  We investigate the magnetic properties of three Mn$_6$ single molecule
magnets by means of inelastic neutron scattering and frequency domain magnetic
resonance spectroscopy. The experimental data reveal that small structural
distortions of the molecular geometry produce a significant effect on the
energy level diagram and therefore on the magnetic properties of the molecule.
We show that the giant spin model completely fails to describe the spin level
structure of the ground spin multiplets. We analyze theoretically the spin
Hamiltonian for the low spin Mn$_6$ molecule (S=4) and we show that the excited
$S$ multiplets play a key role in determining the effective energy barrier for
the magnetization reversal, in analogy to what was previously found for the two
high spin Mn6 (S=12) molecules [S. Carretta et al., Phys. Rev. Lett. 100,
157203 (2008)].
