The successful isolation of cyclo-C18 in experiment means the ground-breaking epoch of carbon rings. Herein, we studied the thermodynamic stabilities of cyclo-Cn (4 ≤ n ≤ 34) with density functional theory. When n = 4N + 2 (N is integer), cyclo-Cn (10 ≤ n ≤ 34) were thermodynamically stable. Especially, cyclo-C10 and cyclo-C14 were thermodynamically, kinetically, dynamically, and optically preferred to cyclo-C18, and were the candidates of zero-dimension carbon rings. The carbon atoms were sp hybridization in cyclo-C10, cyclo-C14 and cyclo-C18. Cyclo-C14 and cyclo-C18 had alternating abnormal single and triple bonds, but cyclo-C10 had equal bonds.Cyclo-C10, cyclo-C14 and cyclo-C18 with large aromaticities had out-plane and in-plane π systems, which were perpendicular to each other. The number of π electrons in out-plane and in-plane π systems followed Hückel rule. Simulated UV-vis-NIR spectra indicated the similar electronic structures of cyclo-C14 and cyclo-C18. IntroductionThe carbon atom attracts a great deal of attentions because it is a fundamental atom in organic compounds and is the constituent atom for many useful materials. For example, there are some pure carbon materials, including zero-dimension fullerenes, [1] one-dimension nanotube, [2] two-dimension graphene, [3] and three-dimension diamond [4] and graphite. They are well-known as the allotropes of carbon atom and are useful in many fields due to their unique electronic structures and physical chemical features. In the past, fullerene is the only zero-dimension allotrope of carbon.Very recently, the successful synthesis and isolation of cyclo-C18 are epoch-making in the carbon chemistry and mean a second zero-dimension allotrope of carbon atom. [5] In fact, the early experiments on pure carbon clusters date back to 1954 using a heated substrate as cluster source. [6] After that, there are several experimental and theoretical studies on the cyclo-Cn. The synthesis and x-ray crystal structure of a direct precursor of cyclo-C18 were described in 1989. The results of time-of-flight mass spectroscopy recognized cyclo-C18 as the predominant fragmentation pattern with the flash heating experiments on this precursor. [7] In addition, Tobe and Diederich et al. synthesized a number of precursors of cyclo-C18 with well-defined cyclic geometries and readily removable groups. These precursors eventually generated cyclo-C18 by laser desorption induced [4 + 2] cycloreversion (retro-Diels-Alder reaction), decarbonylation or [2 + 2] cycloreversion. [8,9] . Rubin revealed that cyclo-C18 can be highly stabilized as a ligand in complex characterized by X-ray crystallography. [10] Furthermore, the mass spectral evidences of C18 are clearly detected during studying the fullerene-formation mechanism. [11] For example, the coalescence of cyclo-C30 predominantly produces buckminsterfullerene (C60), and the small rings cyclo-C18 and cyclo-C24 preferentially produce fullerene C70 through distinct intermediates. [11] The electronic spectra of C18 and C22 were detected in the ...

Fullerenes are important zero-dimensional materials in photoelectric, antioxidant, pharmaceutical, and single-molecular-magnet fields, but the fullereneformation mechanism has been elusive since the discovery of #1812 C 60 _I h in 1985 because of the missing key links and low yield. Therefore, experimental and theoretical research is required to explore some fundamental questions of the fullerene-formation mechanism. Considering the temperature, here we carried out two fullerene-formation models, bottom-up and top-down, for C 2n (50 ≤ 2n ≤ 70) containing optical enantiomers, heptagons, and tetragons via density functional and transition-state theories. The thermodynamically and kinetically preferred pathway for C 2n (50 ≤ 2n ≤ 70) was the bottom-up model instead of the top-down model. Furthermore, this is the first time revealing that the enantiomer and enthalpy play key roles in forming fullerenes C 2n (50 ≤ 2n ≤ 70). Especially, the effect of the enantiomer on the fullerene-formation mechanism had been neglected in previous research. KEYWORDS: density functional theory, thermodynamic and kinetic fullerene-formation mechanisms, competitive relationship between the top-down and bottom-up models, key roles in the top-down model, enantiomer and enthalpy

Four-electron transfer from U to the fullerene cage commonly exists in U@C 2n (2n < 82) so far, while four-and threeelectron transfers, which depend on the cage isomers, simultaneously occur in U@C 82 . Herein, detailed quantum-chemical methods combined with statistical thermodynamic analysis were applied to deeply probe into U@C 84 , which is detected in the mass spectra without any further exploration. With triplet ground states, novel isomers including isolated-pentagon-rule U@C 2 (51579)-C 84 and U@ D 2 (51573)-C 84 as well as nonisolated-pentagon-rule U@C s (51365)-C 84 were identified as thermodynamically optimal. Surprisingly, there were unexpected three-electron transfers, which directly led to one unpaired electron on the cage, in all of the three isomers. Significant covalent interactions between the cage and U successively weakened for U@D 2 (51573)-C 84 , U@C 2 (51579)-C 84 , and U@C s (51365)-C 84 . Besides, the IR absorption spectra were simulated as a reference for further structural identification in the experiment. Last but not least, the potential reaction sites were predicted to facilitate further functionalization and thus achieve promising applications for U@C 84 .

Thermodynamic selectivity occurs between fullerenes and metals in M@C78 (M = La, Ce, Sm), including non-IPR C1(22 595)-C78; the different number of electrons transferred from metals to C78 leads to the first EMF with diradical features.