The [2+1] cycloadditions of dichlorocarbene, silylene, germylene, and oxycarbonylnitrene onto the sidewall of an armchair (5,5) single-wall carbon nanotube (SWNT) have been investigated by means of a two-layered ONIOM (MO:MO) approach. It is shown that (i) the [2+1] cycloaddition on the nanotube sidewall is siteselective, the 1,2-pair site being favored, giving rise to the formation of three-membered ring species, (ii) the additions of dichlorocarbene and oxycarbonylnitrenes require small activation energies, whereas the additions of silylene and germylene are barrierless, (iii) thermal stability of the as-formed SWNT derivatives follows the order oxycarbonyinitrene much greater than dichlorocarbene > silylene > germylene, and (iv) among the four reagents concerned, silylene is the best to be used for the functionalization and purification of SWNTs. Finally, we propose that the [2+1] cycloaddition products of SWNTs can be good starting points for further functionalization of SWNTs because the three-membered rings in these SWNT derivatives (e.g., silacyclopropano-SWNTs and aziridino-SWNTs) would be subject to a great deal of ring-opening reactions that have been well-established for the transformation of their organic analogues (e.g., aziridines and silacyclopropanes) in synthetic organic chemistry.