Abstract
We present a theoretical study of Peierls distortion in carbon rings. We demonstrate using the Longuet-Higgins–Salem model that the appearance of bond alternation in conjugated carbon polymers is independent of the boundary conditions and does in fact appear in carbon rings just as in carbon chains. We use the Hartree–Fock approximation and density functional theory to show that this behaviour is retained at the first principles level.
Similar content being viewed by others
Notes
Developing the model and the corresponding HUGEH code and applying it to various conjugated polymers was a very fruitful collaboration between P.R. Surján and J. Kürti.
References
Peierls RE, Peierls SRE (1955) Quantum theory of solids. Clarendon Press, Oxford
Roth S, Carroll D (2004) One-dimensional metals: conjugated polymers, organic crystals, carbon nanotubes. Wiley, London
Rusznyák Á, Zólyomi V, Kürti J, Yang S, Kertesz M (2005) Bond-length alternation and charge transfer in a linear carbon chain encapsulated within a single-walled carbon nanotube. Phys Rev B 72(15):155420(6)
Yang S, Kertesz M (2006) Bond length alternation and energy band gap of polyyne. J Phys Chem A 110(31):9771–9774
Körzdörfer T, Parrish RM, Sears JS, Sherrill CD, Brédas J-L (2012) On the relationship between bond-length alternation and many-electron self-interaction error. J Chem Phys 137(12):124305(8)
Al-Backri A, Zólyomi V, Lambert CJ (2014) Electronic properties of linear carbon chains: resolving the controversy. J Chem Phys 140(10):104306(4)
Longuet-Higgins HC, Salem L (1959) The alternation of bond lengths in long conjugated chain molecules. Proc R Soc Lond A Math Phys Eng Sci 251(1265):172–185
Kürti J, Surján PR (1992) Embedded units in conjugated polymers. J Math Chem 10(1):313–327
Su WP, Schrieffer JR, Heeger AJ (1980) Soliton excitations in polyacetylene. Phys Rev B 22(4):2099–2111
Heeger AJ, Kivelson S, Schrieffer JR, Su WP (1988) Solitons in conducting polymers. Rev Mod Phys 60:781–851
Surján PR, Kuzmany H (1986) Interruption of conjugations of polyacetylene chains. Phys Rev B 33(4):2615–2624
Sun G, Kürti J, Rajczy P, Kertesz M, Hafner J, Kresse G (2003) Performance of the Vienna ab initio simulation package (VASP) in chemical applications. J Mol Struct THEOCHEM 624(1–3):37–45
Chalifoux WA, Tykwinski RR (2010) Synthesis of polyynes to model the sp-carbon allotrope carbyne. Nat Chem 2(11):967–971
Kirby C, Kroto HW, Walton DRM (1980) The microwave spectrum of cyanohexatriyne, HCCCCCCCN. J Mol Spectrosc 83(2):261–265
Watts JD, Bartlett RJ (1992) A theoretical study of linear carbon cluster monoanions, C-n, and dianions, C2-n (n = 2–10). J Chem Phys 97(5):3445–3457
Monninger G, Förderer M, Gürtler P, Kalhofer S, Petersen S, Nemes L, Szalay PG, Krätschmer W (2002) Vacuum ultraviolet spectroscopy of the carbon molecule C3 in matrix isolated state: experiment and theory. J Phys Chem A 106(24):5779–5788
Zhao C, Kitaura R, Hara H, Irle S, Shinohara H (2011) Growth of linear carbon chains inside thin double-wall carbon nanotubes. J Phys Chem C 115(27):13,166–13,170
Kastner J, Kuzmany H, Kavan L, Dousek FP, Kürti J (1995) Reductive preparation of carbyne with high yield. An in situ Raman scattering study. Macromolecules 28(1):344–353
Heimann R, Evsyukov SE, Kavan L (2012) Carbyne and carbynoid structures. Springer, Berlin
Kürti J, Kuzmany H (1991) Resonance Raman scattering from finite and infinite polymer chains. Phys Rev B 44(2):597–613
Choi CH, Kertesz M (1998) Bond length alternation and aromaticity in large annulenes. J Chem Phys 108(16):6681–6688
Wannere CS, Sattelmeyer KW, Schaefer HF, Schleyer PvR (2004) Aromaticity: the alternating C–C bond length structures of [14]-, [18]-, and [22]annulene. Angew Chem Int Ed 43:4200–4206
Kertész M, Surján PR (1981) Trapping of phase kinks in polyacetylene. Solid State Commun 39(5):611–614
Kürti J, Kuzmany H (1987) Conjugation length and localization in conjugated polymers. In: Kuzmany PDH, Mehring PDM, Roth DS (eds) Springer series in solid-state sciences, vol 76., Electronic properties of conjugated polymersSpringer, Berlin, pp 43–47
Kürti J, Surján PR (1989) Quinoid-aromatic transition in polythiophene-like systems. In: Kuzmany H, Mehring M, Roth S (eds) Electronic properties of conjugated polymers III: basic models and applications: proceedings of an International Winter School, Kirchberg, Tirol, March 11-18, 1989, no. 91 in Springer series in solid-state sciences. Springer, Berlin, p 69
Coulson CA (1951) Bond lengths in conjugated molecules: the present position. Proc R Soc Lond A Math Phys Eng Sci 207(1088):91–100
Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision B.01. Gaussian, Inc., Wallingford CT
Schaman C, Pfeiffer R, Zólyomi V, Kuzmany H, Ajami D, Herges R, Dubay O, Sloan J (2006) The transformation of open picotubes to a closed molecular configuration. Phys Status Solidi B 243:3151–3154
Acknowledgments
The authors acknowledge the financial support from OTKA in Hungary (Grant Number K108676). Je.K. acknowledges beneficial discussions with Sándor Pekker. The authors express their gratitude to Péter Surján on the occasion of Péter’s 60th birthday. Jenő Kürti remembers with pleasure to the many joint works with Péter which resulted in more than ten joint publications, started from 1989.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan”.
Rights and permissions
About this article
Cite this article
Kürti, J., Koltai, J., Gyimesi, B. et al. Hydrocarbon chains and rings: bond length alternation in finite molecules. Theor Chem Acc 134, 114 (2015). https://doi.org/10.1007/s00214-015-1709-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00214-015-1709-4