  We perform inelastic neutron scattering measurements on the molecular
nanomagnet Mn_12-acetate to measure the excitation spectrum up to 45meV (500K).
We isolate magnetic excitations in two groups at 5-6.5meV (60-75K) and
8-10.5meV (95-120K), with higher levels appearing only at 27meV (310K) and
31meV (360K). From a detailed characterization of the transition peaks we show
that all of the low-energy modes appear to be separate S = 9 excitations above
the S = 10 ground state, with the peak at 27meV (310K) corresponding to the
first S = 11 excitation. We consider a general model for the four exchange
interaction parameters of the molecule. The static susceptibility is computed
by high-temperature series expansion and the energy spectrum, matrix elements
and ground-state spin configuration by exact diagonalization. The theoretical
results are matched with experimental observation by inclusion of cluster
anisotropy parameters, revealing strong constraints on possible parameter sets.
We conclude that only a model with dominant exchange couplings J_1 ~ J_2 ~
5.5meV (65K) and small couplings J_3 ~ J_4 ~ 0.6meV (7K) is consistent with the
experimental data.
