Helical versus linear Jahn-Teller distortions in allene and spiropentadiene radical cations

The allene radical cation can be stabilized both by Jahn-Teller distortion of the bond lengths and by torsion of the end-groups. However, only the latter happens and the allene radical cation relaxes into a twisted D₂ symmetry structure with equal double-bond lengths. Here we revisit the Jahn-Teller distortion of allene and spiropentadiene by assessing the possible implications of their helical π-systems in the radical cations. We describe a general relation between the structure and the number of π-electrons in spiroconjugated and linearly conjugated systems. Through constrained optimizations we compare the stabilization achieved by bond-length alternation and axial torsion in the radical cations, which we explain with a simple frontier molecular orbital (MO) picture. While structurally different, allene and spiropentadiene have similar helical frontier MOs. Both cations relax through torsion because the stabilization of their helical frontier MOs is bigger than that which can be achieved by linear π-conjugation. Electrohelicity thus manifests in molecular systems with partial occupation as a helical π-conjugation effect, which evidently provides more stabilization than its linear counterpart in terms of the Jahn-Teller distortion. This mechanism may be a driving factor for the relaxation in a range of spiroconjugated and linearly conjugated cationic systems.