  The role of the bridging ligand on the effective Heisenberg coupling
parameters is analyzed in detail. This analysis strongly suggests that the
ligand-to-metal charge transfer excitations are responsible for a large part of
the final value of the magnetic coupling constant. This permits to suggest a
new variant of the Difference Dedicated Configuration Interaction (DDCI)
method, presently one of the most accurate and reliable for the evaluation of
magnetic effective interactions. This new method treats the bridging ligand
orbitals mediating the interaction at the same level than the magnetic orbitals
and preserves the high quality of the DDCI results while being much less
computationally demanding. The numerical accuracy of the new approach is
illustrated on various systems with one or two magnetic electrons per magnetic
center. The fact that accurate results can be obtained using a rather reduced
configuration interaction space opens the possibility to study more complex
systems with many magnetic centers and/or many electrons per center.
