When finite becomes infinite: convergence properties of vibrational spectra of oligomer chains
We present a computational study of convergence properties of vibrational IR and Raman spectra for a series of increasingly long units of polyethylene, cis- and trans-polyacetylenes, and polyynes. Convergent behavior to the spectra of infinitely long polymers was observed in all cases when chains reached lengths of approximately 60 carbon atoms, both with respect to the positions of the bands and to their intensities. The vibrational spectra of longer chains are practically indistinguishable. The convergence rate depends on the degree of the π conjugation in a studied system: Vibrational spectra for oligoethylenes converge noticeably faster than the spectra for the conjugated systems. The slowest convergence is observed for skeletal motions of the oligomer chains, which may require more than a hundred carbon atoms in the chain to show deviations smaller than 1 cm−1 to the corresponding solid-state calculations. The results suggest that the boundary between the properties of finite and infinite molecular systems fades away for a surprisingly small number of atoms.
KeywordsSimulations of IR and Raman spectra of polymers Convergence in size evolution SCC-DFTB
Ministry of Science and Technology, Taiwan (MOST 105-2113-M-009-018-MY3) and the Center for Emergent Functional Matter Science of National Chiao Tung University from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project funded by the Ministry of Education, Taiwan. We are grateful to the National Center for High-performance Computing, Taiwan for computer time and facilities.
- 29.Chou CP, Li WF, Witek HA, Andrzejak M (2011) Vibrational spectroscopy of linear carbon chains. In: Nemes L, Irle S (eds) Spectroscopy, dynamics and molecular theory of carbon plasmas and vapors. World Scientific, Hackensack, pp 375–415Google Scholar
- 43.Rakovic D, Stepanyan SA, Gribov LA, Panchenko YN (1982) The solution of the inverse spectroscopic problem for the IR spectra of trans- and cis-hexatrienes. J Mol Struct 90:363–377Google Scholar
- 44.Kim JY, Furukawa Y, Sakamoto A, Tasumi M (2002) Raman studies on the self-localized excitations in lightly and heavily doped trans-polyacetylene with sodium. J Phys Chem A 106:8876–8882Google Scholar
- 45.Hendra PJ, Agbenyega JK (1993) The Raman spectra of polymers, 1st edn, chap C. Wiley, Chichester, p 6Google Scholar
- 46.Hummel DO (1991) Atlas of polymer and plastics analysis, 3rd edn. Wiley-VCH, Munich Google Scholar
- 50.Nishimura Y, Lee YP, Irle S, Witek HA (2014) Critical interpretation of CH– and OH– stretching regions for infrared spectra of methanol clusters (CH3OH)n (n = 2–5) using self-consistent-charge density functional tight-binding molecular dynamics simulations. J Chem Phys 141:094303CrossRefPubMedGoogle Scholar