  The magnetic properties of the molecular cluster Mn12Ac are due to the four
Mn3+ ions which have spins S=3/2 and the eight Mn4+ ions with spins S=2. These
spins are coupled by superexchange mechanism. We determine the four exchange
couplings assuming a Heisenberg-type interaction between the ions. We use exact
diagonalization of the spin Hamiltonian by a Lanczos algorithm and we adjust
the couplings to reproduce the magnetization curve of Mn12Ac. We also impose
the constraint of reproducing a gap of 35K between a S=10 ground state and a
first excited state with S=9. We predict that there is an excited level with
S=8 at 37K above the ground state, only slightly above the S=9 excited state
which lies at 35K and the next excited state is a S=9 multiplet at 67K above
the S=10 ground state.
