Article Magnetic Shielding Study of Bonding and Aromaticity in Corannulene and Coronene Peter B. Karadakov Department of Chemistry, University of York, Heslington, York YO10 5DD, UK; [email protected] Abstract: Bonding and aromaticity in the bowl-shaped C5v and planar D5h geometries of corannulene and the planar D6h geometry of coronene are investigated using 3D isosurfaces and 2D contour plots of the isotropic magnetic shielding siso(r) and, for planar geometries, of the out-of-plane component of the shielding tensor szz(r). Corannulene and coronene both feature conjoined shielded “doughnuts” around a peripheral six-membered carbon ring, suggesting strong bonding interactions and aromatic stability; a deshielded region inside the hub ring of corannulene indicates that this ring is antiaromatic, more so in planar corannulene. The switch from the planar to the bowl-shaped geometry of corannulene is shown to enhance both bonding and the local aromaticities of the five- and six-membered rings; these factors, in addition to ring strain reduction, favour the bowl-shaped geometry. The most and least shielded bonds in both corannulene and coronene turn out to be the spoke and hub bonds, respectively. The higher π electron activity over spoke bonds in planar corannulene and coronene is supported by szz(r) contour plots in planes 1 Å above the respective molecular planes; these findings about spoke bonds are somewhat unexpected, given that ring current studies indicate next to no currents over spoke bonds. Keywords: aromaticity; antiaromaticity; corannulene; coronene; magnetic shielding isosurfaces; Citation: Karadakov, P.B. Magnetic magnetic shielding contour plots; shielding over chemical bonds Shielding Study of Bonding and Aromaticity in Corannulene and Coronene. Chemistry 2021, 3, 861–872. https://doi.org/10.3390/ chemistry3030063 1. Introduction The polycyclic aromatic hydrocarbon (PAH) dibenzo[ghi,mno]fluoranthene (C20H10), Academic Editors: Andrea Peluso in which a five-membered central ring is surrounded by five six-membered rings, was and Guglielmo Monaco synthesised by Barth and Lawton in 1966 [1], who gave it the trivial name under which it is currently known, corannulene (see also [2]). The discovery of buckminsterfullerene, C60, Received: 1 August 2021 in 1985 [3], led to an “explosion” of interest in corannulene, as chemists quickly realised Accepted: 9 August 2021 that it was the smallest subunit of the buckyball motif that retains a curved bowl-like Published: 12 August 2021 shape of C5v symmetry. Corannulene is now widely utilised as a polyarene building block for the construction of functional materials [4], and its importance is emphasised by the Publisher’s Note: MDPI stays neutral availability of a process for the kilogram-scale production of this PAH [5]. with regard to jurisdictional claims in Interest in the aromaticity of corannulene was one of the incentives for its initial syn- published maps and institutional affil- thesis: Barth and Lawton thought that ionic resonance structures such as that in Figure1d iations. could give rise to two charged concentric conjugated systems, an inner cyclopentadi- enyl anion and an outer cyclopentadecaheptenyl cation, each of which satisfies Hückel’s 4n + 2 rule. This “annulene-within-an-annulene” (AWA) model could also be expected to apply to planar coronene (C24H12), which has inner and outer rings with 6 π and 14 π Copyright: © 2021 by the author. electrons, respectively. As explained by Zanasi and coworkers [6], the AWA model would Licensee MDPI, Basel, Switzerland. work if the inner and outer annulene rings were uncoupled, which is an unrealistic as- This article is an open access article sumption as the carbon–carbon spoke bonds connecting the two rings have been found to distributed under the terms and be shorter than the hub, flank and rim bonds (see Figure1a for definitions). conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Chemistry 2021, 3, 861–872. https://doi.org/10.3390/chemistry3030063 https://www.mdpi.com/journal/chemistry Chemistry 2021, 3 862 Chemistry 2021, 3, FOR PEER REVIEW 2 FigureFigure 1.1. KekulKekuléé (aa–c–c) andand one ionic resonance structure structure ( (dd)) for for corannulene. corannulene. The The positions positions of of the the carbon–carboncarbon–carbon hubhub (h), spoke (s), flan flankk (f) and rim rim (r) (r) bonds bonds are are shown shown in in (a (a).). The The carbon carbon atoms atoms are are referredreferred toto asas hubhub (involved(involved in two hub bonds), flank flank (involved (involved in in two two flank flank bonds) bonds) and and rim. rim. ValenceValence bondbond (VB) theory provides provides a a simp simplele argument argument against against the the AWA AWA model model [6]: [6 ]: CorannuleneCorannulene has 11 KekulKekuléé resoresonancenance structures structures (see (see Figure Figure 1a–c),1a–c), and and each each of of the the five five spokespoke bondsbonds isis double double in in five five of of these these resonance resonance structures. structures. At At the the moment, moment, it isit notis not possible pos- 1 tosible quantify to quantify the relative the relative importance importance of the of Kekul the éKekuléresonance resonance structures structures of types of Ktypes1,K2 Kand, 2 3 KK3 usingand K modern using modern VB theory, VB because theory, abecause spin-coupled a spin-coupled generalised generalised VB (SCGVB) VB [(SCGVB)7] calculation [7] withcalculation 20 active with orbitals 20 active is still orbitals not computationallyis still not computationally feasible (the feasible overall (the number overall of number unique covalentof unique resonance covalent structuresresonance forstructures a 20-electron for a 20-electron singlet is 16,796; singlet these is 16,796; include, these in include, addition toin theaddition 11 Kekul to theé resonance 11 Kekulé structures,resonance struct a numberures, ofa number less important of less important para-bonded para-bonded structures, similarstructures, to the similar Dewar to structuresthe Dewar instructures benzene, in and benzene, many otherand many structures other withstructures longer with pair separations).longer pair separations). However, chemicalHowever, intuition chemical and intuition SCGVB and experience SCGVB experience with naphthalene with naph- [8] suggestthalene [8] that suggest the weight that the of weight K1, which of K1, includeswhich includes five π fivesextets, π sextets, will will be higher be higher than than the combinedthe combined weight weight of structures of structures K2, K each2, each of whichof which includes includes three threeπ sextets, π sextets, followed followed by by the combinedthe combined weight weight of structures of structures K3, each K3, each of which of which includes includes two π twosextets; π sextets; this emphasizes this empha- the importancesizes the importance of the spoke of the bonds spoke and bonds lends and additional lends additional support tosupport the counter-AWA to the counter-AWA argument. argument.Interestingly, the population analysis results reported by Sygula and Rabideau [9], whichInterestingly, have been quoted the population to “show noanalysis significant results redistribution reported by of Sygula electron and density Rabideau from [9], rim towhich hub” have in corannulene been quoted [10 to], “show include no data significan aboutt the redistribution corannulene of dianions electron anddensity tetraanion from butrim notto hub” about in neutralcorannulene corannulene. [10], include Mulliken data about charges the obtainedcorannulene in the dianions current and study tetraan- show strongion but basis not setabout dependence neutral corannulene. and produce Mullik contradictoryen charges results: obtained the 6-311++G(d,p) in the current chargesstudy suggestshow strong a substantial basis set rim-to-hubdependence charge and produc shift, wherease contradictory the def2-TZVP results: the charges 6-311++G(d,p) suggest a minorcharges hub-to-rim suggest a chargesubstantial shift. rim-to-hub Whereas othercharge types shift, ofwhereas population the def2-TZVP analysis may charges show bettersuggest consistency, a minor hub-to-rim the use ofcharge such shift. methods Wher ineas support other types for orof popu againstlation the analysis AWA model may isshow questionable. better consistency, the use of such methods in support for or against the AWA modelBoth is questionable. corannulene and coronene have been found to feature counter-rotating ring currents,Both with corannulene a diamagnetic and coronene (aromatic) have rim been and fo a paramagneticund to feature (antiaromatic)counter-rotating hub, ring in cur- stark contrastrents, with with a diamagnetic the predictions (aromatic) of the AWA rim and model a paramagnetic [10]. This is (antiaromatic) in line with NICS(0) hub, in results, stark accordingcontrast with to which the predictions the inner ring of the in corannuleneAWA model is[10]. antiaromatic This is in line and with each NICS(0) of the outer results, rings isaccording aromatic, to the which inner the ring inner in coronene ring in corannulene is weakly antiaromatic is antiaromatic or nonaromatic and each of and the eachouter of therings outer is aromatic, rings is aromatic, the inner more ring soin coronene than the outer is weakly rings antiaromatic in corannulene or [nonaromatic10–12]. NICS(0) and is theeach original of the nucleus-independentouter rings is aromatic, chemical more so shift than suggested the