
BEGIN_PROVIDER [double precision, fock_a_tot_3e_bi_orth, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_sss, contrib_sos, contrib_soo,contrib
 fock_a_tot_3e_bi_orth = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   fock_a_tot_3e_bi_orth(a,i) += fock_cs_3e_bi_orth(a,i)
   fock_a_tot_3e_bi_orth(a,i) += fock_a_tmp1_bi_ortho(a,i)
   fock_a_tot_3e_bi_orth(a,i) += fock_a_tmp2_bi_ortho(a,i)
  enddo
 enddo
END_PROVIDER 

BEGIN_PROVIDER [double precision, fock_b_tot_3e_bi_orth, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_sss, contrib_sos, contrib_soo,contrib
 fock_b_tot_3e_bi_orth = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   fock_b_tot_3e_bi_orth(a,i) += fock_cs_3e_bi_orth(a,i)
   fock_b_tot_3e_bi_orth(a,i) += fock_b_tmp2_bi_ortho(a,i)
   fock_b_tot_3e_bi_orth(a,i) += fock_b_tmp1_bi_ortho(a,i)
  enddo
 enddo
END_PROVIDER 

BEGIN_PROVIDER [double precision, fock_cs_3e_bi_orth, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_sss, contrib_sos, contrib_soo, contrib
 double precision :: direct_int, exch_13_int, exch_23_int, exch_12_int, c_3_int, c_minus_3_int
 double precision :: new
 fock_cs_3e_bi_orth = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   
   do j = 1, elec_beta_num
    do k = 1, elec_beta_num
!      call contrib_3e_sss(a,i,j,k,contrib_sss)
!      call contrib_3e_soo(a,i,j,k,contrib_soo)
!      call contrib_3e_sos(a,i,j,k,contrib_sos)
!      contrib = 0.5d0 * (contrib_sss + contrib_soo) + contrib_sos

      call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int )!!! < a k j | i k j >
      call  give_integrals_3_body_bi_ort(a, k, j, j, i, k, c_3_int)      ! < a k j | j i k >
      call  give_integrals_3_body_bi_ort(a, k, j, k, j, i, c_minus_3_int)! < a k j | k j i >
 ! negative terms :: exchange contrib
      call  give_integrals_3_body_bi_ort(a, k, j, j, k, i, exch_13_int)!!! < a k j | j k i > : E_13 
      call  give_integrals_3_body_bi_ort(a, k, j, i, j, k, exch_23_int)!!! < a k j | i j k > : E_23
      call  give_integrals_3_body_bi_ort(a, k, j, k, i, j, exch_12_int)!!! < a k j | k i j > : E_12
      new  = 2.d0 * direct_int + 0.5d0 * (c_3_int + c_minus_3_int - exch_12_int) & 
             -1.5d0 * exch_13_int - exch_23_int
      fock_cs_3e_bi_orth(a,i) += new
    enddo
   enddo
  
  enddo
 enddo
 fock_cs_3e_bi_orth = - fock_cs_3e_bi_orth

END_PROVIDER 


BEGIN_PROVIDER [double precision, fock_a_tmp1_bi_ortho, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_sss, contrib_sos, contrib_soo, contrib
 double precision :: direct_int, exch_13_int, exch_23_int, exch_12_int, c_3_int, c_minus_3_int
 double precision :: new
 fock_a_tmp1_bi_ortho = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   
   do j = elec_beta_num + 1, elec_alpha_num 
    do k = 1, elec_beta_num
      call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int )!!! < a k j | i k j >
      call  give_integrals_3_body_bi_ort(a, k, j, j, i, k, c_3_int)      ! < a k j | j i k >
      call  give_integrals_3_body_bi_ort(a, k, j, k, j, i, c_minus_3_int)! < a k j | k j i >
      call  give_integrals_3_body_bi_ort(a, k, j, j, k, i, exch_13_int)!!! < a k j | j k i > : E_13 
      call  give_integrals_3_body_bi_ort(a, k, j, i, j, k, exch_23_int)!!! < a k j | i j k > : E_23
      call  give_integrals_3_body_bi_ort(a, k, j, k, i, j, exch_12_int)!!! < a k j | k i j > : E_12
      fock_a_tmp1_bi_ortho(a,i) += 1.5d0 * (direct_int - exch_13_int) &
      + 0.5d0 * (c_3_int + c_minus_3_int - exch_23_int - exch_12_int)
    enddo
   enddo

  enddo
 enddo
 fock_a_tmp1_bi_ortho = - fock_a_tmp1_bi_ortho
END_PROVIDER 

BEGIN_PROVIDER [double precision, fock_a_tmp2_bi_ortho, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_sss
 fock_a_tmp2_bi_ortho = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   do j = 1, elec_alpha_num
    do k = elec_beta_num+1, elec_alpha_num
      call contrib_3e_sss(a,i,j,k,contrib_sss)
      fock_a_tmp2_bi_ortho(a,i) += 0.5d0 * contrib_sss
    enddo
   enddo
  enddo
 enddo
END_PROVIDER 





BEGIN_PROVIDER [double precision, fock_b_tmp1_bi_ortho, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: direct_int, exch_13_int, exch_23_int, exch_12_int
 double precision :: new
 fock_b_tmp1_bi_ortho = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   
   do j = 1, elec_beta_num
    do k = elec_beta_num+1, elec_alpha_num
      call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int )!!! < a k j | i k j >
      call  give_integrals_3_body_bi_ort(a, k, j, j, k, i, exch_13_int)!!! < a k j | j k i > : E_13 
      call  give_integrals_3_body_bi_ort(a, k, j, i, j, k, exch_23_int)!!! < a k j | i j k > : E_23
      fock_b_tmp1_bi_ortho(a,i) += 1.5d0 * direct_int - 0.5d0 * exch_23_int - exch_13_int
    enddo
   enddo

  enddo
 enddo
 fock_b_tmp1_bi_ortho = - fock_b_tmp1_bi_ortho
END_PROVIDER 

BEGIN_PROVIDER [double precision, fock_b_tmp2_bi_ortho, (mo_num, mo_num)]
 implicit none
 integer :: i,a,j,k
 double precision :: contrib_soo
 fock_b_tmp2_bi_ortho = 0.d0
 do i = 1, mo_num
  do a = 1, mo_num
   do j = elec_beta_num + 1, elec_alpha_num 
    do k = 1, elec_alpha_num
      call contrib_3e_soo(a,i,j,k,contrib_soo)
      fock_b_tmp2_bi_ortho(a,i) += 0.5d0 * contrib_soo
    enddo
   enddo
  enddo
 enddo
END_PROVIDER 

subroutine contrib_3e_sss(a,i,j,k,integral)
 implicit none
 integer, intent(in) :: a,i,j,k
 BEGIN_DOC
 ! returns the pure same spin contribution to F(a,i) from two orbitals j,k
 END_DOC
 double precision, intent(out) :: integral
 double precision :: direct_int, exch_13_int, exch_23_int, exch_12_int, c_3_int, c_minus_3_int
 call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int )!!! < a k j | i k j >
 call  give_integrals_3_body_bi_ort(a, k, j, j, i, k, c_3_int)      ! < a k j | j i k >
 call  give_integrals_3_body_bi_ort(a, k, j, k, j, i, c_minus_3_int)! < a k j | k j i >
 integral = direct_int + c_3_int + c_minus_3_int 
 ! negative terms :: exchange contrib
 call  give_integrals_3_body_bi_ort(a, k, j, j, k, i, exch_13_int)!!! < a k j | j k i > : E_13 
 call  give_integrals_3_body_bi_ort(a, k, j, i, j, k, exch_23_int)!!! < a k j | i j k > : E_23
 call  give_integrals_3_body_bi_ort(a, k, j, k, i, j, exch_12_int)!!! < a k j | k i j > : E_12
 integral += - exch_13_int - exch_23_int  - exch_12_int 
 integral = -integral
end

subroutine contrib_3e_soo(a,i,j,k,integral)
 implicit none
 integer, intent(in) :: a,i,j,k
 BEGIN_DOC
 ! returns the same spin / opposite spin / opposite spin contribution to F(a,i) from two orbitals j,k
 END_DOC
 double precision, intent(out) :: integral
 double precision :: direct_int, exch_23_int
 call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int) ! < a k j | i k j >
 call  give_integrals_3_body_bi_ort(a, k, j, i, j, k, exch_23_int)! < a k j | i j k > : E_23
 integral = direct_int - exch_23_int 
 integral = -integral
end

subroutine contrib_3e_sos(a,i,j,k,integral)
 implicit none
 integer, intent(in) :: a,i,j,k
 BEGIN_DOC
 ! returns the same spin / opposite spin / same spin contribution to F(a,i) from two orbitals j,k
 END_DOC
 double precision, intent(out) :: integral
 double precision :: direct_int, exch_13_int
 call  give_integrals_3_body_bi_ort(a, k, j, i, k, j, direct_int )! < a k j | i k j >
 call  give_integrals_3_body_bi_ort(a, k, j, j, k, i, exch_13_int)! < a k j | j k i > : E_13 
 integral = direct_int - exch_13_int 
 integral = -integral
end
