Theoretical Studies on the Relative Stabilities of C96 IPR Fullerenes

Three Isolated-Pentagon-Rule Isomers of C96 Fullerene Isolated as Trifluoromethyl Derivatives

The family of experimentally confirmed isolated-pentagon-rule (IPR) isomers of C₉₆ fullerene is extended by trifluoromethylation of a C₉₆ fraction of the fullerene soot, high-performance liquid chromatography separation of CF₃ derivatives, and a single-crystal X-ray diffraction study of C₉₆(CF₃)_n compounds with the use of synchrotron radiation. New cage isomers were revealed in C₉₆(94)(CF₃)_18/20 and C₉₆(182)(CF₃)₁₈ compounds, whereas isomer C₉₆(181), previously known in the adduct with nickel porphyrinate, was confirmed in C₉₆(181)(CF₃)_18/20 derivatives. Common and special features of the addition patterns of CF₃ groups on C₉₆ carbon cages are discussed in more detail. The investigated isomers belong to the most stable C₂-C₉₆(181) and slightly less stable C₁-C₉₆(94) and C₂-C₉₆(182) among the altogether 15 experimentally confirmed IPR isomers of C₉₆ fullerene.

New Isolated-Pentagon-Rule and Skeletally Transformed Isomers of C100 Fullerene Identified by Structure Elucidation of their Chloro Derivatives

High-temperature chlorination of C100 fullerene followed by X-ray structure determination of the chloro derivatives enabled the identification of three isomers of C100 from the fullerene soot, specifically numbers 18, 425, and 417, which obey the isolated pentagon rule (IPR). Among them, isomers C1-C100 (425) and C2-C100 (18) afforded C1-C100 (425)Cl22 and C2-C100 (18)Cl28/30 compounds, respectively, which retain their IPR cage connectivities. In contrast, isomer C2v -C100 (417) gives Cs -C100 (417)Cl28 which undergoes a skeletal transformation by the loss of a C2  fragment, resulting in the formation of a nonclassical (NC) C1-C98 (NC)Cl26 with a heptagon in the carbon cage. Most probably, two nonclassical C1-C100 (NC)Cl18/22 chloro derivatives originate from the IPR isomer C1-C100 (382), although both C1-C100 (344) and even nonclassical C1-C100 (NC) can be also considered as the starting isomers.

Capturing an unstable C100 fullerene as chloride, C100(1)Cl12, with a nanotubular carbon cage

The chlorination of a HPLC C100 fraction afforded C100(1)Cl12 with an unprecedented nanotubular carbon cage of a highly unstable D5d-C100 fullerene.

Structures of chlorinated fullerenes, IPR C₉₆Cl₂₀ and non-classical C₉₄Cl₂₈ and C₉₂Cl₃₂: evidence of the existence of three new isomers of C₉₆

Chlorination of various HPLC fractions of C96 with a mixture of VCl4 and SbCl5 at 340-360 °C and single-crystal X-ray diffraction study of the products led to the identification of three new IPR isomers of C96. The C96(175) isomer forms a stable chloride, C96(175)Cl20, while chlorides of two other new isomers, C96(114) and C96(80), undergo cage shrinkage yielding C94(NC1)Cl28 and C96(NC2)Cl32 with non-classical (NC) cages. These two NC chlorides contain, respectively, one and two heptagons flanked by pairs of fused pentagons and are stabilized by chlorine attachment to the emerging pentagon-pentagon junctions. Thus, the number of the experimentally confirmed C96 isomers has reached nine, which corroborates the empirical rule that the C(6n) fullerenes exhibit particularly rich isomerism.

Sc2(mu2-O) trapped in a fullerene cage: the isolation and structural characterization of Sc2(mu2-O)@C(s)6-C82 and the relevance of the thermal and entropic effects in fullerene isomer selection

The new endohedral fullerene, Sc(2)(mu(2)-O)@C(s)(6)-C(82), has been isolated from the carbon soot obtained by electric arc generation of fullerenes utilizing graphite rods doped with 90% Sc(2)O(3) and 10% Cu (w/w). Sc(2)(mu(2)-O)@C(s)(6)-C(82) has been characterized by single crystal X-ray diffraction, mass spectrometry, and UV/vis spectroscopy. Computational studies have shown that, among the nine isomers that follow the isolated pentagon rule (IPR) for C(82), cage 6 with C(s) symmetry is the most favorable to encapsulate the cluster at T > 1200 K. Sc(2)(mu(2)-O)@C(s)(6)-C(82) is the first example in which the relevance of the thermal and entropic contributions to the stability of the fullerene isomer has been clearly confirmed through the characterization of the X-ray crystal structure.

Prediction of low-energy isomers of large fullerenes from C132 to C160

To predict energetically favored isomers, we used a topological scheme as a prescreening tool to select candidate isomers for each fullerene from C(106) to C(160). Comparison with the PM3 and tight-binding (TB) potential calculated results and few published data for the low-energy isomers of C(106) to C(130) indicates that the prescreening approach is feasible. For each fullerene from C(132) up to C(160), the selected 1000 candidate isomers were further optimized by PM3 and TB potential. The analysis of the semiempirical PM3 and TB results of C(106) to C(160) provides some qualitative features of the large fullerenes. Furthermore, calculations at the B3LYP/6-31G*//B3LYP/3-21G level of theory were carried out on the top ten PM3 and TB low-energy isomers of C(132) to C(160) to accurately predict the stable isomers, and the HOMO-LUMO gap, the ionization energy, and electron affinity of the lowest-energy isomers were also investigated at the same level.

An efficient approach for theoretical study on the low-energy isomers of large fullerenes C90-C140

An approach that consists of a molecular mechanics method based on the second generation reactive empirical bond order (REBO) potential and the more accurate semiempirical method PM3 (Parametric Method No. 3) was proposed to predict the energetically favored isomers of the fullerenes from C90 to C140 at the semiempirical level. All the 578,701 isolated-pentagon-rule isomers of fullerenes from C90 to C140 were enumerated from topological structures and systematically searched using an energy minimization method to select the best 100 low-energy isomers based on the REBO potential for each fullerene. Then these candidate isomers were further optimized by PM3 and ranked again to determine the top low-energy isomers. This approach was applied to calculate the energetically favored isomers of C90-C140. The results of C90-C120 are in good agreement with the published results by quantum-chemical methods. Furthermore, the top five low-energy isomers of C90-C120, as well as C122-C140 which have scarcely been systematically studied before, are also predicted with the approach. The analysis of the structures showed that the hexagon-neighbor rule is an important factor to the stability of C90-C140. The time cost for the systematical search based on the REBO potential was also discussed. It indicates that the approach proposed is efficient for predicting the energetically favored isomers of large fullerenes at the semiempirical level.

On the Structure and Relative Stability of C50 Fullerenes

The complete set of 271 classical fullerene isomers of C50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D(5h) species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D3 structure (with the largest HOMO-LUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D(5h) isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relative-stability interchanges show that the D3 isomer behaves more thermodynamically stable than the D(5h) species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D(5h) and D3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D(5h) symmetry. Some features of higher symmetry C50 nanotube-type isomers are also discussed.