pi-electron delocalization in carbon linear chains

Carbon compounds, as for instance fullerenes and nanotubes, are nowadays among the main actors in the field of nanoscience and nanotechnology. Many different studies and experiments indicate that one-dimensional structures such as linear sp carbon chains are expected in the initial stage of the formation of fullerenes and nanotubes [1-3]. Hydrogen-terminated carbon linear chains have been effectively produced by a submerged electric arc method [4]; one-dimensional carbon nanowires have been observed and characterized at the center of multiwall carbon nanotubes [5]. Recent and successful efforts to synthesize capped polyynic molecules allowed to measure their interesting non-linear optical response [6]. Raman and SERS spectroscopies proved to be a powerful probe to understand the properties of polyconjugated carbon materials [7] and linear carbon chains [8]. In this paper we study the vibrational properties of infinite linear carbon chains based on a density functional perturbation scheme (DFPT) in the framework of pseudo potential theory, as implemented in the PWscf code [9]. We will show that the longitudinal optical phonon branch (LO) is dramatically dependent on Bond-Length Alternation (BLA) especially near Γ and different branches will be found for different BLA values. Similarly to other π-conjugated systems [7], linear carbon chains of increasing lengths show an increasing degree of electronic delocalization and thus a decreasing value of the CC stretching force constants and BLA. First- principles calculations on chains of different lengths will show that their vibrational frequencies can be superimposed on the LO phonon branch for the corresponding BLA value. References [1] R. J. Lagow et al., Science 267, 362, (1995). [2] A. A. Svartsburg et al., Phys. Rev. Lett. 84, 2421 (2000). [3] P. R. C. Kent et al., Phys. Rev. B 62, 15394 (2000). [4] F. Cataldo, Carbon 42, 129-142 (2004). [5] X. Zhao et al., Phys. Rev. Lett. 90, 187401 (2003). [6] A. D. Slepkov et al., J. Chem. Phys. 120, 6807-6810 (2004). [7] (a) M. Gussoni, C. Castiglioni, G. Zerbi, in “Spectroscopy of advanced materials”, Edited by R. J. H. Clark and R. E. Hester, Wiley (1991); (b) V. Hernandez, C. Castiglioni, M. Del Zoppo, G. Zerbi, Phys. Rev. B 50, 9815-9823 (1994); (c) C. Castiglioni, M. Tommasini, G. Zerbi, Phil. Trans. R. Soc. Lond. A 362, 2425-2459 (2004). [8] A. Lucotti et al., Chem. Phys. Lett. 417, 78-82 (2006). [9] S. Baroni, A. Dal Corso, S. De Gironcoli, P. Giannozzi, C. Cavazzoni, G. Ballabio, S. Scandolo, G. Chiarotti, P. Focher, A. Pasquarello, K. Laasonen, A. Trave, R. Car, N. Marzari, A. Kokalj, http://www.pwscf.org/.