The gas-phase hetero Diels–Alder cycloaddition reactions of the sulfur diimides HN
S+N−X, where X = CH3, H, Cl, CN and NO2, with 1,3-butadiene were investigated theoretically at the B3LYP/6-31G* level. The most stable isomers of sulfur diimides have Z,Z-forms, which are more stable than the least stable E,E-forms by 6–11 kcal mol−1. The reactions proceed mostly with HN
S+N−X (2) rather than HN−S+
NX (2′), even with an electron-donor X (=CH3). The activation free energy (ΔG‡) is lower, the stronger the electron-accepting ability of X. The lowest cycloaddition barriers are obtained in the exo-additions of the E,E-isomers, which are lower by ca. 10–13 kcal mol−1 than the highest barrier exo-processes of the Z,Z-isomers. The repulsive interactions between the diene π electrons and the endo lone pair on N (nN), and the steric hindrance of a bulky group, are the two major factors that are responsible for the cycloaddition barrier heights.