BEGIN_PROVIDER [double precision, state_av_full_occ_2_rdm_ab_mo, (n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb)]
 implicit none
 state_av_full_occ_2_rdm_ab_mo = 0.d0
 integer :: i,j,k,l,iorb,jorb,korb,lorb
 BEGIN_DOC
! state_av_full_occ_2_rdm_ab_mo(i,j,k,l) =  STATE AVERAGE physicist notation for 2RDM of alpha/beta + beta/alpha electrons
!
!                                     = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,beta} a_{l,beta} a_{k,alpha} |Psi_{istate}>
!
! WHERE ALL ORBITALS (i,j,k,l) BELONG TO ALL OCCUPIED ORBITALS : core, inactive and active
!
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * N_{\beta} * 2
!
!  !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
!
!  !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
 END_DOC
 PROVIDE n_core_orb list_core
 state_av_full_occ_2_rdm_ab_mo = 0.d0
 !$OMP PARALLEL PRIVATE(i,j,k,l,iorb,jorb,korb,lorb) &
 !$OMP DEFAULT(NONE) SHARED(n_act_orb, n_inact_orb, n_core_orb, &
 !$OMP list_core, list_act, list_inact, no_core_density, &
 !$OMP one_e_dm_mo_alpha_average, one_e_dm_mo_beta_average, &
 !$OMP state_av_act_2_rdm_ab_mo, state_av_full_occ_2_rdm_ab_mo)

 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_act_orb
      korb = list_act(k)
      do l = 1, n_act_orb
       lorb = list_act(l)
       !                                     alph beta alph beta
       state_av_full_occ_2_rdm_ab_mo(lorb,korb,jorb,iorb) = &
        state_av_act_2_rdm_ab_mo(l,k,j,i)
       enddo
      enddo
     enddo
    enddo
 !$OMP END DO
   !! BETA ACTIVE - ALPHA inactive
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_ab_mo(korb,jorb,korb,iorb) = 2.d0 * one_e_dm_mo_beta_average(jorb,iorb)
     enddo
    enddo
   enddo
 !$OMP END DO

   !! ALPHA ACTIVE - BETA inactive
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_ab_mo(jorb,korb,iorb,korb) = 2.d0 * one_e_dm_mo_alpha_average(jorb,iorb)
     enddo
    enddo
   enddo
 !$OMP END DO

   !! ALPHA INACTIVE - BETA INACTIVE
   !!
 !$OMP DO
    do j = 1, n_inact_orb
     jorb = list_inact(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_ab_mo(korb,jorb,korb,jorb) = 2.D0
     enddo
    enddo
 !$OMP END DO

!!!!!!!!!!!!
!!!!!!!!!!!! if "no_core_density" then you don't put the core part
!!!!!!!!!!!! CAN BE USED
   if (.not.no_core_density)then
    !! BETA ACTIVE - ALPHA CORE
    !!
 !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                     alph beta alph beta
       state_av_full_occ_2_rdm_ab_mo(korb,jorb,korb,iorb) = 2.d0 * one_e_dm_mo_beta_average(jorb,iorb)
      enddo
     enddo
    enddo
 !$OMP END DO

    !! ALPHA ACTIVE - BETA CORE
    !!
 !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                     alph beta alph beta
       state_av_full_occ_2_rdm_ab_mo(jorb,korb,iorb,korb) = 2.d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      enddo
     enddo
    enddo
 !$OMP END DO

   !! ALPHA CORE - BETA CORE
   !!
 !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_ab_mo(korb,jorb,korb,jorb) = 2.D0
     enddo
    enddo
 !$OMP END DO
   endif

 !$OMP END PARALLEL
 END_PROVIDER


 BEGIN_PROVIDER [double precision, state_av_full_occ_2_rdm_aa_mo, (n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb)]
 implicit none
 state_av_full_occ_2_rdm_aa_mo = 0.d0
 integer :: i,j,k,l,iorb,jorb,korb,lorb
 BEGIN_DOC
! state_av_full_occ_2_rdm_aa_mo(i,j,k,l) =  STATE AVERAGE physicist notation for 2RDM of alpha/alpha electrons
!
!                                     = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,alpha} a_{l,alpha} a_{k,alpha} |Psi_{istate}>
!
! WHERE ALL ORBITALS (i,j,k,l) BELONG TO ALL OCCUPIED ORBITALS : core, inactive and active
!
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * (N_{\alpha} - 1)
!
!  !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
!
!  !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
 END_DOC

 PROVIDE n_core_orb list_core
 !$OMP PARALLEL PRIVATE(i,j,k,l,iorb,jorb,korb,lorb) &
 !$OMP DEFAULT(NONE) SHARED(n_act_orb, n_inact_orb, n_core_orb, &
 !$OMP list_core, list_act, list_inact, no_core_density, &
 !$OMP one_e_dm_mo_alpha_average, one_e_dm_mo_beta_average, &
 !$OMP state_av_act_2_rdm_aa_mo, state_av_full_occ_2_rdm_aa_mo)
   !! PURE ACTIVE PART ALPHA-ALPHA
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_act_orb
      korb = list_act(k)
      do l = 1, n_act_orb
       lorb = list_act(l)
       state_av_full_occ_2_rdm_aa_mo(lorb,korb,jorb,iorb) =  &
        state_av_act_2_rdm_aa_mo(l,k,j,i)
       enddo
      enddo
     enddo
    enddo
 !$OMP END DO
   !! ALPHA ACTIVE - ALPHA inactive
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                       1     2   1    2    : DIRECT TERM
      state_av_full_occ_2_rdm_aa_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      state_av_full_occ_2_rdm_aa_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      !                                       1     2   1    2    : EXCHANGE TERM
      state_av_full_occ_2_rdm_aa_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      state_av_full_occ_2_rdm_aa_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
     enddo
    enddo
   enddo
 !$OMP END DO

   !! ALPHA INACTIVE - ALPHA INACTIVE
 !$OMP DO
   do j = 1, n_inact_orb
    jorb = list_inact(j)
    do k = 1, n_inact_orb
     korb = list_inact(k)
     state_av_full_occ_2_rdm_aa_mo(korb,jorb,korb,jorb) +=  1.0d0
     state_av_full_occ_2_rdm_aa_mo(korb,jorb,jorb,korb) -=  1.0d0
    enddo
   enddo
 !$OMP END DO

!!!!!!!!!!
!!!!!!!!!! if "no_core_density" then you don't put the core part
!!!!!!!!!! CAN BE USED
   if (.not.no_core_density)then
    !! ALPHA ACTIVE - ALPHA CORE
 !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                       1     2   1    2    : DIRECT TERM
       state_av_full_occ_2_rdm_aa_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       state_av_full_occ_2_rdm_aa_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       !                                       1     2   1    2    : EXCHANGE TERM
       state_av_full_occ_2_rdm_aa_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       state_av_full_occ_2_rdm_aa_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      enddo
     enddo
    enddo
 !$OMP END DO
    !! ALPHA CORE - ALPHA CORE

 !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      state_av_full_occ_2_rdm_aa_mo(korb,jorb,korb,jorb) +=  1.0d0
      state_av_full_occ_2_rdm_aa_mo(korb,jorb,jorb,korb) -=  1.0d0
     enddo
    enddo
 !$OMP END DO
   endif

 !$OMP END PARALLEL
 END_PROVIDER

 BEGIN_PROVIDER [double precision, state_av_full_occ_2_rdm_bb_mo, (n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb)]
 implicit none
 state_av_full_occ_2_rdm_bb_mo = 0.d0
 integer :: i,j,k,l,iorb,jorb,korb,lorb
 BEGIN_DOC
! state_av_full_occ_2_rdm_bb_mo(i,j,k,l) =  STATE AVERAGE physicist notation for 2RDM of beta/beta electrons
!
!                                     = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,beta} a^{\dagger}_{j,beta} a_{l,beta} a_{k,beta} |Psi_{istate}>
!
! WHERE ALL ORBITALS (i,j,k,l) BELONG TO ALL OCCUPIED ORBITALS : core, inactive and active
!
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta} * (N_{\beta} - 1)
!
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
!
!  !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
 END_DOC

 PROVIDE n_core_orb list_core
 !$OMP PARALLEL PRIVATE(i,j,k,l,iorb,jorb,korb,lorb) &
 !$OMP DEFAULT(NONE) SHARED(n_act_orb, n_inact_orb, n_core_orb, &
 !$OMP list_core, list_act, list_inact, no_core_density, &
 !$OMP one_e_dm_mo_alpha_average, one_e_dm_mo_beta_average, &
 !$OMP state_av_act_2_rdm_bb_mo, state_av_full_occ_2_rdm_bb_mo)
   !! PURE ACTIVE PART beta-beta
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_act_orb
      korb = list_act(k)
      do l = 1, n_act_orb
       lorb = list_act(l)
       state_av_full_occ_2_rdm_bb_mo(lorb,korb,jorb,iorb) = &
        state_av_act_2_rdm_bb_mo(l,k,j,i)
       enddo
      enddo
     enddo
    enddo
 !$OMP END DO
   !! beta ACTIVE - beta inactive
   !!
 !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                       1     2   1    2    : DIRECT TERM
      state_av_full_occ_2_rdm_bb_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      state_av_full_occ_2_rdm_bb_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      !                                       1     2   1    2    : EXCHANGE TERM
      state_av_full_occ_2_rdm_bb_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      state_av_full_occ_2_rdm_bb_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
     enddo
    enddo
   enddo
 !$OMP END DO

   !! beta INACTIVE - beta INACTIVE
 !$OMP DO
   do j = 1, n_inact_orb
    jorb = list_inact(j)
    do k = 1, n_inact_orb
     korb = list_inact(k)
     state_av_full_occ_2_rdm_bb_mo(korb,jorb,korb,jorb) +=  1.0d0
     state_av_full_occ_2_rdm_bb_mo(korb,jorb,jorb,korb) -=  1.0d0
    enddo
   enddo
 !$OMP END DO

!!!!!!!!!!!!
!!!!!!!!!!!! if "no_core_density" then you don't put the core part
!!!!!!!!!!!! CAN BE USED
   if (.not.no_core_density)then
    !! beta ACTIVE - beta CORE
 !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                       1     2   1    2    : DIRECT TERM
       state_av_full_occ_2_rdm_bb_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       state_av_full_occ_2_rdm_bb_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       !                                       1     2   1    2    : EXCHANGE TERM
       state_av_full_occ_2_rdm_bb_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       state_av_full_occ_2_rdm_bb_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      enddo
     enddo
    enddo
 !$OMP END DO
    !! beta CORE - beta CORE

 !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      state_av_full_occ_2_rdm_bb_mo(korb,jorb,korb,jorb) +=  1.0d0
      state_av_full_occ_2_rdm_bb_mo(korb,jorb,jorb,korb) -=  1.0d0
     enddo
    enddo
 !$OMP END DO
   endif
 !$OMP END PARALLEL

 END_PROVIDER

 BEGIN_PROVIDER [double precision, state_av_full_occ_2_rdm_spin_trace_mo, (n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb,n_core_inact_act_orb)]
 implicit none
 state_av_full_occ_2_rdm_spin_trace_mo = 0.d0
 integer :: i,j,k,l,iorb,jorb,korb,lorb
 BEGIN_DOC
! state_av_full_occ_2_rdm_bb_mo(i,j,k,l) =  STATE AVERAGE physicist notation for 2RDM of beta/beta electrons
!
!                                     = \sum_{istate} w(istate) * \sum_{sigma,sigma'} <Psi_{istate}| a^{\dagger}_{i,sigma} a^{\dagger'}_{j,sigma} a_{l,sigma'} a_{k,sigma} |Psi_{istate}>
!
!
! WHERE ALL ORBITALS (i,j,k,l) BELONG TO ALL OCCUPIED ORBITALS : core, inactive and active
!
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec} * (N_{elec} - 1)
!
!  !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
!
!  !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
 END_DOC

 PROVIDE n_core_orb list_core

 !$OMP PARALLEL PRIVATE(i,j,k,l,iorb,jorb,korb,lorb) &
 !$OMP DEFAULT(NONE) SHARED(n_act_orb, n_inact_orb, n_core_orb, &
 !$OMP list_core, list_act, list_inact, no_core_density, &
 !$OMP one_e_dm_mo_alpha_average, one_e_dm_mo_beta_average, &
 !$OMP state_av_act_2_rdm_spin_trace_mo, state_av_full_occ_2_rdm_spin_trace_mo)
   !!!!!!!!!!!!!!!!
   !!!!!!!!!!!!!!!!
   !! PURE ACTIVE PART SPIN-TRACE
   !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_act_orb
      korb = list_act(k)
      do l = 1, n_act_orb
       lorb = list_act(l)
       state_av_full_occ_2_rdm_spin_trace_mo(lorb,korb,jorb,iorb) += &
        state_av_act_2_rdm_spin_trace_mo(l,k,j,i)
       enddo
      enddo
     enddo
    enddo
   !$OMP END DO

   !!!!!!!!!!!!!!!!
   !!!!!!!!!!!!!!!!
   !!!!! BETA-BETA !!!!!
   !! beta ACTIVE - beta inactive
   !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                       1     2   1    2    : DIRECT TERM
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      !                                       1     2   1    2    : EXCHANGE TERM
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
     enddo
    enddo
   enddo
   !$OMP END DO
   !! beta INACTIVE - beta INACTIVE
   !$OMP DO
   do j = 1, n_inact_orb
    jorb = list_inact(j)
    do k = 1, n_inact_orb
     korb = list_inact(k)
     state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) +=  1.0d0
     state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,jorb,korb) -=  1.0d0
    enddo
   enddo
   !$OMP END DO
   if (.not.no_core_density)then
    !! beta ACTIVE - beta CORE
    !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                       1     2   1    2    : DIRECT TERM
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       !                                       1     2   1    2    : EXCHANGE TERM
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      enddo
     enddo
    enddo
    !$OMP END DO
    !! beta CORE - beta CORE
    !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) +=  1.0d0
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,jorb,korb) -=  1.0d0
     enddo
    enddo
    !$OMP END DO
   endif

   !!!!!!!!!!!!!!!!
   !!!!!!!!!!!!!!!!
   !!!!! ALPHA-ALPHA !!!!!
   !! ALPHA ACTIVE - ALPHA inactive
   !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                       1     2   1    2    : DIRECT TERM
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      !                                       1     2   1    2    : EXCHANGE TERM
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
     enddo
    enddo
   enddo
   !$OMP END DO
   !! ALPHA INACTIVE - ALPHA INACTIVE
   !$OMP DO
   do j = 1, n_inact_orb
    jorb = list_inact(j)
    do k = 1, n_inact_orb
     korb = list_inact(k)
     state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) +=  1.0d0
     state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,jorb,korb) -=  1.0d0
    enddo
   enddo
   !$OMP END DO
   if (.not.no_core_density)then
    !! ALPHA ACTIVE - ALPHA CORE
    !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !                                       1     2   1    2    : DIRECT TERM
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) +=  1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       !                                       1     2   1    2    : EXCHANGE TERM
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,korb,iorb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,iorb,korb) += -1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      enddo
     enddo
    enddo
    !$OMP END DO
    !! ALPHA CORE - ALPHA CORE
    !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) +=  1.0d0
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,jorb,korb) -=  1.0d0
     enddo
    enddo
    !$OMP END DO
   endif

   !!!!!!!!!!!!!!!!
   !!!!!!!!!!!!!!!!
   !!!!! ALPHA-BETA + BETA-ALPHA !!!!!
   !$OMP DO
   do i = 1, n_act_orb
    iorb = list_act(i)
    do j = 1, n_act_orb
     jorb = list_act(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      ! ALPHA INACTIVE - BETA ACTIVE
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) += 1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      !                                     beta alph beta alph
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) += 1.0d0 * one_e_dm_mo_beta_average(jorb,iorb)
      ! BETA INACTIVE - ALPHA ACTIVE
      !                                     beta alph beta alpha
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) += 1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) += 1.0d0 * one_e_dm_mo_alpha_average(jorb,iorb)
     enddo
    enddo
   enddo
   !$OMP END DO
   !! ALPHA INACTIVE - BETA INACTIVE
    !$OMP DO
    do j = 1, n_inact_orb
     jorb = list_inact(j)
     do k = 1, n_inact_orb
      korb = list_inact(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) += 1.0d0
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,jorb,korb) += 1.0d0
     enddo
    enddo
    !$OMP END DO

!!!!!!!!!!!!
!!!!!!!!!!!! if "no_core_density" then you don't put the core part
!!!!!!!!!!!! CAN BE USED
   if (.not.no_core_density)then
    !$OMP DO
    do i = 1, n_act_orb
     iorb = list_act(i)
     do j = 1, n_act_orb
      jorb = list_act(j)
      do k = 1, n_core_orb
       korb = list_core(k)
       !! BETA ACTIVE - ALPHA CORE
       !                                     alph beta alph beta
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) += 1.0D0 * one_e_dm_mo_beta_average(jorb,iorb)
       !                                     beta alph beta alph
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) += 1.0D0 * one_e_dm_mo_beta_average(jorb,iorb)
       !! ALPHA ACTIVE - BETA CORE
       !                                     alph beta alph beta
       state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,iorb,korb) += 1.0D0 * one_e_dm_mo_alpha_average(jorb,iorb)
       !                                     beta alph beta alph
       state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,iorb) += 1.0D0 * one_e_dm_mo_alpha_average(jorb,iorb)
      enddo
     enddo
    enddo
    !$OMP END DO
   !! ALPHA CORE - BETA CORE
    !$OMP DO
    do j = 1, n_core_orb
     jorb = list_core(j)
     do k = 1, n_core_orb
      korb = list_core(k)
      !                                     alph beta alph beta
      state_av_full_occ_2_rdm_spin_trace_mo(korb,jorb,korb,jorb) += 1.0D0
      state_av_full_occ_2_rdm_spin_trace_mo(jorb,korb,jorb,korb) += 1.0D0
     enddo
    enddo
    !$OMP END DO

   endif
  !$OMP END PARALLEL

 END_PROVIDER