Fourth-order magnetic anisotropy and tunnel splittings in Mn(12) from spin-orbit-vibron interactions

From density-functional-theory 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.