Molecular magnets exhibit many novel nanostructure magnetic properties
and potential application, while most of the present studies
concentrate on the collective spin dynamics and quantum magnetic
tunneling of molecular spin based on a phenomenal Heisenberg spin
model, the spin is the only relevant freedom degree. This work focus
on the microscopic origin of the spin interaction in molecular magnets
Mn_{12}Ac, we find the orbital freedom degree plays roles in the S=10
groundstate and the spin dynamics. Starting from the
orbital-degenerate Hubbard model, we obtain the superexchange magnetic
coupling matrix for different orbitals between Mn ions by the
second-order perturbation approach, orbital-dependent couplings among
Mn ions stablize the S=10 configuration as realistic ground state and
the groundstate energy gap by the exact diagonalization. Therefore the
anisotropic spin interaction in Mn_{12}Ac is attributed to the
spatial-symmetry-broken orbital interaction, the orbital dynamics is
thus involved in the spin dynamics.