Chirality in curved polyaromatic systems

Carbon allotropes constituted of sp(2)-hybridised carbon atoms display a variety of properties that arise from their delocalised Pi-conjugated electronic structure. Apart from carbon's planar allotropic form graphene, bent or curved structures, such as carbon nanotubes or fullerenes, respectively, have been discovered. In this Tutorial Review, we analyse and conceptually categorise chiral synthetic molecular fragments of non-planar sp(2)-carbon allotropes, including hypothetical forms of carbon that have been proposed to exist as stable entities. Two types of molecular systems composed of equally or differently sized rings are examined: bent with zero Gaussian curvature and curved with positive or negative Gaussian curvature. To affirm that a system is chiral, two conditions must be fulfilled: (1) both reflective symmetry elements, an inversion centre and a mirror plane, must be absent and (2) the system must be stereochemically rigid. It is therefore crucial to not only consider the symmetry of a given system as if it was a rigid object but also its structural dynamics. These principles serve as guidelines for the design of molecular fragments that encode and transcribe chirality into larger systems.