Not very long ago the main concept of the connection between the electronic structure and chemical reactivity of CNTs was based on the Haddon approach,23 which attributed the reactivity of fullerenes to the strain engendered by their spherical geometry as rešected in pyramidalization angles of carbon atoms. It was suggested that the curvature-induced pyramidalization and misalignment of the π orbitals of the carbon atoms24,25 induces a local strain in a defect-free CNT. This concept made allowance for explaining the difference between the reactivity of a CNT end cap and that of a sidewall in favor of the former, and gave a simple explanation of the reactivity increase while the CNT diameter decreases. Further development of the approach turned out to be useful for considering the reactivity of the convex and concave sidewalls of CNTs toward addition reactions.12,13

The Haddon approach was quite productive but basically empirical, while more sophisticated theoretical approaches were needed. Various density functional theory (DFT) techniques actively explored in recent years with respect to the chemical functionalization of carbon nanotubes, to name a few,15-22 were a natural response to the requirement. However, a lot of severe limitations were usually implied when using the technique. This concerns:

1. The aromaticity concept attributed to the electronic structure of the tubes, which results in the closed-shell approximation for wave functions (that concerns the restricted DFT approach)

2. The periodic boundary conditions along the tubes, which restrict the tube area consideration to the sidewall only, leaving the tube ends, the most active spots on the tube, as was shown,26 outside the consideration

3. The absence of atomically matched characteristics that could exhibit the chemical reactivity of the tube atoms

4. A postfactum character of simulations that were aimed at obtaining energy and structural data consistent with experimental œndings by adapting the functionals used

As was the case with fullerenes, the most crucial is the œrst assumption in view of weakly interacting odd electrons in carbon nanotubes. When the problem is considered in the framework of the aromaticity concept, this means strong coupling between the electrons so that odd electrons are covalently coupled in pairs, similarly to π electrons of the benzene molecule. The only UBS DFT calculation that is known so far27 concerns a thorough analysis of the singlet state of cyclacenes and short zigzag CNTs. It was shown that the energy of the UBS DFT singlet state was lower than that of the restricted DFT singlet that pointed to the open-shell character of the singlet state. This œnding is of great importance, exhibiting the falsity of aromaticity-based concept for quantitative description of the electronic states of carbon nanotubes on the DFT platform.