! ---

BEGIN_PROVIDER [ double precision, three_body_ints_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num, mo_num)]

 BEGIN_DOC
! matrix element of the -L  three-body operator
!
! notice the -1 sign: in this way three_body_ints_bi_ort can be directly used to compute Slater rules :)
 END_DOC

 implicit none
 integer          :: i, j, k, l, m, n
 double precision :: integral, wall1, wall0
 character*(128)  :: name_file

  three_body_ints_bi_ort = 0.d0
  print *, ' Providing the three_body_ints_bi_ort ...'
  call wall_time(wall0)
  name_file = 'six_index_tensor'

! if(read_three_body_ints_bi_ort)then
!  call read_fcidump_3_tc(three_body_ints_bi_ort)
! else
!  if(read_three_body_ints_bi_ort)then
!   print*,'Reading three_body_ints_bi_ort from disk ...'
!   call read_array_6_index_tensor(mo_num,three_body_ints_bi_ort,name_file)
!  else

  !provide x_W_ki_bi_ortho_erf_rk
  provide mos_r_in_r_array_transp mos_l_in_r_array_transp
  provide int2_grad1_u12_ao_transp final_grid_points int2_grad1_u12_bimo_t
  provide mo_l_coef mo_r_coef mos_l_in_r_array_transp mos_r_in_r_array_transp n_points_final_grid


 !$OMP PARALLEL                       &
 !$OMP DEFAULT (NONE)                 &
 !$OMP PRIVATE (i,j,k,l,m,n,integral) &
 !$OMP SHARED (mo_num,three_body_ints_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, mo_num
        do k = 1, mo_num
          do l = 1, mo_num
            do n = 1, mo_num
              call give_integrals_3_body_bi_ort(n, l, k, m, j, i, integral)

              three_body_ints_bi_ort(n,l,k,m,j,i) = -1.d0 * integral
            enddo
          enddo
        enddo
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL
!  endif
! endif

  call wall_time(wall1)
  print *, ' wall time for three_body_ints_bi_ort', wall1 - wall0
  call print_memory_usage()
! if(write_three_body_ints_bi_ort)then
!  print*,'Writing three_body_ints_bi_ort on disk ...'
!  call write_array_6_index_tensor(mo_num,three_body_ints_bi_ort,name_file)
!  call ezfio_set_three_body_ints_bi_ort_io_three_body_ints_bi_ort("Read")
! endif

END_PROVIDER

! ---

subroutine give_integrals_3_body_bi_ort_spin( n, sigma_n, l, sigma_l, k, sigma_k &
                                            , m, sigma_m, j, sigma_j, i, sigma_i &
                                            , integral)

  BEGIN_DOC
  !
  ! < n l k | L | m j i > with a BI-ORTHONORMAL SPIN-ORBITALS
  ! 
  ! /!\ L is defined without the 1/6 factor
  !
  END_DOC

  implicit none
  integer,          intent(in)  :: n, l, k, m, j, i
  double precision, intent(in)  :: sigma_n, sigma_l, sigma_k, sigma_m, sigma_j, sigma_i
  double precision, intent(out) :: integral
  integer                       :: ipoint
  double precision              :: weight, tmp
  logical, external             :: is_same_spin

  integral = 0.d0

  if( is_same_spin(sigma_n, sigma_m) .and. &
      is_same_spin(sigma_l, sigma_j) .and. &
      is_same_spin(sigma_k, sigma_i) ) then

    PROVIDE mo_l_coef mo_r_coef
    PROVIDE int2_grad1_u12_bimo_t

    do ipoint = 1, n_points_final_grid

      tmp =     mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
                * ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,l,j)    &
                  + int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,l,j)    &
                  + int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,l,j) )

      tmp = tmp + mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
                * ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,k,i)    &
                  + int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,k,i)    &
                  + int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )

      tmp = tmp + mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
                * ( int2_grad1_u12_bimo_t(ipoint,1,l,j) * int2_grad1_u12_bimo_t(ipoint,1,k,i)    &
                  + int2_grad1_u12_bimo_t(ipoint,2,l,j) * int2_grad1_u12_bimo_t(ipoint,2,k,i)    &
                  + int2_grad1_u12_bimo_t(ipoint,3,l,j) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )

      integral = integral + tmp * final_weight_at_r_vector(ipoint)
    enddo

  endif

  return
end subroutine give_integrals_3_body_bi_ort_spin

! ---

subroutine give_integrals_3_body_bi_ort(n, l, k, m, j, i, integral)

  BEGIN_DOC
  !
  ! < n l k | L | m j i > with a BI-ORTHONORMAL MOLECULAR ORBITALS
  !
  ! /!\ L is defined without the 1/6 factor
  !
  END_DOC

  implicit none
  integer,          intent(in)  :: n, l, k, m, j, i
  double precision, intent(out) :: integral
  integer                       :: ipoint
  double precision              :: weight, tmp

  PROVIDE mo_l_coef mo_r_coef
  PROVIDE int2_grad1_u12_bimo_t

  integral = 0.d0
  ! (n, l, k, m, j, i)
  do ipoint = 1, n_points_final_grid

    tmp =     mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
              * ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,l,j)    &
                + int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,l,j)    &
                + int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,l,j) )

    tmp = tmp + mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
              * ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,k,i)    &
                + int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,k,i)    &
                + int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )

    tmp = tmp + mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
              * ( int2_grad1_u12_bimo_t(ipoint,1,l,j) * int2_grad1_u12_bimo_t(ipoint,1,k,i)    &
                + int2_grad1_u12_bimo_t(ipoint,2,l,j) * int2_grad1_u12_bimo_t(ipoint,2,k,i)    &
                + int2_grad1_u12_bimo_t(ipoint,3,l,j) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )

    integral = integral + tmp * final_weight_at_r_vector(ipoint)
  enddo

end

! ---

subroutine give_integrals_3_body_bi_ort_old(n, l, k, m, j, i, integral)

  BEGIN_DOC
  !
  ! < n l k | L | m j i > with a BI-ORTHONORMAL MOLECULAR ORBITALS
  !
  ! /!\ L is defined without the 1/6 factor
  !
  END_DOC

  implicit none
  integer,          intent(in)  :: n, l, k, m, j, i
  double precision, intent(out) :: integral
  integer                       :: ipoint
  double precision              :: weight

  integral = 0.d0
  do ipoint = 1, n_points_final_grid
    weight = final_weight_at_r_vector(ipoint)
    integral += weight * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i)        &
              * ( int2_grad1_u12_bimo_transp(n,m,1,ipoint) * int2_grad1_u12_bimo_transp(l,j,1,ipoint) &
                + int2_grad1_u12_bimo_transp(n,m,2,ipoint) * int2_grad1_u12_bimo_transp(l,j,2,ipoint) &
                + int2_grad1_u12_bimo_transp(n,m,3,ipoint) * int2_grad1_u12_bimo_transp(l,j,3,ipoint) )
    integral += weight * mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j)        &
              * ( int2_grad1_u12_bimo_transp(n,m,1,ipoint) * int2_grad1_u12_bimo_transp(k,i,1,ipoint) &
                + int2_grad1_u12_bimo_transp(n,m,2,ipoint) * int2_grad1_u12_bimo_transp(k,i,2,ipoint) &
                + int2_grad1_u12_bimo_transp(n,m,3,ipoint) * int2_grad1_u12_bimo_transp(k,i,3,ipoint) )
    integral += weight * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m)        &
              * ( int2_grad1_u12_bimo_transp(l,j,1,ipoint) * int2_grad1_u12_bimo_transp(k,i,1,ipoint) &
                + int2_grad1_u12_bimo_transp(l,j,2,ipoint) * int2_grad1_u12_bimo_transp(k,i,2,ipoint) &
                + int2_grad1_u12_bimo_transp(l,j,3,ipoint) * int2_grad1_u12_bimo_transp(k,i,3,ipoint) )

  enddo

end subroutine give_integrals_3_body_bi_ort_old

! ---

subroutine give_integrals_3_body_bi_ort_ao(n, l, k, m, j, i, integral)

  BEGIN_DOC
  !
  ! < n l k | L | m j i > with a BI-ORTHONORMAL ATOMIC ORBITALS
  !
  ! /!\ L is defined without the 1/6 factor
  !
  END_DOC

  implicit none
  integer,          intent(in)  :: n, l, k, m, j, i
  double precision, intent(out) :: integral
  integer                       :: ipoint
  double precision              :: weight

  integral = 0.d0
  do ipoint = 1, n_points_final_grid
    weight = final_weight_at_r_vector(ipoint)

    integral += weight * aos_in_r_array_transp(ipoint,k) * aos_in_r_array_transp(ipoint,i) &
              * ( int2_grad1_u12_ao_t(ipoint,1,n,m) * int2_grad1_u12_ao_t(ipoint,1,l,j)    &
                + int2_grad1_u12_ao_t(ipoint,2,n,m) * int2_grad1_u12_ao_t(ipoint,2,l,j)    &
                + int2_grad1_u12_ao_t(ipoint,3,n,m) * int2_grad1_u12_ao_t(ipoint,3,l,j) )
    integral += weight * aos_in_r_array_transp(ipoint,l) * aos_in_r_array_transp(ipoint,j) &
              * ( int2_grad1_u12_ao_t(ipoint,1,n,m) * int2_grad1_u12_ao_t(ipoint,1,k,i)    &
                + int2_grad1_u12_ao_t(ipoint,2,n,m) * int2_grad1_u12_ao_t(ipoint,2,k,i)    &
                + int2_grad1_u12_ao_t(ipoint,3,n,m) * int2_grad1_u12_ao_t(ipoint,3,k,i) )
    integral += weight * aos_in_r_array_transp(ipoint,n) * aos_in_r_array_transp(ipoint,m) &
              * ( int2_grad1_u12_ao_t(ipoint,1,l,j) * int2_grad1_u12_ao_t(ipoint,1,k,i)    &
                + int2_grad1_u12_ao_t(ipoint,2,l,j) * int2_grad1_u12_ao_t(ipoint,2,k,i)    &
                + int2_grad1_u12_ao_t(ipoint,3,l,j) * int2_grad1_u12_ao_t(ipoint,3,k,i) )

  enddo

end subroutine give_integrals_3_body_bi_ort_ao

! ---