Coupling of the electron spin to local molecular vibrations is an important phenomenon that leads to relaxation of the magnetic moment (spin-lattice relaxation). Slowing down of magnetic relaxation is the main aim when improving the properties of molecular nanomagnets, intended for application in magnetic data storage. Experimentally, spectral features related to spin-phonon coupling have been observed in infrared and Raman spectra. The coupling of the spin system to phonons can be modeled by a Hamiltonian of the following form (similar models were previously considered in, e.g., Refs. 22,24,26,43):