(t_3c_O, t_3c_help_1)
    1379          36 :       CALL dbt_create(t_3c_O, t_3c_help_2)
    1380          36 :       CALL dbt_create(t_2c_AO, t_R_occ)
    1381          36 :       CALL dbt_create(t_2c_AO, t_R_virt)
    1382          36 :       CALL dbt_create(t_3c_M, t_3c_ints)
    1383          36 :       CALL dbt_create(t_3c_M, t_3c_work)
    1384             : 
    1385             :       !Before entring the loop, need to compute the 2c tensors B = (1 + Q(w))^-1 - 1, for each
    1386             :       !frequency grid point, before doing the transformation to the time grid
    1387         416 :       ALLOCATE (t_B(num_integ_points))
    1388         128 :       DO jquad = 1, num_integ_points
    1389         128 :          CALL dbt_create(t_2c_RI, t_B(jquad))
    1390             :       END DO
    1391             : 
    1392         200 :       ALLOCATE (mat_P_tau(num_integ_points))
    1393         128 :       DO jquad = 1, num_integ_points
    1394          92 :          ALLOCATE (mat_P_tau(jquad)%matrix)
    1395         128 :          CALL dbcsr_create(mat_P_tau(jquad)%matrix, template=mat_P_omega(jquad, ispin)%matrix)
    1396             :       END DO
    1397             : 
    1398          36 :       CALL dbcsr_create(dbcsr_work_symm, template=force_data%G_PQ, matrix_type=dbcsr_type_symmetric)
    1399          36 :       CALL dbt_create(dbcsr_work_symm, t_2c_tmp)
    1400             : 
    1401             :       !loop over freqeuncies
    1402         128 :       DO iquad = 1, num_integ_points
    1403          92 :          omega = tj(iquad)
    1404             : 
    1405             :          !calculate (1 + Q(w))^-1 - 1 for the given freq.
    1406             :          !Always take spin alpha (get 2*alpha in closed shell, and alpha+beta in open-shell)
    1407          92 :          CALL dbcsr_copy(dbcsr_work_symm, mat_P_omega(iquad, 1)%matrix)
    1408          92 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work_symm, t_2c_tmp)
    1409          92 :          CALL dbt_copy(t_2c_tmp, t_2c_RI, move_data=.TRUE.)
    1410             : 
    1411             :          CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_2c_RI_2, &
    1412             :                            contract_1=[2], notcontract_1=[1], &
    1413             :                            contract_2=[1], notcontract_2=[2], &
    1414             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1415          92 :                            flop=flop, unit_nr=unit_nr_dbcsr)
    1416          92 :          dbcsr_nflop = dbcsr_nflop + flop
    1417             :          CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_2c_RI_2, 0.0_dp, t_2c_RI, &
    1418             :                            contract_1=[1], notcontract_1=[2], &
    1419             :                            contract_2=[1], notcontract_2=[2], &
    1420             :                            map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1421          92 :                            flop=flop, unit_nr=unit_nr_dbcsr)
    1422          92 :          CALL dbt_copy(t_2c_RI, t_2c_tmp, move_data=.TRUE.)
    1423          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, dbcsr_work_symm)
    1424          92 :          CALL dbcsr_add_on_diag(dbcsr_work_symm, 1.0_dp)
    1425             : 
    1426          92 :          CALL cp_dbcsr_cholesky_decompose(dbcsr_work_symm, para_env=para_env, blacs_env=blacs_env)
    1427          92 :          CALL cp_dbcsr_cholesky_invert(dbcsr_work_symm, para_env=para_env, blacs_env=blacs_env, uplo_to_full=.TRUE.)
    1428             : 
    1429          92 :          CALL dbcsr_add_on_diag(dbcsr_work_symm, -1.0_dp)
    1430             : 
    1431         372 :          DO jquad = 1, num_integ_points
    1432         244 :             tau = tau_tj(jquad)
    1433             : 
    1434             :             !the P matrix to time.
    1435         244 :             weight = weights_cos_tf_w_to_t(jquad, iquad)*COS(tau*omega)
    1436         244 :             IF (open_shell) THEN
    1437          64 :                IF (ispin == 1) THEN
    1438             :                   !mat_P_omega contains the sum of alpha and beta spin => we only want alpha
    1439          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 1)%matrix, 1.0_dp, weight)
    1440          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 2)%matrix, 1.0_dp, -weight)
    1441             :                ELSE
    1442          32 :                   CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 2)%matrix, 1.0_dp, weight)
    1443             :                END IF
    1444             :             ELSE
    1445             :                !factor 0.5 because originam matrix Q is scaled by 2 in RPA (spin)
    1446         180 :                weight = 0.5_dp*weight
    1447         180 :                CALL dbcsr_add(mat_P_tau(jquad)%matrix, mat_P_omega(iquad, 1)%matrix, 1.0_dp, weight)
    1448             :             END IF
    1449             : 
    1450             :             !convert B matrix to time
    1451         244 :             weight = weights_cos_tf_t_to_w(iquad, jquad)*COS(tau*omega)*wj(iquad)
    1452         244 :             CALL dbt_copy_matrix_to_tensor(dbcsr_work_symm, t_2c_tmp)
    1453         244 :             CALL dbt_scale(t_2c_tmp, weight)
    1454         336 :             CALL dbt_copy(t_2c_tmp, t_B(jquad), summation=.TRUE., move_data=.TRUE.)
    1455             :          END DO
    1456             :       END DO
    1457          36 :       CALL dbt_destroy(t_2c_tmp)
    1458          36 :       CALL dbcsr_release(dbcsr_work_symm)
    1459          36 :       CALL dbt_clear(t_2c_RI)
    1460          36 :       CALL dbt_clear(t_2c_RI_2)
    1461             : 
    1462             :       !Pre-define the sparsity of t_3c_4 as a function of the derivatives
    1463          36 :       occ_der_AO = 0; nze_der_AO = 0
    1464          36 :       occ_der_RI = 0; nze_der_RI = 0
    1465         144 :       DO i_xyz = 1, 3
    1466         360 :          DO i_mem = 1, cut_memory
    1467             :             CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(i_mem, i_xyz)%ind, &
    1468         216 :                                    force_data%t_3c_der_RI_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    1469         216 :             CALL get_tensor_occupancy(force_data%t_3c_der_RI(i_xyz), nze, occ)
    1470         216 :             occ_der_RI = occ_der_RI + occ
    1471         216 :             nze_der_RI = nze_der_RI + nze
    1472         216 :             CALL dbt_copy(force_data%t_3c_der_RI(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
    1473             : 
    1474             :             CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(i_mem, i_xyz)%ind, &
    1475         216 :                                    force_data%t_3c_der_AO_comp(i_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    1476         216 :             CALL get_tensor_occupancy(force_data%t_3c_der_AO(i_xyz), nze, occ)
    1477         216 :             occ_der_AO = occ_der_AO + occ
    1478         216 :             nze_der_AO = nze_der_AO + nze
    1479         216 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, order=[1, 3, 2], summation=.TRUE.)
    1480         756 :             CALL dbt_copy(force_data%t_3c_der_AO(i_xyz), t_3c_sparse, summation=.TRUE., move_data=.TRUE.)
    1481             :          END DO
    1482             :       END DO
    1483          36 :       occ_der_RI = occ_der_RI/3.0_dp
    1484          36 :       occ_der_AO = occ_der_AO/3.0_dp
    1485          36 :       nze_der_RI = nze_der_RI/3
    1486          36 :       nze_der_AO = nze_der_AO/3
    1487             : 
    1488          36 :       CALL dbcsr_create(R_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1489          36 :       CALL dbcsr_create(R_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1490          36 :       CALL dbcsr_create(dbcsr_work_symm, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_symmetric)
    1491          36 :       CALL dbcsr_create(dbcsr_work1, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1492          36 :       CALL dbcsr_create(dbcsr_work2, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1493          36 :       CALL dbcsr_create(dbcsr_work3, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1494          36 :       CALL dbcsr_create(exp_occ, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1495          36 :       CALL dbcsr_create(exp_virt, template=matrix_s(1)%matrix, matrix_type=dbcsr_type_no_symmetry)
    1496          36 :       IF (use_virial) CALL dbcsr_create(virial_ovlp, template=dbcsr_work1)
    1497             : 
    1498          36 :       CALL dbt_batched_contract_init(t_3c_0, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
    1499          36 :       CALL dbt_batched_contract_init(t_3c_1, batch_range_2=mc_ranges, batch_range_3=mc_ranges)
    1500          36 :       CALL dbt_batched_contract_init(t_3c_3, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1501          36 :       CALL dbt_batched_contract_init(t_M_occ, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1502          36 :       CALL dbt_batched_contract_init(t_M_virt, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1503             : 
    1504          36 :       CALL dbt_batched_contract_init(t_3c_ints, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1505          36 :       CALL dbt_batched_contract_init(t_3c_work, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges)
    1506             : 
    1507             :       CALL dbt_batched_contract_init(t_3c_4, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1508          36 :                                      batch_range_3=mc_ranges)
    1509             :       CALL dbt_batched_contract_init(t_3c_5, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1510          36 :                                      batch_range_3=mc_ranges)
    1511             :       CALL dbt_batched_contract_init(t_3c_6, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1512          36 :                                      batch_range_3=mc_ranges)
    1513             :       CALL dbt_batched_contract_init(t_3c_7, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1514          36 :                                      batch_range_3=mc_ranges)
    1515             :       CALL dbt_batched_contract_init(t_3c_8, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1516          36 :                                      batch_range_3=mc_ranges)
    1517             :       CALL dbt_batched_contract_init(t_3c_sparse, batch_range_1=mc_ranges_RI, batch_range_2=mc_ranges, &
    1518          36 :                                      batch_range_3=mc_ranges)
    1519             : 
    1520          36 :       fac = 1.0_dp/fourpi*mp2_env%ri_rpa%scale_rpa
    1521          36 :       IF (open_shell) fac = 0.5_dp*fac
    1522             : 
    1523          36 :       work_virial = 0.0_dp
    1524          36 :       work_virial_ovlp = 0.0_dp
    1525         128 :       DO jquad = 1, num_integ_points
    1526          92 :          tau = tau_tj(jquad)
    1527          92 :          occ_ddint = 0; nze_ddint = 0
    1528             : 
    1529          92 :          CALL para_env%sync()
    1530          92 :          t1 = m_walltime()
    1531             : 
    1532             :          !Deal with the force contributions where there is no explicit 3-center quantities, i.e. the
    1533             :          !forces due to the metric and potential derivatives
    1534          92 :          CALL dbt_create(mat_P_tau(jquad)%matrix, t_2c_tmp)
    1535          92 :          CALL dbt_copy_matrix_to_tensor(mat_P_tau(jquad)%matrix, t_2c_tmp)
    1536          92 :          CALL dbt_copy(t_2c_tmp, t_P, move_data=.TRUE.)
    1537          92 :          CALL dbt_filter(t_P, eps_filter)
    1538          92 :          CALL dbt_destroy(t_2c_tmp)
    1539             : 
    1540             :          CALL perform_2c_ops(force, t_KBKT, force_data, fac, t_B(jquad), t_P, t_2c_RI, t_2c_RI_2, &
    1541          92 :                              use_virial, atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
    1542          92 :          CALL get_tensor_occupancy(t_KBKT, nze_KBK, occ_KBK)
    1543             : 
    1544             :          !Calculate the pseudo-density matrix in tensor form. There are a few useless arguments for SOS-MP2
    1545             :          CALL compute_mat_dm_global(fm_scaled_dm_occ_tau, fm_scaled_dm_virt_tau, tau_tj, num_integ_points, &
    1546             :                                     nmo, fm_mo_coeff_occ(ispin), fm_mo_coeff_virt(ispin), &
    1547             :                                     fm_mo_coeff_occ_scaled, fm_mo_coeff_virt_scaled, mat_dm_occ, mat_dm_virt, &
    1548             :                                     matrix_s, ispin, Eigenval(:, ispin), e_fermi, eps_filter, &
    1549             :                                     mp2_env%ri_rpa_im_time%memory_info, unit_nr, &
    1550          92 :                                     jquad, .FALSE., .FALSE., qs_env, dummy_int, dummy_ptr, para_env)
    1551             : 
    1552          92 :          CALL dbt_create(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
    1553          92 :          CALL dbt_copy_matrix_to_tensor(mat_dm_occ(jquad, 1)%matrix, t_2c_tmp)
    1554          92 :          CALL dbt_copy(t_2c_tmp, t_dm_occ, move_data=.TRUE.)
    1555          92 :          CALL dbt_filter(t_dm_occ, eps_filter)
    1556          92 :          CALL dbt_destroy(t_2c_tmp)
    1557             : 
    1558          92 :          CALL dbt_create(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
    1559          92 :          CALL dbt_copy_matrix_to_tensor(mat_dm_virt(jquad, 1)%matrix, t_2c_tmp)
    1560          92 :          CALL dbt_copy(t_2c_tmp, t_dm_virt, move_data=.TRUE.)
    1561          92 :          CALL dbt_filter(t_dm_virt, eps_filter)
    1562          92 :          CALL dbt_destroy(t_2c_tmp)
    1563             : 
    1564             :          !Deal with the 3-center quantities.
    1565             :          CALL perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
    1566             :                              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, &
    1567             :                              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, &
    1568             :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
    1569             :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
    1570             :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
    1571          92 :                              unit_nr_dbcsr, mp2_env)
    1572             : 
    1573          92 :          CALL timeset(routineN//"_dbcsr", handle2)
    1574             :          !We go back to DBCSR matrices from now on
    1575             :          !Note: R matrices are in fact symmetric, but use a normal type for convenience
    1576          92 :          CALL dbt_create(matrix_s(1)%matrix, t_2c_tmp)
    1577          92 :          CALL dbt_copy(t_R_occ, t_2c_tmp, move_data=.TRUE.)
    1578          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_occ)
    1579             : 
    1580          92 :          CALL dbt_copy(t_R_virt, t_2c_tmp, move_data=.TRUE.)
    1581          92 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, R_virt)
    1582             : 
    1583             :          !Iteratively calculate the Y1 and Y2 matrices
    1584          92 :          CALL dbcsr_copy(dbcsr_work_symm, matrix_ks(ispin)%matrix)
    1585          92 :          CALL dbcsr_add(dbcsr_work_symm, matrix_s(1)%matrix, 1.0_dp, -e_fermi)
    1586             :          CALL dbcsr_multiply('N', 'N', tau, force_data%P_occ(ispin)%matrix, &
    1587          92 :                              dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1588          92 :          CALL build_Y_matrix(Y_1, dbcsr_work1, force_data%P_occ(ispin)%matrix, R_virt, eps_filter)
    1589          92 :          CALL matrix_exponential(exp_occ, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
    1590             : 
    1591             :          CALL dbcsr_multiply('N', 'N', -tau, force_data%P_virt(ispin)%matrix, &
    1592          92 :                              dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1593          92 :          CALL build_Y_matrix(Y_2, dbcsr_work1, force_data%P_virt(ispin)%matrix, R_occ, eps_filter)
    1594          92 :          CALL matrix_exponential(exp_virt, dbcsr_work1, 1.0_dp, 1.0_dp, eps_filter)
    1595             : 
    1596             :          !The force contribution coming from [-S^-1*(e^-tau*P_virt*F)^T*R_occ*S^-1
    1597             :          !                                    +tau*S^-1*Y_2^T*F*S^-1] * der_S
    1598             :          !as well as -tau*e_fermi*Y_1*P^occ + tau*e_fermi*Y_2*P^virt
    1599          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, R_occ, force_data%inv_ovlp, 0.0_dp, dbcsr_work1)
    1600          92 :          CALL dbcsr_multiply('T', 'N', 1.0_dp, exp_virt, dbcsr_work1, 0.0_dp, dbcsr_work3)
    1601          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, force_data%inv_ovlp, dbcsr_work3, 0.0_dp, dbcsr_work2)
    1602             : 
    1603          92 :          CALL dbcsr_multiply('N', 'T', tau, force_data%inv_ovlp, Y_2, 0.0_dp, dbcsr_work3)
    1604          92 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, dbcsr_work3, dbcsr_work_symm, 0.0_dp, dbcsr_work1)
    1605          92 :          CALL dbcsr_multiply('N', 'N', -1.0_dp, dbcsr_work1, force_data%inv_ovlp, 1.0_dp, dbcsr_work2)
    1606             : 
    1607          92 :          CALL dbcsr_multiply('N', 'T', tau*e_fermi, force_data%P_occ(ispin)%matrix, Y_1, 1.0_dp, dbcsr_work2)
    1608          92 :          CALL dbcsr_multiply('N', 'T', -tau*e_fermi, force_data%P_virt(ispin)%matrix, Y_2, 1.0_dp, dbcsr_work2)
    1609             : 
    1610          92 :          CALL dbt_copy_matrix_to_tensor(dbcsr_work2, t_2c_tmp)
    1611          92 :          CALL dbt_copy(t_2c_tmp, t_2c_AO, move_data=.TRUE.)
    1612             : 
    1613          92 :          pref = -1.0_dp*fac
    1614             :          CALL get_2c_der_force(force, t_2c_AO, force_data%t_2c_der_ovlp, atom_of_kind, &
    1615          92 :                                kind_of, force_data%idx_to_at_AO, pref, do_ovlp=.TRUE.)
    1616             : 
    1617          92 :          IF (use_virial) CALL dbcsr_add(virial_ovlp, dbcsr_work2, 1.0_dp, pref)
    1618             : 
    1619             :          !The final contribution from Tr[(tau*Y_1*P_occ - tau*Y_2*P_virt) * der_F]
    1620             :          CALL dbcsr_multiply('N', 'N', fac*tau, Y_1, force_data%P_occ(ispin)%matrix, 1.0_dp, &
    1621          92 :                              force_data%sum_YP_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1622             :          CALL dbcsr_multiply('N', 'N', -fac*tau, Y_2, force_data%P_virt(ispin)%matrix, 1.0_dp, &
    1623          92 :                              force_data%sum_YP_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1624             : 
    1625          92 :          spin_fac = 0.5_dp*fac
    1626          92 :          IF (open_shell) spin_fac = 2.0_dp*spin_fac
    1627             :          !Build-up the RHS of the response equation.
    1628             :          CALL dbcsr_multiply('N', 'N', 1.0_dp*spin_fac, R_virt, exp_occ, 1.0_dp, &
    1629          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1630             :          CALL dbcsr_multiply('N', 'N', -1.0_dp*spin_fac, R_occ, exp_virt, 1.0_dp, &
    1631          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1632             :          CALL dbcsr_multiply('N', 'N', tau*spin_fac, dbcsr_work_symm, Y_1, 1.0_dp, &
    1633          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1634             :          CALL dbcsr_multiply('N', 'N', tau*spin_fac, dbcsr_work_symm, Y_2, 1.0_dp, &
    1635          92 :                              force_data%sum_O_tau(ispin)%matrix, retain_sparsity=.TRUE.)
    1636             : 
    1637          92 :          CALL timestop(handle2)
    1638             : 
    1639             :          !Print some info
    1640          92 :          CALL para_env%sync()
    1641          92 :          t2 = m_walltime()
    1642          92 :          dbcsr_time = dbcsr_time + t2 - t1
    1643             : 
    1644          92 :          IF (unit_nr > 0) THEN
    1645             :             WRITE (unit_nr, '(/T3,A,1X,I3,A)') &
    1646          46 :                'RPA_LOW_SCALING_INFO| Info for time point', jquad, '    (gradients)'
    1647             :             WRITE (unit_nr, '(T6,A,T56,F25.6)') &
    1648          46 :                'Time:', t2 - t1
    1649             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1650          46 :                'Occupancy of 3c AO derivs:', REAL(nze_der_AO, dp), '/', occ_der_AO*100, '%'
    1651             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1652          46 :                'Occupancy of 3c RI derivs:', REAL(nze_der_RI, dp), '/', occ_der_RI*100, '%'
    1653             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1654          46 :                'Occupancy of the Docc * Dvirt * 3c-int tensor', REAL(nze_ddint, dp), '/', occ_ddint*100, '%'
    1655             :             WRITE (unit_nr, '(T6,A,T63,ES7.1,1X,A1,1X,F7.3,A1)') &
    1656          46 :                'Occupancy of KBK^T 2c-tensor:', REAL(nze_KBK, dp), '/', occ_KBK*100, '%'
    1657          46 :             CALL m_flush(unit_nr)
    1658             :          END IF
    1659             : 
    1660             :          !intermediate clean-up
    1661          92 :          CALL dbcsr_release(Y_1)
    1662          92 :          CALL dbcsr_release(Y_2)
    1663         496 :          CALL dbt_destroy(t_2c_tmp)
    1664             : 
    1665             :       END DO !jquad
    1666             : 
    1667          36 :       CALL dbt_batched_contract_finalize(t_3c_0)
    1668          36 :       CALL dbt_batched_contract_finalize(t_3c_1)
    1669          36 :       CALL dbt_batched_contract_finalize(t_3c_3)
    1670          36 :       CALL dbt_batched_contract_finalize(t_M_occ)
    1671          36 :       CALL dbt_batched_contract_finalize(t_M_virt)
    1672             : 
    1673          36 :       CALL dbt_batched_contract_finalize(t_3c_ints)
    1674          36 :       CALL dbt_batched_contract_finalize(t_3c_work)
    1675             : 
    1676          36 :       CALL dbt_batched_contract_finalize(t_3c_4)
    1677          36 :       CALL dbt_batched_contract_finalize(t_3c_5)
    1678          36 :       CALL dbt_batched_contract_finalize(t_3c_6)
    1679          36 :       CALL dbt_batched_contract_finalize(t_3c_7)
    1680          36 :       CALL dbt_batched_contract_finalize(t_3c_8)
    1681          36 :       CALL dbt_batched_contract_finalize(t_3c_sparse)
    1682             : 
    1683             :       !Calculate the 2c and 3c contributions to the virial
    1684          36 :       IF (use_virial) THEN
    1685           2 :          CALL dbt_copy(force_data%t_3c_virial_split, force_data%t_3c_virial, move_data=.TRUE.)
    1686             :          CALL calc_3c_virial(work_virial, force_data%t_3c_virial, 1.0_dp, qs_env, force_data%nl_3c, &
    1687             :                              basis_set_ri_aux, basis_set_ao, basis_set_ao, mp2_env%ri_metric, &
    1688           2 :                              der_eps=mp2_env%ri_rpa_im_time%eps_filter, op_pos=1)
    1689             : 
    1690             :          CALL calc_2c_virial(work_virial, force_data%RI_virial_met, 1.0_dp, qs_env, force_data%nl_2c_met, &
    1691           2 :                              basis_set_ri_aux, basis_set_ri_aux, mp2_env%ri_metric)
    1692           2 :          CALL dbcsr_clear(force_data%RI_virial_met)
    1693             : 
    1694           2 :          IF (.NOT. force_data%do_periodic) THEN
    1695             :             CALL calc_2c_virial(work_virial, force_data%RI_virial_pot, 1.0_dp, qs_env, force_data%nl_2c_pot, &
    1696           0 :                                 basis_set_ri_aux, basis_set_ri_aux, mp2_env%potential_parameter)
    1697           0 :             CALL dbcsr_clear(force_data%RI_virial_pot)
    1698             :          END IF
    1699             : 
    1700           2 :          identity_pot%potential_type = do_potential_id
    1701             :          CALL calc_2c_virial(work_virial_ovlp, virial_ovlp, 1.0_dp, qs_env, force_data%nl_2c_ovlp, &
    1702           2 :                              basis_set_ao, basis_set_ao, identity_pot)
    1703           2 :          CALL dbcsr_release(virial_ovlp)
    1704             : 
    1705           8 :          DO k_xyz = 1, 3
    1706          26 :             DO j_xyz = 1, 3
    1707          78 :                DO i_xyz = 1, 3
    1708             :                   virial%pv_mp2(i_xyz, j_xyz) = virial%pv_mp2(i_xyz, j_xyz) &
    1709          54 :                                                 - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1710             :                   virial%pv_overlap(i_xyz, j_xyz) = virial%pv_overlap(i_xyz, j_xyz) &
    1711          54 :                                                     - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1712             :                   virial%pv_virial(i_xyz, j_xyz) = virial%pv_virial(i_xyz, j_xyz) &
    1713             :                                                    - work_virial(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz) &
    1714          72 :                                                    - work_virial_ovlp(i_xyz, k_xyz)*cell%hmat(j_xyz, k_xyz)
    1715             :                END DO
    1716             :             END DO
    1717             :          END DO
    1718             :       END IF
    1719             : 
    1720             :       !Calculate the periodic contributions of (P|Q) to the force and the virial
    1721          36 :       work_virial = 0.0_dp
    1722          36 :       IF (force_data%do_periodic) THEN
    1723          18 :          IF (mp2_env%eri_method == do_eri_gpw) THEN
    1724           6 :             CALL get_2c_gpw_forces(force_data%G_PQ, force, work_virial, use_virial, mp2_env, qs_env)
    1725          12 :          ELSE IF (mp2_env%eri_method == do_eri_mme) THEN
    1726          12 :             CALL get_2c_mme_forces(force_data%G_PQ, force, mp2_env, qs_env)
    1727          12 :             IF (use_virial) CPABORT("Stress tensor not available with MME intrgrals")
    1728             :          ELSE
    1729           0 :             CPABORT("Periodic case not possible with OS integrals")
    1730             :          END IF
    1731          18 :          CALL dbcsr_clear(force_data%G_PQ)
    1732             :       END IF
    1733             : 
    1734          36 :       IF (use_virial) THEN
    1735          26 :          virial%pv_mp2 = virial%pv_mp2 + work_virial
    1736          26 :          virial%pv_virial = virial%pv_virial + work_virial
    1737           2 :          virial%pv_calculate = .FALSE.
    1738             : 
    1739           6 :          DO ibasis = 1, SIZE(basis_set_ao)
    1740           4 :             orb_basis => basis_set_ao(ibasis)%gto_basis_set
    1741           4 :             CALL init_interaction_radii_orb_basis(orb_basis, eps_pgf_orb_old)
    1742           4 :             ri_basis => basis_set_ri_aux(ibasis)%gto_basis_set
    1743           6 :             CALL init_interaction_radii_orb_basis(ri_basis, eps_pgf_orb_old)
    1744             :          END DO
    1745             :       END IF
    1746             : 
    1747             :       !clean-up
    1748          36 :       IF (ASSOCIATED(dummy_ptr)) DEALLOCATE (dummy_ptr)
    1749         128 :       DO jquad = 1, num_integ_points
    1750         128 :          CALL dbt_destroy(t_B(jquad))
    1751             :       END DO
    1752          36 :       CALL dbt_destroy(t_P)
    1753          36 :       CALL dbt_destroy(t_3c_0)
    1754          36 :       CALL dbt_destroy(t_3c_1)
    1755          36 :       CALL dbt_destroy(t_3c_3)
    1756          36 :       CALL dbt_destroy(t_3c_4)
    1757          36 :       CALL dbt_destroy(t_3c_5)
    1758          36 :       CALL dbt_destroy(t_3c_6)
    1759          36 :       CALL dbt_destroy(t_3c_7)
    1760          36 :       CALL dbt_destroy(t_3c_8)
    1761          36 :       CALL dbt_destroy(t_3c_sparse)
    1762          36 :       CALL dbt_destroy(t_3c_help_1)
    1763          36 :       CALL dbt_destroy(t_3c_help_2)
    1764          36 :       CALL dbt_destroy(t_3c_ints)
    1765          36 :       CALL dbt_destroy(t_3c_work)
    1766          36 :       CALL dbt_destroy(t_R_occ)
    1767          36 :       CALL dbt_destroy(t_R_virt)
    1768          36 :       CALL dbt_destroy(t_dm_occ)
    1769          36 :       CALL dbt_destroy(t_dm_virt)
    1770          36 :       CALL dbt_destroy(t_KBKT)
    1771          36 :       CALL dbt_destroy(t_M_occ)
    1772          36 :       CALL dbt_destroy(t_M_virt)
    1773          36 :       CALL dbcsr_release(R_occ)
    1774          36 :       CALL dbcsr_release(R_virt)
    1775          36 :       CALL dbcsr_release(dbcsr_work_symm)
    1776          36 :       CALL dbcsr_release(dbcsr_work1)
    1777          36 :       CALL dbcsr_release(dbcsr_work2)
    1778          36 :       CALL dbcsr_release(dbcsr_work3)
    1779          36 :       CALL dbcsr_release(exp_occ)
    1780          36 :       CALL dbcsr_release(exp_virt)
    1781             : 
    1782          36 :       CALL dbt_destroy(t_2c_RI)
    1783          36 :       CALL dbt_destroy(t_2c_RI_2)
    1784          36 :       CALL dbt_destroy(t_2c_AO)
    1785          36 :       CALL dbcsr_deallocate_matrix_set(mat_dm_occ)
    1786          36 :       CALL dbcsr_deallocate_matrix_set(mat_dm_virt)
    1787          36 :       CALL dbcsr_deallocate_matrix_set(mat_P_tau)
    1788             : 
    1789          36 :       CALL timestop(handle)
    1790             : 
    1791         236 :    END SUBROUTINE calc_rpa_loop_forces
    1792             : 
    1793             : ! **************************************************************************************************
    1794             : !> \brief This subroutines performs the 2c tensor operations that are common accros low-scaling RPA
    1795             : !>        and SOS-MP2, including forces and virial
    1796             : !> \param force ...
    1797             : !> \param t_KBKT returns the 2c tensor product of K*B*K^T
    1798             : !> \param force_data ...
    1799             : !> \param fac ...
    1800             : !> \param t_B depending on RPA or SOS-MP2, t_B contains (1 + Q)^-1 - 1 or simply Q, respectively
    1801             : !> \param t_P ...
    1802             : !> \param t_2c_RI ...
    1803             : !> \param t_2c_RI_2 ...
    1804             : !> \param use_virial ...
    1805             : !> \param atom_of_kind ...
    1806             : !> \param kind_of ...
    1807             : !> \param eps_filter ...
    1808             : !> \param dbcsr_nflop ...
    1809             : !> \param unit_nr_dbcsr ...
    1810             : ! **************************************************************************************************
    1811         170 :    SUBROUTINE perform_2c_ops(force, t_KBKT, force_data, fac, t_B, t_P, t_2c_RI, t_2c_RI_2, use_virial, &
    1812         170 :                              atom_of_kind, kind_of, eps_filter, dbcsr_nflop, unit_nr_dbcsr)
    1813             : 
    1814             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1815             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_KBKT
    1816             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1817             :       REAL(dp), INTENT(IN)                               :: fac
    1818             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_B, t_P, t_2c_RI, t_2c_RI_2
    1819             :       LOGICAL, INTENT(IN)                                :: use_virial
    1820             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: atom_of_kind, kind_of
    1821             :       REAL(dp), INTENT(IN)                               :: eps_filter
    1822             :       INTEGER(int_8), INTENT(INOUT)                      :: dbcsr_nflop
    1823             :       INTEGER, INTENT(IN)                                :: unit_nr_dbcsr
    1824             : 
    1825             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'perform_2c_ops'
    1826             : 
    1827             :       INTEGER                                            :: handle
    1828             :       INTEGER(int_8)                                     :: flop
    1829             :       REAL(dp)                                           :: pref
    1830        2890 :       TYPE(dbt_type)                                     :: t_2c_tmp, t_2c_virial
    1831             : 
    1832         170 :       CALL timeset(routineN, handle)
    1833             : 
    1834         170 :       IF (use_virial) CALL dbt_create(force_data%RI_virial_pot, t_2c_virial)
    1835             : 
    1836             :       !P^T*K*B + P*K*B^T (note we calculate and save K*B*K^T for later, and P=P^T)
    1837             :       CALL dbt_contract(1.0_dp, force_data%t_2c_K, t_B, 0.0_dp, t_2c_RI, &
    1838             :                         contract_1=[2], notcontract_1=[1], &
    1839             :                         contract_2=[1], notcontract_2=[2], &
    1840             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1841         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1842         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1843             : 
    1844             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_KBKT, &
    1845             :                         contract_1=[2], notcontract_1=[1], &
    1846             :                         contract_2=[2], notcontract_2=[1], &
    1847             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1848         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1849         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1850             : 
    1851             :       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
    1852             :                         contract_1=[2], notcontract_1=[1], &
    1853             :                         contract_2=[1], notcontract_2=[2], &
    1854             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1855         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1856         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1857         170 :       CALL dbt_clear(t_2c_RI)
    1858             :       !t_2c_RI_2 currently holds 2*P^T*K*B = P^T*K*B + P*K*B^T (because of symmetry)
    1859             : 
    1860             :       !For the metric contribution, we need S^-1*(P^T*K*B + P*K*B^T)*K^T
    1861             :       CALL dbt_contract(1.0_dp, force_data%t_2c_inv_metric, t_2c_RI_2, 0.0_dp, t_2c_RI, &
    1862             :                         contract_1=[2], notcontract_1=[1], &
    1863             :                         contract_2=[1], notcontract_2=[2], &
    1864             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1865         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1866         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1867             : 
    1868             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_K, 0.0_dp, t_2c_RI_2, &
    1869             :                         contract_1=[2], notcontract_1=[1], &
    1870             :                         contract_2=[2], notcontract_2=[1], &
    1871             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1872         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1873         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1874             : 
    1875             :       !Here we do the trace for the force
    1876         170 :       pref = -1.0_dp*fac
    1877             :       CALL get_2c_der_force(force, t_2c_RI_2, force_data%t_2c_der_metric, atom_of_kind, &
    1878         170 :                             kind_of, force_data%idx_to_at_RI, pref, do_mp2=.TRUE.)
    1879         170 :       IF (use_virial) THEN
    1880          12 :          CALL dbt_copy(t_2c_RI_2, t_2c_virial)
    1881          12 :          CALL dbt_scale(t_2c_virial, pref)
    1882          12 :          CALL dbt_copy_tensor_to_matrix(t_2c_virial, force_data%RI_virial_met, summation=.TRUE.)
    1883          12 :          CALL dbt_clear(t_2c_virial)
    1884             :       END IF
    1885             : 
    1886             :       !For the potential contribution, we need S^-1*(P^T*K*B + P*K*B^T)*V^-0.5
    1887             :       !some of it is still in t_2c_RI: ( S^-1*(P^T*K*B + P*K*B^T) )
    1888             :       CALL dbt_contract(1.0_dp, t_2c_RI, force_data%t_2c_pot_msqrt, 0.0_dp, t_2c_RI_2, &
    1889             :                         contract_1=[2], notcontract_1=[1], &
    1890             :                         contract_2=[1], notcontract_2=[2], &
    1891             :                         map_1=[1], map_2=[2], filter_eps=eps_filter, &
    1892         170 :                         flop=flop, unit_nr=unit_nr_dbcsr)
    1893         170 :       dbcsr_nflop = dbcsr_nflop + flop
    1894             : 
    1895             :       !Here we do the trace for the force. In the periodic case, we store the matrix in G_PQ for later
    1896         170 :       pref = 0.5_dp*fac
    1897         170 :       IF (force_data%do_periodic) THEN
    1898          76 :          CALL dbt_scale(t_2c_RI_2, pref)
    1899          76 :          CALL dbt_create(force_data%G_PQ, t_2c_tmp)
    1900          76 :          CALL dbt_copy(t_2c_RI_2, t_2c_tmp, move_data=.TRUE.)
    1901          76 :          CALL dbt_copy_tensor_to_matrix(t_2c_tmp, force_data%G_PQ, summation=.TRUE.)
    1902          76 :          CALL dbt_destroy(t_2c_tmp)
    1903             :       ELSE
    1904             :          CALL get_2c_der_force(force, t_2c_RI_2, force_data%t_2c_der_pot, atom_of_kind, &
    1905          94 :                                kind_of, force_data%idx_to_at_RI, pref, do_mp2=.TRUE.)
    1906             : 
    1907          94 :          IF (use_virial) THEN
    1908           0 :             CALL dbt_copy(t_2c_RI_2, t_2c_virial)
    1909           0 :             CALL dbt_scale(t_2c_virial, pref)
    1910           0 :             CALL dbt_copy_tensor_to_matrix(t_2c_virial, force_data%RI_virial_pot, summation=.TRUE.)
    1911           0 :             CALL dbt_clear(t_2c_virial)
    1912             :          END IF
    1913             :       END IF
    1914             : 
    1915         170 :       CALL dbt_clear(t_2c_RI)
    1916         170 :       CALL dbt_clear(t_2c_RI_2)
    1917             : 
    1918         170 :       IF (use_virial) CALL dbt_destroy(t_2c_virial)
    1919             : 
    1920         170 :       CALL timestop(handle)
    1921             : 
    1922         170 :    END SUBROUTINE perform_2c_ops
    1923             : 
    1924             : ! **************************************************************************************************
    1925             : !> \brief This subroutines performs the 3c tensor operations that are common accros low-scaling RPA
    1926             : !>        and SOS-MP2, including forces and virial
    1927             : !> \param force ...
    1928             : !> \param t_R_occ ...
    1929             : !> \param t_R_virt ...
    1930             : !> \param force_data ...
    1931             : !> \param fac ...
    1932             : !> \param cut_memory ...
    1933             : !> \param n_mem_RI ...
    1934             : !> \param t_KBKT ...
    1935             : !> \param t_dm_occ ...
    1936             : !> \param t_dm_virt ...
    1937             : !> \param t_3c_O ...
    1938             : !> \param t_3c_M ...
    1939             : !> \param t_M_occ ...
    1940             : !> \param t_M_virt ...
    1941             : !> \param t_3c_0 ...
    1942             : !> \param t_3c_1 ...
    1943             : !> \param t_3c_3 ...
    1944             : !> \param t_3c_4 ...
    1945             : !> \param t_3c_5 ...
    1946             : !> \param t_3c_6 ...
    1947             : !> \param t_3c_7 ...
    1948             : !> \param t_3c_8 ...
    1949             : !> \param t_3c_sparse ...
    1950             : !> \param t_3c_help_1 ...
    1951             : !> \param t_3c_help_2 ...
    1952             : !> \param t_3c_ints ...
    1953             : !> \param t_3c_work ...
    1954             : !> \param starts_array_mc ...
    1955             : !> \param ends_array_mc ...
    1956             : !> \param batch_start_RI ...
    1957             : !> \param batch_end_RI ...
    1958             : !> \param t_3c_O_compressed ...
    1959             : !> \param t_3c_O_ind ...
    1960             : !> \param use_virial ...
    1961             : !> \param atom_of_kind ...
    1962             : !> \param kind_of ...
    1963             : !> \param eps_filter ...
    1964             : !> \param occ_ddint ...
    1965             : !> \param nze_ddint ...
    1966             : !> \param dbcsr_nflop ...
    1967             : !> \param unit_nr_dbcsr ...
    1968             : !> \param mp2_env ...
    1969             : ! **************************************************************************************************
    1970         170 :    SUBROUTINE perform_3c_ops(force, t_R_occ, t_R_virt, force_data, fac, cut_memory, n_mem_RI, &
    1971             :                              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, &
    1972             :                              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, &
    1973         170 :                              t_3c_ints, t_3c_work, starts_array_mc, ends_array_mc, batch_start_RI, &
    1974         170 :                              batch_end_RI, t_3c_O_compressed, t_3c_O_ind, use_virial, &
    1975         170 :                              atom_of_kind, kind_of, eps_filter, occ_ddint, nze_ddint, dbcsr_nflop, &
    1976             :                              unit_nr_dbcsr, mp2_env)
    1977             : 
    1978             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    1979             :       TYPE(dbt_type), INTENT(INOUT)                      :: t_R_occ, t_R_virt
    1980             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    1981             :       REAL(dp), INTENT(IN)                               :: fac
    1982             :       INTEGER, INTENT(IN)                                :: cut_memory, n_mem_RI
    1983             :       TYPE(dbt_type), INTENT(INOUT) :: t_KBKT, t_dm_occ, t_dm_virt, t_3c_O, t_3c_M, t_M_occ, &
    1984             :          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, &
    1985             :          t_3c_help_1, t_3c_help_2, t_3c_ints, t_3c_work
    1986             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: starts_array_mc, ends_array_mc, &
    1987             :                                                             batch_start_RI, batch_end_RI
    1988             :       TYPE(hfx_compression_type), DIMENSION(:)           :: t_3c_O_compressed
    1989             :       TYPE(block_ind_type), DIMENSION(:), INTENT(INOUT)  :: t_3c_O_ind
    1990             :       LOGICAL, INTENT(IN)                                :: use_virial
    1991             :       INTEGER, DIMENSION(:), INTENT(IN)                  :: atom_of_kind, kind_of
    1992             :       REAL(dp), INTENT(IN)                               :: eps_filter
    1993             :       REAL(dp), INTENT(INOUT)                            :: occ_ddint
    1994             :       INTEGER(int_8), INTENT(INOUT)                      :: nze_ddint, dbcsr_nflop
    1995             :       INTEGER, INTENT(IN)                                :: unit_nr_dbcsr
    1996             :       TYPE(mp2_type)                                     :: mp2_env
    1997             : 
    1998             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'perform_3c_ops'
    1999             : 
    2000             :       INTEGER                                            :: dummy_int, handle, handle2, i_mem, &
    2001             :                                                             i_xyz, j_mem, k_mem
    2002             :       INTEGER(int_8)                                     :: flop, nze
    2003             :       INTEGER, DIMENSION(2, 1)                           :: ibounds, jbounds, kbounds
    2004             :       INTEGER, DIMENSION(2, 2)                           :: bounds_2c
    2005             :       INTEGER, DIMENSION(2, 3)                           :: bounds_cpy
    2006             :       INTEGER, DIMENSION(3)                              :: bounds_3c
    2007             :       REAL(dp)                                           :: memory, occ, pref
    2008         170 :       TYPE(block_ind_type), ALLOCATABLE, DIMENSION(:, :) :: blk_indices
    2009             :       TYPE(hfx_compression_type), ALLOCATABLE, &
    2010         170 :          DIMENSION(:, :)                                 :: store_3c
    2011             : 
    2012         170 :       CALL timeset(routineN, handle)
    2013             : 
    2014         170 :       CALL dbt_get_info(t_3c_M, nfull_total=bounds_3c)
    2015             : 
    2016             :       !Pre-compute and compress KBK^T * (pq|R)
    2017      360910 :       ALLOCATE (store_3c(n_mem_RI, cut_memory))
    2018        1700 :       ALLOCATE (blk_indices(n_mem_RI, cut_memory))
    2019         170 :       memory = 0.0_dp
    2020         170 :       CALL timeset(routineN//"_pre_3c", handle2)
    2021             :       !temporarily build the full int 3c tensor
    2022         170 :       CALL dbt_copy(t_3c_O, t_3c_0)
    2023         510 :       DO i_mem = 1, cut_memory
    2024             :          CALL decompress_tensor(t_3c_O, t_3c_O_ind(i_mem)%ind, t_3c_O_compressed(i_mem), &
    2025         340 :                                 mp2_env%ri_rpa_im_time%eps_compress)
    2026         340 :          CALL dbt_copy(t_3c_O, t_3c_ints)
    2027         340 :          CALL dbt_copy(t_3c_O, t_3c_0, move_data=.TRUE., summation=.TRUE.)
    2028             : 
    2029        1190 :          DO k_mem = 1, n_mem_RI
    2030        2040 :             kbounds(:, 1) = [batch_start_RI(k_mem), batch_end_RI(k_mem)]
    2031             : 
    2032         680 :             CALL alloc_containers(store_3c(k_mem, i_mem), 1)
    2033             : 
    2034             :             !contract witht KBK^T over the RI index and store
    2035         680 :             CALL dbt_batched_contract_init(t_KBKT)
    2036             :             CALL dbt_contract(1.0_dp, t_KBKT, t_3c_ints, 0.0_dp, t_3c_work, &
    2037             :                               contract_1=[2], notcontract_1=[1], &
    2038             :                               contract_2=[1], notcontract_2=[2, 3], &
    2039             :                               map_1=[1], map_2=[2, 3], filter_eps=eps_filter, &
    2040         680 :                               bounds_2=kbounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2041         680 :             CALL dbt_batched_contract_finalize(t_KBKT)
    2042         680 :             dbcsr_nflop = dbcsr_nflop + flop
    2043             : 
    2044         680 :             CALL dbt_copy(t_3c_work, t_3c_M, move_data=.TRUE.)
    2045             :             CALL compress_tensor(t_3c_M, blk_indices(k_mem, i_mem)%ind, store_3c(k_mem, i_mem), &
    2046        1020 :                                  mp2_env%ri_rpa_im_time%eps_compress, memory)
    2047             :          END DO
    2048             :       END DO !i_mem
    2049         170 :       CALL dbt_clear(t_3c_M)
    2050         170 :       CALL dbt_copy(t_3c_M, t_3c_ints)
    2051         170 :       CALL timestop(handle2)
    2052             : 
    2053         170 :       CALL dbt_batched_contract_init(t_R_occ)
    2054         170 :       CALL dbt_batched_contract_init(t_R_virt)
    2055         510 :       DO i_mem = 1, cut_memory
    2056        1020 :          ibounds(:, 1) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2057             : 
    2058             :          !Compute the matrices M (integrals in t_3c_0)
    2059         340 :          CALL timeset(routineN//"_3c_M", handle2)
    2060         340 :          CALL dbt_batched_contract_init(t_dm_occ)
    2061             :          CALL dbt_contract(1.0_dp, t_3c_0, t_dm_occ, 0.0_dp, t_3c_1, &
    2062             :                            contract_1=[3], notcontract_1=[1, 2], &
    2063             :                            contract_2=[1], notcontract_2=[2], &
    2064             :                            map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2065         340 :                            bounds_3=ibounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2066         340 :          dbcsr_nflop = dbcsr_nflop + flop
    2067         340 :          CALL dbt_batched_contract_finalize(t_dm_occ)
    2068         340 :          CALL dbt_copy(t_3c_1, t_M_occ, order=[1, 3, 2], move_data=.TRUE.)
    2069             : 
    2070         340 :          CALL dbt_batched_contract_init(t_dm_virt)
    2071             :          CALL dbt_contract(1.0_dp, t_3c_0, t_dm_virt, 0.0_dp, t_3c_1, &
    2072             :                            contract_1=[3], notcontract_1=[1, 2], &
    2073             :                            contract_2=[1], notcontract_2=[2], &
    2074             :                            map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2075         340 :                            bounds_3=ibounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2076         340 :          dbcsr_nflop = dbcsr_nflop + flop
    2077         340 :          CALL dbt_batched_contract_finalize(t_dm_virt)
    2078         340 :          CALL dbt_copy(t_3c_1, t_M_virt, order=[1, 3, 2], move_data=.TRUE.)
    2079         340 :          CALL timestop(handle2)
    2080             : 
    2081             :          !Compute the R matrices
    2082         340 :          CALL timeset(routineN//"_3c_R", handle2)
    2083        1020 :          DO k_mem = 1, n_mem_RI
    2084             :             CALL decompress_tensor(t_3c_M, blk_indices(k_mem, i_mem)%ind, store_3c(k_mem, i_mem), &
    2085         680 :                                    mp2_env%ri_rpa_im_time%eps_compress)
    2086         680 :             CALL dbt_copy(t_3c_M, t_3c_3, move_data=.TRUE.)
    2087             : 
    2088             :             CALL dbt_contract(1.0_dp, t_M_occ, t_3c_3, 1.0_dp, t_R_occ, &
    2089             :                               contract_1=[1, 2], notcontract_1=[3], &
    2090             :                               contract_2=[1, 2], notcontract_2=[3], &
    2091             :                               map_1=[1], map_2=[2], filter_eps=eps_filter, &
    2092         680 :                               flop=flop, unit_nr=unit_nr_dbcsr)
    2093         680 :             dbcsr_nflop = dbcsr_nflop + flop
    2094             : 
    2095             :             CALL dbt_contract(1.0_dp, t_M_virt, t_3c_3, 1.0_dp, t_R_virt, &
    2096             :                               contract_1=[1, 2], notcontract_1=[3], &
    2097             :                               contract_2=[1, 2], notcontract_2=[3], &
    2098             :                               map_1=[1], map_2=[2], filter_eps=eps_filter, &
    2099         680 :                               flop=flop, unit_nr=unit_nr_dbcsr)
    2100        1020 :             dbcsr_nflop = dbcsr_nflop + flop
    2101             :          END DO
    2102         340 :          CALL dbt_copy(t_3c_M, t_3c_3)
    2103         340 :          CALL dbt_copy(t_3c_M, t_M_virt)
    2104         340 :          CALL timestop(handle2)
    2105             : 
    2106         340 :          CALL dbt_copy(t_M_occ, t_3c_4, move_data=.TRUE.)
    2107             : 
    2108        1020 :          DO j_mem = 1, cut_memory
    2109        2040 :             jbounds(:, 1) = [starts_array_mc(j_mem), ends_array_mc(j_mem)]
    2110             : 
    2111        2040 :             bounds_cpy(:, 1) = [1, bounds_3c(1)]
    2112        2040 :             bounds_cpy(:, 2) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2113        2040 :             bounds_cpy(:, 3) = [starts_array_mc(j_mem), ends_array_mc(j_mem)]
    2114         680 :             CALL dbt_copy(t_3c_sparse, t_3c_7, bounds=bounds_cpy)
    2115             : 
    2116         680 :             CALL dbt_batched_contract_init(t_dm_virt)
    2117        2040 :             DO k_mem = 1, n_mem_RI
    2118        4080 :                bounds_2c(:, 1) = [batch_start_RI(k_mem), batch_end_RI(k_mem)]
    2119        4080 :                bounds_2c(:, 2) = [starts_array_mc(i_mem), ends_array_mc(i_mem)]
    2120             : 
    2121        1360 :                CALL timeset(routineN//"_3c_dm", handle2)
    2122             : 
    2123             :                !Calculate (mu nu| P) * D_occ * D_virt
    2124             :                !Note: technically need M_occ*D_virt + M_virt*D_occ, but it is equivalent to 2*M_occ*D_virt
    2125             :                CALL dbt_contract(2.0_dp, t_3c_4, t_dm_virt, 0.0_dp, t_3c_5, &
    2126             :                                  contract_1=[3], notcontract_1=[1, 2], &
    2127             :                                  contract_2=[1], notcontract_2=[2], &
    2128             :                                  map_1=[1, 2], map_2=[3], filter_eps=eps_filter, &
    2129        1360 :                                  bounds_2=bounds_2c, bounds_3=jbounds, flop=flop, unit_nr=unit_nr_dbcsr)
    2130        1360 :                dbcsr_nflop = dbcsr_nflop + flop
    2131             : 
    2132        1360 :                CALL get_tensor_occupancy(t_3c_5, nze, occ)
    2133        1360 :                nze_ddint = nze_ddint + nze
    2134        1360 :                occ_ddint = occ_ddint + occ
    2135             : 
    2136        1360 :                CALL dbt_copy(t_3c_5, t_3c_6, move_data=.TRUE.)
    2137        1360 :                CALL timestop(handle2)
    2138             : 
    2139             :                !Calculate the contraction of the above with K*B*K^T
    2140        1360 :                CALL timeset(routineN//"_3c_KBK", handle2)
    2141        1360 :                CALL dbt_batched_contract_init(t_KBKT)
    2142             :                CALL dbt_contract(1.0_dp, t_KBKT, t_3c_6, 0.0_dp, t_3c_7, &
    2143             :                                  contract_1=[2], notcontract_1=[1], &
    2144             :                                  contract_2=[1], notcontract_2=[2, 3], &
    2145             :                                  map_1=[1], map_2=[2, 3], &
    2146        1360 :                                  retain_sparsity=.TRUE., flop=flop, unit_nr=unit_nr_dbcsr)
    2147        1360 :                dbcsr_nflop = dbcsr_nflop + flop
    2148        1360 :                CALL dbt_batched_contract_finalize(t_KBKT)
    2149        1360 :                CALL timestop(handle2)
    2150        6120 :                CALL dbt_copy(t_3c_7, t_3c_8, summation=.TRUE.)
    2151             : 
    2152             :             END DO !k_mem
    2153        1020 :             CALL dbt_batched_contract_finalize(t_dm_virt)
    2154             :          END DO !j_mem
    2155             : 
    2156         340 :          CALL dbt_copy(t_3c_8, t_3c_help_1, move_data=.TRUE.)
    2157             : 
    2158         340 :          pref = 1.0_dp*fac
    2159        1020 :          DO k_mem = 1, cut_memory
    2160        2720 :             DO i_xyz = 1, 3
    2161        2040 :                CALL dbt_clear(force_data%t_3c_der_RI(i_xyz))
    2162             :                CALL decompress_tensor(force_data%t_3c_der_RI(i_xyz), force_data%t_3c_der_RI_ind(k_mem, i_xyz)%ind, &
    2163        2720 :                                       force_data%t_3c_der_RI_comp(k_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    2164             :             END DO
    2165             :             CALL get_force_from_3c_trace(force, t_3c_help_1, force_data%t_3c_der_RI, atom_of_kind, kind_of, &
    2166        1020 :                                          force_data%idx_to_at_RI, pref, do_mp2=.TRUE., deriv_dim=1)
    2167             :          END DO
    2168             : 
    2169         340 :          IF (use_virial) THEN
    2170          24 :             CALL dbt_copy(t_3c_help_1, t_3c_help_2)
    2171          24 :             CALL dbt_scale(t_3c_help_2, pref)
    2172          24 :             CALL dbt_copy(t_3c_help_2, force_data%t_3c_virial_split, summation=.TRUE., move_data=.TRUE.)
    2173             :          END IF
    2174             : 
    2175         340 :          CALL dbt_copy(t_3c_help_1, t_3c_help_2)
    2176         340 :          CALL dbt_copy(t_3c_help_1, t_3c_help_2, order=[1, 3, 2], move_data=.TRUE., summation=.TRUE.)
    2177        1020 :          DO k_mem = 1, cut_memory
    2178        2720 :             DO i_xyz = 1, 3
    2179        2040 :                CALL dbt_clear(force_data%t_3c_der_AO(i_xyz))
    2180             :                CALL decompress_tensor(force_data%t_3c_der_AO(i_xyz), force_data%t_3c_der_AO_ind(k_mem, i_xyz)%ind, &
    2181        2720 :                                       force_data%t_3c_der_AO_comp(k_mem, i_xyz), mp2_env%ri_rpa_im_time%eps_compress)
    2182             :             END DO
    2183             :             CALL get_force_from_3c_trace(force, t_3c_help_2, force_data%t_3c_der_AO, atom_of_kind, kind_of, &
    2184        1020 :                                          force_data%idx_to_at_AO, pref, do_mp2=.TRUE., deriv_dim=3)
    2185             :          END DO
    2186             : 
    2187        1190 :          CALL dbt_clear(t_3c_help_2)
    2188             :       END DO !i_mem
    2189         170 :       CALL dbt_batched_contract_finalize(t_R_occ)
    2190         170 :       CALL dbt_batched_contract_finalize(t_R_virt)
    2191             : 
    2192         510 :       DO k_mem = 1, n_mem_RI
    2193        1190 :          DO i_mem = 1, cut_memory
    2194        1020 :             CALL dealloc_containers(store_3c(k_mem, i_mem), dummy_int)
    2195             :          END DO
    2196             :       END DO
    2197         850 :       DEALLOCATE (store_3c, blk_indices)
    2198             : 
    2199         170 :       CALL timestop(handle)
    2200             : 
    2201         340 :    END SUBROUTINE perform_3c_ops
    2202             : 
    2203             : ! **************************************************************************************************
    2204             : !> \brief All the forces that can be calculated after the loop on the Laplace quaradture, using
    2205             : !>        terms collected during the said loop. This inludes the z-vector equation and its reponse
    2206             : !>        forces, as well as the force coming from the trace with the derivative of the KS matrix
    2207             : !> \param force_data ...
    2208             : !> \param unit_nr ...
    2209             : !> \param qs_env ...
    2210             : ! **************************************************************************************************
    2211          50 :    SUBROUTINE calc_post_loop_forces(force_data, unit_nr, qs_env)
    2212             : 
    2213             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    2214             :       INTEGER, INTENT(IN)                                :: unit_nr
    2215             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2216             : 
    2217             :       CHARACTER(len=*), PARAMETER :: routineN = 'calc_post_loop_forces'
    2218             : 
    2219             :       INTEGER                                            :: handle, ispin, nao, nao_aux, nocc, nspins
    2220             :       LOGICAL                                            :: do_exx
    2221             :       REAL(dp)                                           :: focc
    2222             :       TYPE(admm_type), POINTER                           :: admm_env
    2223             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    2224          50 :       TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:)        :: cpmos, mo_occ
    2225             :       TYPE(cp_fm_type), POINTER                          :: mo_coeff
    2226          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: dbcsr_p_work, matrix_p_mp2, &
    2227          50 :                                                             matrix_p_mp2_admm, matrix_s, &
    2228          50 :                                                             matrix_s_aux, work_admm, YP_admm
    2229             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2230             :       TYPE(linres_control_type), POINTER                 :: linres_control
    2231          50 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    2232             :       TYPE(qs_p_env_type), POINTER                       :: p_env
    2233             :       TYPE(section_vals_type), POINTER                   :: hfx_section, lr_section
    2234             : 
    2235          50 :       NULLIFY (linres_control, p_env, dft_control, matrix_s, mos, mo_coeff, fm_struct, lr_section, &
    2236          50 :                dbcsr_p_work, YP_admm, matrix_p_mp2, admm_env, work_admm, matrix_s_aux, matrix_p_mp2_admm)
    2237             : 
    2238          50 :       CALL timeset(routineN, handle)
    2239             : 
    2240          50 :       CALL get_qs_env(qs_env, dft_control=dft_control, matrix_s=matrix_s, mos=mos)
    2241          50 :       nspins = dft_control%nspins
    2242             : 
    2243             :       ! Setting up for the z-vector equation
    2244             : 
    2245             :       ! Initialize linres_control
    2246          50 :       lr_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%LOW_SCALING%CPHF")
    2247             : 
    2248          50 :       ALLOCATE (linres_control)
    2249          50 :       CALL section_vals_val_get(lr_section, "MAX_ITER", i_val=linres_control%max_iter)
    2250          50 :       CALL section_vals_val_get(lr_section, "EPS_CONV", r_val=linres_control%eps)
    2251          50 :       CALL section_vals_val_get(lr_section, "PRECONDITIONER", i_val=linres_control%preconditioner_type)
    2252          50 :       CALL section_vals_val_get(lr_section, "ENERGY_GAP", r_val=linres_control%energy_gap)
    2253             : 
    2254          50 :       linres_control%do_kernel = .TRUE.
    2255          50 :       linres_control%lr_triplet = .FALSE.
    2256          50 :       linres_control%converged = .FALSE.
    2257          50 :       linres_control%eps_filter = qs_env%mp2_env%ri_rpa_im_time%eps_filter
    2258             : 
    2259          50 :       CALL set_qs_env(qs_env, linres_control=linres_control)
    2260             : 
    2261          50 :       IF (unit_nr > 0) THEN
    2262          25 :          WRITE (unit_nr, *)
    2263          25 :          WRITE (unit_nr, '(T3,A)') 'MP2_CPHF| Iterative solution of Z-Vector equations'
    2264          25 :          WRITE (unit_nr, '(T3,A,T45,ES8.1)') 'MP2_CPHF| Convergence threshold:', linres_control%eps
    2265          25 :          WRITE (unit_nr, '(T3,A,T45,I8)') 'MP2_CPHF| Maximum number of iterations: ', linres_control%max_iter
    2266             :       END IF
    2267             : 
    2268         350 :       ALLOCATE (p_env)
    2269          50 :       CALL p_env_create(p_env, qs_env, orthogonal_orbitals=.TRUE., linres_control=linres_control)
    2270          50 :       CALL p_env_psi0_changed(p_env, qs_env)
    2271             : 
    2272             :       ! Matrix allocation
    2273          50 :       CALL dbcsr_allocate_matrix_set(p_env%p1, nspins)
    2274          50 :       CALL dbcsr_allocate_matrix_set(p_env%w1, nspins)
    2275          50 :       CALL dbcsr_allocate_matrix_set(dbcsr_p_work, nspins)
    2276         112 :       DO ispin = 1, nspins
    2277          62 :          ALLOCATE (p_env%p1(ispin)%matrix, p_env%w1(ispin)%matrix, dbcsr_p_work(ispin)%matrix)
    2278          62 :          CALL dbcsr_create(matrix=p_env%p1(ispin)%matrix, template=matrix_s(1)%matrix)
    2279          62 :          CALL dbcsr_create(matrix=p_env%w1(ispin)%matrix, template=matrix_s(1)%matrix)
    2280          62 :          CALL dbcsr_create(matrix=dbcsr_p_work(ispin)%matrix, template=matrix_s(1)%matrix)
    2281          62 :          CALL dbcsr_copy(p_env%p1(ispin)%matrix, matrix_s(1)%matrix)
    2282          62 :          CALL dbcsr_copy(p_env%w1(ispin)%matrix, matrix_s(1)%matrix)
    2283          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, matrix_s(1)%matrix)
    2284          62 :          CALL dbcsr_set(p_env%p1(ispin)%matrix, 0.0_dp)
    2285          62 :          CALL dbcsr_set(p_env%w1(ispin)%matrix, 0.0_dp)
    2286         112 :          CALL dbcsr_set(dbcsr_p_work(ispin)%matrix, 0.0_dp)
    2287             :       END DO
    2288             : 
    2289          50 :       IF (dft_control%do_admm) THEN
    2290          16 :          CALL get_admm_env(qs_env%admm_env, matrix_s_aux_fit=matrix_s_aux)
    2291          16 :          CALL dbcsr_allocate_matrix_set(p_env%p1_admm, nspins)
    2292          16 :          CALL dbcsr_allocate_matrix_set(work_admm, nspins)
    2293          36 :          DO ispin = 1, nspins
    2294          20 :             ALLOCATE (p_env%p1_admm(ispin)%matrix, work_admm(ispin)%matrix)
    2295          20 :             CALL dbcsr_create(p_env%p1_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2296          20 :             CALL dbcsr_copy(p_env%p1_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2297          20 :             CALL dbcsr_set(p_env%p1_admm(ispin)%matrix, 0.0_dp)
    2298          20 :             CALL dbcsr_create(work_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2299          20 :             CALL dbcsr_copy(work_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2300          36 :             CALL dbcsr_set(work_admm(ispin)%matrix, 0.0_dp)
    2301             :          END DO
    2302             :       END IF
    2303             : 
    2304             :       ! Preparing the RHS of the z-vector equation
    2305          50 :       CALL prepare_for_response(force_data, qs_env)
    2306         374 :       ALLOCATE (cpmos(nspins), mo_occ(nspins))
    2307         112 :       DO ispin = 1, nspins
    2308          62 :          CALL get_mo_set(mo_set=mos(ispin), mo_coeff=mo_coeff, nao=nao, homo=nocc)
    2309          62 :          NULLIFY (fm_struct)
    2310             :          CALL cp_fm_struct_create(fm_struct, ncol_global=nocc, &
    2311          62 :                                   template_fmstruct=mo_coeff%matrix_struct)
    2312          62 :          CALL cp_fm_create(cpmos(ispin), fm_struct)
    2313          62 :          CALL cp_fm_set_all(cpmos(ispin), 0.0_dp)
    2314          62 :          CALL cp_fm_create(mo_occ(ispin), fm_struct)
    2315          62 :          CALL cp_fm_to_fm(mo_coeff, mo_occ(ispin), nocc)
    2316         174 :          CALL cp_fm_struct_release(fm_struct)
    2317             :       END DO
    2318             : 
    2319             :       ! in case of EXX, need to add the HF Hamiltonian to the RHS of the Z-vector equation
    2320             :       ! Strategy: we take the ks_matrix, remove the current xc contribution, and then add the RPA HF one
    2321          50 :       do_exx = .FALSE.
    2322          50 :       IF (qs_env%mp2_env%method == ri_rpa_method_gpw) THEN
    2323          28 :          hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%RI_RPA%HF")
    2324          28 :          CALL section_vals_get(hfx_section, explicit=do_exx)
    2325             :       END IF
    2326             : 
    2327          50 :       IF (do_exx) THEN
    2328             :          CALL add_exx_to_rhs(rhs=force_data%sum_O_tau, &
    2329             :                              qs_env=qs_env, &
    2330             :                              ext_hfx_section=hfx_section, &
    2331             :                              x_data=qs_env%mp2_env%ri_rpa%x_data, &
    2332             :                              recalc_integrals=.FALSE., &
    2333             :                              do_admm=qs_env%mp2_env%ri_rpa%do_admm, &
    2334             :                              do_exx=do_exx, &
    2335          18 :                              reuse_hfx=qs_env%mp2_env%ri_rpa%reuse_hfx)
    2336             :       END IF
    2337             : 
    2338          50 :       focc = 2.0_dp
    2339          50 :       IF (nspins == 1) focc = 4.0_dp
    2340         112 :       DO ispin = 1, nspins
    2341          62 :          CALL get_mo_set(mo_set=mos(ispin), mo_coeff=mo_coeff, homo=nocc)
    2342             :          CALL cp_dbcsr_sm_fm_multiply(force_data%sum_O_tau(ispin)%matrix, mo_occ(ispin), &
    2343             :                                       cpmos(ispin), nocc, &
    2344         112 :                                       alpha=focc, beta=0.0_dp)
    2345             :       END DO
    2346             : 
    2347             :       ! The z-vector equation and associated forces
    2348          50 :       CALL response_equation_new(qs_env, p_env, cpmos, unit_nr)
    2349             : 
    2350             :       ! Save the mp2 density matrix
    2351          50 :       CALL get_qs_env(qs_env, matrix_p_mp2=matrix_p_mp2)
    2352          50 :       IF (ASSOCIATED(matrix_p_mp2)) CALL dbcsr_deallocate_matrix_set(matrix_p_mp2)
    2353         112 :       DO ispin = 1, nspins
    2354          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, p_env%p1(ispin)%matrix)
    2355         112 :          CALL dbcsr_add(dbcsr_p_work(ispin)%matrix, force_data%sum_YP_tau(ispin)%matrix, 1.0_dp, 1.0_dp)
    2356             :       END DO
    2357          50 :       CALL set_ks_env(qs_env%ks_env, matrix_p_mp2=dbcsr_p_work)
    2358             : 
    2359          50 :       IF (dft_control%do_admm) THEN
    2360          16 :          CALL dbcsr_allocate_matrix_set(YP_admm, nspins)
    2361          16 :          CALL get_qs_env(qs_env, matrix_p_mp2_admm=matrix_p_mp2_admm, admm_env=admm_env)
    2362          16 :          nao = admm_env%nao_orb
    2363          16 :          nao_aux = admm_env%nao_aux_fit
    2364          16 :          IF (ASSOCIATED(matrix_p_mp2_admm)) CALL dbcsr_deallocate_matrix_set(matrix_p_mp2_admm)
    2365          36 :          DO ispin = 1, nspins
    2366             : 
    2367             :             !sum_YP_tau in the auxiliary basis
    2368          20 :             CALL copy_dbcsr_to_fm(force_data%sum_YP_tau(ispin)%matrix, admm_env%work_orb_orb)
    2369             :             CALL parallel_gemm('N', 'N', nao_aux, nao, nao, 1.0_dp, admm_env%A, admm_env%work_orb_orb, &
    2370          20 :                                0.0_dp, admm_env%work_aux_orb)
    2371             :             CALL parallel_gemm('N', 'T', nao_aux, nao_aux, nao, 1.0_dp, admm_env%work_aux_orb, admm_env%A, &
    2372          20 :                                0.0_dp, admm_env%work_aux_aux)
    2373          20 :             CALL copy_fm_to_dbcsr(admm_env%work_aux_aux, work_admm(ispin)%matrix, keep_sparsity=.TRUE.)
    2374             : 
    2375             :             !save the admm representation od sum_YP_tau
    2376          20 :             ALLOCATE (YP_admm(ispin)%matrix)
    2377          20 :             CALL dbcsr_create(YP_admm(ispin)%matrix, template=work_admm(ispin)%matrix)
    2378          20 :             CALL dbcsr_copy(YP_admm(ispin)%matrix, work_admm(ispin)%matrix)
    2379             : 
    2380          36 :             CALL dbcsr_add(work_admm(ispin)%matrix, p_env%p1_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    2381             : 
    2382             :          END DO
    2383          16 :          CALL set_ks_env(qs_env%ks_env, matrix_p_mp2_admm=work_admm)
    2384             :       END IF
    2385             : 
    2386             :       !Calculate the response force and the force from the trace with F
    2387          50 :       CALL update_im_time_forces(p_env, force_data%sum_O_tau, force_data%sum_YP_tau, YP_admm, qs_env)
    2388             : 
    2389             :       !clean-up
    2390          50 :       IF (dft_control%do_admm) CALL dbcsr_deallocate_matrix_set(YP_admm)
    2391             : 
    2392          50 :       CALL cp_fm_release(cpmos)
    2393          50 :       CALL cp_fm_release(mo_occ)
    2394          50 :       CALL p_env_release(p_env)
    2395          50 :       DEALLOCATE (p_env)
    2396             : 
    2397          50 :       CALL timestop(handle)
    2398             : 
    2399         100 :    END SUBROUTINE calc_post_loop_forces
    2400             : 
    2401             : ! **************************************************************************************************
    2402             : !> \brief Prepares the RHS of the z-vector equation. Apply the xc and HFX kernel on the previously
    2403             : !>        stored sum_YP_tau density, and add it to the final force_data%sum_O_tau quantity
    2404             : !> \param force_data ...
    2405             : !> \param qs_env ...
    2406             : ! **************************************************************************************************
    2407          50 :    SUBROUTINE prepare_for_response(force_data, qs_env)
    2408             : 
    2409             :       TYPE(im_time_force_type), INTENT(INOUT)            :: force_data
    2410             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2411             : 
    2412             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'prepare_for_response'
    2413             : 
    2414             :       INTEGER                                            :: handle, ispin, nao, nao_aux, nspins
    2415             :       LOGICAL                                            :: do_hfx, do_tau, do_tau_admm
    2416             :       REAL(dp)                                           :: ehartree
    2417             :       TYPE(admm_type), POINTER                           :: admm_env
    2418          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: dbcsr_p_work, ker_tau_admm, matrix_s, &
    2419          50 :                                                             matrix_s_aux, work_admm
    2420             :       TYPE(dbcsr_type)                                   :: dbcsr_work
    2421             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2422             :       TYPE(pw_c1d_gs_type)                               :: rhoz_tot_gspace, zv_hartree_gspace
    2423          50 :       TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER        :: rhoz_g
    2424             :       TYPE(pw_env_type), POINTER                         :: pw_env
    2425             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    2426             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2427             :       TYPE(pw_r3d_rs_type)                               :: zv_hartree_rspace
    2428          50 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rhoz_r, tauz_r, v_xc, v_xc_tau
    2429             :       TYPE(qs_rho_type), POINTER                         :: rho, rho_aux_fit
    2430             :       TYPE(section_vals_type), POINTER                   :: hfx_section, xc_section
    2431             :       TYPE(task_list_type), POINTER                      :: task_list_aux_fit
    2432             : 
    2433          50 :       NULLIFY (pw_env, rhoz_r, rhoz_g, tauz_r, v_xc, v_xc_tau, &
    2434          50 :                poisson_env, auxbas_pw_pool, dft_control, admm_env, xc_section, rho, rho_aux_fit, &
    2435          50 :                task_list_aux_fit, ker_tau_admm, work_admm, dbcsr_p_work, matrix_s, hfx_section)
    2436             : 
    2437          50 :       CALL timeset(routineN, handle)
    2438             : 
    2439          50 :       CALL get_qs_env(qs_env, dft_control=dft_control, pw_env=pw_env, rho=rho, matrix_s=matrix_s)
    2440          50 :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool, poisson_env=poisson_env)
    2441          50 :       nspins = dft_control%nspins
    2442             : 
    2443          50 :       CALL dbcsr_allocate_matrix_set(dbcsr_p_work, nspins)
    2444         112 :       DO ispin = 1, nspins
    2445          62 :          ALLOCATE (dbcsr_p_work(ispin)%matrix)
    2446          62 :          CALL dbcsr_create(matrix=dbcsr_p_work(ispin)%matrix, template=matrix_s(1)%matrix)
    2447          62 :          CALL dbcsr_copy(dbcsr_p_work(ispin)%matrix, matrix_s(1)%matrix)
    2448         112 :          CALL dbcsr_set(dbcsr_p_work(ispin)%matrix, 0.0_dp)
    2449             :       END DO
    2450             : 
    2451             :       !Apply the kernel on the density saved in force_data%sum_YP_tau
    2452         374 :       ALLOCATE (rhoz_r(nspins), rhoz_g(nspins))
    2453         112 :       DO ispin = 1, nspins
    2454          62 :          CALL auxbas_pw_pool%create_pw(rhoz_r(ispin))
    2455         112 :          CALL auxbas_pw_pool%create_pw(rhoz_g(ispin))
    2456             :       END DO
    2457          50 :       CALL auxbas_pw_pool%create_pw(rhoz_tot_gspace)
    2458          50 :       CALL auxbas_pw_pool%create_pw(zv_hartree_rspace)
    2459          50 :       CALL auxbas_pw_pool%create_pw(zv_hartree_gspace)
    2460             : 
    2461          50 :       CALL pw_zero(rhoz_tot_gspace)
    2462         112 :       DO ispin = 1, nspins
    2463             :          CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=force_data%sum_YP_tau(ispin)%matrix, &
    2464          62 :                                  rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin))
    2465         112 :          CALL pw_axpy(rhoz_g(ispin), rhoz_tot_gspace)
    2466             :       END DO
    2467             : 
    2468             :       CALL pw_poisson_solve(poisson_env, rhoz_tot_gspace, ehartree, &
    2469          50 :                             zv_hartree_gspace)
    2470             : 
    2471          50 :       CALL pw_transfer(zv_hartree_gspace, zv_hartree_rspace)
    2472          50 :       CALL pw_scale(zv_hartree_rspace, zv_hartree_rspace%pw_grid%dvol)
    2473             : 
    2474          50 :       CALL qs_rho_get(rho, tau_r_valid=do_tau)
    2475          50 :       IF (do_tau) THEN
    2476             :          BLOCK
    2477             :             TYPE(pw_c1d_gs_type) :: tauz_g
    2478          24 :             ALLOCATE (tauz_r(nspins))
    2479           8 :             CALL auxbas_pw_pool%create_pw(tauz_g)
    2480          16 :             DO ispin = 1, nspins
    2481           8 :                CALL auxbas_pw_pool%create_pw(tauz_r(ispin))
    2482             : 
    2483             :                CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=force_data%sum_YP_tau(ispin)%matrix, &
    2484          16 :                                        rho=tauz_r(ispin), rho_gspace=tauz_g, compute_tau=.TRUE.)
    2485             :             END DO
    2486          16 :             CALL auxbas_pw_pool%give_back_pw(tauz_g)
    2487             :          END BLOCK
    2488             :       END IF
    2489             : 
    2490          50 :       IF (dft_control%do_admm) THEN
    2491          16 :          CALL get_qs_env(qs_env, admm_env=admm_env)
    2492          16 :          xc_section => admm_env%xc_section_primary
    2493             :       ELSE
    2494          34 :          xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    2495             :       END IF
    2496             : 
    2497             :       !Primary XC kernel
    2498          50 :       CALL create_kernel(qs_env, v_xc, v_xc_tau, rho, rhoz_r, rhoz_g, tauz_r, xc_section)
    2499             : 
    2500         112 :       DO ispin = 1, nspins
    2501          62 :          CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    2502          62 :          CALL pw_axpy(zv_hartree_rspace, v_xc(ispin))
    2503             :          CALL integrate_v_rspace(qs_env=qs_env, &
    2504             :                                  v_rspace=v_xc(ispin), &
    2505             :                                  hmat=dbcsr_p_work(ispin), &
    2506          62 :                                  calculate_forces=.FALSE.)
    2507             : 
    2508         112 :          CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    2509             :       END DO
    2510          50 :       CALL auxbas_pw_pool%give_back_pw(rhoz_tot_gspace)
    2511          50 :       CALL auxbas_pw_pool%give_back_pw(zv_hartree_rspace)
    2512          50 :       CALL auxbas_pw_pool%give_back_pw(zv_hartree_gspace)
    2513          50 :       DEALLOCATE (v_xc)
    2514             : 
    2515          50 :       IF (do_tau) THEN
    2516          16 :          DO ispin = 1, nspins
    2517           8 :             CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    2518             :             CALL integrate_v_rspace(qs_env=qs_env, &
    2519             :                                     v_rspace=v_xc_tau(ispin), &
    2520             :                                     hmat=dbcsr_p_work(ispin), &
    2521             :                                     compute_tau=.TRUE., &
    2522           8 :                                     calculate_forces=.FALSE.)
    2523          16 :             CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    2524             :          END DO
    2525           8 :          DEALLOCATE (v_xc_tau)
    2526             :       END IF
    2527             : 
    2528             :       !Auxiliary xc kernel (admm)
    2529          50 :       IF (dft_control%do_admm) THEN
    2530          16 :          CALL get_qs_env(qs_env, admm_env=admm_env)
    2531             :          CALL get_admm_env(admm_env, matrix_s_aux_fit=matrix_s_aux, &
    2532          16 :                            task_list_aux_fit=task_list_aux_fit, rho_aux_fit=rho_aux_fit)
    2533             : 
    2534          16 :          CALL qs_rho_get(rho_aux_fit, tau_r_valid=do_tau_admm)
    2535             : 
    2536          16 :          CALL dbcsr_allocate_matrix_set(work_admm, nspins)
    2537          16 :          CALL dbcsr_allocate_matrix_set(ker_tau_admm, nspins)
    2538          36 :          DO ispin = 1, nspins
    2539          20 :             ALLOCATE (work_admm(ispin)%matrix, ker_tau_admm(ispin)%matrix)
    2540          20 :             CALL dbcsr_create(work_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2541          20 :             CALL dbcsr_copy(work_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2542          20 :             CALL dbcsr_set(work_admm(ispin)%matrix, 0.0_dp)
    2543          20 :             CALL dbcsr_create(ker_tau_admm(ispin)%matrix, template=matrix_s_aux(1)%matrix)
    2544          20 :             CALL dbcsr_copy(ker_tau_admm(ispin)%matrix, matrix_s_aux(1)%matrix)
    2545          36 :             CALL dbcsr_set(ker_tau_admm(ispin)%matrix, 0.0_dp)
    2546             :          END DO
    2547             : 
    2548             :          !get the density in the auxuliary density
    2549          16 :          CPASSERT(ASSOCIATED(admm_env%work_orb_orb))
    2550          16 :          CPASSERT(ASSOCIATED(admm_env%work_aux_orb))
    2551          16 :          CPASSERT(ASSOCIATED(admm_env%work_aux_aux))
    2552          16 :          nao = admm_env%nao_orb
    2553          16 :          nao_aux = admm_env%nao_aux_fit
    2554          36 :          DO ispin = 1, nspins
    2555          20 :             CALL copy_dbcsr_to_fm(force_data%sum_YP_tau(ispin)%matrix, admm_env%work_orb_orb)
    2556             :             CALL parallel_gemm('N', 'N', nao_aux, nao, nao, 1.0_dp, admm_env%A, admm_env%work_orb_orb, &
    2557          20 :                                0.0_dp, admm_env%work_aux_orb)
    2558             :             CALL parallel_gemm('N', 'T', nao_aux, nao_aux, nao, 1.0_dp, admm_env%work_aux_orb, admm_env%A, &
    2559          20 :                                0.0_dp, admm_env%work_aux_aux)
    2560          36 :             CALL copy_fm_to_dbcsr(admm_env%work_aux_aux, ker_tau_admm(ispin)%matrix, keep_sparsity=.TRUE.)
    2561             :          END DO
    2562             : 
    2563          16 :          IF (.NOT. qs_env%admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    2564          36 :             DO ispin = 1, nspins
    2565          20 :                CALL pw_zero(rhoz_r(ispin))
    2566          20 :                CALL pw_zero(rhoz_g(ispin))
    2567             :                CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=ker_tau_admm(ispin)%matrix, &
    2568             :                                        rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin), &
    2569          36 :                                        basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    2570             :             END DO
    2571             : 
    2572          16 :             IF (do_tau_admm) THEN
    2573             :                BLOCK
    2574             :                   TYPE(pw_c1d_gs_type) :: tauz_g
    2575           0 :                   CALL auxbas_pw_pool%create_pw(tauz_g)
    2576           0 :                   DO ispin = 1, nspins
    2577           0 :                      CALL pw_zero(tauz_r(ispin))
    2578             :                      CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=ker_tau_admm(ispin)%matrix, &
    2579             :                                              rho=tauz_r(ispin), rho_gspace=tauz_g, &
    2580             :                                              basis_type="AUX_FIT", task_list_external=task_list_aux_fit, &
    2581           0 :                                              compute_tau=.TRUE.)
    2582             :                   END DO
    2583           0 :                   CALL auxbas_pw_pool%give_back_pw(tauz_g)
    2584             :                END BLOCK
    2585             :             END IF
    2586             : 
    2587          16 :             xc_section => admm_env%xc_section_aux
    2588          16 :             CALL create_kernel(qs_env, v_xc, v_xc_tau, rho_aux_fit, rhoz_r, rhoz_g, tauz_r, xc_section)
    2589             : 
    2590          36 :             DO ispin = 1, nspins
    2591          20 :                CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    2592             :                CALL integrate_v_rspace(qs_env=qs_env, &
    2593             :                                        v_rspace=v_xc(ispin), &
    2594             :                                        hmat=work_admm(ispin), &
    2595             :                                        calculate_forces=.FALSE., &
    2596             :                                        basis_type="AUX_FIT", &
    2597          20 :                                        task_list_external=task_list_aux_fit)
    2598          36 :                CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    2599             :             END DO
    2600          16 :             DEALLOCATE (v_xc)
    2601             : 
    2602          16 :             IF (do_tau_admm) THEN
    2603           0 :                DO ispin = 1, nspins
    2604           0 :                   CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    2605             :                   CALL integrate_v_rspace(qs_env=qs_env, &
    2606             :                                           v_rspace=v_xc_tau(ispin), &
    2607             :                                           hmat=work_admm(ispin), &
    2608             :                                           calculate_forces=.FALSE., &
    2609             :                                           basis_type="AUX_FIT", &
    2610             :                                           task_list_external=task_list_aux_fit, &
    2611           0 :                                           compute_tau=.TRUE.)
    2612           0 :                   CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    2613             :                END DO
    2614           0 :                DEALLOCATE (v_xc_tau)
    2615             :             END IF
    2616             :          END IF !admm
    2617             :       END IF
    2618             : 
    2619         112 :       DO ispin = 1, nspins
    2620          62 :          CALL auxbas_pw_pool%give_back_pw(rhoz_r(ispin))
    2621         112 :          CALL auxbas_pw_pool%give_back_pw(rhoz_g(ispin))
    2622             :       END DO
    2623          50 :       DEALLOCATE (rhoz_r, rhoz_g)
    2624             : 
    2625          50 :       IF (do_tau) THEN
    2626          16 :          DO ispin = 1, nspins
    2627          16 :             CALL auxbas_pw_pool%give_back_pw(tauz_r(ispin))
    2628             :          END DO
    2629           8 :          DEALLOCATE (tauz_r)
    2630             :       END IF
    2631             : 
    2632             :       !HFX kernel
    2633          50 :       hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%HF")
    2634          50 :       CALL section_vals_get(hfx_section, explicit=do_hfx)
    2635          50 :       IF (do_hfx) THEN
    2636          32 :          IF (dft_control%do_admm) THEN
    2637          16 :             CALL tddft_hfx_matrix(work_admm, ker_tau_admm, qs_env, .FALSE., .FALSE.)
    2638             : 
    2639             :             !Going back to primary basis
    2640          16 :             CALL dbcsr_create(dbcsr_work, template=dbcsr_p_work(1)%matrix)
    2641          16 :             CALL dbcsr_copy(dbcsr_work, dbcsr_p_work(1)%matrix)
    2642          16 :             CALL dbcsr_set(dbcsr_work, 0.0_dp)
    2643          36 :             DO ispin = 1, nspins
    2644          20 :                CALL copy_dbcsr_to_fm(work_admm(ispin)%matrix, admm_env%work_aux_aux)
    2645             :                CALL parallel_gemm('N', 'N', nao_aux, nao, nao_aux, 1.0_dp, admm_env%work_aux_aux, admm_env%A, &
    2646          20 :                                   0.0_dp, admm_env%work_aux_orb)
    2647             :                CALL parallel_gemm('T', 'N', nao, nao, nao_aux, 1.0_dp, admm_env%A, admm_env%work_aux_orb, &
    2648          20 :                                   0.0_dp, admm_env%work_orb_orb)
    2649          20 :                CALL copy_fm_to_dbcsr(admm_env%work_orb_orb, dbcsr_work, keep_sparsity=.TRUE.)
    2650          36 :                CALL dbcsr_add(dbcsr_p_work(ispin)%matrix, dbcsr_work, 1.0_dp, 1.0_dp)
    2651             :             END DO
    2652          16 :             CALL dbcsr_release(dbcsr_work)
    2653          16 :             CALL dbcsr_deallocate_matrix_set(ker_tau_admm)
    2654             :          ELSE
    2655          16 :             CALL tddft_hfx_matrix(dbcsr_p_work, force_data%sum_YP_tau, qs_env, .FALSE., .FALSE.)
    2656             :          END IF
    2657             :       END IF
    2658             : 
    2659         112 :       DO ispin = 1, nspins
    2660         112 :          CALL dbcsr_add(force_data%sum_O_tau(ispin)%matrix, dbcsr_p_work(ispin)%matrix, 1.0_dp, 1.0_dp)
    2661             :       END DO
    2662             : 
    2663          50 :       CALL dbcsr_deallocate_matrix_set(dbcsr_p_work)
    2664          50 :       CALL dbcsr_deallocate_matrix_set(work_admm)
    2665             : 
    2666          50 :       CALL timestop(handle)
    2667             : 
    2668         200 :    END SUBROUTINE prepare_for_response
    2669             : 
    2670             : ! **************************************************************************************************
    2671             : !> \brief Calculate the force and virial due to the (P|Q) GPW integral derivatives
    2672             : !> \param G_PQ ...
    2673             : !> \param force ...
    2674             : !> \param h_stress ...
    2675             : !> \param use_virial ...
    2676             : !> \param mp2_env ...
    2677             : !> \param qs_env ...
    2678             : ! **************************************************************************************************
    2679          12 :    SUBROUTINE get_2c_gpw_forces(G_PQ, force, h_stress, use_virial, mp2_env, qs_env)
    2680             : 
    2681             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: G_PQ
    2682             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    2683             :       REAL(dp), DIMENSION(3, 3), INTENT(INOUT)           :: h_stress
    2684             :       LOGICAL, INTENT(IN)                                :: use_virial
    2685             :       TYPE(mp2_type), INTENT(INOUT)                      :: mp2_env
    2686             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2687             : 
    2688             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'get_2c_gpw_forces'
    2689             : 
    2690             :       INTEGER :: atom_a, color, handle, i, i_RI, i_xyz, iatom, igrid_level, ikind, ipgf, iset, j, &
    2691             :          j_RI, jatom, lb_RI, n_RI, natom, ncoa, ncoms, nkind, nproc, nseta, o1, offset, pdims(2), &
    2692             :          sgfa, ub_RI
    2693          24 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, iproc_map, kind_of, &
    2694          12 :                                                             sizes_RI
    2695          24 :       INTEGER, DIMENSION(:), POINTER                     :: col_dist, la_max, la_min, npgfa, nsgfa, &
    2696          12 :                                                             row_dist
    2697          12 :       INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, pgrid
    2698             :       LOGICAL                                            :: found, one_proc_group
    2699             :       REAL(dp)                                           :: cutoff_old, radius, relative_cutoff_old
    2700          12 :       REAL(dp), ALLOCATABLE, DIMENSION(:)                :: e_cutoff_old, wf_vector
    2701             :       REAL(dp), DIMENSION(3)                             :: force_a, force_b, ra
    2702             :       REAL(dp), DIMENSION(3, 3)                          :: my_virial_a, my_virial_b
    2703          12 :       REAL(KIND=dp), DIMENSION(:, :), POINTER            :: h_tmp, I_ab, pab, pblock, sphi_a, zeta
    2704          12 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    2705             :       TYPE(cell_type), POINTER                           :: cell
    2706             :       TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
    2707             :       TYPE(dbcsr_type)                                   :: tmp_G_PQ
    2708             :       TYPE(dft_control_type), POINTER                    :: dft_control
    2709             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    2710          12 :          DIMENSION(:), TARGET                            :: basis_set_ri_aux
    2711             :       TYPE(gto_basis_set_type), POINTER                  :: basis_set_a
    2712          12 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    2713             :       TYPE(mp_para_env_type), POINTER                    :: para_env, para_env_ext
    2714             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
    2715          12 :          POINTER                                         :: sab_orb
    2716          12 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    2717          48 :       TYPE(pw_c1d_gs_type)                               :: dvg(3), pot_g, rho_g, rho_g_copy
    2718             :       TYPE(pw_env_type), POINTER                         :: pw_env_ext
    2719             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    2720             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    2721             :       TYPE(pw_r3d_rs_type)                               :: psi_L, rho_r
    2722          12 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    2723          12 :       TYPE(realspace_grid_type), DIMENSION(:), POINTER   :: rs_v
    2724             :       TYPE(task_list_type), POINTER                      :: task_list_ext
    2725             : 
    2726          12 :       NULLIFY (sab_orb, task_list_ext, particle_set, qs_kind_set, dft_control, pw_env_ext, auxbas_pw_pool, &
    2727          12 :                poisson_env, atomic_kind_set, para_env, cell, rs_v, mos, basis_set_a)
    2728             : 
    2729          12 :       CALL timeset(routineN, handle)
    2730             : 
    2731             :       CALL get_qs_env(qs_env, dft_control=dft_control, para_env=para_env, sab_orb=sab_orb, &
    2732             :                       natom=natom, nkind=nkind, qs_kind_set=qs_kind_set, particle_set=particle_set, &
    2733          12 :                       mos=mos, cell=cell, atomic_kind_set=atomic_kind_set)
    2734             : 
    2735             :       !The idea is to use GPW to compute the integrals and derivatives. Because the potential needs
    2736             :       !to be calculated for each phi_j (column) of all AO pairs, and because that is expensive, we want
    2737             :       !to minimize the amount of time we do that. Therefore, we work with a special distribution, where
    2738             :       !each column of the resulting DBCSR matrix is mapped to a sub-communicator.
    2739             : 
    2740             :       !Try to get the optimal pdims (we want a grid that is flat: many cols, few rows)
    2741          12 :       IF (para_env%num_pe <= natom) THEN
    2742             :          pdims(1) = 1
    2743             :          pdims(2) = para_env%num_pe
    2744             :       ELSE
    2745           0 :          DO i = natom, 1, -1
    2746           0 :             IF (MODULO(para_env%num_pe, i) == 0) THEN
    2747           0 :                pdims(1) = para_env%num_pe/i
    2748           0 :                pdims(2) = i
    2749           0 :                EXIT
    2750             :             END IF
    2751             :          END DO
    2752             :       END IF
    2753             : 
    2754          48 :       ALLOCATE (row_dist(natom), col_dist(natom))
    2755          48 :       DO iatom = 1, natom
    2756          48 :          row_dist(iatom) = MODULO(iatom, pdims(1))
    2757             :       END DO
    2758          48 :       DO jatom = 1, natom
    2759          48 :          col_dist(jatom) = MODULO(jatom, pdims(2))
    2760             :       END DO
    2761             : 
    2762          48 :       ALLOCATE (pgrid(0:pdims(1) - 1, 0:pdims(2) - 1))
    2763          12 :       nproc = 0
    2764          24 :       DO i = 0, pdims(1) - 1
    2765          48 :          DO j = 0, pdims(2) - 1
    2766          24 :             pgrid(i, j) = nproc
    2767          36 :             nproc = nproc + 1
    2768             :          END DO
    2769             :       END DO
    2770             : 
    2771          12 :       CALL dbcsr_distribution_new(dbcsr_dist, group=para_env%get_handle(), pgrid=pgrid, row_dist=row_dist, col_dist=col_dist)
    2772             : 
    2773             :       !The temporary DBCSR integrals and derivatives matrices in this flat distribution
    2774          12 :       CALL dbcsr_create(tmp_G_PQ, template=G_PQ, matrix_type=dbcsr_type_no_symmetry, dist=dbcsr_dist)
    2775          12 :       CALL dbcsr_complete_redistribute(G_PQ, tmp_G_PQ)
    2776             : 
    2777          84 :       ALLOCATE (basis_set_ri_aux(nkind), sizes_RI(natom))
    2778          12 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    2779          12 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_RI, basis=basis_set_ri_aux)
    2780          48 :       n_RI = SUM(sizes_RI)
    2781             : 
    2782          12 :       one_proc_group = mp2_env%mp2_num_proc == 1
    2783          12 :       ALLOCATE (para_env_ext)
    2784          12 :       IF (one_proc_group) THEN
    2785             :          !one subgroup per proc
    2786           4 :          CALL para_env_ext%from_split(para_env, para_env%mepos)
    2787             :       ELSE
    2788             :          !Split the communicator accross the columns of the matrix
    2789           8 :          ncoms = MIN(pdims(2), para_env%num_pe/mp2_env%mp2_num_proc)
    2790          16 :          DO i = 0, pdims(1) - 1
    2791          32 :             DO j = 0, pdims(2) - 1
    2792          24 :                IF (pgrid(i, j) == para_env%mepos) color = MODULO(j + 1, ncoms)
    2793             :             END DO
    2794             :          END DO
    2795           8 :          CALL para_env_ext%from_split(para_env, color)
    2796             :       END IF
    2797             : 
    2798             :       !sab_orb and task_list_ext are essentially dummies
    2799             :       CALL prepare_gpw(qs_env, dft_control, e_cutoff_old, cutoff_old, relative_cutoff_old, para_env_ext, pw_env_ext, &
    2800          12 :                        auxbas_pw_pool, poisson_env, task_list_ext, rho_r, rho_g, pot_g, psi_L, sab_orb)
    2801             : 
    2802          12 :       IF (use_virial) THEN
    2803           4 :          CALL auxbas_pw_pool%create_pw(rho_g_copy)
    2804          16 :          DO i_xyz = 1, 3
    2805          16 :             CALL auxbas_pw_pool%create_pw(dvg(i_xyz))
    2806             :          END DO
    2807             :       END IF
    2808             : 
    2809          36 :       ALLOCATE (wf_vector(n_RI))
    2810             : 
    2811          12 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    2812             : 
    2813          36 :       ALLOCATE (iproc_map(natom))
    2814             : 
    2815             :       !Loop over the atomic blocks
    2816          48 :       DO jatom = 1, natom
    2817             : 
    2818             :          !Only calculate if on the correct sub-communicator/proc
    2819          36 :          IF (one_proc_group) THEN
    2820          48 :             iproc_map = 0
    2821          48 :             DO iatom = 1, natom
    2822          48 :                IF (pgrid(row_dist(iatom), col_dist(jatom)) == para_env%mepos) iproc_map(iatom) = 1
    2823             :             END DO
    2824          30 :             IF (.NOT. ANY(iproc_map == 1)) CYCLE
    2825             :          ELSE
    2826          24 :             IF (.NOT. MODULO(col_dist(jatom) + 1, ncoms) == color) CYCLE
    2827             :          END IF
    2828             : 
    2829          60 :          lb_RI = SUM(sizes_RI(1:jatom - 1))
    2830          30 :          ub_RI = lb_RI + sizes_RI(jatom)
    2831         872 :          DO j_RI = lb_RI + 1, ub_RI
    2832             : 
    2833       69720 :             wf_vector = 0.0_dp
    2834         830 :             wf_vector(j_RI) = 1.0_dp
    2835             : 
    2836             :             CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, qs_kind_set, cell, &
    2837             :                                     particle_set, pw_env_ext, dft_control%qs_control%eps_rho_rspace, &
    2838         830 :                                     basis_type="RI_AUX")
    2839             : 
    2840         830 :             IF (use_virial) THEN
    2841         166 :                CALL calc_potential_gpw(rho_r, rho_g, poisson_env, pot_g, mp2_env%potential_parameter, dvg)
    2842             : 
    2843       13944 :                wf_vector = 0.0_dp
    2844         664 :                DO iatom = 1, natom
    2845             :                   !only compute if i,j atom pair on correct proc
    2846         498 :                   IF (one_proc_group) THEN
    2847         498 :                      IF (.NOT. iproc_map(iatom) == 1) CYCLE
    2848             :                   END IF
    2849             : 
    2850         498 :                   CALL dbcsr_get_block_p(tmp_G_PQ, iatom, jatom, pblock, found)
    2851         498 :                   IF (.NOT. found) CYCLE
    2852             : 
    2853         996 :                   i_RI = SUM(sizes_RI(1:iatom - 1))
    2854       14940 :                   wf_vector(i_RI + 1:i_RI + sizes_RI(iatom)) = pblock(:, j_RI - lb_RI)
    2855             :                END DO
    2856             : 
    2857         166 :                CALL pw_copy(rho_g, rho_g_copy)
    2858             :                CALL collocate_function(wf_vector, psi_L, rho_g, atomic_kind_set, qs_kind_set, cell, &
    2859             :                                        particle_set, pw_env_ext, dft_control%qs_control%eps_rho_rspace, &
    2860         166 :                                        basis_type="RI_AUX")
    2861             : 
    2862             :                CALL calc_potential_gpw(psi_L, rho_g, poisson_env, pot_g, mp2_env%potential_parameter, &
    2863         166 :                                        no_transfer=.TRUE.)
    2864             :                CALL virial_gpw_potential(rho_g_copy, pot_g, rho_g, dvg, h_stress, &
    2865         166 :                                          mp2_env%potential_parameter, para_env_ext)
    2866             :             ELSE
    2867         664 :                CALL calc_potential_gpw(rho_r, rho_g, poisson_env, pot_g, mp2_env%potential_parameter)
    2868             :             END IF
    2869             : 
    2870         830 :             NULLIFY (rs_v)
    2871         830 :             CALL pw_env_get(pw_env_ext, rs_grids=rs_v)
    2872         830 :             CALL potential_pw2rs(rs_v, rho_r, pw_env_ext)
    2873             : 
    2874        3356 :             DO iatom = 1, natom
    2875             : 
    2876             :                !only compute if i,j atom pair on correct proc
    2877        2490 :                IF (one_proc_group) THEN
    2878         498 :                   IF (.NOT. iproc_map(iatom) == 1) CYCLE
    2879             :                END IF
    2880             : 
    2881        2490 :                force_a(:) = 0.0_dp
    2882        2490 :                force_b(:) = 0.0_dp
    2883        2490 :                IF (use_virial) THEN
    2884         498 :                   my_virial_a = 0.0_dp
    2885         498 :                   my_virial_b = 0.0_dp
    2886             :                END IF
    2887             : 
    2888        2490 :                ikind = kind_of(iatom)
    2889        2490 :                atom_a = atom_of_kind(iatom)
    2890             : 
    2891        2490 :                basis_set_a => basis_set_ri_aux(ikind)%gto_basis_set
    2892        2490 :                first_sgfa => basis_set_a%first_sgf
    2893        2490 :                la_max => basis_set_a%lmax
    2894        2490 :                la_min => basis_set_a%lmin
    2895        2490 :                nseta = basis_set_a%nset
    2896        2490 :                nsgfa => basis_set_a%nsgf_set
    2897        2490 :                sphi_a => basis_set_a%sphi
    2898        2490 :                zeta => basis_set_a%zet
    2899        2490 :                npgfa => basis_set_a%npgf
    2900             : 
    2901        2490 :                ra(:) = pbc(particle_set(iatom)%r, cell)
    2902             : 
    2903        2490 :                CALL dbcsr_get_block_p(tmp_G_PQ, iatom, jatom, pblock, found)
    2904        2490 :                IF (.NOT. found) CYCLE
    2905             : 
    2906             :                offset = 0
    2907       15936 :                DO iset = 1, nseta
    2908       14442 :                   ncoa = npgfa(iset)*ncoset(la_max(iset))
    2909       14442 :                   sgfa = first_sgfa(1, iset)
    2910             : 
    2911      131472 :                   ALLOCATE (h_tmp(ncoa, 1)); h_tmp = 0.0_dp
    2912       99102 :                   ALLOCATE (I_ab(nsgfa(iset), 1)); I_ab = 0.0_dp
    2913      117030 :                   ALLOCATE (pab(ncoa, 1)); pab = 0.0_dp
    2914             : 
    2915       97110 :                   I_ab(1:nsgfa(iset), 1) = 2.0_dp*pblock(offset + 1:offset + nsgfa(iset), j_RI - lb_RI)
    2916             :                   CALL dgemm("N", "N", ncoa, 1, nsgfa(iset), 1.0_dp, sphi_a(1, sgfa), SIZE(sphi_a, 1), &
    2917       14442 :                              I_ab(1, 1), nsgfa(iset), 0.0_dp, pab(1, 1), ncoa)
    2918             : 
    2919       43326 :                   igrid_level = gaussian_gridlevel(pw_env_ext%gridlevel_info, MINVAL(zeta(:, iset)))
    2920             : 
    2921             :                   ! The last three parameters are used to check whether a given function is within the own range.
    2922             :                   ! Here, it is always the case, so let's enforce it because mod(0, 1)==0
    2923       14442 :                   IF (map_gaussian_here(rs_v(igrid_level), cell%h_inv, ra, 0, 1, 0)) THEN
    2924       28884 :                      DO ipgf = 1, npgfa(iset)
    2925       14442 :                         o1 = (ipgf - 1)*ncoset(la_max(iset))
    2926       14442 :                         igrid_level = gaussian_gridlevel(pw_env_ext%gridlevel_info, zeta(ipgf, iset))
    2927             : 
    2928             :                         radius = exp_radius_very_extended(la_min=la_min(iset), la_max=la_max(iset), &
    2929             :                                                           lb_min=0, lb_max=0, ra=ra, rb=ra, rp=ra, &
    2930             :                                                           zetp=zeta(ipgf, iset), &
    2931             :                                                           eps=dft_control%qs_control%eps_gvg_rspace, &
    2932       14442 :                                                           prefactor=1.0_dp, cutoff=1.0_dp)
    2933             : 
    2934             :                         CALL integrate_pgf_product( &
    2935             :                            la_max=la_max(iset), zeta=zeta(ipgf, iset), la_min=la_min(iset), &
    2936             :                            lb_max=0, zetb=0.0_dp, lb_min=0, &
    2937             :                            ra=ra, rab=(/0.0_dp, 0.0_dp, 0.0_dp/), &
    2938             :                            rsgrid=rs_v(igrid_level), &
    2939             :                            hab=h_tmp, pab=pab, &
    2940             :                            o1=o1, &
    2941             :                            o2=0, &
    2942             :                            radius=radius, &
    2943             :                            calculate_forces=.TRUE., &
    2944             :                            force_a=force_a, force_b=force_b, &
    2945       28884 :                            use_virial=use_virial, my_virial_a=my_virial_a, my_virial_b=my_virial_b)
    2946             : 
    2947             :                      END DO
    2948             : 
    2949             :                   END IF
    2950             : 
    2951       14442 :                   offset = offset + nsgfa(iset)
    2952       15936 :                   DEALLOCATE (pab, h_tmp, I_ab)
    2953             :                END DO !iset
    2954             : 
    2955        5976 :                force(ikind)%mp2_non_sep(:, atom_a) = force(ikind)%mp2_non_sep(:, atom_a) + force_a + force_b
    2956       10790 :                IF (use_virial) h_stress = h_stress + my_virial_a + my_virial_b
    2957             : 
    2958             :             END DO !iatom
    2959             :          END DO !j_RI
    2960             :       END DO !jatom
    2961             : 
    2962          12 :       IF (use_virial) THEN
    2963           4 :          CALL auxbas_pw_pool%give_back_pw(rho_g_copy)
    2964          16 :          DO i_xyz = 1, 3
    2965          16 :             CALL auxbas_pw_pool%give_back_pw(dvg(i_xyz))
    2966             :          END DO
    2967             :       END IF
    2968             : 
    2969             :       CALL cleanup_gpw(qs_env, e_cutoff_old, cutoff_old, relative_cutoff_old, para_env_ext, pw_env_ext, &
    2970          12 :                        task_list_ext, auxbas_pw_pool, rho_r, rho_g, pot_g, psi_L)
    2971             : 
    2972          12 :       CALL dbcsr_release(tmp_G_PQ)
    2973          12 :       CALL dbcsr_distribution_release(dbcsr_dist)
    2974          12 :       DEALLOCATE (col_dist, row_dist, pgrid)
    2975             : 
    2976          12 :       CALL mp_para_env_release(para_env_ext)
    2977             : 
    2978          12 :       CALL timestop(handle)
    2979             : 
    2980          48 :    END SUBROUTINE get_2c_gpw_forces
    2981             : 
    2982             : ! **************************************************************************************************
    2983             : !> \brief Calculate the forces due to the (P|Q) MME integral derivatives
    2984             : !> \param G_PQ ...
    2985             : !> \param force ...
    2986             : !> \param mp2_env ...
    2987             : !> \param qs_env ...
    2988             : ! **************************************************************************************************
    2989          16 :    SUBROUTINE get_2c_mme_forces(G_PQ, force, mp2_env, qs_env)
    2990             : 
    2991             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: G_PQ
    2992             :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    2993             :       TYPE(mp2_type), INTENT(INOUT)                      :: mp2_env
    2994             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    2995             : 
    2996             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'get_2c_mme_forces'
    2997             : 
    2998             :       INTEGER :: atom_a, atom_b, G_count, handle, i_xyz, iatom, ikind, iset, jatom, jkind, jset, &
    2999             :          natom, nkind, nseta, nsetb, offset_hab_a, offset_hab_b, R_count, sgfa, sgfb
    3000          16 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, kind_of
    3001          16 :       INTEGER, DIMENSION(:), POINTER                     :: la_max, la_min, lb_max, lb_min, npgfa, &
    3002          16 :                                                             npgfb, nsgfa, nsgfb
    3003          16 :       INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, first_sgfb
    3004             :       LOGICAL                                            :: found
    3005             :       REAL(dp)                                           :: new_force, pref
    3006          16 :       REAL(dp), ALLOCATABLE, DIMENSION(:, :)             :: hab
    3007          16 :       REAL(dp), ALLOCATABLE, DIMENSION(:, :, :)          :: hdab
    3008          16 :       REAL(dp), DIMENSION(:, :), POINTER                 :: pblock
    3009             :       REAL(KIND=dp), DIMENSION(3)                        :: ra, rb
    3010          16 :       REAL(KIND=dp), DIMENSION(:, :), POINTER            :: sphi_a, sphi_b, zeta, zetb
    3011          16 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    3012             :       TYPE(cell_type), POINTER                           :: cell
    3013             :       TYPE(dbcsr_iterator_type)                          :: iter
    3014             :       TYPE(gto_basis_set_p_type), ALLOCATABLE, &
    3015          16 :          DIMENSION(:), TARGET                            :: basis_set_ri_aux
    3016             :       TYPE(gto_basis_set_type), POINTER                  :: basis_set_a, basis_set_b
    3017             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    3018          16 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    3019          16 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    3020             : 
    3021          16 :       NULLIFY (qs_kind_set, basis_set_a, basis_set_b, pblock, particle_set, &
    3022          16 :                cell, la_max, la_min, lb_min, npgfa, lb_max, npgfb, nsgfa, &
    3023          16 :                nsgfb, first_sgfa, first_sgfb, sphi_a, sphi_b, zeta, zetb, &
    3024          16 :                atomic_kind_set, para_env)
    3025             : 
    3026          16 :       CALL timeset(routineN, handle)
    3027             : 
    3028             :       CALL get_qs_env(qs_env, qs_kind_set=qs_kind_set, nkind=nkind, particle_set=particle_set, &
    3029          16 :                       cell=cell, atomic_kind_set=atomic_kind_set, natom=natom, para_env=para_env)
    3030             : 
    3031          16 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of, atom_of_kind=atom_of_kind)
    3032             : 
    3033          80 :       ALLOCATE (basis_set_ri_aux(nkind))
    3034          16 :       CALL basis_set_list_setup(basis_set_ri_aux, "RI_AUX", qs_kind_set)
    3035             : 
    3036          16 :       G_count = 0; R_count = 0
    3037             : 
    3038          16 :       CALL dbcsr_iterator_start(iter, G_PQ)
    3039         116 :       DO WHILE (dbcsr_iterator_blocks_left(iter))
    3040             : 
    3041         100 :          CALL dbcsr_iterator_next_block(iter, row=iatom, column=jatom)
    3042         100 :          CALL dbcsr_get_block_p(G_PQ, iatom, jatom, pblock, found)
    3043         100 :          IF (.NOT. found) CYCLE
    3044         100 :          IF (iatom > jatom) CYCLE
    3045          64 :          pref = 2.0_dp
    3046          64 :          IF (iatom == jatom) pref = 1.0_dp
    3047             : 
    3048          64 :          ikind = kind_of(iatom)
    3049          64 :          jkind = kind_of(jatom)
    3050             : 
    3051          64 :          atom_a = atom_of_kind(iatom)
    3052          64 :          atom_b = atom_of_kind(jatom)
    3053             : 
    3054          64 :          basis_set_a => basis_set_ri_aux(ikind)%gto_basis_set
    3055          64 :          first_sgfa => basis_set_a%first_sgf
    3056          64 :          la_max => basis_set_a%lmax
    3057          64 :          la_min => basis_set_a%lmin
    3058          64 :          nseta = basis_set_a%nset
    3059          64 :          nsgfa => basis_set_a%nsgf_set
    3060          64 :          sphi_a => basis_set_a%sphi
    3061          64 :          zeta => basis_set_a%zet
    3062          64 :          npgfa => basis_set_a%npgf
    3063             : 
    3064          64 :          basis_set_b => basis_set_ri_aux(jkind)%gto_basis_set
    3065          64 :          first_sgfb => basis_set_b%first_sgf
    3066          64 :          lb_max => basis_set_b%lmax
    3067          64 :          lb_min => basis_set_b%lmin
    3068          64 :          nsetb = basis_set_b%nset
    3069          64 :          nsgfb => basis_set_b%nsgf_set
    3070          64 :          sphi_b => basis_set_b%sphi
    3071          64 :          zetb => basis_set_b%zet
    3072          64 :          npgfb => basis_set_b%npgf
    3073             : 
    3074          64 :          ra(:) = pbc(particle_set(iatom)%r, cell)
    3075          64 :          rb(:) = pbc(particle_set(jatom)%r, cell)
    3076             : 
    3077         256 :          ALLOCATE (hab(basis_set_a%nsgf, basis_set_b%nsgf))
    3078         256 :          ALLOCATE (hdab(3, basis_set_a%nsgf, basis_set_b%nsgf))
    3079       47944 :          hab(:, :) = 0.0_dp
    3080      187912 :          hdab(:, :, :) = 0.0_dp
    3081             : 
    3082          64 :          offset_hab_a = 0
    3083         756 :          DO iset = 1, nseta
    3084         692 :             sgfa = first_sgfa(1, iset)
    3085             : 
    3086         692 :             offset_hab_b = 0
    3087        6340 :             DO jset = 1, nsetb
    3088        5648 :                sgfb = first_sgfb(1, jset)
    3089             : 
    3090             :                CALL integrate_set_2c(mp2_env%eri_mme_param%par, mp2_env%potential_parameter, la_min(iset), &
    3091             :                                      la_max(iset), lb_min(jset), lb_max(jset), npgfa(iset), npgfb(jset), &
    3092             :                                      zeta(:, iset), zetb(:, jset), ra, rb, hab, nsgfa(iset), nsgfb(jset), &
    3093             :                                      offset_hab_a, offset_hab_b, 0, 0, sphi_a, sphi_b, sgfa, sgfb, &
    3094             :                                      nsgfa(iset), nsgfb(jset), do_eri_mme, hdab=hdab, &
    3095        5648 :                                      G_count=G_count, R_count=R_count)
    3096             : 
    3097        6340 :                offset_hab_b = offset_hab_b + nsgfb(jset)
    3098             :             END DO
    3099         756 :             offset_hab_a = offset_hab_a + nsgfa(iset)
    3100             :          END DO
    3101             : 
    3102         256 :          DO i_xyz = 1, 3
    3103      143832 :             new_force = pref*SUM(pblock(:, :)*hdab(i_xyz, :, :))
    3104         192 :             force(ikind)%mp2_non_sep(i_xyz, atom_a) = force(ikind)%mp2_non_sep(i_xyz, atom_a) + new_force
    3105         256 :             force(jkind)%mp2_non_sep(i_xyz, atom_b) = force(jkind)%mp2_non_sep(i_xyz, atom_b) - new_force
    3106             :          END DO
    3107             : 
    3108         216 :          DEALLOCATE (hab, hdab)
    3109             :       END DO
    3110          16 :       CALL dbcsr_iterator_stop(iter)
    3111             : 
    3112          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)
    3113             : 
    3114          16 :       CALL timestop(handle)
    3115             : 
    3116          48 :    END SUBROUTINE get_2c_mme_forces
    3117             : 
    3118             : ! **************************************************************************************************
    3119             : !> \brief This routines gather all the force updates due to the response density and the trace with F
    3120             : !>        Also update the forces due to the SCF density for XC and exact exchange
    3121             : !> \param p_env the p_env coming from the response calculation
    3122             : !> \param matrix_hz the matrix going into the RHS of the response equation
    3123             : !> \param matrix_p_F the density matrix with which we evaluate Trace[P*F]
    3124             : !> \param matrix_p_F_admm ...
    3125             : !> \param qs_env ...
    3126             : !> \note very much inspired from the response_force routine in response_solver.F, especially for virial
    3127             : ! **************************************************************************************************
    3128          50 :    SUBROUTINE update_im_time_forces(p_env, matrix_hz, matrix_p_F, matrix_p_F_admm, qs_env)
    3129             : 
    3130             :       TYPE(qs_p_env_type), POINTER                       :: p_env
    3131             :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_hz, matrix_p_F, matrix_p_F_admm
    3132             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3133             : 
    3134             :       CHARACTER(len=*), PARAMETER :: routineN = 'update_im_time_forces'
    3135             : 
    3136             :       INTEGER                                            :: handle, i, idens, ispin, n_rep_hf, nao, &
    3137             :                                                             nao_aux, nder, nimages, nocc, nspins
    3138          50 :       INTEGER, DIMENSION(:, :, :), POINTER               :: cell_to_index
    3139             :       LOGICAL                                            :: do_exx, do_hfx, do_tau, do_tau_admm, &
    3140             :                                                             use_virial
    3141             :       REAL(dp)                                           :: dummy_real1, dummy_real2, ehartree, &
    3142             :                                                             eps_ppnl, exc, focc
    3143             :       REAL(dp), DIMENSION(3, 3)                          :: h_stress, pv_loc
    3144             :       TYPE(admm_type), POINTER                           :: admm_env
    3145          50 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
    3146          50 :       TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: current_density, current_density_admm, &
    3147          50 :          current_mat_h, matrix_p_mp2, matrix_p_mp2_admm, matrix_s, matrix_s_aux_fit, matrix_w, &
    3148          50 :          rho_ao, rho_ao_aux, scrm, scrm_admm
    3149          50 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: dbcsr_work_h, dbcsr_work_p
    3150             :       TYPE(dbcsr_type)                                   :: dbcsr_work
    3151             :       TYPE(dft_control_type), POINTER                    :: dft_control
    3152          50 :       TYPE(hfx_type), DIMENSION(:, :), POINTER           :: x_data
    3153          50 :       TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos
    3154             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    3155             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
    3156          50 :          POINTER                                         :: sab_orb, sac_ae, sac_ppl, sap_ppnl
    3157          50 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
    3158             :       TYPE(pw_c1d_gs_type)                               :: rho_tot_gspace, rhoz_tot_gspace, &
    3159             :                                                             zv_hartree_gspace
    3160          50 :       TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER        :: rhoz_g
    3161             :       TYPE(pw_env_type), POINTER                         :: pw_env
    3162             :       TYPE(pw_poisson_type), POINTER                     :: poisson_env
    3163             :       TYPE(pw_pool_type), POINTER                        :: auxbas_pw_pool
    3164             :       TYPE(pw_r3d_rs_type)                               :: vh_rspace, vhxc_rspace, zv_hartree_rspace
    3165          50 :       TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER        :: rhoz_r, tauz_r, v_xc, v_xc_tau, &
    3166          50 :                                                             vadmm_rspace, vtau_rspace, vxc_rspace
    3167          50 :       TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
    3168          50 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
    3169             :       TYPE(qs_rho_type), POINTER                         :: rho, rho_aux_fit
    3170             :       TYPE(section_vals_type), POINTER                   :: hfx_section, xc_section
    3171             :       TYPE(task_list_type), POINTER                      :: task_list_aux_fit
    3172             :       TYPE(virial_type), POINTER                         :: virial
    3173             : 
    3174          50 :       NULLIFY (scrm, rho, dft_control, matrix_p_mp2, matrix_s, matrix_p_mp2_admm, admm_env, sab_orb, &
    3175          50 :                cell_to_index, dbcsr_work_p, dbcsr_work_h, sac_ae, sac_ppl, sap_ppnl, force, virial, &
    3176          50 :                qs_kind_set, atomic_kind_set, particle_set, pw_env, poisson_env, auxbas_pw_pool, &
    3177          50 :                task_list_aux_fit, matrix_s_aux_fit, scrm_admm, rho_aux_fit, rho_ao_aux, x_data, &
    3178          50 :                hfx_section, xc_section, para_env, rhoz_g, rhoz_r, tauz_r, v_xc, v_xc_tau, &
    3179          50 :                vxc_rspace, vtau_rspace, vadmm_rspace, rho_ao, matrix_w)
    3180             : 
    3181          50 :       CALL timeset(routineN, handle)
    3182             : 
    3183             :       CALL get_qs_env(qs_env, rho=rho, dft_control=dft_control, matrix_s=matrix_s, admm_env=admm_env, &
    3184             :                       sab_orb=sab_orb, sac_ae=sac_ae, sac_ppl=sac_ppl, sap_ppnl=sap_ppnl, force=force, &
    3185             :                       virial=virial, particle_set=particle_set, qs_kind_set=qs_kind_set, &
    3186          50 :                       atomic_kind_set=atomic_kind_set, x_data=x_data, para_env=para_env)
    3187          50 :       nspins = dft_control%nspins
    3188             : 
    3189          50 :       use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
    3190          50 :       IF (use_virial) virial%pv_calculate = .TRUE.
    3191             : 
    3192             :       !Whether we replace the force/energy of SCF XC with HF in RPA
    3193          50 :       do_exx = .FALSE.
    3194          50 :       IF (qs_env%mp2_env%method == ri_rpa_method_gpw) THEN
    3195          28 :          hfx_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC%WF_CORRELATION%RI_RPA%HF")
    3196          28 :          CALL section_vals_get(hfx_section, explicit=do_exx)
    3197             :       END IF
    3198             : 
    3199             :       !Get the mp2 density matrix which is p_env%p1 + matrix_p_F
    3200          50 :       CALL get_qs_env(qs_env, matrix_p_mp2=matrix_p_mp2, matrix_p_mp2_admm=matrix_p_mp2_admm)
    3201             : 
    3202             :       !The kinetic term (only response density)
    3203          50 :       NULLIFY (scrm)
    3204          50 :       IF (nspins == 2) CALL dbcsr_add(matrix_p_mp2(1)%matrix, matrix_p_mp2(2)%matrix, 1.0_dp, 1.0_dp)
    3205             :       CALL build_kinetic_matrix(qs_env%ks_env, matrix_t=scrm, &
    3206             :                                 matrix_name="KINETIC ENERGY MATRIX", &
    3207             :                                 basis_type="ORB", &
    3208             :                                 sab_nl=sab_orb, calculate_forces=.TRUE., &
    3209          50 :                                 matrix_p=matrix_p_mp2(1)%matrix)
    3210          50 :       IF (nspins == 2) CALL dbcsr_add(matrix_p_mp2(1)%matrix, matrix_p_mp2(2)%matrix, 1.0_dp, -1.0_dp)
    3211          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3212             : 
    3213             :       !The pseudo-potential terms (only reponse density)
    3214          50 :       CALL dbcsr_allocate_matrix_set(scrm, nspins)
    3215         112 :       DO ispin = 1, nspins
    3216          62 :          ALLOCATE (scrm(ispin)%matrix)
    3217          62 :          CALL dbcsr_create(scrm(ispin)%matrix, template=matrix_s(1)%matrix)
    3218          62 :          CALL dbcsr_copy(scrm(ispin)%matrix, matrix_s(1)%matrix)
    3219         112 :          CALL dbcsr_set(scrm(ispin)%matrix, 0.0_dp)
    3220             :       END DO
    3221             : 
    3222          50 :       nder = 1
    3223          50 :       nimages = 1
    3224          50 :       NULLIFY (cell_to_index)
    3225         424 :       ALLOCATE (dbcsr_work_p(nspins, 1), dbcsr_work_h(nspins, 1))
    3226         112 :       DO ispin = 1, nspins
    3227          62 :          dbcsr_work_p(ispin, 1)%matrix => matrix_p_mp2(ispin)%matrix
    3228         112 :          dbcsr_work_h(ispin, 1)%matrix => scrm(ispin)%matrix
    3229             :       END DO
    3230             : 
    3231          50 :       IF (ASSOCIATED(sac_ae)) THEN
    3232             :          CALL build_core_ae(dbcsr_work_h, dbcsr_work_p, force, &
    3233             :                             virial, .TRUE., use_virial, nder, &
    3234             :                             qs_kind_set, atomic_kind_set, particle_set, &
    3235           0 :                             sab_orb, sac_ae, nimages, cell_to_index)
    3236             :       END IF
    3237             : 
    3238          50 :       IF (ASSOCIATED(sac_ppl)) THEN
    3239             :          CALL build_core_ppl(dbcsr_work_h, dbcsr_work_p, force, &
    3240             :                              virial, .TRUE., use_virial, nder, &
    3241             :                              qs_kind_set, atomic_kind_set, particle_set, &
    3242          50 :                              sab_orb, sac_ppl, nimages, cell_to_index, "ORB")
    3243             :       END IF
    3244             : 
    3245          50 :       IF (ASSOCIATED(sap_ppnl)) THEN
    3246          50 :          eps_ppnl = dft_control%qs_control%eps_ppnl
    3247             :          CALL build_core_ppnl(dbcsr_work_h, dbcsr_work_p, force, &
    3248             :                               virial, .TRUE., use_virial, nder, &
    3249             :                               qs_kind_set, atomic_kind_set, particle_set, &
    3250          50 :                               sab_orb, sap_ppnl, eps_ppnl, nimages, cell_to_index, "ORB")
    3251             :       END IF
    3252          50 :       DEALLOCATE (dbcsr_work_p, dbcsr_work_h)
    3253             : 
    3254          50 :       IF (use_virial) THEN
    3255           4 :          h_stress = 0.0_dp
    3256          52 :          virial%pv_xc = 0.0_dp
    3257           4 :          NULLIFY (vxc_rspace, vtau_rspace, vadmm_rspace)
    3258             :          CALL ks_ref_potential(qs_env, vh_rspace, vxc_rspace, vtau_rspace, vadmm_rspace, &
    3259           4 :                                dummy_real1, dummy_real2, h_stress)
    3260          52 :          virial%pv_ehartree = virial%pv_ehartree + h_stress/REAL(para_env%num_pe, dp)
    3261          52 :          virial%pv_virial = virial%pv_virial + h_stress/REAL(para_env%num_pe, dp)
    3262           4 :          IF (.NOT. do_exx) THEN
    3263             :             !if RPA EXX, then do not consider XC virial (replaced by RPA%HF virial)
    3264          52 :             virial%pv_exc = virial%pv_exc - virial%pv_xc
    3265          52 :             virial%pv_virial = virial%pv_virial - virial%pv_xc
    3266             :          END IF
    3267             :       ELSE
    3268          46 :          CALL ks_ref_potential(qs_env, vh_rspace, vxc_rspace, vtau_rspace, vadmm_rspace, dummy_real1, dummy_real2)
    3269             :       END IF
    3270          50 :       do_tau = ASSOCIATED(vtau_rspace)
    3271             : 
    3272             :       !Core forces from the SCF
    3273          50 :       CALL integrate_v_core_rspace(vh_rspace, qs_env)
    3274             : 
    3275             :       !The Hartree-xc potential term, P*dVHxc (mp2 + SCF density x deriv of the SCF potential)
    3276             :       !Get the total density
    3277          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
    3278         112 :       DO ispin = 1, nspins
    3279         112 :          CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, 1.0_dp)
    3280             :       END DO
    3281             : 
    3282          50 :       CALL get_qs_env(qs_env, pw_env=pw_env)
    3283             :       CALL pw_env_get(pw_env, auxbas_pw_pool=auxbas_pw_pool, &
    3284          50 :                       poisson_env=poisson_env)
    3285          50 :       CALL auxbas_pw_pool%create_pw(vhxc_rspace)
    3286             : 
    3287          98 :       IF (use_virial) pv_loc = virial%pv_virial
    3288             : 
    3289          50 :       IF (do_exx) THEN
    3290             :          !Only want response XC contribution, but SCF+response Hartree contribution
    3291          44 :          DO ispin = 1, nspins
    3292             :             !Hartree
    3293          26 :             CALL pw_transfer(vh_rspace, vhxc_rspace)
    3294             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3295             :                                     hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3296          26 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3297             :             !XC
    3298          26 :             CALL pw_transfer(vxc_rspace(ispin), vhxc_rspace)
    3299             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3300             :                                     hmat=scrm(ispin), pmat=matrix_p_mp2(ispin), &
    3301          26 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3302          44 :             IF (do_tau) THEN
    3303             :                CALL integrate_v_rspace(v_rspace=vtau_rspace(ispin), &
    3304             :                                        hmat=scrm(ispin), pmat=matrix_p_mp2(ispin), &
    3305           0 :                                        qs_env=qs_env, calculate_forces=.TRUE., compute_tau=.TRUE.)
    3306             :             END IF
    3307             :          END DO
    3308             :       ELSE
    3309          68 :          DO ispin = 1, nspins
    3310          36 :             CALL pw_transfer(vh_rspace, vhxc_rspace)
    3311          36 :             CALL pw_axpy(vxc_rspace(ispin), vhxc_rspace)
    3312             :             CALL integrate_v_rspace(v_rspace=vhxc_rspace, &
    3313             :                                     hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3314          36 :                                     qs_env=qs_env, calculate_forces=.TRUE.)
    3315          68 :             IF (do_tau) THEN
    3316             :                CALL integrate_v_rspace(v_rspace=vtau_rspace(ispin), &
    3317             :                                        hmat=scrm(ispin), pmat=rho_ao(ispin), &
    3318           8 :                                        qs_env=qs_env, calculate_forces=.TRUE., compute_tau=.TRUE.)
    3319             :             END IF
    3320             :          END DO
    3321             :       END IF
    3322          50 :       CALL auxbas_pw_pool%give_back_pw(vhxc_rspace)
    3323             : 
    3324          98 :       IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3325             : 
    3326             :       !The admm projection contribution (mp2 + SCF densities). If EXX, then only mp2 density
    3327          50 :       IF (dft_control%do_admm) THEN
    3328             :          CALL get_admm_env(admm_env, task_list_aux_fit=task_list_aux_fit, rho_aux_fit=rho_aux_fit, &
    3329          16 :                            matrix_s_aux_fit=matrix_s_aux_fit)
    3330          16 :          CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux)
    3331          16 :          CALL dbcsr_allocate_matrix_set(scrm_admm, nspins)
    3332          36 :          DO ispin = 1, nspins
    3333          20 :             ALLOCATE (scrm_admm(ispin)%matrix)
    3334          20 :             CALL dbcsr_create(scrm_admm(ispin)%matrix, template=matrix_s_aux_fit(1)%matrix)
    3335          20 :             CALL dbcsr_copy(scrm_admm(ispin)%matrix, matrix_s_aux_fit(1)%matrix)
    3336          36 :             CALL dbcsr_set(scrm_admm(ispin)%matrix, 0.0_dp)
    3337             :          END DO
    3338             : 
    3339          64 :          IF (use_virial) pv_loc = virial%pv_virial
    3340          16 :          IF (.NOT. qs_env%admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    3341          36 :             DO ispin = 1, nspins
    3342          36 :                IF (do_exx) THEN
    3343             :                   CALL integrate_v_rspace(v_rspace=vadmm_rspace(ispin), &
    3344             :                                           hmat=scrm_admm(ispin), pmat=matrix_p_mp2_admm(ispin), &
    3345             :                                           qs_env=qs_env, calculate_forces=.TRUE., &
    3346           8 :                                           basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3347             :                ELSE
    3348          12 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    3349             :                   CALL integrate_v_rspace(v_rspace=vadmm_rspace(ispin), &
    3350             :                                           hmat=scrm_admm(ispin), pmat=rho_ao_aux(ispin), &
    3351             :                                           qs_env=qs_env, calculate_forces=.TRUE., &
    3352          12 :                                           basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3353          12 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, -1.0_dp)
    3354             :                END IF
    3355             :             END DO
    3356             :          END IF
    3357          64 :          IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3358             : 
    3359          16 :          CALL tddft_hfx_matrix(scrm_admm, rho_ao_aux, qs_env, .FALSE., .FALSE.)
    3360             : 
    3361          16 :          IF (do_exx) THEN
    3362           4 :             CALL admm_projection_derivative(qs_env, scrm_admm, matrix_p_mp2)
    3363             :          ELSE
    3364          12 :             CALL admm_projection_derivative(qs_env, scrm_admm, rho_ao)
    3365             :          END IF
    3366             :       END IF
    3367             : 
    3368             :       !The exact-exchange term (mp2 + SCF densities)
    3369          50 :       xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    3370          50 :       hfx_section => section_vals_get_subs_vals(xc_section, "HF")
    3371          50 :       CALL section_vals_get(hfx_section, explicit=do_hfx)
    3372             : 
    3373          50 :       IF (do_hfx) THEN
    3374          32 :          CALL section_vals_get(hfx_section, n_repetition=n_rep_hf)
    3375          32 :          CPASSERT(n_rep_hf == 1)
    3376          80 :          IF (use_virial) virial%pv_fock_4c = 0.0_dp
    3377             : 
    3378             :          !In case of EXX, only want to response HFX forces, as the SCF will change according to RI_RPA%HF
    3379          32 :          IF (do_exx) THEN
    3380           8 :             IF (dft_control%do_admm) THEN
    3381           4 :                CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3382           4 :                CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux, rho_ao_kp=dbcsr_work_p)
    3383           4 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3384             : 
    3385             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3386             :                                             x_data(1, 1)%general_parameter%fraction, &
    3387             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2_admm, &
    3388           0 :                                             use_virial=use_virial, resp_only=.TRUE.)
    3389             :                ELSE
    3390             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2_admm, hfx_section, para_env, &
    3391           4 :                                                1, use_virial, resp_only=.TRUE.)
    3392             :                END IF
    3393             :             ELSE
    3394           8 :                DO ispin = 1, nspins
    3395           8 :                   CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, -1.0_dp)
    3396             :                END DO
    3397           4 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3398           4 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3399             : 
    3400             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3401             :                                             x_data(1, 1)%general_parameter%fraction, &
    3402             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2, &
    3403           0 :                                             use_virial=use_virial, resp_only=.TRUE.)
    3404             :                ELSE
    3405             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2, hfx_section, para_env, &
    3406           4 :                                                1, use_virial, resp_only=.TRUE.)
    3407             :                END IF
    3408           8 :                DO ispin = 1, nspins
    3409           8 :                   CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, 1.0_dp)
    3410             :                END DO
    3411             :             END IF !admm
    3412             : 
    3413             :          ELSE !No Exx
    3414          24 :             IF (dft_control%do_admm) THEN
    3415          12 :                CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3416          12 :                CALL qs_rho_get(rho_aux_fit, rho_ao=rho_ao_aux, rho_ao_kp=dbcsr_work_p)
    3417          24 :                DO ispin = 1, nspins
    3418          24 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, 1.0_dp)
    3419             :                END DO
    3420          12 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3421             : 
    3422             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3423             :                                             x_data(1, 1)%general_parameter%fraction, &
    3424             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2_admm, &
    3425           0 :                                             use_virial=use_virial, resp_only=.FALSE.)
    3426             :                ELSE
    3427             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2_admm, hfx_section, para_env, &
    3428          12 :                                                1, use_virial, resp_only=.FALSE.)
    3429             :                END IF
    3430          24 :                DO ispin = 1, nspins
    3431          24 :                   CALL dbcsr_add(rho_ao_aux(ispin)%matrix, matrix_p_mp2_admm(ispin)%matrix, 1.0_dp, -1.0_dp)
    3432             :                END DO
    3433             :             ELSE
    3434          12 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3435          12 :                IF (x_data(1, 1)%do_hfx_ri) THEN
    3436             : 
    3437             :                   CALL hfx_ri_update_forces(qs_env, x_data(1, 1)%ri_data, nspins, &
    3438             :                                             x_data(1, 1)%general_parameter%fraction, &
    3439             :                                             rho_ao=dbcsr_work_p, rho_ao_resp=matrix_p_mp2, &
    3440           0 :                                             use_virial=use_virial, resp_only=.FALSE.)
    3441             :                ELSE
    3442             :                   CALL derivatives_four_center(qs_env, dbcsr_work_p, matrix_p_mp2, hfx_section, para_env, &
    3443          12 :                                                1, use_virial, resp_only=.FALSE.)
    3444             :                END IF
    3445             :             END IF
    3446             :          END IF !do_exx
    3447             : 
    3448          32 :          IF (use_virial) THEN
    3449          52 :             virial%pv_exx = virial%pv_exx - virial%pv_fock_4c
    3450          52 :             virial%pv_virial = virial%pv_virial - virial%pv_fock_4c
    3451             :          END IF
    3452             :       END IF
    3453             : 
    3454             :       !retrieve the SCF density
    3455          50 :       CALL qs_rho_get(rho, rho_ao=rho_ao)
    3456         112 :       DO ispin = 1, nspins
    3457         112 :          CALL dbcsr_add(rho_ao(ispin)%matrix, matrix_p_mp2(ispin)%matrix, 1.0_dp, -1.0_dp)
    3458             :       END DO
    3459             : 
    3460             :       !From here, we need to do everything twice. Once for the response density, and once for the
    3461             :       !density that is used for the trace Tr[P*F]. The reason is that the former is needed for the
    3462             :       !eventual overlap contribution from matrix_wz
    3463             :       !Only with the mp2 density
    3464             : 
    3465         436 :       ALLOCATE (current_density(nspins), current_mat_h(nspins), current_density_admm(nspins))
    3466         150 :       DO idens = 1, 2
    3467         224 :          DO ispin = 1, nspins
    3468         224 :             IF (idens == 1) THEN
    3469          62 :                current_density(ispin)%matrix => matrix_p_F(ispin)%matrix
    3470          62 :                current_mat_h(ispin)%matrix => scrm(ispin)%matrix
    3471          62 :                IF (dft_control%do_admm) current_density_admm(ispin)%matrix => matrix_p_F_admm(ispin)%matrix
    3472             :             ELSE
    3473          62 :                current_density(ispin)%matrix => p_env%p1(ispin)%matrix
    3474          62 :                current_mat_h(ispin)%matrix => matrix_hz(ispin)%matrix
    3475          62 :                IF (dft_control%do_admm) current_density_admm(ispin)%matrix => p_env%p1_admm(ispin)%matrix
    3476             :             END IF
    3477             :          END DO
    3478             : 
    3479             :          !The core-denstiy derivative
    3480         748 :          ALLOCATE (rhoz_r(nspins), rhoz_g(nspins))
    3481         224 :          DO ispin = 1, nspins
    3482         124 :             CALL auxbas_pw_pool%create_pw(rhoz_r(ispin))
    3483         224 :             CALL auxbas_pw_pool%create_pw(rhoz_g(ispin))
    3484             :          END DO
    3485         100 :          CALL auxbas_pw_pool%create_pw(rhoz_tot_gspace)
    3486         100 :          CALL auxbas_pw_pool%create_pw(zv_hartree_rspace)
    3487         100 :          CALL auxbas_pw_pool%create_pw(zv_hartree_gspace)
    3488             : 
    3489         100 :          CALL pw_zero(rhoz_tot_gspace)
    3490         224 :          DO ispin = 1, nspins
    3491             :             CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3492         124 :                                     rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin))
    3493         224 :             CALL pw_axpy(rhoz_g(ispin), rhoz_tot_gspace)
    3494             :          END DO
    3495             : 
    3496         100 :          IF (use_virial) THEN
    3497             : 
    3498           8 :             CALL get_qs_env(qs_env, rho=rho)
    3499           8 :             CALL auxbas_pw_pool%create_pw(rho_tot_gspace)
    3500             : 
    3501           8 :             CALL calc_rho_tot_gspace(rho_tot_gspace, qs_env, rho)
    3502             : 
    3503           8 :             h_stress(:, :) = 0.0_dp
    3504             :             CALL pw_poisson_solve(poisson_env, &
    3505             :                                   density=rhoz_tot_gspace, &
    3506             :                                   ehartree=ehartree, &
    3507             :                                   vhartree=zv_hartree_gspace, &
    3508             :                                   h_stress=h_stress, &
    3509           8 :                                   aux_density=rho_tot_gspace)
    3510             : 
    3511           8 :             CALL auxbas_pw_pool%give_back_pw(rho_tot_gspace)
    3512             : 
    3513             :             !Green contribution
    3514         104 :             virial%pv_ehartree = virial%pv_ehartree + 2.0_dp*h_stress/REAL(para_env%num_pe, dp)
    3515         104 :             virial%pv_virial = virial%pv_virial + 2.0_dp*h_stress/REAL(para_env%num_pe, dp)
    3516             : 
    3517             :          ELSE
    3518             :             CALL pw_poisson_solve(poisson_env, rhoz_tot_gspace, ehartree, &
    3519          92 :                                   zv_hartree_gspace)
    3520             :          END IF
    3521             : 
    3522         100 :          CALL pw_transfer(zv_hartree_gspace, zv_hartree_rspace)
    3523         100 :          CALL pw_scale(zv_hartree_rspace, zv_hartree_rspace%pw_grid%dvol)
    3524         100 :          CALL integrate_v_core_rspace(zv_hartree_rspace, qs_env)
    3525             : 
    3526         100 :          IF (do_tau) THEN
    3527             :             BLOCK
    3528             :                TYPE(pw_c1d_gs_type) :: tauz_g
    3529          16 :                CALL auxbas_pw_pool%create_pw(tauz_g)
    3530          48 :                ALLOCATE (tauz_r(nspins))
    3531          32 :                DO ispin = 1, nspins
    3532          16 :                   CALL auxbas_pw_pool%create_pw(tauz_r(ispin))
    3533             : 
    3534             :                   CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3535          32 :                                           rho=tauz_r(ispin), rho_gspace=tauz_g, compute_tau=.TRUE.)
    3536             :                END DO
    3537          16 :                CALL auxbas_pw_pool%give_back_pw(tauz_g)
    3538             :             END BLOCK
    3539             :          END IF
    3540             : 
    3541             :          !Volume contribution to the virial
    3542         100 :          IF (use_virial) THEN
    3543             :             !Volume contribution
    3544             :             exc = 0.0_dp
    3545          16 :             DO ispin = 1, nspins
    3546             :                exc = exc + pw_integral_ab(rhoz_r(ispin), vxc_rspace(ispin))/ &
    3547          16 :                      vxc_rspace(ispin)%pw_grid%dvol
    3548             :             END DO
    3549           8 :             IF (ASSOCIATED(vtau_rspace)) THEN
    3550           0 :                DO ispin = 1, nspins
    3551             :                   exc = exc + pw_integral_ab(tauz_r(ispin), vtau_rspace(ispin))/ &
    3552           0 :                         vtau_rspace(ispin)%pw_grid%dvol
    3553             :                END DO
    3554             :             END IF
    3555          32 :             DO i = 1, 3
    3556          24 :                virial%pv_ehartree(i, i) = virial%pv_ehartree(i, i) - 4.0_dp*ehartree/REAL(para_env%num_pe, dp)
    3557          24 :                virial%pv_exc(i, i) = virial%pv_exc(i, i) - exc/REAL(para_env%num_pe, dp)
    3558             :                virial%pv_virial(i, i) = virial%pv_virial(i, i) - 4.0_dp*ehartree/REAL(para_env%num_pe, dp) &
    3559          32 :                                         - exc/REAL(para_env%num_pe, dp)
    3560             :             END DO
    3561             :          END IF
    3562             : 
    3563             :          !The xc-kernel term.
    3564         100 :          IF (dft_control%do_admm) THEN
    3565          32 :             CALL get_qs_env(qs_env, admm_env=admm_env)
    3566          32 :             xc_section => admm_env%xc_section_primary
    3567             :          ELSE
    3568          68 :             xc_section => section_vals_get_subs_vals(qs_env%input, "DFT%XC")
    3569             :          END IF
    3570             : 
    3571         196 :          IF (use_virial) virial%pv_xc = 0.0_dp
    3572             : 
    3573             :          CALL create_kernel(qs_env, &
    3574             :                             vxc=v_xc, &
    3575             :                             vxc_tau=v_xc_tau, &
    3576             :                             rho=rho, &
    3577             :                             rho1_r=rhoz_r, &
    3578             :                             rho1_g=rhoz_g, &
    3579             :                             tau1_r=tauz_r, &
    3580             :                             xc_section=xc_section, &
    3581             :                             compute_virial=use_virial, &
    3582         100 :                             virial_xc=virial%pv_xc)
    3583             : 
    3584         100 :          IF (use_virial) THEN
    3585         104 :             virial%pv_exc = virial%pv_exc + virial%pv_xc
    3586         104 :             virial%pv_virial = virial%pv_virial + virial%pv_xc
    3587             : 
    3588         104 :             pv_loc = virial%pv_virial
    3589             :          END IF
    3590             : 
    3591         100 :          CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3592         224 :          DO ispin = 1, nspins
    3593         124 :             CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    3594         124 :             CALL pw_axpy(zv_hartree_rspace, v_xc(ispin))
    3595             :             CALL integrate_v_rspace(qs_env=qs_env, &
    3596             :                                     v_rspace=v_xc(ispin), &
    3597             :                                     hmat=current_mat_h(ispin), &
    3598             :                                     pmat=dbcsr_work_p(ispin, 1), &
    3599         124 :                                     calculate_forces=.TRUE.)
    3600         224 :             CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    3601             :          END DO
    3602         100 :          CALL auxbas_pw_pool%give_back_pw(rhoz_tot_gspace)
    3603         100 :          CALL auxbas_pw_pool%give_back_pw(zv_hartree_rspace)
    3604         100 :          CALL auxbas_pw_pool%give_back_pw(zv_hartree_gspace)
    3605         100 :          DEALLOCATE (v_xc)
    3606             : 
    3607         100 :          IF (do_tau) THEN
    3608          32 :             DO ispin = 1, nspins
    3609          16 :                CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    3610             :                CALL integrate_v_rspace(qs_env=qs_env, &
    3611             :                                        v_rspace=v_xc_tau(ispin), &
    3612             :                                        hmat=current_mat_h(ispin), &
    3613             :                                        pmat=dbcsr_work_p(ispin, 1), &
    3614             :                                        compute_tau=.TRUE., &
    3615          16 :                                        calculate_forces=.TRUE.)
    3616          32 :                CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    3617             :             END DO
    3618          16 :             DEALLOCATE (v_xc_tau)
    3619             :          END IF
    3620             : 
    3621         196 :          IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3622             : 
    3623         100 :          IF (do_hfx) THEN
    3624          64 :             IF (dft_control%do_admm) THEN
    3625          72 :                DO ispin = 1, nspins
    3626          72 :                   CALL dbcsr_set(scrm_admm(ispin)%matrix, 0.0_dp)
    3627             :                END DO
    3628          32 :                CALL qs_rho_get(rho_aux_fit, tau_r_valid=do_tau_admm)
    3629             : 
    3630          32 :                IF (.NOT. admm_env%aux_exch_func == do_admm_aux_exch_func_none) THEN
    3631          32 :                   CALL get_admm_env(admm_env, rho_aux_fit=rho_aux_fit)
    3632          72 :                   DO ispin = 1, nspins
    3633          40 :                      CALL pw_zero(rhoz_r(ispin))
    3634          40 :                      CALL pw_zero(rhoz_g(ispin))
    3635             :                      CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density_admm(ispin)%matrix, &
    3636             :                                              rho=rhoz_r(ispin), rho_gspace=rhoz_g(ispin), &
    3637          72 :                                              basis_type="AUX_FIT", task_list_external=task_list_aux_fit)
    3638             :                   END DO
    3639             : 
    3640          32 :                   IF (do_tau_admm) THEN
    3641             :                      BLOCK
    3642             :                         TYPE(pw_c1d_gs_type) :: tauz_g
    3643           0 :                         CALL auxbas_pw_pool%create_pw(tauz_g)
    3644           0 :                         DO ispin = 1, nspins
    3645           0 :                            CALL pw_zero(tauz_r(ispin))
    3646             :                            CALL calculate_rho_elec(ks_env=qs_env%ks_env, matrix_p=current_density(ispin)%matrix, &
    3647             :                                                    rho=tauz_r(ispin), rho_gspace=tauz_g, &
    3648             :                                                    basis_type="AUX_FIT", task_list_external=task_list_aux_fit, &
    3649           0 :                                                    compute_tau=.TRUE.)
    3650             :                         END DO
    3651           0 :                         CALL auxbas_pw_pool%give_back_pw(tauz_g)
    3652             :                      END BLOCK
    3653             :                   END IF
    3654             : 
    3655             :                   !Volume contribution to the virial
    3656          32 :                   IF (use_virial) THEN
    3657             :                      exc = 0.0_dp
    3658          16 :                      DO ispin = 1, nspins
    3659             :                         exc = exc + pw_integral_ab(rhoz_r(ispin), vadmm_rspace(ispin))/ &
    3660          16 :                               vadmm_rspace(ispin)%pw_grid%dvol
    3661             :                      END DO
    3662          32 :                      DO i = 1, 3
    3663          24 :                         virial%pv_exc(i, i) = virial%pv_exc(i, i) - exc/REAL(para_env%num_pe, dp)
    3664          32 :                         virial%pv_virial(i, i) = virial%pv_virial(i, i) - exc/REAL(para_env%num_pe, dp)
    3665             :                      END DO
    3666             : 
    3667         104 :                      virial%pv_xc = 0.0_dp
    3668             :                   END IF
    3669             : 
    3670          32 :                   xc_section => admm_env%xc_section_aux
    3671             :                   CALL create_kernel(qs_env, v_xc, v_xc_tau, rho_aux_fit, rhoz_r, rhoz_g, tauz_r, xc_section, &
    3672          32 :                                      compute_virial=use_virial, virial_xc=virial%pv_xc)
    3673             : 
    3674          32 :                   IF (use_virial) THEN
    3675         104 :                      virial%pv_exc = virial%pv_exc + virial%pv_xc
    3676         104 :                      virial%pv_virial = virial%pv_virial + virial%pv_xc
    3677             : 
    3678         104 :                      pv_loc = virial%pv_virial
    3679             :                   END IF
    3680             : 
    3681          32 :                   CALL qs_rho_get(rho_aux_fit, rho_ao_kp=dbcsr_work_p)
    3682          72 :                   DO ispin = 1, nspins
    3683          40 :                      CALL pw_scale(v_xc(ispin), v_xc(ispin)%pw_grid%dvol)
    3684             :                      CALL integrate_v_rspace(qs_env=qs_env, &
    3685             :                                              v_rspace=v_xc(ispin), &
    3686             :                                              hmat=scrm_admm(ispin), &
    3687             :                                              pmat=dbcsr_work_p(ispin, 1), &
    3688             :                                              calculate_forces=.TRUE., &
    3689             :                                              basis_type="AUX_FIT", &
    3690          40 :                                              task_list_external=task_list_aux_fit)
    3691          72 :                      CALL auxbas_pw_pool%give_back_pw(v_xc(ispin))
    3692             :                   END DO
    3693          32 :                   DEALLOCATE (v_xc)
    3694             : 
    3695          32 :                   IF (do_tau_admm) THEN
    3696           0 :                      DO ispin = 1, nspins
    3697           0 :                         CALL pw_scale(v_xc_tau(ispin), v_xc_tau(ispin)%pw_grid%dvol)
    3698             :                         CALL integrate_v_rspace(qs_env=qs_env, &
    3699             :                                                 v_rspace=v_xc_tau(ispin), &
    3700             :                                                 hmat=scrm_admm(ispin), &
    3701             :                                                 pmat=dbcsr_work_p(ispin, 1), &
    3702             :                                                 calculate_forces=.TRUE., &
    3703             :                                                 basis_type="AUX_FIT", &
    3704             :                                                 task_list_external=task_list_aux_fit, &
    3705           0 :                                                 compute_tau=.TRUE.)
    3706           0 :                         CALL auxbas_pw_pool%give_back_pw(v_xc_tau(ispin))
    3707             :                      END DO
    3708           0 :                      DEALLOCATE (v_xc_tau)
    3709             :                   END IF
    3710             : 
    3711         128 :                   IF (use_virial) virial%pv_ehartree = virial%pv_ehartree + (virial%pv_virial - pv_loc)
    3712             :                END IF
    3713             : 
    3714          32 :                CALL tddft_hfx_matrix(scrm_admm, current_density_admm, qs_env, .FALSE., .FALSE.)
    3715             : 
    3716          32 :                CALL qs_rho_get(rho, rho_ao_kp=dbcsr_work_p)
    3717          32 :                CALL admm_projection_derivative(qs_env, scrm_admm, dbcsr_work_p(:, 1))
    3718             : 
    3719             :                !If response density, need to get matrix_hz contribution
    3720          32 :                CALL dbcsr_create(dbcsr_work, template=matrix_s(1)%matrix)
    3721          32 :                IF (idens == 2) THEN
    3722          16 :                   nao = admm_env%nao_orb
    3723          16 :                   nao_aux = admm_env%nao_aux_fit
    3724          36 :                   DO ispin = 1, nspins
    3725          20 :                      CALL dbcsr_copy(dbcsr_work, matrix_hz(ispin)%matrix)
    3726          20 :                      CALL dbcsr_set(dbcsr_work, 0.0_dp)
    3727             : 
    3728             :                      CALL cp_dbcsr_sm_fm_multiply(scrm_admm(ispin)%matrix, admm_env%A, &
    3729          20 :                                                   admm_env%work_aux_orb, nao)
    3730             :                      CALL parallel_gemm('T', 'N', nao, nao, nao_aux, &
    3731             :                                         1.0_dp, admm_env%A, admm_env%work_aux_orb, 0.0_dp, &
    3732          20 :                                         admm_env%work_orb_orb)
    3733          20 :                      CALL copy_fm_to_dbcsr(admm_env%work_orb_orb, dbcsr_work, keep_sparsity=.TRUE.)
    3734          36 :                      CALL dbcsr_add(matrix_hz(ispin)%matrix, dbcsr_work, 1.0_dp, 1.0_dp)
    3735             :                   END DO
    3736             :                END IF
    3737             : 
    3738          32 :                CALL dbcsr_release(dbcsr_work)
    3739             :             ELSE !no admm
    3740             : 
    3741             :                !Need the contribution to matrix_hz as well
    3742          32 :                IF (idens == 2) THEN
    3743          16 :                   CALL tddft_hfx_matrix(matrix_hz, current_density, qs_env, .FALSE., .FALSE.)
    3744             :                END IF
    3745             :             END IF !admm
    3746             :          END IF !do_hfx
    3747             : 
    3748         224 :          DO ispin = 1, nspins
    3749         124 :             CALL auxbas_pw_pool%give_back_pw(rhoz_r(ispin))
    3750         224 :             CALL auxbas_pw_pool%give_back_pw(rhoz_g(ispin))
    3751             :          END DO
    3752         100 :          DEALLOCATE (rhoz_r, rhoz_g)
    3753             : 
    3754         150 :          IF (do_tau) THEN
    3755          32 :             DO ispin = 1, nspins
    3756          32 :                CALL auxbas_pw_pool%give_back_pw(tauz_r(ispin))
    3757             :             END DO
    3758          16 :             DEALLOCATE (tauz_r)
    3759             :          END IF
    3760             :       END DO !idens
    3761          50 :       CALL dbcsr_deallocate_matrix_set(scrm_admm)
    3762             : 
    3763          50 :       DEALLOCATE (current_density, current_mat_h, current_density_admm)
    3764          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3765             : 
    3766             :       !The energy weighted and overlap term. ONLY with the response density
    3767          50 :       focc = 2.0_dp
    3768          50 :       IF (nspins == 2) focc = 1.0_dp
    3769          50 :       CALL get_qs_env(qs_env, mos=mos)
    3770         112 :       DO ispin = 1, nspins
    3771          62 :          CALL get_mo_set(mo_set=mos(ispin), homo=nocc)
    3772             :          CALL calculate_whz_matrix(mos(ispin)%mo_coeff, matrix_hz(ispin)%matrix, &
    3773         112 :                                    p_env%w1(ispin)%matrix, focc, nocc)
    3774             :       END DO
    3775          50 :       IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, p_env%w1(2)%matrix, 1.0_dp, 1.0_dp)
    3776             : 
    3777             :       !Add to it the SCF W matrix, except if EXX (because taken care of by HF response)
    3778          50 :       IF (.NOT. do_exx) THEN
    3779          32 :          CALL compute_matrix_w(qs_env, calc_forces=.TRUE.)
    3780          32 :          CALL get_qs_env(qs_env, matrix_w=matrix_w)
    3781          32 :          CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(1)%matrix, 1.0_dp, 1.0_dp)
    3782          32 :          IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(2)%matrix, 1.0_dp, 1.0_dp)
    3783             :       END IF
    3784             : 
    3785          50 :       NULLIFY (scrm)
    3786             :       CALL build_overlap_matrix(qs_env%ks_env, matrix_s=scrm, &
    3787             :                                 matrix_name="OVERLAP MATRIX", &
    3788             :                                 basis_type_a="ORB", basis_type_b="ORB", &
    3789             :                                 sab_nl=sab_orb, calculate_forces=.TRUE., &
    3790          50 :                                 matrix_p=p_env%w1(1)%matrix)
    3791             : 
    3792          50 :       IF (.NOT. do_exx) THEN
    3793          32 :          CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(1)%matrix, 1.0_dp, -1.0_dp)
    3794          32 :          IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, matrix_w(2)%matrix, 1.0_dp, -1.0_dp)
    3795          68 :          DO ispin = 1, nspins
    3796          68 :             CALL dbcsr_set(matrix_w(ispin)%matrix, 0.0_dp)
    3797             :          END DO
    3798             :       END IF
    3799             : 
    3800          50 :       IF (nspins == 2) CALL dbcsr_add(p_env%w1(1)%matrix, p_env%w1(2)%matrix, 1.0_dp, -1.0_dp)
    3801          50 :       CALL dbcsr_deallocate_matrix_set(scrm)
    3802             : 
    3803          50 :       IF (use_virial) virial%pv_calculate = .FALSE.
    3804             : 
    3805             :       !clean-up
    3806          50 :       CALL auxbas_pw_pool%give_back_pw(vh_rspace)
    3807             : 
    3808         112 :       DO ispin = 1, nspins
    3809          62 :          CALL auxbas_pw_pool%give_back_pw(vxc_rspace(ispin))
    3810          62 :          IF (ASSOCIATED(vtau_rspace)) THEN
    3811           8 :             CALL auxbas_pw_pool%give_back_pw(vtau_rspace(ispin))
    3812             :          END IF
    3813         112 :          IF (ASSOCIATED(vadmm_rspace)) THEN
    3814          20 :             CALL auxbas_pw_pool%give_back_pw(vadmm_rspace(ispin))
    3815             :          END IF
    3816             :       END DO
    3817          50 :       DEALLOCATE (vxc_rspace)
    3818          50 :       IF (ASSOCIATED(vtau_rspace)) DEALLOCATE (vtau_rspace)
    3819          50 :       IF (ASSOCIATED(vadmm_rspace)) DEALLOCATE (vadmm_rspace)
    3820             : 
    3821          50 :       CALL timestop(handle)
    3822             : 
    3823         100 :    END SUBROUTINE update_im_time_forces
    3824             : 
    3825             : ! **************************************************************************************************
    3826             : !> \brief Iteratively builds the matrix Y = sum_k Y_k until convergence, where
    3827             : !>        Y_k = 1/k*2^n (A/2^n) Y_k-1 + 1/k!*2^n * PR(n) * (A/2^n)^(k-1)
    3828             : !>        n is chosen such that the norm of A is < 1 (and e^A converges fast)
    3829             : !>        PR(n) =  e^(A/2^n)*PR(n-1) + PR(n-1)*e^(A/2^n), PR(0) = P*R^T
    3830             : !> \param Y ...
    3831             : !> \param A ...
    3832             : !> \param P ...
    3833             : !> \param R ...
    3834             : !> \param filter_eps ...
    3835             : ! **************************************************************************************************
    3836         340 :    SUBROUTINE build_Y_matrix(Y, A, P, R, filter_eps)
    3837             : 
    3838             :       TYPE(dbcsr_type), INTENT(OUT)                      :: Y
    3839             :       TYPE(dbcsr_type), INTENT(INOUT)                    :: A, P, R
    3840             :       REAL(dp), INTENT(IN)                               :: filter_eps
    3841             : 
    3842             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'build_Y_matrix'
    3843             : 
    3844             :       INTEGER                                            :: handle, k, n
    3845             :       REAL(dp)                                           :: norm_scalar, threshold
    3846             :       TYPE(dbcsr_type)                                   :: A2n, exp_A2n, PRn, work, work2, Yk
    3847             : 
    3848         340 :       CALL timeset(routineN, handle)
    3849             : 
    3850         340 :       threshold = 1.0E-16_dp
    3851             : 
    3852             :       !Find n such that norm(A) < 1 and we insure convergence of the exponential
    3853         340 :       norm_scalar = dbcsr_frobenius_norm(A)
    3854             : 
    3855             :       !checked: result invariant with value of n
    3856         340 :       n = 1
    3857         466 :       DO
    3858         806 :          IF ((norm_scalar/2.0_dp**n) < 1.0_dp) EXIT
    3859         466 :          n = n + 1
    3860             :       END DO
    3861             : 
    3862             :       !Calculate PR(n) recursively
    3863         340 :       CALL dbcsr_create(PRn, template=A, matrix_type=dbcsr_type_no_symmetry)
    3864         340 :       CALL dbcsr_create(work, template=A, matrix_type=dbcsr_type_no_symmetry)
    3865         340 :       CALL dbcsr_multiply('N', 'N', 1.0_dp, P, R, 0.0_dp, work, filter_eps=filter_eps)
    3866         340 :       CALL dbcsr_create(exp_A2n, template=A, matrix_type=dbcsr_type_no_symmetry)
    3867             : 
    3868        1146 :       DO k = 1, n
    3869         806 :          CALL matrix_exponential(exp_A2n, A, 1.0_dp, 0.5_dp**k, threshold)
    3870         806 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, exp_A2n, work, 0.0_dp, PRn, filter_eps=filter_eps)
    3871         806 :          CALL dbcsr_multiply('N', 'N', 1.0_dp, work, exp_A2n, 1.0_dp, PRn, filter_eps=filter_eps)
    3872        1146 :          CALL dbcsr_copy(work, PRn)
    3873             :       END DO
    3874         340 :       CALL dbcsr_release(exp_A2n)
    3875             : 
    3876             :       !Calculate Y iteratively, until convergence
    3877         340 :       CALL dbcsr_create(A2n, template=A, matrix_type=dbcsr_type_no_symmetry)
    3878         340 :       CALL dbcsr_copy(A2n, A)
    3879         340 :       CALL dbcsr_scale(A2n, 0.5_dp**n)
    3880         340 :       CALL dbcsr_create(Y, template=A, matrix_type=dbcsr_type_no_symmetry)
    3881         340 :       CALL dbcsr_create(Yk, template=A, matrix_type=dbcsr_type_no_symmetry)
    3882         340 :       CALL dbcsr_create(work2, template=A, matrix_type=dbcsr_type_no_symmetry)
    3883             : 
    3884             :       !k=1
    3885         340 :       CALL dbcsr_scale(PRn, 0.5_dp**n)
    3886         340 :       CALL dbcsr_copy(work, PRn)
    3887         340 :       CALL dbcsr_copy(work2, PRn)
    3888         340 :       CALL dbcsr_add(Y, PRn, 1.0_dp, 1.0_dp)
    3889             : 
    3890         340 :       k = 1
    3891        1908 :       DO
    3892        2248 :          k = k + 1
    3893        2248 :          CALL dbcsr_multiply('N', 'N', 1.0_dp/REAL(k, dp), A2n, work, 0.0_dp, Yk, filter_eps=filter_eps)
    3894        2248 :          CALL dbcsr_multiply('N', 'N', 1.0_dp/REAL(k, dp), work2, A2n, 0.0_dp, PRn, filter_eps=filter_eps)
    3895             : 
    3896        2248 :          CALL dbcsr_add(Yk, PRn, 1.0_dp, 1.0_dp)
    3897        2248 :          CALL dbcsr_add(Y, Yk, 1.0_dp, 1.0_dp)
    3898             : 
    3899        2248 :          IF (dbcsr_frobenius_norm(Yk) < threshold) EXIT
    3900        1908 :          CALL dbcsr_copy(work, Yk)
    3901        1908 :          CALL dbcsr_copy(work2, PRn)
    3902             :       END DO
    3903             : 
    3904         340 :       CALL dbcsr_release(work)
    3905         340 :       CALL dbcsr_release(work2)
    3906         340 :       CALL dbcsr_release(PRn)
    3907         340 :       CALL dbcsr_release(A2n)
    3908         340 :       CALL dbcsr_release(Yk)
    3909             : 
    3910         340 :       CALL timestop(handle)
    3911             : 
    3912         340 :    END SUBROUTINE build_Y_matrix
    3913             : 
    3914             : ! **************************************************************************************************
    3915             : !> \brief Overwrites the "optimal" Laplace quadrature with that of the first step
    3916             : !> \param tj ...
    3917             : !> \param wj ...
    3918             : !> \param tau_tj ...
    3919             : !> \param tau_wj ...
    3920             : !> \param weights_cos_tf_t_to_w ...
    3921             : !> \param weights_cos_tf_w_to_t ...
    3922             : !> \param do_laplace ...
    3923             : !> \param do_im_time ...
    3924             : !> \param num_integ_points ...
    3925             : !> \param unit_nr ...
    3926             : !> \param qs_env ...
    3927             : ! **************************************************************************************************
    3928         202 :    SUBROUTINE keep_initial_quad(tj, wj, tau_tj, tau_wj, weights_cos_tf_t_to_w, weights_cos_tf_w_to_t, &
    3929             :                                 do_laplace, do_im_time, num_integ_points, unit_nr, qs_env)
    3930             : 
    3931             :       REAL(dp), ALLOCATABLE, DIMENSION(:), INTENT(INOUT) :: tj, wj, tau_tj, tau_wj
    3932             :       REAL(dp), ALLOCATABLE, DIMENSION(:, :), &
    3933             :          INTENT(INOUT)                                   :: weights_cos_tf_t_to_w, &
    3934             :                                                             weights_cos_tf_w_to_t
    3935             :       LOGICAL, INTENT(IN)                                :: do_laplace, do_im_time
    3936             :       INTEGER, INTENT(IN)                                :: num_integ_points, unit_nr
    3937             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    3938             : 
    3939             :       INTEGER                                            :: jquad
    3940             : 
    3941         202 :       IF (do_laplace .OR. do_im_time) THEN
    3942         164 :          IF (.NOT. ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tau_tj)) THEN
    3943         384 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tau_tj(0:num_integ_points))
    3944         384 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tau_wj(num_integ_points))
    3945        1112 :             qs_env%mp2_env%ri_rpa_im_time%tau_tj(:) = tau_tj(:)
    3946         984 :             qs_env%mp2_env%ri_rpa_im_time%tau_wj(:) = tau_wj(:)
    3947             :          ELSE
    3948             :             !If weights already stored, we overwrite the new ones
    3949         188 :             tau_tj(:) = qs_env%mp2_env%ri_rpa_im_time%tau_tj(:)
    3950         152 :             tau_wj(:) = qs_env%mp2_env%ri_rpa_im_time%tau_wj(:)
    3951             :          END IF
    3952             :       END IF
    3953         202 :       IF (.NOT. do_laplace) THEN
    3954         144 :          IF (.NOT. ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tj)) THEN
    3955         354 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%tj(num_integ_points))
    3956         354 :             ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%wj(num_integ_points))
    3957         976 :             qs_env%mp2_env%ri_rpa_im_time%tj(:) = tj(:)
    3958         976 :             qs_env%mp2_env%ri_rpa_im_time%wj(:) = wj(:)
    3959         118 :             IF (do_im_time) THEN
    3960         360 :                ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(num_integ_points, num_integ_points))
    3961         360 :                ALLOCATE (qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(num_integ_points, num_integ_points))
    3962        9746 :                qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(:, :) = weights_cos_tf_t_to_w(:, :)
    3963        9746 :                qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(:, :) = weights_cos_tf_w_to_t(:, :)
    3964             :             END IF
    3965             :          ELSE
    3966         110 :             tj(:) = qs_env%mp2_env%ri_rpa_im_time%tj(:)
    3967         110 :             wj(:) = qs_env%mp2_env%ri_rpa_im_time%wj(:)
    3968          26 :             IF (do_im_time) THEN
    3969         184 :                weights_cos_tf_t_to_w(:, :) = qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_t_to_w(:, :)
    3970         184 :                weights_cos_tf_w_to_t(:, :) = qs_env%mp2_env%ri_rpa_im_time%weights_cos_tf_w_to_t(:, :)
    3971             :             END IF
    3972             :          END IF
    3973             :       END IF
    3974         202 :       IF (unit_nr > 0) THEN
    3975             :          !Printing order same as in mp2_grids.F for consistency
    3976         101 :          IF (ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tj) .AND. (.NOT. do_laplace)) THEN
    3977             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") &
    3978          72 :                "MINIMAX_INFO| Number of integration points:", num_integ_points
    3979             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T54,A,T72,A)") &
    3980          72 :                "MINIMAX_INFO| Minimax params (freq grid, scaled):", "Weights", "Abscissas"
    3981         543 :             DO jquad = 1, num_integ_points
    3982         543 :                WRITE (UNIT=unit_nr, FMT="(T41,F20.10,F20.10)") wj(jquad), tj(jquad)
    3983             :             END DO
    3984          72 :             CALL m_flush(unit_nr)
    3985             :          END IF
    3986         101 :          IF (ASSOCIATED(qs_env%mp2_env%ri_rpa_im_time%tau_tj)) THEN
    3987             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") &
    3988          82 :                "MINIMAX_INFO| Number of integration points:", num_integ_points
    3989             :             WRITE (UNIT=unit_nr, FMT="(T3,A,T54,A,T72,A)") &
    3990          82 :                "MINIMAX_INFO| Minimax params (time grid, scaled):", "Weights", "Abscissas"
    3991         568 :             DO jquad = 1, num_integ_points
    3992         568 :                WRITE (UNIT=unit_nr, FMT="(T41,F20.10,F20.10)") tau_wj(jquad), tau_tj(jquad)
    3993             :             END DO
    3994          82 :             CALL m_flush(unit_nr)
    3995             :          END IF
    3996             :       END IF
    3997             : 
    3998         202 :    END SUBROUTINE keep_initial_quad
    3999             : 
    4000             : END MODULE rpa_im_time_force_methods

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