Do Diradicals Behave Like Radicals?

This review sets out to understand the reactivity of diradicals, and how that may differ from monoradicals. We also offer a thorough survey and critical evaluation of various measures of diradical character in the literature. The review divides into three parts:

1. We delineate the electronic structure of a diradical with its two degenerate or nearly degenerate singly occupied molecular orbital (SOMO) levels. The well-known appropriate wave functions and energy ordering of low-lying electronic states—one triplet state and three singlet states—of a diradical are introduced. The continuum of electronic structure from diradicals to diradicaloids and finally to closed-shell molecules is described, depending on increasing gaps between the HOMO and LUMO of a molecule. A classification of diradicals based on whether or not the two SOMOs can be located on different sites of the molecule emerges as useful in determining the ground state spin of a diradical. We then move on to a discussion of a delocalized to localized orbital transformation that can be made for the lowest singlet state of diradicals, a transformation that interchanges “closed-shell” to “open-shell” descriptions. The resulting seeming ambiguity in state description is better viewed as a duality, a view that proves to be extremely useful in understanding the dual reactivity of singlet diradicals.
2. In the second, longest part of this paper, we move to reactivity, examining with a consistent level of theory activation energies of prototypical radical reactions -- dimerization, hydrogen abstraction, addition to ethylene -- for some typical organic diradicals and diradicaloids, in their two lowest spin states. The following molecules are studied, and the findings compared to experiment: (1) alkyl chain diradicals vs. alkyl chain radicals: (2) cyclobutadiene vs. 3-cyclobutenyl; (3) trimethylenemethane vs 2-methylallyl; (4) para and meta-quinodimethane vs. benzyl; (5) dioxygen vs peroxyl and hydroxyl. Differences and similarities in reactivity of diradicals vs. monoradicals, based on either a localized or delocalized view, whichever is suitable, are then discussed. The localized perspective seems to work best for radical-type reactions, while the delocalized view is convenient for "closed-shell-type" reactions, such as electrophilic/nucleophilic reactions and concerted pericyclic reactions. The evolution of the exchange integral Kxy along a reaction coordinate plays a determinative role in setting activation energies. The spin densities measure the likelihoods of different sites to undergo radical-like reaction, and the singlet-triplet gap is found to determine the difference between the reaction modes of triplet diradicals and singlet diradical(oid)s. In general, singlet diradical(oid)s exhibit both diradical-like and closed-shell reactivities.
3. The third part of this work begins with an extensive, comparative, and critical survey of available measures of diradical character in the literature. The relationship between diradical character and electron correlation is discussed. We analyze in detail the consequences of diradical character for H2 dissociation, ozone and its sulfur analogues, polyenes, and polyacenes. Finally, we mention briefly, providing leading references, some other types of diradical(oid)s not discussed in detail in the review, such as arynes, main group and transition metal-based diradicals.