Account of three-body interactions in the lattice dynamics method

The lattice dynamics method is extended with the account of three-body interaction potential in the harmonic approximation. Analytic expressions for the force constants and dynamical matrix elements are presented. Dynamical matrix element responsible for indirect interaction of atoms is single out. Modeling calculations of phonon spectra at the center of Brillouin zone for empty silicon clathrate structures Si34 and Si46 have been performed.