Analysis of the relationship between reaction energies of electrophilic SWNT additions and sidewall curvature: Chiral nanotubes

The relationship of reaction energies for CH₂/NH/O exo- and endo-[2 + 1] cycloadditions to chiral single-walled carbon nanotube (SWNT) sidewalls with the inverse tube diameter (1/d) was investigated using density functional theory (DFT) and density functional tight binding (DFTB) methods. We considered additions to the three nonequivalent C-C bond types t (bond most parallel to tube axis), d ("diagonal" bond, slightly skewed), and p (bond most perpendicular to tube axis), using hydrogen-terminated (2n,n) SWNT model systems with n = 2-8. Exoadditions are classified into two types, one where the original C-C bond is broken (exo(l)), and one where it remains intact (exo(s)) in the addition complex. Endoadditions are found to always belong to the latter (endo(s)) type. It is found that (a) exoadditions are more exothermic than endo additions, and (b) that exoadditions are more exothermic with larger bond-tube axis angle (p > d > t). A nearly perfect linear relationship between the total reaction energy ΔE and 1/d holds only for individual endo, exo(s) and exo(l) addition series to specific t/d/p bonds, while ΔE, as well as the SWNT deformation energy (DEF) and the interaction energy (INT) between deformed SWNT and deformed addends, are quadratically dependent on 1/d, when both negative (endo) and positive (exo(s)) bond curvatures are considered in linear regression analysis. Energy decomposition analysis shows that for endo- and exo(s)- series the curvature dependence of ΔE is dominated by INT, while for exo(l) series, this quantity is dominated by DEF.