Finite-Length Models of Carbon Nanotubes Based on Clar Sextet Theory

Abstract

Finite-length models of metallic and semiconducting carbon nanotubes (CNTs) based on Clar sextet theory of aromatic systems are proposed. For metallic CNTs, the electronic properties of finite-length models converge monotonically to the values expected for quasi-monodimensional metallic systems. For semiconducting CNTs, the use of finite-length models as proposed in this work leads to a fast convergence of the electronic properties to the values expected for the corresponding infinite-length nanotube.

Clar’s Theory, π-Electron Distribution, and Geometry of Graphene Nanoribbons

“…[44][45][46] It has also been applied to graphene-related systems, 46,47 carbon nanotubes, [48][49][50] and to ribbons 51,52 to some extent.…”

Semiempirical calculations on the electronic properties of finite-length models of carbon nanotubes based on Clar sextet theory

“…As discussed in previous work [11,15], Clar sextet theory can be conveniently applied to the hexagonal network of the CNT sidewall by defining two translational basis vectors, which reflect the translational symmetry of a fully benzenoid graphene sheet and are connected to the 2-dimensional (n,m) vector basis of the nanotubes sidewall [18] by algebraic relationships [11]. The Clar vector basis allows the definition of a primitive cell of the CNTs, from which the infinite CNT can be generated by application of a screw axis operation along the nanotube principal axis [15].…”

“…The Clar vector basis allows the definition of a primitive cell of the CNTs, from which the infinite CNT can be generated by application of a screw axis operation along the nanotube principal axis [15]. Ormsby and King demonstrated [11] that the description of the sidewall in terms of the primitive Clar cell leads to a classification of the CNTs based on the parameter R, which is defined as: R=(n-m, 3), where n and m are the nanotube chiral vectors.…”

“…Finite-length models of nanotubes were built by starting from the corresponding periodic unit cell, as provided by the Materials Studio Builder, recutting and saturating the edges of the FLCCs with hydrogen atoms as described in Ref. [15]. Geometries were optimised at the AM1 level of theory as implemented in the VAMP module [17] of Materials Studio and electronic properties were evaluated at the same level.…”

“…This approach allowed the construction of finite length models of CNTs which are good representatives of their infinite counterparts. In particular, models defined in terms of finite-length Clar clusters (FLCCs) [15] provide accurate electronic properties, as demonstrated for calculations performed at the DFT level [15], and exhibit several computational advantages. Moreover, methods based on semiempirical potentials and particularly the AM1 method [16] allow to describe correctly the electronic structure and the reactivity of CNTs, as for example demonstrated by Orsmy and King in the study of hydrogenation reactions at the sidewall [12].…”