The radical cation of allene is an oft-studied system, in part because the vertical structure constitutes one of the simplest D 2d symmetry conical intersections. Processes relating to the removal of an electron from allene are thus governed by complex non-Born-Oppenheimer dynamics. The vertical cation relaxes by a Jahn-Teller (JT) distortion into a chiral D 2 symmetry energy minimum. The radical cation of spiropentadiene is a similar case, and we shall elaborate on their neutral and cationic electronic structures in terms of their helical π-orbitals. The π-system of allene can be represented in two different ways by its canonical frontier molecular orbitals (MOs). The degenerate highest occupied MO (HOMO) and HOMO-1 can be symmetry adapted to the different symmetry operations of the D 2d point group. The two mirror plane elements and the two offaxis C 2 rotation axes are shown in Figure . The conventional rectilinear π-MOs of allene are symmetry-adapted to the mirror operations. If we instead symmetry-adapt the π-MOs to the two rotation operations we get the two helical orbitals shown in Figure . The choice between these two pictures is arbitrary. The mixing of the π-systems is mediated by the p-orbitals on the central carbon, which forms a basis with continuous overlap bea , Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, Ecole Polytechnique federale de Lausanne (EPFL), 1015 Lausanne, Switzerland; E-mail: clemence.corminboeuf@epfl.ch † Electronic Supplementary Information (ESI) available: