  From density-functional-theory (DFT) based methods we calculate the
vibrational spectrum of the Mn_{12}O_{12}(COOH)_{16}(H_2 O)_4 molecular magnet.
Calculated infrared intensities are in accord with experimental studies. There
have been no ab initio attempts at determining which interactions account for
the fourth-order anisotropy. We show that vibrationally induced distortions of
the molecule contribute to the fourth-order anisotropy Hamiltonian and that the
magnitude and sign of the effect (-6.2 K) is in good agreement with all
experiments. Vibrationally induced tunnel splittings in isotopically pure and
natural samples are predicted.
