! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_direct_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the direct terms 
  !
  ! three_e_3_idx_direct_bi_ort(m,j,i) = <mji|-L|mji>
  ! 
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  PROVIDE mo_l_coef mo_r_coef

  three_e_3_idx_direct_bi_ort = 0.d0
  print *, ' Providing the three_e_3_idx_direct_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

  !$OMP PARALLEL                 &
  !$OMP DEFAULT (NONE)           &
  !$OMP PRIVATE (i,j,m,integral) & 
  !$OMP SHARED (mo_num,three_e_3_idx_direct_bi_ort)
  !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, m, j, i, integral)
        three_e_3_idx_direct_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
  !$OMP END DO
  !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_direct_bi_ort(m,j,i) = three_e_3_idx_direct_bi_ort(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_direct_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_cycle_1_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the first cyclic permutation 
  !
  ! three_e_3_idx_cycle_1_bi_ort(m,j,i) = <mji|-L|jim>
  !
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  three_e_3_idx_cycle_1_bi_ort = 0.d0
  print *, ' Providing the three_e_3_idx_cycle_1_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_cycle_1_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, j, i, m, integral)
        three_e_3_idx_cycle_1_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_cycle_1_bi_ort(m,j,i) = three_e_3_idx_cycle_1_bi_ort(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_cycle_1_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_cycle_2_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the second cyclic permutation 
  !
  ! three_e_3_idx_direct_bi_ort(m,j,i) = <mji|-L|imj>
  !
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  PROVIDE mo_l_coef mo_r_coef

  three_e_3_idx_cycle_2_bi_ort = 0.d0
  print *, ' Providing the three_e_3_idx_cycle_2_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_cycle_2_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, i, m, j, integral)
        three_e_3_idx_cycle_2_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_cycle_2_bi_ort(m,j,i) = three_e_3_idx_cycle_2_bi_ort(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_cycle_2_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_exch23_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 2 and 3
  !
  ! three_e_3_idx_exch23_bi_ort(m,j,i) = <mji|-L|jmi>
  ! 
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  PROVIDE mo_l_coef mo_r_coef

  three_e_3_idx_exch23_bi_ort = 0.d0
  print*,'Providing the three_e_3_idx_exch23_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_exch23_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, j, m, i, integral)
        three_e_3_idx_exch23_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_exch23_bi_ort(m,j,i) = three_e_3_idx_exch23_bi_ort(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_exch23_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_exch13_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 3
  !
  ! three_e_3_idx_exch13_bi_ort(m,j,i) = <mji|-L|ijm>
  ! 
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer :: i,j,m
  double precision :: integral, wall1, wall0

  PROVIDE mo_l_coef mo_r_coef

  three_e_3_idx_exch13_bi_ort = 0.d0
  print *, ' Providing the three_e_3_idx_exch13_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_exch13_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, i, j, m,integral)
        three_e_3_idx_exch13_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_exch13_bi_ort(m,j,i) = three_e_3_idx_exch13_bi_ort(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_exch13_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_exch12_bi_ort, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 2
  !
  ! three_e_3_idx_exch12_bi_ort(m,j,i) = <mji|-L|mij>
  ! 
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  PROVIDE mo_l_coef mo_r_coef

  three_e_3_idx_exch12_bi_ort = 0.d0
  print *, ' Providing the three_e_3_idx_exch12_bi_ort ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_exch12_bi_ort)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, m, i, j, integral)
        three_e_3_idx_exch12_bi_ort(m,j,i) = -1.d0 * integral 
      enddo
    enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_exch12_bi_ort', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---

BEGIN_PROVIDER [ double precision, three_e_3_idx_exch12_bi_ort_new, (mo_num, mo_num, mo_num)]

  BEGIN_DOC
  !
  ! matrix element of the -L  three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 2
  !
  ! three_e_3_idx_exch12_bi_ort_new(m,j,i) = <mji|-L|mij>
  ! 
  ! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
  !
  END_DOC

  implicit none
  integer          :: i, j, m
  double precision :: integral, wall1, wall0

  three_e_3_idx_exch12_bi_ort_new = 0.d0
  print *, ' Providing the three_e_3_idx_exch12_bi_ort_new ...'
  call wall_time(wall0)

  provide mos_r_in_r_array_transp mos_l_in_r_array_transp

 !$OMP PARALLEL                 &
 !$OMP DEFAULT (NONE)           &
 !$OMP PRIVATE (i,j,m,integral) & 
 !$OMP SHARED (mo_num,three_e_3_idx_exch12_bi_ort_new)
 !$OMP DO SCHEDULE (dynamic)
  do i = 1, mo_num
    do j = 1, mo_num
      do m = j, mo_num
        call give_integrals_3_body_bi_ort(m, j, i, m, i, j, integral)
        three_e_3_idx_exch12_bi_ort_new(m,j,i) = -1.d0 * integral 
    enddo
   enddo
  enddo
 !$OMP END DO
 !$OMP END PARALLEL

  do i = 1, mo_num
    do j = 1, mo_num
      do m = 1, j
        three_e_3_idx_exch12_bi_ort_new(m,j,i) = three_e_3_idx_exch12_bi_ort_new(j,m,i)
      enddo
    enddo
  enddo

  call wall_time(wall1)
  print *, ' wall time for three_e_3_idx_exch12_bi_ort_new', wall1 - wall0
  call print_memory_usage()

END_PROVIDER 

! ---