The electronic terms of the finite-length nanotubes, generated by edge states: A CASSCF study

• Published in: International journal of quantum chemistry Vol. 111; no. 11; pp. 2592 - 2601
• Main Authors: Pavlov, Mikhail, Ermilov, Alexander
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.09.2011
• Subjects: antiferromagnetic coupling; carbon nanotubes; CASSCF; edge states; Heisenburg Hamiltonian
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.22650

Low‐lying electronic terms of the hydrocarbons [C7]q (q = 1,3…9) were calculated within CASSCF approach. The [C7]q are H‐terminated finite fragment of zigzag carbon nanotube (7,0) containing q cyclacene units. Each [C7]q with odd q has D7h point symmetry. All systems [Cn]q with arbitrary n and q have a specific set of the one‐electron states characterized by the exponential decay along the cylinder axis that has been estimated within the Huckel model. These MOs are localized near bases of the cylinder and they are frontier in all systems [Cn]q. By hypothesis, the low‐lying electronic terms of the hydrocarbons [C7]q (q = 1,3…9) are defined by four quasi‐degenerate MOs e3′, e3″, which were included in the active space CASSCF. Low‐lying electronic terms possess tier structure and systems with various q have the same order of states. The distance between tiers tends to asymptotic limit with increasing q. In this case, states in each tier become quasi‐degenerate. The lowest tier consists of close set of states 1A ′1, 3A ″2, 5A ′1, and each is characterized by single occupation of the localized MOs. Ground state of [C7]q is singlet; values of splitting are well described by Heisenberg hamiltonaian. The calculation results can be interpreted as reducing interaction of states localized on opposite cylinder bases with increasing fragment length. According to CASSCF, this interaction reduces exponentially in exact accordance with the similar characteristics of the localized MOs. There is a reason to believe that the value of splitting decreases less rapidly with increasing q if level of calculation is improved. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011