LCOV - code coverage report
Current view: top level - src - rpa_im_time_force_methods.F (source / functions) Coverage Total Hit
Test: CP2K Regtests (git:42dac4a) Lines: 97.4 % 1935 1885
Test Date: 2025-07-25 12:55:17 Functions: 100.0 % 12 12

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

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