Analysis of the Relationship between Reaction Energies of Electrophilic SWNT Additions and Sidewall Curvature: Chiral Nanotubes

The relationship of reaction energies for CH 2 /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 (2 n, 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 Δ E and 1/ d holds only for individual endo, exo( s ) and exo( l ) addition series to specific t / d / p bonds, while Δ E, 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 Δ E is dominated by INT, while for exo( l ) series, this quantity is dominated by DEF.