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

Abstract

Low-lying electronic terms of the hydrocarbons [C 7 ] q (q ¼ 1,3…9) were calculated within CASSCF approach. The [C 7 ] q are H-terminated finite fragment of zigzag carbon nanotube (7,0) containing q cyclacene units. Each [C 7 ] q with odd q has D 7h point symmetry. All systems [C n ] 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 [C n ] q . By hypothesis, the low-lying electronic terms of the hydrocarbons [C 7 ] q (q ¼ 1,3…9) are defined by four quasidegenerate MOs e 3 0 , e 3 00 , 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, and each is characterized by single occupation of the localized MOs. Ground state of [C 7 ] 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.

Potential magnetic properties of nanotubes (n, 0) with Klein and Fujita edges

“…Equation (13') has the same structure as the well known expression for the zigzag type NT energy bands [2]: (14) where and l = 1, 2 … n; is the size of the unit cell of an NT (n, 0) along the tube axis (rotary symmetry axis C n ). The dispersion curve describing the energy bands of an infinite NT is obtained from the continuous change in the interval [-1, 1].…”

“…As in [14,15], an NT fragment containing q [n]cyclacene layers (Fig. 1a) and having both Fujita type edges are denoted as [C n ] q .…”

“…However, qualitative prediction allows us to specify criteria for developing the calculation methods we for mulated in [14]. It is wise to select localized MOs as the active space in multiconfiguration CASSCF cal culations.…”

“…It is most productive to construct hypothetical states of the individual bases [14] in order to interpret the vertical spectrum. Indeed, three electrons are localized on the Fujita edge, and a hypothetical state of 4 B 2 (down) with the electron configuration of can be attributed to them.…”

“…In earlier works, we described edge states for zig zag type NTs with edges where the terminal carbon atoms are connected to hydrogen atoms [14,15]. An edge of this type is called a Fujita edge.…”