Vibrational spectroscopy of linear carbon chains

A detailed theoretical study of geometric, electronic, vibrational, and spec-troscopic properties of linear carbon chains is presented. The study is supplemented with an extensive survey of available experimental and theo-retical results. Our calculations constitute a bridge between the quantum-chemical and solid-state simulations, using the SCC-DFTB (self-consistent-charge density-functional tight-binding) methodology. The computed equi-librium geometry, electronic band structure, and phonon dispersion curves of infinite carbon chains are compared with analogous results obtained for finite oligomers. A surprisingly fast convergence of all the studied properties of the finite systems to the infinite limit and a rather short-ranged influence of the terminal sections of the chain are observed. The molecular calculations display analogues of well known solid state physics phenomena, such as Peierls distortion or Kohn anomaly. The presented IR and Raman spectra of finite chains show that the infinite limit is approached rapidly both in the frequency and intensity domain. For a constant mass sample, the intensity of the IR signal is inversely proportional to the number of carbons atoms in the chain, while the intensity of the main Raman band becomes independent on the chain length. The satellite bands and terminal group vibrations disappear from the Raman spectra already for relatively short chains.