  The magnetic energy-level diagrams for models of the Mn12 and V15 molecule
are calculated using the Lanczos method with full orthogonalization and a
Chebyshev-polynomial-based projector method. The effect of the
Dzyaloshinskii-Moriya interaction on the appearance of energy-level repulsions
and its relevance to the observation of steps in the time-dependent
magnetization data is studied. We assess the usefulness of simplified models
for the description of the zero-temperature magnetization dynamics.
