  A two-orbital two-electron diatomic model resembling LiH is used to
investigate the differences between the exact L\"owdin-Shull and approximate
Hartree-Fock-Bogoliubov and Baerends-Buijse density matrix functionals in the
medium- to long-distance dissociation region. In case of homolytic dissociation
(one electron on each atom), the approximate functionals fail to generate the
correct energy due to a compromise between the Hartree-Fock component (which
favors partial charge transfer) and the strong correlation component (which
hampers charge transfer). The exact functional is able to generate the
physically correct answer by enforcing the equi-charge distribution of the
bonding and antibonding orbitals. Besides, the approximate functionals also
have issues in correctly describing heterolytic dissociation (two electrons on
one atom) due to the strong correlation component hampering charge transfer. In
this work, we propose a new scheme in which the homolytic dissociation problem
for approximate functionals is avoided by adding a Lagrange multiplier that
enforces equi-charge distribution of the bonding and antibonding orbitals. The
symmety based nature of the findings implies that they are most likely
transferable to other cases in which one uses an approximate one-particle
method in conjunction with a symmetrical particle-hole correction factor.
