Anharmonic effects of periodic molecular systems in the vibron model approximation

The vibron model approximation to take into account anharmonic effects in periodic systems is discussed. This is achieved by considering a simple one-dimensional molecular crystal with four degrees of freedom. In this case the lattice dynamical treatment is separated into two sets of modes, the modes associated to the molecular degrees of freedom and those corresponding to the motions of the centre of mass of the molecules. The non-interacting molecular modes are studied in detail, and analytical expressions for the energies and wave functions for the two-phonon manifold are obtained. A local-normal mode transition as a function of the interaction parameters is identified, similar to that in isolated molecular systems.