BEGIN_PROVIDER [double precision, spin_population, (ao_num_align,ao_num)]
 implicit none
 integer :: i,j
 BEGIN_DOC
! spin population on the ao basis :
! spin_population(i,j) = rho_AO(alpha)(i,j) - rho_AO(beta)(i,j) * <AO_i|AO_j>
 END_DOC
 spin_population = 0.d0
 do i = 1, ao_num
  do j = 1, ao_num
   spin_population(j,i) = one_body_spin_density_ao(i,j) * ao_overlap(i,j)
  enddo
 enddo
END_PROVIDER

BEGIN_PROVIDER [double precision, spin_population_angular_momentum, (0:ao_l_max)]
 implicit none
 integer :: i
 double precision :: accu
 spin_population_angular_momentum = 0.d0
 do i = 1,  ao_num
  spin_population_angular_momentum(ao_l(i)) += spin_gross_orbital_product(i)
 enddo

END_PROVIDER 


BEGIN_PROVIDER [double precision, spin_gross_orbital_product, (ao_num)]
 implicit none
 spin_gross_orbital_product = 0.d0
 integer :: i,j
 BEGIN_DOC
! gross orbital product for the spin population
 END_DOC
 do i = 1, ao_num
  do j = 1, ao_num
   spin_gross_orbital_product(i) += spin_population(j,i)
  enddo
 enddo

END_PROVIDER

BEGIN_PROVIDER [double precision, mulliken_spin_densities, (nucl_num)]
 implicit none
 integer :: i,j
 BEGIN_DOC
!ATOMIC SPIN POPULATION (ALPHA MINUS BETA)
 END_DOC
 mulliken_spin_densities = 0.d0
 do i = 1, ao_num
  mulliken_spin_densities(ao_nucl(i)) += spin_gross_orbital_product(i)
 enddo

END_PROVIDER

 BEGIN_PROVIDER [double precision, electronic_population_alpha, (ao_num_align,ao_num)]
&BEGIN_PROVIDER [double precision, electronic_population_beta, (ao_num_align,ao_num)]
 implicit none
 integer :: i,j
 BEGIN_DOC
! spin population on the ao basis :
! spin_population(i,j) = rho_AO(alpha)(i,j) - rho_AO(beta)(i,j) * <AO_i|AO_j>
 END_DOC
 electronic_population_alpha = 0.d0
 electronic_population_beta = 0.d0
 do i = 1, ao_num
  do j = 1, ao_num
   electronic_population_alpha(j,i) = one_body_dm_ao_alpha(i,j) * ao_overlap(i,j)
   electronic_population_beta(j,i) = one_body_dm_ao_beta(i,j) * ao_overlap(i,j)
  enddo
 enddo

END_PROVIDER

 BEGIN_PROVIDER [double precision, gross_orbital_product_alpha, (ao_num)]
&BEGIN_PROVIDER [double precision, gross_orbital_product_beta, (ao_num)]
 implicit none
 spin_gross_orbital_product = 0.d0
 integer :: i,j
 BEGIN_DOC
! gross orbital product 
 END_DOC
 do i = 1, ao_num
  do j = 1, ao_num
   gross_orbital_product_alpha(i) += electronic_population_alpha(j,i)
   gross_orbital_product_beta(i) += electronic_population_beta(j,i)
  enddo
 enddo

END_PROVIDER

 BEGIN_PROVIDER [double precision, mulliken_densities_alpha, (nucl_num)]
&BEGIN_PROVIDER [double precision, mulliken_densities_beta, (nucl_num)]
 implicit none
 integer :: i,j
 BEGIN_DOC
!
 END_DOC
 mulliken_densities_alpha = 0.d0
 mulliken_densities_beta = 0.d0
 do i = 1, ao_num
  mulliken_densities_alpha(ao_nucl(i)) += gross_orbital_product_alpha(i)
  mulliken_densities_beta(ao_nucl(i)) += gross_orbital_product_beta(i)
 enddo

END_PROVIDER