Localized Vibration States in Molecular Lattices

In molecular lattices besides small translational motions of the molecules small librational motions are possible. In general there is a coupling between the two types of motion. If there are defects in the lattice, localized vibrational states can occur, both for translational and librational modes. These modes are investigated using the simple model of a linear lattice of dumpbell‐molecules. From a general discussion of the Green's function it follows that the frequencies of the localized librational states can occur in the region of the spectrum which in the ideal lattice is dominated by the translational modes and vice versa. Also both kinds of localized state can have frequencies in regions where there are no ideal lattice frequencies. Further, it is possible to have more localized librational than translational states.