The viability of 1,3-dipolar cycloadditions of a series of 1,3-dipolar molecules (azomethine ylide, ozone, nitrone, nitrile imine, nitrile ylide, nitrile oxide, diazomethane, and methyl azide) onto the sidewalls of carbon nanotubes has been assessed theoretically by means of a two-layered ONIOM approach. The theoretical calculations predict the following: (i) other than the 18-valence-electron azomethine ylide and ozone, the 16-valence-electron nitrile ylide and nitrile imine are the best candidates for experimentalists to try; (ii) upon 1,3-dipolar cycloaddition, a 1,3-diople molecule is di-sigma-bonded to a pair of carbon atoms on the sidewall of SWNT, forming a five-membered ring surface species; (iii) the as-formed 1,3-dipole-SWNT bonding is much weaker than that in the products of the molecular 1,3-DC reactions and can be plausibly broken by heating at elevated temperatures; (iv) the sidewalls of the armchair (n,n) SWNTs (n = 5-10) are subject to the 1,3-DCs of ozone and azomethine ylides; (v) both the 1,3-DC reactivity and retro-1,3-DC reactivity are moderately dependent on the diameters of SWNTs, implying the feasibility of making use of the heterogeneous 1,3-DC chemistry to purify and separate SWNTs diameter-specifically.