xtb_coulomb.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2026 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
! **************************************************************************************************
!> \brief Calculation of Coulomb contributions in xTB
!> \author JGH
! **************************************************************************************************
MODULE xtb_coulomb
   USE ai_contraction,                  ONLY: block_add,&
                                              contraction
   USE ai_overlap,                      ONLY: overlap_ab
   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind_set
   USE atprop_types,                    ONLY: atprop_array_init,&
                                              atprop_type
   USE basis_set_types,                 ONLY: gto_basis_set_p_type,&
                                              gto_basis_set_type
   USE cell_types,                      ONLY: cell_type,&
                                              get_cell,&
                                              pbc
   USE cp_control_types,                ONLY: dft_control_type,&
                                              xtb_control_type
   USE cp_dbcsr_api,                    ONLY: dbcsr_add,&
                                              dbcsr_get_block_p,&
                                              dbcsr_iterator_blocks_left,&
                                              dbcsr_iterator_next_block,&
                                              dbcsr_iterator_start,&
                                              dbcsr_iterator_stop,&
                                              dbcsr_iterator_type,&
                                              dbcsr_p_type
   USE distribution_1d_types,           ONLY: distribution_1d_type
   USE ewald_environment_types,         ONLY: ewald_env_get,&
                                              ewald_environment_type
   USE ewald_methods_tb,                ONLY: tb_ewald_overlap,&
                                              tb_spme_evaluate
   USE ewald_pw_types,                  ONLY: ewald_pw_type
   USE kinds,                           ONLY: dp
   USE kpoint_types,                    ONLY: get_kpoint_info,&
                                              kpoint_type
   USE mathconstants,                   ONLY: oorootpi,&
                                              pi
   USE message_passing,                 ONLY: mp_para_env_type
   USE orbital_pointers,                ONLY: ncoset
   USE particle_types,                  ONLY: particle_type
   USE pw_poisson_types,                ONLY: do_ewald_ewald,&
                                              do_ewald_none,&
                                              do_ewald_pme,&
                                              do_ewald_spme
   USE qmmm_tb_coulomb,                 ONLY: build_tb_coulomb_qmqm
   USE qs_dftb3_methods,                ONLY: build_dftb3_diagonal
   USE qs_energy_types,                 ONLY: qs_energy_type
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_force_types,                  ONLY: qs_force_type
   USE qs_integral_utils,               ONLY: basis_set_list_setup,&
                                              get_memory_usage
   USE qs_kind_types,                   ONLY: get_qs_kind,&
                                              qs_kind_type
   USE qs_neighbor_list_types,          ONLY: get_iterator_info,&
                                              neighbor_list_iterate,&
                                              neighbor_list_iterator_create,&
                                              neighbor_list_iterator_p_type,&
                                              neighbor_list_iterator_release,&
                                              neighbor_list_set_p_type
   USE qs_rho_types,                    ONLY: qs_rho_get,&
                                              qs_rho_type
   USE sap_kind_types,                  ONLY: clist_type,&
                                              release_sap_int,&
                                              sap_int_type
   USE virial_methods,                  ONLY: virial_pair_force
   USE virial_types,                    ONLY: virial_type
   USE xtb_types,                       ONLY: get_xtb_atom_param,&
                                              xtb_atom_type
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
 
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xtb_coulomb'
 
   PUBLIC :: build_xtb_coulomb, gamma_rab_sr, dgamma_rab_sr, xtb_dsint_list
 
CONTAINS
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param ks_matrix ...
!> \param rho ...
!> \param charges ...
!> \param mcharge ...
!> \param energy ...
!> \param calculate_forces ...
!> \param just_energy ...
! **************************************************************************************************
   SUBROUTINE build_xtb_coulomb(qs_env, ks_matrix, rho, charges, mcharge, energy, &
                                calculate_forces, just_energy)
 
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: ks_matrix
      TYPE(qs_rho_type), POINTER                         :: rho
      REAL(dp), DIMENSION(:, :), INTENT(in)              :: charges
      REAL(dp), DIMENSION(:), INTENT(in)                 :: mcharge
      TYPE(qs_energy_type), POINTER                      :: energy
      LOGICAL, INTENT(in)                                :: calculate_forces, just_energy
 
      CHARACTER(len=*), PARAMETER                        :: routinen = 'build_xtb_coulomb'
 
      INTEGER :: atom_i, atom_j, ewald_type, handle, i, ia, iac, iatom, ic, icol, ikind, img, &
         irow, is, j, jatom, jkind, la, lb, lmaxa, lmaxb, natom, natorb_a, natorb_b, ni, nimg, nj, &
         nkind, nmat, za, zb
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: atom_of_kind, kind_of
      INTEGER, DIMENSION(25)                             :: laoa, laob
      INTEGER, DIMENSION(3)                              :: cellind, periodic
      INTEGER, DIMENSION(5)                              :: occ
      INTEGER, DIMENSION(:, :, :), POINTER               :: cell_to_index
      LOGICAL                                            :: defined, do_ewald, do_gamma_stress, &
                                                            found, use_virial
      REAL(kind=dp)                                      :: alpha, deth, dr, ecsr, etaa, etab, f1, &
                                                            f2, fi, gmij, kg, rcut, rcuta, rcutb, &
                                                            zeff
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:)           :: xgamma, zeffk
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: gammab, gcij, gmcharge
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: gchrg
      REAL(kind=dp), DIMENSION(25)                       :: gcint
      REAL(kind=dp), DIMENSION(3)                        :: fij, rij
      REAL(kind=dp), DIMENSION(5)                        :: kappaa, kappab
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: dsblock, ksblock, pblock, sblock
      REAL(kind=dp), DIMENSION(:, :, :), POINTER         :: dsint
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(atprop_type), POINTER                         :: atprop
      TYPE(cell_type), POINTER                           :: cell
      TYPE(dbcsr_iterator_type)                          :: iter
      TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: matrix_p, matrix_s
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(distribution_1d_type), POINTER                :: local_particles
      TYPE(ewald_environment_type), POINTER              :: ewald_env
      TYPE(ewald_pw_type), POINTER                       :: ewald_pw
      TYPE(kpoint_type), POINTER                         :: kpoints
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(neighbor_list_iterator_p_type), &
         DIMENSION(:), POINTER                           :: nl_iterator
      TYPE(neighbor_list_set_p_type), DIMENSION(:), &
         POINTER                                         :: n_list
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_force_type), DIMENSION(:), POINTER         :: force
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(sap_int_type), DIMENSION(:), POINTER          :: sap_int
      TYPE(virial_type), POINTER                         :: virial
      TYPE(xtb_atom_type), POINTER                       :: xtb_atom_a, xtb_atom_b, xtb_kind
      TYPE(xtb_control_type), POINTER                    :: xtb_control
 
      CALL timeset(routinen, handle)
 
      NULLIFY (matrix_p, matrix_s, virial, atprop, dft_control)
 
      CALL get_qs_env(qs_env, &
                      qs_kind_set=qs_kind_set, &
                      particle_set=particle_set, &
                      cell=cell, &
                      virial=virial, &
                      atprop=atprop, &
                      dft_control=dft_control)
 
      xtb_control => dft_control%qs_control%xtb_control
 
      use_virial = .false.
      IF (calculate_forces) THEN
         use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
      END IF
 
      do_gamma_stress = .false.
      IF (.NOT. just_energy .AND. use_virial) THEN
         IF (dft_control%nimages == 1) do_gamma_stress = .true.
      END IF
 
      IF (atprop%energy) THEN
         CALL get_qs_env(qs_env=qs_env, particle_set=particle_set)
         natom = SIZE(particle_set)
         CALL atprop_array_init(atprop%atecoul, natom)
      END IF
 
      IF (calculate_forces) THEN
         nmat = 4
      ELSE
         nmat = 1
      END IF
 
      CALL get_qs_env(qs_env, nkind=nkind, natom=natom)
      ALLOCATE (gchrg(natom, 5, nmat))
      gchrg = 0._dp
      ALLOCATE (gmcharge(natom, nmat))
      gmcharge = 0._dp
 
      ! short range contribution (gamma)
      ! loop over all atom pairs (sab_xtbe)
      kg = xtb_control%kg
      NULLIFY (n_list)
      CALL get_qs_env(qs_env=qs_env, sab_xtbe=n_list)
      IF (.NOT. ASSOCIATED(n_list)) THEN
         cpabort("sab_xtbe neighbor list is not associated in build_xtb_coulomb")
      END IF
      CALL neighbor_list_iterator_create(nl_iterator, n_list)
      DO WHILE (neighbor_list_iterate(nl_iterator) == 0)
         CALL get_iterator_info(nl_iterator, ikind=ikind, jkind=jkind, &
                                iatom=iatom, jatom=jatom, r=rij, cell=cellind)
         CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_atom_a)
         CALL get_xtb_atom_param(xtb_atom_a, defined=defined, natorb=natorb_a)
         IF (.NOT. defined .OR. natorb_a < 1) cycle
         CALL get_qs_kind(qs_kind_set(jkind), xtb_parameter=xtb_atom_b)
         CALL get_xtb_atom_param(xtb_atom_b, defined=defined, natorb=natorb_b)
         IF (.NOT. defined .OR. natorb_b < 1) cycle
         ! atomic parameters
         CALL get_xtb_atom_param(xtb_atom_a, eta=etaa, lmax=lmaxa, kappa=kappaa, rcut=rcuta)
         CALL get_xtb_atom_param(xtb_atom_b, eta=etab, lmax=lmaxb, kappa=kappab, rcut=rcutb)
         ! gamma matrix
         ni = lmaxa + 1
         nj = lmaxb + 1
         ALLOCATE (gammab(ni, nj))
         rcut = rcuta + rcutb
         dr = sqrt(sum(rij(:)**2))
         CALL gamma_rab_sr(gammab, dr, ni, kappaa, etaa, nj, kappab, etab, kg, rcut)
         gchrg(iatom, 1:ni, 1) = gchrg(iatom, 1:ni, 1) + matmul(gammab, charges(jatom, 1:nj))
         IF (iatom /= jatom) THEN
            gchrg(jatom, 1:nj, 1) = gchrg(jatom, 1:nj, 1) + matmul(charges(iatom, 1:ni), gammab)
         END IF
         IF (calculate_forces) THEN
            IF (dr > 1.e-6_dp) THEN
               CALL dgamma_rab_sr(gammab, dr, ni, kappaa, etaa, nj, kappab, etab, kg, rcut)
               DO i = 1, 3
                  gchrg(iatom, 1:ni, i + 1) = gchrg(iatom, 1:ni, i + 1) &
                                              + matmul(gammab, charges(jatom, 1:nj))*rij(i)/dr
                  IF (iatom /= jatom) THEN
                     gchrg(jatom, 1:nj, i + 1) = gchrg(jatom, 1:nj, i + 1) &
                                                 - matmul(charges(iatom, 1:ni), gammab)*rij(i)/dr
                  END IF
               END DO
               IF (use_virial) THEN
                  gcint(1:ni) = matmul(gammab, charges(jatom, 1:nj))
                  DO i = 1, 3
                     fij(i) = -sum(charges(iatom, 1:ni)*gcint(1:ni))*rij(i)/dr
                  END DO
                  fi = 1.0_dp
                  IF (iatom == jatom) fi = 0.5_dp
                  CALL virial_pair_force(virial%pv_virial, fi, fij, rij)
               END IF
            END IF
         END IF
         DEALLOCATE (gammab)
      END DO
      CALL neighbor_list_iterator_release(nl_iterator)
 
      ! 1/R contribution
 
      IF (xtb_control%coulomb_lr) THEN
         do_ewald = xtb_control%do_ewald
         IF (do_ewald) THEN
            ! Ewald sum
            NULLIFY (ewald_env, ewald_pw)
            CALL get_qs_env(qs_env=qs_env, &
                            ewald_env=ewald_env, ewald_pw=ewald_pw)
            CALL get_cell(cell=cell, periodic=periodic, deth=deth)
            CALL ewald_env_get(ewald_env, alpha=alpha, ewald_type=ewald_type)
            CALL get_qs_env(qs_env=qs_env, sab_tbe=n_list)
            CALL tb_ewald_overlap(gmcharge, mcharge, alpha, n_list, virial, use_virial)
            SELECT CASE (ewald_type)
            CASE DEFAULT
               cpabort("Invalid Ewald type")
            CASE (do_ewald_none)
               cpabort("Not allowed with xTB/DFTB")
            CASE (do_ewald_ewald)
               cpabort("Standard Ewald not implemented in xTB/DFTB")
            CASE (do_ewald_pme)
               cpabort("PME not implemented in xTB/DFTB")
            CASE (do_ewald_spme)
               CALL tb_spme_evaluate(ewald_env, ewald_pw, particle_set, cell, &
                                     gmcharge, mcharge, calculate_forces, virial, use_virial)
            END SELECT
         ELSE
            ! direct sum
            CALL get_qs_env(qs_env=qs_env, &
                            local_particles=local_particles)
            DO ikind = 1, SIZE(local_particles%n_el)
               DO ia = 1, local_particles%n_el(ikind)
                  iatom = local_particles%list(ikind)%array(ia)
                  DO jatom = 1, iatom - 1
                     rij = particle_set(iatom)%r - particle_set(jatom)%r
                     rij = pbc(rij, cell)
                     dr = sqrt(sum(rij(:)**2))
                     IF (dr > 1.e-6_dp) THEN
                        gmcharge(iatom, 1) = gmcharge(iatom, 1) + mcharge(jatom)/dr
                        gmcharge(jatom, 1) = gmcharge(jatom, 1) + mcharge(iatom)/dr
                        DO i = 2, nmat
                           gmcharge(iatom, i) = gmcharge(iatom, i) + rij(i - 1)*mcharge(jatom)/dr**3
                           gmcharge(jatom, i) = gmcharge(jatom, i) - rij(i - 1)*mcharge(iatom)/dr**3
                        END DO
                        IF (use_virial) THEN
                           DO i = 1, 3
                              fij(i) = mcharge(iatom)*mcharge(jatom)*rij(i)/dr**3
                           END DO
                           CALL virial_pair_force(virial%pv_virial, 1.0_dp, fij, rij)
                        END IF
                     END IF
                  END DO
               END DO
            END DO
         END IF
      END IF
 
      ! global sum of gamma*p arrays
      CALL get_qs_env(qs_env=qs_env, &
                      atomic_kind_set=atomic_kind_set, &
                      force=force, para_env=para_env)
      CALL para_env%sum(gmcharge(:, 1))
      CALL para_env%sum(gchrg(:, :, 1))
 
      IF (xtb_control%coulomb_lr) THEN
         IF (do_ewald) THEN
            ! add self charge interaction and background charge contribution
            gmcharge(:, 1) = gmcharge(:, 1) - 2._dp*alpha*oorootpi*mcharge(:)
            IF (any(periodic(:) == 1)) THEN
               gmcharge(:, 1) = gmcharge(:, 1) - pi/alpha**2/deth
            END IF
         END IF
      END IF
 
      ! energy
      CALL get_atomic_kind_set(atomic_kind_set=atomic_kind_set, &
                               kind_of=kind_of, &
                               atom_of_kind=atom_of_kind)
      ecsr = 0.0_dp
      DO iatom = 1, natom
         ikind = kind_of(iatom)
         CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_kind)
         CALL get_xtb_atom_param(xtb_kind, lmax=ni)
         ni = ni + 1
         ecsr = ecsr + sum(charges(iatom, 1:ni)*gchrg(iatom, 1:ni, 1))
      END DO
 
      energy%hartree = energy%hartree + 0.5_dp*ecsr
      energy%hartree = energy%hartree + 0.5_dp*sum(mcharge(:)*gmcharge(:, 1))
 
      IF (atprop%energy) THEN
         CALL get_qs_env(qs_env=qs_env, local_particles=local_particles)
         DO ikind = 1, SIZE(local_particles%n_el)
            CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_kind)
            CALL get_xtb_atom_param(xtb_kind, lmax=ni, occupation=occ)
            ni = ni + 1
            zeff = sum(real(occ, kind=dp))
            DO ia = 1, local_particles%n_el(ikind)
               iatom = local_particles%list(ikind)%array(ia)
               atprop%atecoul(iatom) = atprop%atecoul(iatom) + &
                                       0.5_dp*sum(real(occ(1:ni), kind=dp)*gchrg(iatom, 1:ni, 1))
               atprop%atecoul(iatom) = atprop%atecoul(iatom) + &
                                       0.5_dp*zeff*gmcharge(iatom, 1)
            END DO
         END DO
      END IF
 
      IF (calculate_forces) THEN
         DO iatom = 1, natom
            ikind = kind_of(iatom)
            atom_i = atom_of_kind(iatom)
            CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_kind)
            CALL get_xtb_atom_param(xtb_kind, lmax=ni)
            ! short range
            ni = ni + 1
            DO i = 1, 3
               fij(i) = sum(charges(iatom, 1:ni)*gchrg(iatom, 1:ni, i + 1))
            END DO
            force(ikind)%rho_elec(1, atom_i) = force(ikind)%rho_elec(1, atom_i) - fij(1)
            force(ikind)%rho_elec(2, atom_i) = force(ikind)%rho_elec(2, atom_i) - fij(2)
            force(ikind)%rho_elec(3, atom_i) = force(ikind)%rho_elec(3, atom_i) - fij(3)
            ! long range
            DO i = 1, 3
               fij(i) = gmcharge(iatom, i + 1)*mcharge(iatom)
            END DO
            force(ikind)%rho_elec(1, atom_i) = force(ikind)%rho_elec(1, atom_i) - fij(1)
            force(ikind)%rho_elec(2, atom_i) = force(ikind)%rho_elec(2, atom_i) - fij(2)
            force(ikind)%rho_elec(3, atom_i) = force(ikind)%rho_elec(3, atom_i) - fij(3)
         END DO
      END IF
 
      IF (.NOT. just_energy) THEN
         CALL get_qs_env(qs_env=qs_env, matrix_s_kp=matrix_s)
         CALL qs_rho_get(rho, rho_ao_kp=matrix_p)
 
         nimg = dft_control%nimages
         NULLIFY (cell_to_index)
         IF (nimg > 1) THEN
            NULLIFY (kpoints)
            CALL get_qs_env(qs_env=qs_env, kpoints=kpoints)
            CALL get_kpoint_info(kpoint=kpoints, cell_to_index=cell_to_index)
         END IF
 
         IF (calculate_forces .AND. SIZE(matrix_p, 1) == 2) THEN
            DO img = 1, nimg
               CALL dbcsr_add(matrix_p(1, img)%matrix, matrix_p(2, img)%matrix, &
                              alpha_scalar=1.0_dp, beta_scalar=1.0_dp)
            END DO
         END IF
 
         NULLIFY (sap_int)
         IF (do_gamma_stress) THEN
            ! derivative overlap integral (non collapsed)
            CALL xtb_dsint_list(qs_env, sap_int)
         END IF
 
         IF (nimg == 1) THEN
            ! no k-points; all matrices have been transformed to periodic bsf
            CALL dbcsr_iterator_start(iter, matrix_s(1, 1)%matrix)
            DO WHILE (dbcsr_iterator_blocks_left(iter))
               CALL dbcsr_iterator_next_block(iter, irow, icol, sblock)
               ikind = kind_of(irow)
               jkind = kind_of(icol)
 
               ! atomic parameters
               CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_atom_a)
               CALL get_qs_kind(qs_kind_set(jkind), xtb_parameter=xtb_atom_b)
               CALL get_xtb_atom_param(xtb_atom_a, z=za, lao=laoa)
               CALL get_xtb_atom_param(xtb_atom_b, z=zb, lao=laob)
 
               ni = SIZE(sblock, 1)
               nj = SIZE(sblock, 2)
               ALLOCATE (gcij(ni, nj))
               DO i = 1, ni
                  DO j = 1, nj
                     la = laoa(i) + 1
                     lb = laob(j) + 1
                     gcij(i, j) = 0.5_dp*(gchrg(irow, la, 1) + gchrg(icol, lb, 1))
                  END DO
               END DO
               gmij = 0.5_dp*(gmcharge(irow, 1) + gmcharge(icol, 1))
               DO is = 1, SIZE(ks_matrix, 1)
                  NULLIFY (ksblock)
                  CALL dbcsr_get_block_p(matrix=ks_matrix(is, 1)%matrix, &
                                         row=irow, col=icol, block=ksblock, found=found)
                  cpassert(found)
                  ksblock = ksblock - gcij*sblock
                  ksblock = ksblock - gmij*sblock
               END DO
               IF (calculate_forces) THEN
                  atom_i = atom_of_kind(irow)
                  atom_j = atom_of_kind(icol)
                  NULLIFY (pblock)
                  CALL dbcsr_get_block_p(matrix=matrix_p(1, 1)%matrix, &
                                         row=irow, col=icol, block=pblock, found=found)
                  cpassert(found)
                  DO i = 1, 3
                     NULLIFY (dsblock)
                     CALL dbcsr_get_block_p(matrix=matrix_s(1 + i, 1)%matrix, &
                                            row=irow, col=icol, block=dsblock, found=found)
                     cpassert(found)
                     fij(i) = 0.0_dp
                     ! short range
                     fi = -2.0_dp*sum(pblock*dsblock*gcij)
                     force(ikind)%rho_elec(i, atom_i) = force(ikind)%rho_elec(i, atom_i) + fi
                     force(jkind)%rho_elec(i, atom_j) = force(jkind)%rho_elec(i, atom_j) - fi
                     fij(i) = fij(i) + fi
                     ! long range
                     fi = -2.0_dp*gmij*sum(pblock*dsblock)
                     force(ikind)%rho_elec(i, atom_i) = force(ikind)%rho_elec(i, atom_i) + fi
                     force(jkind)%rho_elec(i, atom_j) = force(jkind)%rho_elec(i, atom_j) - fi
                     fij(i) = fij(i) + fi
                  END DO
               END IF
               DEALLOCATE (gcij)
            END DO
            CALL dbcsr_iterator_stop(iter)
            ! stress tensor (needs recalculation of overlap integrals)
            IF (do_gamma_stress) THEN
               DO ikind = 1, nkind
                  DO jkind = 1, nkind
                     iac = ikind + nkind*(jkind - 1)
                     IF (.NOT. ASSOCIATED(sap_int(iac)%alist)) cycle
                     ! atomic parameters
                     CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_atom_a)
                     CALL get_qs_kind(qs_kind_set(jkind), xtb_parameter=xtb_atom_b)
                     CALL get_xtb_atom_param(xtb_atom_a, lao=laoa, natorb=ni)
                     CALL get_xtb_atom_param(xtb_atom_b, lao=laob, natorb=nj)
                     DO ia = 1, sap_int(iac)%nalist
                        IF (.NOT. ASSOCIATED(sap_int(iac)%alist(ia)%clist)) cycle
                        iatom = sap_int(iac)%alist(ia)%aatom
                        DO ic = 1, sap_int(iac)%alist(ia)%nclist
                           jatom = sap_int(iac)%alist(ia)%clist(ic)%catom
                           rij = sap_int(iac)%alist(ia)%clist(ic)%rac
                           dr = sqrt(sum(rij(:)**2))
                           IF (dr > 1.e-6_dp) THEN
                              dsint => sap_int(iac)%alist(ia)%clist(ic)%acint
                              ALLOCATE (gcij(ni, nj))
                              DO i = 1, ni
                                 DO j = 1, nj
                                    la = laoa(i) + 1
                                    lb = laob(j) + 1
                                    gcij(i, j) = 0.5_dp*(gchrg(iatom, la, 1) + gchrg(jatom, lb, 1))
                                 END DO
                              END DO
                              gmij = 0.5_dp*(gmcharge(iatom, 1) + gmcharge(jatom, 1))
                              icol = max(iatom, jatom)
                              irow = min(iatom, jatom)
                              NULLIFY (pblock)
                              CALL dbcsr_get_block_p(matrix=matrix_p(1, 1)%matrix, &
                                                     row=irow, col=icol, block=pblock, found=found)
                              cpassert(found)
                              fij = 0.0_dp
                              DO i = 1, 3
                                 ! short/long range
                                 IF (irow == iatom) THEN
                                    f1 = -2.0_dp*sum(pblock*dsint(:, :, i)*gcij)
                                    f2 = -2.0_dp*gmij*sum(pblock*dsint(:, :, i))
                                 ELSE
                                    f1 = -2.0_dp*sum(transpose(pblock)*dsint(:, :, i)*gcij)
                                    f2 = -2.0_dp*gmij*sum(transpose(pblock)*dsint(:, :, i))
                                 END IF
                                 fij(i) = f1 + f2
                              END DO
                              DEALLOCATE (gcij)
                              fi = 1.0_dp
                              IF (iatom == jatom) fi = 0.5_dp
                              CALL virial_pair_force(virial%pv_virial, fi, fij, rij)
                           END IF
                        END DO
                     END DO
                  END DO
               END DO
            END IF
         ELSE
            NULLIFY (n_list)
            CALL get_qs_env(qs_env=qs_env, sab_orb=n_list)
            CALL neighbor_list_iterator_create(nl_iterator, n_list)
            DO WHILE (neighbor_list_iterate(nl_iterator) == 0)
               CALL get_iterator_info(nl_iterator, ikind=ikind, jkind=jkind, &
                                      iatom=iatom, jatom=jatom, r=rij, cell=cellind)
 
               icol = max(iatom, jatom)
               irow = min(iatom, jatom)
 
               ic = cell_to_index(cellind(1), cellind(2), cellind(3))
               cpassert(ic > 0)
 
               NULLIFY (sblock)
               CALL dbcsr_get_block_p(matrix=matrix_s(1, ic)%matrix, &
                                      row=irow, col=icol, block=sblock, found=found)
               cpassert(found)
 
               ! atomic parameters
               CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_atom_a)
               CALL get_qs_kind(qs_kind_set(jkind), xtb_parameter=xtb_atom_b)
               CALL get_xtb_atom_param(xtb_atom_a, z=za, lao=laoa)
               CALL get_xtb_atom_param(xtb_atom_b, z=zb, lao=laob)
 
               ni = SIZE(sblock, 1)
               nj = SIZE(sblock, 2)
               ALLOCATE (gcij(ni, nj))
               DO i = 1, ni
                  DO j = 1, nj
                     IF (irow == iatom) THEN
                        la = laoa(i) + 1
                        lb = laob(j) + 1
                        gcij(i, j) = 0.5_dp*(gchrg(iatom, la, 1) + gchrg(jatom, lb, 1))
                     ELSE
                        la = laoa(j) + 1
                        lb = laob(i) + 1
                        gcij(i, j) = 0.5_dp*(gchrg(iatom, la, 1) + gchrg(jatom, lb, 1))
                     END IF
                  END DO
               END DO
               gmij = 0.5_dp*(gmcharge(iatom, 1) + gmcharge(jatom, 1))
               DO is = 1, SIZE(ks_matrix, 1)
                  NULLIFY (ksblock)
                  CALL dbcsr_get_block_p(matrix=ks_matrix(is, ic)%matrix, &
                                         row=irow, col=icol, block=ksblock, found=found)
                  cpassert(found)
                  ksblock = ksblock - gcij*sblock
                  ksblock = ksblock - gmij*sblock
               END DO
 
               IF (calculate_forces) THEN
                  atom_i = atom_of_kind(iatom)
                  atom_j = atom_of_kind(jatom)
                  IF (irow /= iatom) THEN
                     gmij = -gmij
                     gcij = -gcij
                  END IF
                  NULLIFY (pblock)
                  CALL dbcsr_get_block_p(matrix=matrix_p(1, ic)%matrix, &
                                         row=irow, col=icol, block=pblock, found=found)
                  cpassert(found)
                  DO i = 1, 3
                     NULLIFY (dsblock)
                     CALL dbcsr_get_block_p(matrix=matrix_s(1 + i, ic)%matrix, &
                                            row=irow, col=icol, block=dsblock, found=found)
                     cpassert(found)
                     fij(i) = 0.0_dp
                     ! short range
                     fi = -2.0_dp*sum(pblock*dsblock*gcij)
                     force(ikind)%rho_elec(i, atom_i) = force(ikind)%rho_elec(i, atom_i) + fi
                     force(jkind)%rho_elec(i, atom_j) = force(jkind)%rho_elec(i, atom_j) - fi
                     fij(i) = fij(i) + fi
                     ! long range
                     fi = -2.0_dp*gmij*sum(pblock*dsblock)
                     force(ikind)%rho_elec(i, atom_i) = force(ikind)%rho_elec(i, atom_i) + fi
                     force(jkind)%rho_elec(i, atom_j) = force(jkind)%rho_elec(i, atom_j) - fi
                     fij(i) = fij(i) + fi
                  END DO
                  IF (use_virial) THEN
                     dr = sqrt(sum(rij(:)**2))
                     IF (dr > 1.e-6_dp) THEN
                        fi = 1.0_dp
                        IF (iatom == jatom) fi = 0.5_dp
                        CALL virial_pair_force(virial%pv_virial, fi, fij, rij)
                     END IF
                  END IF
               END IF
               DEALLOCATE (gcij)
 
            END DO
            CALL neighbor_list_iterator_release(nl_iterator)
         END IF
 
         IF (calculate_forces .AND. SIZE(matrix_p, 1) == 2) THEN
            DO img = 1, nimg
               CALL dbcsr_add(matrix_p(1, img)%matrix, matrix_p(2, img)%matrix, &
                              alpha_scalar=1.0_dp, beta_scalar=-1.0_dp)
            END DO
         END IF
      END IF
 
      IF (xtb_control%tb3_interaction) THEN
         CALL get_qs_env(qs_env, nkind=nkind)
         ALLOCATE (zeffk(nkind), xgamma(nkind))
         DO ikind = 1, nkind
            CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_kind)
            CALL get_xtb_atom_param(xtb_kind, xgamma=xgamma(ikind), zeff=zeffk(ikind))
         END DO
         ! Diagonal 3rd order correction (DFTB3)
         CALL build_dftb3_diagonal(qs_env, ks_matrix, rho, mcharge, energy, xgamma, zeffk, &
                                   sap_int, calculate_forces, just_energy)
         DEALLOCATE (zeffk, xgamma)
      END IF
 
      ! QMMM
      IF (qs_env%qmmm .AND. qs_env%qmmm_periodic) THEN
         CALL build_tb_coulomb_qmqm(qs_env, ks_matrix, rho, mcharge, energy, &
                                    calculate_forces, just_energy)
      END IF
 
      IF (do_gamma_stress) THEN
         CALL release_sap_int(sap_int)
      END IF
 
      CALL timestop(handle)
 
   END SUBROUTINE build_xtb_coulomb
 
! **************************************************************************************************
!> \brief  Computes the short-range gamma parameter from
!>         Nataga-Mishimoto-Ohno-Klopman formula for xTB
!>         WARNING: The xTB function (gamma - 1/r) has still an l-dependent longrange (1/r^3)
!>                  behaviour. We use a cutoff function to smoothly remove this part.
!>                  However, this will change energies and effect final results.
!>
!> \param gmat ...
!> \param rab ...
!> \param nla ...
!> \param kappaa ...
!> \param etaa ...
!> \param nlb ...
!> \param kappab ...
!> \param etab ...
!> \param kg ...
!> \param rcut ...
!> \par History
!>      10.2018 JGH
!> \version 1.1
! **************************************************************************************************
   SUBROUTINE gamma_rab_sr(gmat, rab, nla, kappaa, etaa, nlb, kappab, etab, kg, rcut)
      REAL(dp), DIMENSION(:, :), INTENT(INOUT)           :: gmat
      REAL(dp), INTENT(IN)                               :: rab
      INTEGER, INTENT(IN)                                :: nla
      REAL(dp), DIMENSION(:), INTENT(IN)                 :: kappaa
      REAL(dp), INTENT(IN)                               :: etaa
      INTEGER, INTENT(IN)                                :: nlb
      REAL(dp), DIMENSION(:), INTENT(IN)                 :: kappab
      REAL(dp), INTENT(IN)                               :: etab, kg, rcut
 
      REAL(kind=dp), PARAMETER                           :: rsmooth = 1.0_dp
 
      INTEGER                                            :: i, j
      REAL(kind=dp)                                      :: fcut, r, rk, x
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: eta
 
      ALLOCATE (eta(nla, nlb))
      eta = 0.0_dp
 
      DO j = 1, nlb
         DO i = 1, nla
            eta(i, j) = 1._dp/(etaa*(1._dp + kappaa(i))) + 1._dp/(etab*(1._dp + kappab(j)))
            eta(i, j) = 2._dp/eta(i, j)
         END DO
      END DO
 
      gmat = 0.0_dp
      IF (rab < 1.e-6_dp) THEN
         ! on site terms
         gmat(:, :) = eta(:, :)
      ELSEIF (rab > rcut) THEN
         ! do nothing
      ELSE
         rk = rab**kg
         eta = eta**(-kg)
         IF (rab < rcut - rsmooth) THEN
            fcut = 1.0_dp
         ELSE
            r = rab - (rcut - rsmooth)
            x = r/rsmooth
            fcut = -6._dp*x**5 + 15._dp*x**4 - 10._dp*x**3 + 1._dp
         END IF
         gmat(:, :) = fcut*(1._dp/(rk + eta(:, :)))**(1._dp/kg) - fcut/rab
      END IF
 
      DEALLOCATE (eta)
 
   END SUBROUTINE gamma_rab_sr
 
! **************************************************************************************************
!> \brief  Computes the derivative of the short-range gamma parameter from
!>         Nataga-Mishimoto-Ohno-Klopman formula for xTB
!>         WARNING: The xTB function (gamma - 1/r) has still an l-dependent longrange (1/r^3)
!>                  behaviour. We use a cutoff function to smoothly remove this part.
!>                  However, this will change energies and effect final results.
!>
!> \param dgmat ...
!> \param rab ...
!> \param nla ...
!> \param kappaa ...
!> \param etaa ...
!> \param nlb ...
!> \param kappab ...
!> \param etab ...
!> \param kg ...
!> \param rcut ...
!> \par History
!>      10.2018 JGH
!> \version 1.1
! **************************************************************************************************
   SUBROUTINE dgamma_rab_sr(dgmat, rab, nla, kappaa, etaa, nlb, kappab, etab, kg, rcut)
      REAL(dp), DIMENSION(:, :), INTENT(INOUT)           :: dgmat
      REAL(dp), INTENT(IN)                               :: rab
      INTEGER, INTENT(IN)                                :: nla
      REAL(dp), DIMENSION(:), INTENT(IN)                 :: kappaa
      REAL(dp), INTENT(IN)                               :: etaa
      INTEGER, INTENT(IN)                                :: nlb
      REAL(dp), DIMENSION(:), INTENT(IN)                 :: kappab
      REAL(dp), INTENT(IN)                               :: etab, kg, rcut
 
      REAL(kind=dp), PARAMETER                           :: rsmooth = 1.0_dp
 
      INTEGER                                            :: i, j
      REAL(kind=dp)                                      :: dfcut, fcut, r, rk, x
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: eta
 
      ALLOCATE (eta(nla, nlb))
 
      DO j = 1, nlb
         DO i = 1, nla
            eta(i, j) = 1._dp/(etaa*(1._dp + kappaa(i))) + 1._dp/(etab*(1._dp + kappab(j)))
            eta(i, j) = 2._dp/eta(i, j)
         END DO
      END DO
 
      IF (rab < 1.e-6) THEN
         ! on site terms
         dgmat(:, :) = 0.0_dp
      ELSEIF (rab > rcut) THEN
         dgmat(:, :) = 0.0_dp
      ELSE
         eta = eta**(-kg)
         rk = rab**kg
         IF (rab < rcut - rsmooth) THEN
            fcut = 1.0_dp
            dfcut = 0.0_dp
         ELSE
            r = rab - (rcut - rsmooth)
            x = r/rsmooth
            fcut = -6._dp*x**5 + 15._dp*x**4 - 10._dp*x**3 + 1._dp
            dfcut = -30._dp*x**4 + 60._dp*x**3 - 30._dp*x**2
            dfcut = dfcut/rsmooth
         END IF
         dgmat(:, :) = dfcut*(1._dp/(rk + eta(:, :)))**(1._dp/kg)
         dgmat(:, :) = dgmat(:, :) - dfcut/rab + fcut/rab**2
         dgmat(:, :) = dgmat(:, :) - fcut/(rk + eta(:, :))*(1._dp/(rk + eta(:, :)))**(1._dp/kg)*rk/rab
      END IF
 
      DEALLOCATE (eta)
 
   END SUBROUTINE dgamma_rab_sr
 
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param sap_int ...
! **************************************************************************************************
   SUBROUTINE xtb_dsint_list(qs_env, sap_int)
 
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(sap_int_type), DIMENSION(:), POINTER          :: sap_int
 
      CHARACTER(LEN=*), PARAMETER                        :: routinen = 'xtb_dsint_list'
 
      INTEGER :: handle, i, iac, iatom, ikind, ilist, iset, jatom, jkind, jneighbor, jset, ldsab, &
         n1, n2, natorb_a, natorb_b, ncoa, ncob, nkind, nlist, nneighbor, nseta, nsetb, sgfa, sgfb
      INTEGER, DIMENSION(3)                              :: cell
      INTEGER, DIMENSION(:), POINTER                     :: la_max, la_min, lb_max, lb_min, npgfa, &
                                                            npgfb, nsgfa, nsgfb
      INTEGER, DIMENSION(:, :), POINTER                  :: first_sgfa, first_sgfb
      LOGICAL                                            :: defined
      REAL(kind=dp)                                      :: dr
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: owork
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :, :)     :: oint, sint
      REAL(kind=dp), DIMENSION(3)                        :: rij
      REAL(kind=dp), DIMENSION(:), POINTER               :: set_radius_a, set_radius_b
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: rpgfa, rpgfb, scon_a, scon_b, zeta, zetb
      TYPE(clist_type), POINTER                          :: clist
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER  :: basis_set_list
      TYPE(gto_basis_set_type), POINTER                  :: basis_set_a, basis_set_b
      TYPE(neighbor_list_iterator_p_type), &
         DIMENSION(:), POINTER                           :: nl_iterator
      TYPE(neighbor_list_set_p_type), DIMENSION(:), &
         POINTER                                         :: sab_orb
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
      TYPE(xtb_atom_type), POINTER                       :: xtb_atom_a, xtb_atom_b
 
      CALL timeset(routinen, handle)
 
      CALL get_qs_env(qs_env=qs_env, nkind=nkind)
      cpassert(.NOT. ASSOCIATED(sap_int))
      ALLOCATE (sap_int(nkind*nkind))
      DO i = 1, nkind*nkind
         NULLIFY (sap_int(i)%alist, sap_int(i)%asort, sap_int(i)%aindex)
         sap_int(i)%nalist = 0
      END DO
 
      CALL get_qs_env(qs_env=qs_env, &
                      qs_kind_set=qs_kind_set, &
                      dft_control=dft_control, &
                      sab_orb=sab_orb)
 
      ! set up basis set lists
      ALLOCATE (basis_set_list(nkind))
      CALL basis_set_list_setup(basis_set_list, "ORB", qs_kind_set)
 
      ! loop over all atom pairs with a non-zero overlap (sab_orb)
      CALL neighbor_list_iterator_create(nl_iterator, sab_orb)
      DO WHILE (neighbor_list_iterate(nl_iterator) == 0)
         CALL get_iterator_info(nl_iterator, ikind=ikind, jkind=jkind, iatom=iatom, &
                                jatom=jatom, nlist=nlist, ilist=ilist, nnode=nneighbor, &
                                inode=jneighbor, cell=cell, r=rij)
         iac = ikind + nkind*(jkind - 1)
         !
         CALL get_qs_kind(qs_kind_set(ikind), xtb_parameter=xtb_atom_a)
         CALL get_xtb_atom_param(xtb_atom_a, defined=defined, natorb=natorb_a)
         IF (.NOT. defined .OR. natorb_a < 1) cycle
         CALL get_qs_kind(qs_kind_set(jkind), xtb_parameter=xtb_atom_b)
         CALL get_xtb_atom_param(xtb_atom_b, defined=defined, natorb=natorb_b)
         IF (.NOT. defined .OR. natorb_b < 1) cycle
 
         dr = sqrt(sum(rij(:)**2))
 
         ! integral list
         IF (.NOT. ASSOCIATED(sap_int(iac)%alist)) THEN
            sap_int(iac)%a_kind = ikind
            sap_int(iac)%p_kind = jkind
            sap_int(iac)%nalist = nlist
            ALLOCATE (sap_int(iac)%alist(nlist))
            DO i = 1, nlist
               NULLIFY (sap_int(iac)%alist(i)%clist)
               sap_int(iac)%alist(i)%aatom = 0
               sap_int(iac)%alist(i)%nclist = 0
            END DO
         END IF
         IF (.NOT. ASSOCIATED(sap_int(iac)%alist(ilist)%clist)) THEN
            sap_int(iac)%alist(ilist)%aatom = iatom
            sap_int(iac)%alist(ilist)%nclist = nneighbor
            ALLOCATE (sap_int(iac)%alist(ilist)%clist(nneighbor))
            DO i = 1, nneighbor
               sap_int(iac)%alist(ilist)%clist(i)%catom = 0
            END DO
         END IF
         clist => sap_int(iac)%alist(ilist)%clist(jneighbor)
         clist%catom = jatom
         clist%cell = cell
         clist%rac = rij
         ALLOCATE (clist%acint(natorb_a, natorb_b, 3))
         NULLIFY (clist%achint)
         clist%acint = 0._dp
         clist%nsgf_cnt = 0
         NULLIFY (clist%sgf_list)
 
         ! overlap
         basis_set_a => basis_set_list(ikind)%gto_basis_set
         IF (.NOT. ASSOCIATED(basis_set_a)) cycle
         basis_set_b => basis_set_list(jkind)%gto_basis_set
         IF (.NOT. ASSOCIATED(basis_set_b)) cycle
         ! basis ikind
         first_sgfa => basis_set_a%first_sgf
         la_max => basis_set_a%lmax
         la_min => basis_set_a%lmin
         npgfa => basis_set_a%npgf
         nseta = basis_set_a%nset
         nsgfa => basis_set_a%nsgf_set
         rpgfa => basis_set_a%pgf_radius
         set_radius_a => basis_set_a%set_radius
         scon_a => basis_set_a%scon
         zeta => basis_set_a%zet
         ! basis jkind
         first_sgfb => basis_set_b%first_sgf
         lb_max => basis_set_b%lmax
         lb_min => basis_set_b%lmin
         npgfb => basis_set_b%npgf
         nsetb = basis_set_b%nset
         nsgfb => basis_set_b%nsgf_set
         rpgfb => basis_set_b%pgf_radius
         set_radius_b => basis_set_b%set_radius
         scon_b => basis_set_b%scon
         zetb => basis_set_b%zet
 
         ldsab = get_memory_usage(qs_kind_set, "ORB", "ORB")
         ALLOCATE (oint(ldsab, ldsab, 4), owork(ldsab, ldsab))
         ALLOCATE (sint(natorb_a, natorb_b, 4))
         sint = 0.0_dp
 
         DO iset = 1, nseta
            ncoa = npgfa(iset)*ncoset(la_max(iset))
            n1 = npgfa(iset)*(ncoset(la_max(iset)) - ncoset(la_min(iset) - 1))
            sgfa = first_sgfa(1, iset)
            DO jset = 1, nsetb
               IF (set_radius_a(iset) + set_radius_b(jset) < dr) cycle
               ncob = npgfb(jset)*ncoset(lb_max(jset))
               n2 = npgfb(jset)*(ncoset(lb_max(jset)) - ncoset(lb_min(jset) - 1))
               sgfb = first_sgfb(1, jset)
               CALL overlap_ab(la_max(iset), la_min(iset), npgfa(iset), rpgfa(:, iset), zeta(:, iset), &
                               lb_max(jset), lb_min(jset), npgfb(jset), rpgfb(:, jset), zetb(:, jset), &
                               rij, sab=oint(:, :, 1), dab=oint(:, :, 2:4))
               ! Contraction
               DO i = 1, 4
                  CALL contraction(oint(:, :, i), owork, ca=scon_a(:, sgfa:), na=n1, ma=nsgfa(iset), &
                                   cb=scon_b(:, sgfb:), nb=n2, mb=nsgfb(jset), fscale=1.0_dp, trans=.false.)
                  CALL block_add("IN", owork, nsgfa(iset), nsgfb(jset), sint(:, :, i), &
                                 sgfa, sgfb, trans=.false.)
               END DO
            END DO
         END DO
         ! update dS/dR matrix
         clist%acint(1:natorb_a, 1:natorb_b, 1:3) = sint(1:natorb_a, 1:natorb_b, 2:4)
 
         DEALLOCATE (oint, owork, sint)
 
      END DO
      CALL neighbor_list_iterator_release(nl_iterator)
 
      DEALLOCATE (basis_set_list)
 
      CALL timestop(handle)
 
   END SUBROUTINE xtb_dsint_list
 
END MODULE xtb_coulomb