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Electronic Structure and Stability of C80 Fullerene IPR Isomers a
Ayrat R. Khamatgalimov & Valeri I. Kovalenko
a
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A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Scientific Center, Russian Academy of Sciences, Kazan, Russia Available online: 11 Jul 2011
To cite this article: Ayrat R. Khamatgalimov & Valeri I. Kovalenko (2011): Electronic Structure and Stability of C80 Fullerene IPR Isomers, Fullerenes, Nanotubes and Carbon Nanostructures, 19:7, 599-604 To link to this article: http://dx.doi.org/10.1080/1536383X.2010.504951
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Fullerenes, Nanotubes, and Carbon Nanostructures, 19: 599–604, 2011 Copyright © Taylor & Francis Group, LLC ISSN: 1536-383X print / 1536-4046 online DOI: 10.1080/1536383X.2010.504951
Electronic Structure and Stability of C80 Fullerene IPR Isomers AYRAT R. KHAMATGALIMOV AND VALERI I. KOVALENKO
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A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Scientific Center, Russian Academy of Sciences, Kazan, Russia The distribution of single, double and delocalized π - bonds in molecules of seven IPR isomers of fullerene C80 has been shown. Phenalenyl-radical substructures are the reason for molecular instability of unstable isomers. A distortion of hexagons and pentagons has been shown to be a property of molecules of all isomers of fullerene S80 , but maximum distortions, similarly to C70 , occur in hexagons with delocalized π – bonds that do not affect fullerene stability. Keywords IPR fullerene, stability, structure, cycle distortion
Searching the criteria of stability of fullerene molecules is an important task considering the perspective of their practical applications. Only two isomers, 1 (D5d ) and 2 (D2 ), of seven isolated-pentagon-rule (IPR) isomers of fullerene S80 have been obtained and characterized as empty molecules (1–3). Isomer 1 (D5d ) was suggested as the most probable cage structure for third isomer of Dy3 N@C80 endohedral metallofullerene (4), and isomer 2 (D2 ) was also produced as exohedral derivative C80 Cl12 (5). A third representative of the family, isomer 5 (C2v ), was identified as an exohedral derivative C80 (CF3 )12 (6). Isomers 6 (D5h ) and 7 (Ih ) exist only as endohedral metallofullerenes (for a recent review, see 7,8). Isomer 3 (C2v ) was recently observed as metallofullerene La@C80 and Yb@C80 (9,10). The reason why other isomers are not obtained has not been determined. Generally, the instability of fullerenes can be caused by the presence of unpaired electrons in a molecule (an open shell) or by local strain of a cage (11). “Missing” fullerenes C74 and C72 are typical examples of these two types of instability (12). In the present work, we attempt to establish how the instability of fullerene S80 isomers is connected with their electronic and geometrical structures and to predict the possibility of their production. For this purpose, the analysis of energy and geometrical parameters of molecules of seven S80 fullerene IPR isomers was carried out on the basis of earlier developed criteria (13) followed by DFT calculations. The molecular structures of all IPR isomers were fully optimized using DFT B3LYP functional with 6-31G basis. Because some radical isomers were considered as triplets, the quantum-chemical calculations and geometry optimizations were carried out in both singlet and triplet configurations. Because some radical isomers were considered triplets, Address correspondence to Ayrat R. Khamatgalimov, A.E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Scientific Center, Russian Academy of Sciences, 8 Arbuzov str., Kazan, 420088, Russia. E-mail:
[email protected]
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in a course of DFT calculations we used unrestricted Kohn–Sham methodology. For comparison, optimizations of singlet state of these isomers were carried out using a restricted Kohn–Sham methodology. In the first step, geometry optimization was performed without the symmetry constraint. The calculations showed that in isomers 1–5 the equilibrium geometry was very close to the topologic symmetry of each isomer. Therefore, a subsequent optimization was carried out with the corresponding symmetry constraint. Molecular symmetries decreasing of isomers 6 and 7 noted earlier (14–17) was observed in our results. To improve energies, geometry optimization was followed by single-point calculation with 6-31G∗ and 6-31+G∗ basis. To ensure the calculated structures were indeed minima, vibrational analyses were performed using the same methods. All calculations were carried out using the GAUSSIAN 98 program [18]. Results are presented in the form of Schlegel diagrams with distribution of single, double and delocalized π - bonds in molecules of these isomers (Figures 1 and 2).
Figure 1. Schlegel diagrams of stable (experimentally produced and characterized) IPR isomers of fullerene S80 (hereinafter, all pentagons are marked grey; single and double bonds are marked with single and double lines, respectively; the delocalized π -bonds are marked by circles; the centres of symmetry axes are depicted by points).
Figure 2. Schlegel diagrams of unstable IPR isomers of fullerene S80 (the delocalized π -bonds are marked with dotted lines).
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Electronic Structure of C80 Fullerene
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While analyzing the structures of experimentally produced isomers, the similarity with C60 and C70 fullerenes should be noted (Figure 1): in the structure of isomers 1 (D5d ) pentagons consist only of single bonds, the alternation of single and double bonds in hexagons takes place; similarly to S70 , two s-indacene substructures with delocalized π - bonds are observed in isomer 2 (D2 ). The appearance of indacene substructure can be an example of the existence of multiple totally symmetric Kekulé structures (π -tautomerism) (19). The presence of phenalenyl substructures in the structures of other isomers not produced as empty molecules (Figure 2) assumes the radical character of its electron shell that, as well as in a case of fullerene S74 [12], can be the reasons for their instability. Undoubtedly, the higher the number of unpaired electrons on fullerene shell, the less stable the structure. Thus the production of not yet obtained isomers 3–7 is possible only as endohedral metallofullerenes or exohedral derivatives. The obtained results of bonds distribution are fully supported by DFT calculations. Previous computations suggest isomers 1 (D5d ) and 2 (D2 ) as the lowest-energy structures in the set (3,15,17,20–27) confirmed by the authors (Table 1). Considerable temperature effects on the relative stabilities in the system are reported (17,21,22,26). Quantumchemical calculations of other unstable isomers show that the lowest energy wave functions are a triplet radical that is in a good agreement with our estimations (Table 1). Isomers 1 (D5d ) and 2 (D2 ) are found to have singlet ground states similar to the results of (16,17). However, unlike our results, in (16) singlet states had also isomers 3 (C2v ); therefore, the authors supposed that in addition to already experimentally accessible isomers 1 (D5d ) and 2 (D2 ), this isomer might be extracted from soot. Nevertheless, this isomer has not yet been produced. The conclusion that all other IPR isomers cannot be extracted as they are either radicals or have nearly zero singlet–triplet splittings (16,17) also agree with our results. Additional confirmation that triplets are the ground states of these isomers has been revealed by checking the wave function stability, which showed, that in case of a singlet state of these isomers, the RHF-to-UHF instability was observed. This means that triplet
Table 1 Relative energies E (kcal/mol), HOMO-LUMO gaps (eV) of seven IPR isomers of C80 fullerene E
HOMO-LUMO
Fullerene C80 isomers
6-31G
6-31G∗
6-31+G∗
6-31G
6-31G∗
6-31+G∗
1 (singlet) (D5d ) 2 (singlet) (D2 ) 3 (singlet) (C2v ) (triplet) 4 (singlet) (D3 ) (triplet) 5 (singlet) (C2v ) (triplet) 6 (singlet Cs ) (triplet D5h ) 7 (singlet D2h ) (triplet C2h )
1.83 0.00 7.12 3.24 9.54 7.85 9.02 4.64 11.85 11.88 29.67 30.11
4.25 0.00 7.60 12.58 16.84 14.95 9.43 4.21 11.60 45.20 40.91 27.71
2.83 0.00 9.39 4.71 9.45 7.04 10.73 6.11 12.51 11.97 27.45 28.56
1.05 1.39 0.81 0.96 0.78 0.92 0.67 0.95 0.65 0.64 0.76 0.73
0.99 1.35 0.78 0.92 0.74 0.96 0.65 0.97 0.63 0.63 0.77 0.74
0.97 1.33 0.67 0.94 0.73 0.94 0.63 0.95 0.63 0.64 0.76 0.73
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is a lower-lying state than singlet. The wave functions of triplet states are stable under the perturbations considered. The deficiency of a charge distribution and spin densities of radical isomers of C80 fullerene are mainly concentrated on phenalenyl-radical and indacene substructures. A detailed comparative analysis of bond lengths and bond angles did not display substantial deviations of these main geometrical parameters of fullerene molecules in question. All of them are close to typical values for most stable fullerenes C60 and C70 . This observation is quite obvious, since structures of these isomers are close to spherical. However, the results of the analysis of dihedral angles inside hexagons and pentagons are more impressive. The high distortion of the fullerene cage, that is, the high aplanarity of hexagons and pentagons, reflects local strain of a fullerene molecule (28) and directly connects with its thermodynamic instability. If all hexagons and pentagons in molecule of fullerene S60 are plain, then in fullerene S70 there are small distortions of hexagons and pentagons (29) and high distortion in five hexagons with delocalized π –bonds that do not affect fullerene stability (28). This fact is remarkable considering the common standpoint that in general delocalization is typical for plain classical aromatic molecules (e.g., benzene, naphthalene); however, fullerenes have curvature. A compensating effect for retention of π delocalization in such hexagons is the most probable explanation of a cycle distortion (28). An analysis of molecular geometry of studied IPR isomers of C80 shows that all have no high local strain. In all isomers of fullerene C80 there are distortions of all cycles, but similar to C70 the maximum distortions are in hexagons with delocalized π –bonds. Therefore, the main reason for instability of “empty” isomers 3-4-5-6-7 is the presence of radical substructures such as phenalenyl-radical, whereas isomers 1-2 with closed electronic shell are stable. Thus, production of isomers 3-7 as “empty” molecules seems unlikely. In fact, isomers 3 (C2v ), 6 (D5h ) and 7 (Ih ) exist as endohedral metallofullerenes (4,7–9), and one may assume a possible further extracting of isomers 4 (D3 ) and 5 (C2v ) in this form. Thus, the distribution of single, double and delocalized π -bonds in molecules of seven IPR isomers of fullerene C80 has been shown. Phenalenyl-radical substructures have been shown to be the reason for molecular instability of unstable isomers. A distortion of hexagons and pentagons has been shown to be a property of molecules of all IPR isomers of fullerene S80 , but maximum distortions, similar to C70 , occur in hexagons with delocalized π –bonds that do not affect fullerene stability.
Note After submission of this article, the isomer 5(C2v ) was isolated and characterized for the first time as an endohedral derivative (Kurihara, H., Lu, X., Iiduka, Y., Mizorogi, N., Slanina, Z., Tsuchiya, T., Akasaka, T. and Nagase, S. Sc2 C2 @C80 rather than Sc2 @C82 : Templated formation of unexpected C2v (5)-C80 and temperature-dependent dynamic formation of internal Sc2 C2 cluster. J. Am. Chem. Soc., 133:2382–2385).
Acknowledgments We are grateful to Yekaterina Kovalenko for her assistance in preparing the paper. Calculations were performed in the Supercomputer Center of Kazan Scientific Centre of the RAS. This work is supported by the Grant of President of Russian Federation.
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