Structure and Electronic Properties of Fullerenes C₅₂^q+: Is C₅₂²⁺ an Exception to the Pentagon Adjacency Penalty Rule?

Abstract

The structure, vibrational spectra and electronic properties of the neutral, singly and doubly charged C52 fullerenes were studied by means of the Hartree-Fock method and density functional theory. Different isomers were considered, in particular those with the lowest possible number (five or six) of adjacent pentagons, and an isomer with a four-atom ring. For neutral and singly charged species, the most stable isomer is that with the lowest number of adjacent pentagons, namely five. However, for C(52)2+, the most stable structure has six adjacent pentagons. This finding, which contradicts the pentagon adjacency penalty rule, is a consequence of complete filling of the HOMO pi shell and the near-perfect sphericity of the most stable isomer. The simulated vibrational spectra show important differences in the positions and intensities of the vibrations for the different isomers.

Ab initio calculation of carbon clusters. II. Relative stabilities of fullerene and nonfullerene C24

“…However, few theoretical studies have shown that nonclassical fullerenes, especially those containing 4-MRs, can compete with classical fullerenes in chemical stabilities. [14][15][16][17][18][19][20][21] We note that a nonclassical fullerene C 62 containing a 4-MR has been synthesized and detected experimentally. 21 There have been increasing research interests in small to medium-sized ͑n =20-36͒ carbon clusters since the discovery of the C 60 .…”

“…[7][8][9][10][11][12][13]17,[22][23][24][25][26][27][28][29][30][31] In our previous paper ͑Paper I 26 ͒, we studied relative stabilities of various isomers of carbon cluster C 20 using high-level ab initio methods. In that study, the bowl-shaped "fullerene fragment" corannulene was theoretically identified as the ground-state isomer of C 20 , which has a lower energy than the ͑only͒ classical fullerene isomer of C 20 . Indeed, the bowl-shaped isomer of C 20 has been experimentally detected in photoelectron spectroscopy ͑PES͒ experiment.…”

“…Accordingly, the intracluster covalent bonding must be strong enough or at least stronger than the clustercluster interaction. As for fullerenes containing fourmembered rings ͑4-MRs͒, the stress induced by large curvature may be better released in C 24 than in larger nonclassical fullerenes such as C 40 , 14,15 C 52 , 20 and C 62 , 21 so that nonclassical fullerene isomers of C 24 can be energetically competitive.…”

From C58to C62and back: Stability, structural similarity, and ring current

“…On the theoretical side, all mathematically possible classical isomers from C 20 to C 90 and beyond have been studied, and the consensus is that the stable classical isomers typically satisfy a more general rule, i.e., that pentagon adjacencies are minimized [3]. This has also been called the pentagon-adjacency-penalty rule (PAPR) [4,5]. The focus of studies of classical fullerenes is now moving on to applications [6,7].…”

Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

“…Furthermore, even for those non-IPR isomers, the ones with fewer pentagon-pentagon adjacencies are usually more stable than others, i.e. they obey pentagon adjacency penalty rule (PAPR) [8][9][10] . To our knowledge, the exceptions to IPR and PAPR are in the cases of C 72 [11] and C 50 [12] , respectively.…”