Modeling phonons of carbon nanowires

The modeling of the vibrational structure of materials is of great help for the use of vibrational spectroscopy for structural characterization. This is especially true in presence of conjugated ππ electrons where the delocalized nature of ππ orbitals produces long-range interactions responsible for a marked dependence of the vibrational states on the confinement. This effect is due to the finite size of the molecules as well as to chemical and/or structural defects or to the presence of nanocrystals. To model the vibrational states we adopt a semiempirical model developed in the framework of a tight binding theory for ππ electrons (Hückel theory). This treatment has been already successfully applied in the past to the study of the vibrational dynamics of polyynes, graphene and carbon nanotubes and it is here extended to the case of sp linear carbon chains (polyynes). It is shown that the effect of the confinement on the vibrational features is influenced by the presence of a Kohn anomaly in the limit of a cumulenic structure. This behaviour is shared by all conjugated carbon materials irrespective of the hybridization of C atoms (sp22 or sp).