  We present a detailed study of the influence of various interactions on the
spin quantum tunneling in a Mn12 wheel molecule. The effects of single-ion and
exchange (spin-orbit) anisotropy are first considered, followed by an analysis
of the roles played by secondary influences, e.g. disorder, dipolar and
hyperfine fields, and magnetoacoustic interactions. Special attention is paid
to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is
done within the framework of a 12-spin microscopic model, and also using
simplified dimer and tetramer approximations in which the electronic spins are
grouped in 2 or 4 blocks, respectively. If the molecule is inversion symmetric,
the DM interaction between the dimer halves must be zero. In an inversion
symmetric tetramer, two independent DM vectors are allowed, but no new
tunneling transitions are generated by the DM interaction. Experiments on the
Mn12 wheel can only be explained if the molecular inversion symmetry is broken,
and we explore this in detail using both models, focussing on the asymmetric
disposition and rounding of Berry phase minima associated with quantum
interference between states of opposite parity. A remarkable behavior exists
for the `Berry phase zeroes' as a function of the directions of the internal DM
vectors and the external transverse field. A rather drastic breaking of the
molecular inversion-symmetry is required to explain the experiments; in the
tetramer model this requires a reorientation of the DM vectors on one half of
the molecule by nearly 180 degrees. This cannot be attributed to sample
disorder. These results are of general interest for the quantum dynamics of
tunneling spins, and lead to some interesting experimental predictions.
