title: Chirality in curved polyaromatic systems.
abstract: Carbon allotropes constituted of sp2-hybridised carbon atoms display a variety of properties that arise from their delocalised π-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 sp2-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.
authors.affiliation: Department of Chemistry, University of Basel, St. Johanns-Ring 19, 4056 Basel, Switzerland. marcel.mayor@unibas.ch and Department of Chemistry, University of Oxford, Chemistry Research Laboratory, Mansfield Road, OX1 3TA Oxford, UK.
authors.forename: Michel
authors.identifier: http://orcid.org/0000-0002-6107-2310
authors.initials: M
authors.lastname: Rickhaus
authors.affiliation: Department of Chemistry, University of Basel, St. Johanns-Ring 19, 4056 Basel, Switzerland. marcel.mayor@unibas.ch and Institute for Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), P. O. Box 3640, 76021 Karlsruhe, Germany and Lehn Institute of Functional Materials (LIFM), Sun Yat-Sen University, Guangzhou, P. R. China.
authors.forename: Marcel
authors.identifier: http://orcid.org/0000-0002-8094-7813
authors.initials: M
authors.lastname: Mayor
authors.affiliation: Department of Chemistry, University of Basel, St. Johanns-Ring 19, 4056 Basel, Switzerland. marcel.mayor@unibas.ch.
authors.forename: Michal
authors.identifier: http://orcid.org/0000-0001-5595-431X
authors.initials: M
authors.lastname: Juríček