Why is phenyl azide so unreactive in [3+2] cycloaddition reactions? Demystifying Sustmann's paradigmatic parabola

The [3 + 2] cycloaddition (32CA) reactions of phenyl azide with a series of 25 ethylenes of different electronic activation have been studied within Molecular Electron Density Theory (MEDT) at the omega B97X-D/6-311G(d,p) computational level to understand the low reactivity of azides participating in 32CA reactions. Analysis of the reactivity indices allows characterizing phenyl azide as a moderate electrophile and a moderate nucleophile. The relative reaction rate constants k(r) of twelve selected 32CA reactions, together with the electrophilicity omega and nucleophilicity N indices of the corresponding ethylenes, allow us to classify these 32CA reactions into four groups: (i) group A, involving supernucleophilic ethylenes and displaying a k(r) > 10(4); (ii) group B, involving strained cyclic ethylenes and displaying a k(r) < 10(2); (iii) group C, involving strongly electrophilic ethylenes and displaying a k(r) <= 10(2), and (iv) group D, involving moderately electrophilic and nucleophilic ethylenes and displaying a k(r) < 2. These four groups are characterized in Sustmann's parabolic correlation, which results from an inaccurate interpretation of the reactivity of phenyl azide, which is not an ambiphilic species but rather a moderate electrophile that reacts efficiently only with supernucleophilic ethylenes in reverse electron density flux (REDF) zw-type 32CA reactions.

Automated summary

In this study, the [3 + 2] cycloaddition reactions of phenyl azide with different electronically activated ethylenes were investigated. The reactivity of phenyl azide as both an electrophile and a nucleophile was characterized. The reactions were classified into four groups based on the relative reaction rate constants and electrophilicity and nucleophilicity indices of the ethylenes. The results contradict the existing parabolic correlation model.