The reactions of hydrogen isocyanide (HN=C) with various simple alkynes (HC=C-X, with X = H, CH3, NH2, F), formally [2 + 1] cycloadditions, have been studied by density functional theory (DFT) with the hybrid exchange correlation B3LYP functional and a 6-311G(d,p) basis set, as well as by MO theory with CCSD(T) calculations. For each reaction, the intrinsic reaction coordinate (IRC) pathway has been constructed. It is shown that each [2 + 1] cycloaddition is nonconcerted but proceeds in two steps: rate-determining addition of HN=C to a carbon atom of HC=CX, giving rise to a zwitterion intermediate, followed by a ring closure of the latter, yielding finally cyclopropenimine. In all cases, HN=C behaves as an electrophile. The activation energies corresponding to both possible initial attacks of HN=C are distinguishable, introducing thus a site selectivity and an asynchronism of bond formation in the initial step, for which a rationalization using DFT-based reactivity descriptors and the local HSAB principle has been proposed. Except for HC=C-F, initial attack on the unsubstituted alkyne carbon is preferred. The hardness and polarizability profiles along the IRC reaction paths of the supersystem have also been constructed. In some cases, there are no clear-cut extrema; in other cases, there is a minimum in the hardness profile and a maximum in the polarizability profile, but these extrema do not coincide with the energy maximum and are rather shifted toward the side having the closest value, following apparently a generalized Hammond postulate. While the higher hardness-lower polarizability criterion seems to hold true, there is no obvious relationship between hardness and energy. The activation energy (E-act) vs hardness difference relationship recently derived by Gazquez turns out to be successful in the interpretation of the calculated E-act sequences.