Chlorination of IPR C100 fullerene affords unconventional C96 Cl20 with a nonclassical cage containing three heptagons

M@C78 (M = U, Th): Inherent Topological Connectivity Existed in Thermodynamically Stable Isomers and the Possibility of an Endohedral Fullerene Containing One Heptagon Ring

The density functional theory combined with statistical thermodynamic analyses of M@C₇₈ (M = U and Th) demonstrated that four isomers, M@D_3h(24109)-C₇₈, M@C_2v(24107)-C₇₈, M@C₁(22595)-C₇₈, and M@C₁(23349)-C₇₈, and a nonclassical isomer, M@C₁(id7)-C₇₈, containing one heptagon ring possess outstanding thermodynamic stabilities in the two M@C₇₈ series. Especially, the M@C₁(id7)-C₇₈ isomer is the first nonclassical C₇₈ fullerene that can exist stably. Importantly, these five fullerene cages are found to be related in the form of Stone-Wales (SW) transformations. Geometric analyses disclosed that, unlike lanthanide metals, actinide metals are more likely to bond with sumanene-type hexagonal rings when they are encapsulated in IPR C₇₈ cages. Frontier molecular orbital analysis showed that both U and Th atoms donate four electrons to the C₇₈ carbon cages.

Capturing nonclassical C70 with double heptagons in low-pressure combustion

A double-heptagon-containing C₇₀H₆ (dihept-C₇₀H₆) was isolated and unambiguously characterized in the soot of low-pressure combustion, which shares the identical heptagonal cage as dihept-C₇₀Cl₆ previously identified in the products of carbon arc, and thus represents the first nonclassical fullerene isolable in both carbon arc and combustion.

Combinatorics of Supergiant Fullerenes: Enumeration of Polysubstituted Isomers, Chirality, Nuclear Magnetic Resonance, Electron Spin Resonance Patterns, and Vibrational Modes from C70 to C150000

We have developed combinatorial techniques for the enumeration of isomers of polysubstituted giant fullerenes through icosahedral C₁₅₀₀₀₀ and applied the techniques to chirality of the isomers, NMR spectroscopy, and group theoretical analysis of the vibrational modes of supergiant fullerenes. We have employed a combination of distance-degree vectorial sequences, self-returning walk sequences followed by our generalization of Sheehan's version of Pólya's theorem, and Möbius inversion technique extended to all irreducible representations of the point groups of giant fullerenes. The concept of shell equivalence classes was utilized to analyze supergiant fullerenes. We have applied these techniques to golden fullerenes in the series C_60m² for m of up to 50 or C₁₅₀₀₀₀ as well as giant fullerenes in the series C_180m² and C₇₀(D_5h). We have employed computational and combinatorial tools to enumerate both chiral and achiral isomers of substituted and hetero giant fullerenes as well as NMR-generating functions for the giant fullerenes. The techniques also provide efficient tools to enumerate all of the vibrational modes of giant fullerenes in terms of the shell partitions. General combinatorial formulae are obtained for larger polysubstituted golden fullerenes of the series C_60m² for any m, and thus the techniques are applied to larger fullerenes such as C₁₅₀₀₀₀. New insights into chirality measures, NMR, ESR hyperfine structures, and vibrational modes of supergiant fullerenes are provided using the novel combinatorial techniques.

Structural Studies of Giant Empty and Endohedral Fullerenes

Structure elucidations of giant fullerenes composed of 100 or more carbon atoms are severely hampered by their extremely low yield, poor solubility and huge numbers of possible cage isomers. High-temperature exohedral chlorination followed by X-ray single crystal diffraction studies of the chloro derivatives offers a practical solution for structure elucidations of giant fullerenes. Various isomers of giant fullerenes have been determined by this method, specially, non-classical giant fullerenes containing heptagons generated by the skeletal transformations of carbon cages. Alternatively, giant fullerenes can be also stabilized by encapsulating metal atoms or clusters through intramolecular electron transfer from the encapsulated species to the outer fullerene cage. In this review, we present a comprehensive overview on synthesis, separation and structural elucidation of giant fullerenes. The isomer structures, chlorination patterns of a series of giant fullerenes C_2n (2n = 100-108) and heptagon-containing non-classical fullerenes derived from giant fullerenes are summarized. On the other hand, giant endohedral fullerenes bearing different endohedral species are also discussed. At the end, we propose an outlook on the future development of giant fullerenes.

Combinatorics of Edge Symmetry: Chiral and Achiral Edge Colorings of Icosahedral Giant Fullerenes: C80, C180, and C240

We develop the combinatorics of edge symmetry and edge colorings under the action of the edge group for icosahedral giant fullerenes from C80 to C240. We use computational symmetry techniques that employ Sheehan’s modification of Pόlya’s theorem and the Möbius inversion method together with generalized character cycle indices. These techniques are applied to generate edge group symmetry comprised of induced edge permutations and thus colorings of giant fullerenes under the edge symmetry action for all irreducible representations. We primarily consider high-symmetry icosahedral fullerenes such as C80 with a chamfered dodecahedron structure, icosahedral C180, and C240 with a chamfered truncated icosahedron geometry. These symmetry-based combinatorial techniques enumerate both achiral and chiral edge colorings of such giant fullerenes with or without constraints. Our computed results show that there are several equivalence classes of edge colorings for giant fullerenes, most of which are chiral. The techniques can be applied to superaromaticity, sextet polynomials, the rapid computation of conjugated circuits and resonance energies, chirality measures, etc., through the enumeration of equivalence classes of edge colorings.

Strain Release of Fused Pentagons in Fullerene Cages by Chemical Functionalization

According to the isolated pentagon rule (IPR), for stable fullerenes, the 12 pentagons should be isolated from one another by hexagons, otherwise the fused pentagons will result in an increase in the local steric strain of the fullerene cage. However, the successful isolation of more than 100 endohedral and exohedral fullerenes containing fused pentagons over the past 20 years has shown that strain release of fused pentagons in fullerene cages is feasible. Herein, we present a general overview on fused-pentagon-containing (i.e. non-IPR) fullerenes through an exhaustive review of all the types of fused-pentagon-containing fullerenes reported to date. We clarify how the strain of fused pentagons can be released in different manners, and provide an in-depth understanding of the role of fused pentagons in the stability, electronic properties, and chemical reactivity of fullerene cages.

Double Negatively Curved C70 Growth through a Heptagon-Involving Pathway

All previously reported C₇₀ isomers have positive curvature and contain 12 pentagons in addition to hexagons. Herein, we report a new C₇₀ species with two negatively curved heptagon moieties and 14 pentagons. This unconventional heptafullerene[70] containing two symmetric heptagons, referred to as dihept-C₇₀ , grows in the carbon arc by a theoretically supported pathway in which the carbon cluster of a previously reported C₆₆ species undergoes successive C₂ insertion via a known heptafullerene[68] intermediate with low energy barriers. As identified by X-ray crystallography, the occurrence of heptagons facilitates a reduction in the angle of the π-orbital axis vector in the fused pentagons to stabilize dihept-C₇₀ . Chlorination at the intersection of a heptagon and two adjacent pentagons can greatly enlarge the HOMO-LUMO gap, which makes dihept-C₇₀ Cl₆ isolable by chromatography. The synthesis of dihept-C₇₀ Cl₆ offers precious clues with respect to the fullerene formation mechanism in the carbon-clustering process.

Chlorination-Promoted Skeletal Transformations of Fullerenes

Classical fullerenes are built of pentagonal and hexagonal rings, and the conventional syntheses produce only those isomers that obey the isolated-pentagon rule (IPR), where all pentagonal rings are separated from each other by hexagonal rings. Upon exohedral derivatization, the IPR fullerene cages normally retain their connectivity pattern. However, it has been discovered that high-temperature chlorination of fullerenes with SbCl₅ or VCl₄ can induce skeletal transformations that alter the carbon cage topology, as directly evidenced by single crystal X-ray diffraction studies of the chlorinated products of a series of fullerenes in the broad range of C₆₀ to C₁₀₂. Two general types of transformations have been identified: (i) the Stone-Wales rearrangement (SWR) that consists of a rotation of a C-C bond by 90°, and (ii) the removal of a C-C bond, i.e., C₂ loss (C2L). Single- or multistep SWR and/or C2L transformations afford either classical non-IPR fullerenes bearing fused pentagons (highlighted in red in the TOC picture) or nonclassical (NCx) fullerenes with x = 1-3 heptagonal rings (highlighted in blue in the TOC picture) often flanked by fused pentagons. Several subtypes of the SWR and C2L processes can be further discerned depending on the local topology of the transformed region of the cage. Under the chlorination conditions, the non-IPR and NC carbon cages that would be energetically unfavorable and mostly labile in their pristine state are instantaneously stabilized by chlorination of the pentagon-pentagon junctions and by delimitation of the original spherical π-system into smaller favorable aromatic fragments. The significance of the chlorination-promoted skeletal transformations within the realm of fullerene chemistry is demonstrated by the growing body of examples. To date, these include single- and multistep SWRs in the buckminsterfullerene C₆₀ and in the higher fullerenes C₇₆(1), C₇₈(2), C₈₂(3), and C102(19), single and multistep C2Ls (i.e., cage shrinkage) in C₈₆(16), C₈₈(33), C₉₀(28), C₉₂(50), C₉₆(80), C₉₆(114), and C102(19), and multistep combinations of SWRs and C2Ls in C₈₈(3), C₈₈(33), and C₁₀₀(18), (IPR isomer numbering in parentheses is according to the spiral algorithm). Remarkably, an IPR precursor can give rise to versatile transformed chlorinated fullerene cages formed via branched pathways. The products can be recovered either in their initial chlorinated form or as more soluble CF₃/F derivatives obtained by an additional trifluoromethylation workup. Reconstruction of the skeletal transformation pathways is often complicated due to the lack of the isolable intermediate products in the multistep cases. Therefore, it is usually based on the principle of selecting the shortest pathways between the starting and the final cage. The quantum-chemical calculations illustrate the detailed mechanisms of the SWR and C2L transformations and the thermodynamic driving forces behind them. A particularly important aspect is the interplay between the chlorination patterns and the regiochemistry of the skeletal transformations.

Crystallographic identification of Eu@C2n (2n = 88, 86 and 84): completing a transformation map for existing metallofullerenes

Revealing the transformation routes among existing fullerene isomers is key to understanding the formation mechanism of fullerenes which is still unclear now because of the absence of typical key links. Herein, we have crystallographically identified four new fullerene cages, namely, C 2(27)-C88, C 1(7)-C86, C 2(13)-C84 and C 2(11)-C84, in the form of Eu@C2n , which are important links to complete a transformation map that contains as many as 98% (176 compounds in total) of the reported metallofullerenes with clear cage structures (C2n , 2n = 86-74). Importantly, the mutual transformations between the metallofullerene isomers included in the map require only one or two well-established steps (Stone-Wales transformation and/or C2 insertion/extrusion). Moreover, structural analysis demonstrates that the unique C 2(27)-C88 cage may serve as a key point in the map and is directly transformable from a graphene fragment. Thus, our work provides important insights into the formation mechanism of fullerenes.

Salvaging Reactive Fullerenes from Soot by Exohedral Derivatization

The awesome allotropy of carbon yields innumerable topologically possible cage structures of molecular carbon. This field is also related to endohedral metallofullerenes constructed by metal-atom encapsulation. Stable and soluble empty fullerenes and endohedral metallofullerenes are available in pure form in macroscopic amounts from carbon arc production or other physical processes followed by extraction and subsequent chromatographic separation. However, many other unidentified fullerene species, which must be reactive and insoluble in their pristine forms, remain in soot. These "missing" species must have extremely small HOMO-LUMO gaps and may have unconventional cage structures. Recent progress in this field has demonstrated that reactive fullerenes can be salvaged by exohedral derivatization, which can stabilize the reactive carbon cages. This concept provides a means of preparing macroscopic amounts of unconventional fullerenes as their derivatives.

Formation of C2v-C72(11188)Cl4: A Particularly Stable Non-IPR Fullerene

Halogenation has been one of the most used strategies to explore the reactivity of empty carbon cages. In particular, the higher reactivity of non-IPR fullerenes, i.e., those fullerenes that do not satisfy the isolated pentagon rule (IPR), has been used to functionalize and capture these less stable fullerenes. Here, we have explored the stability of the non-IPR isomer C₇₂(11188) with C_2v symmetry, which is topologically linked to the only IPR isomer of C₇₀, as well as its reactivity to chlorination. DFT calculations and Car-Parrinello molecular dynamics simulations suggest that chlorination takes places initially in nonspecific sites, once carbon cages are formed. When the temperature in the arc reactor decreases sufficiently, Cl atoms are trapped on the fullerene surface, migrating from not-so-favored positions to reach the most favored sites in the pentalene. We have also discussed why cage C_2v-C₇₂(11188) is found to take four chlorines, whereas cage C₁-C₇₄(14049) is observed to capture 10 of them, even though these two fullerenes are closely related by a simple C₂ insertion.

Chlorination-promoted skeletal transformation of IPR C76 discovered via trifluoromethylation under the formation of non-IPR C76(CF3)nFm

High-temperature chlorination of IPR D₂-C₇₆ followed by trifluoromethylation resulted in X-ray structures of non-classical, non-IPR C₇₆(CF₃)₁₄, C₇₆(CF₃)₁₄F₂, and C₇₆(CF₃)₁₆F₆.

Relative Stability of Empty Exohedral Fullerenes: π Delocalization versus Strain and Steric Hindrance

Predicting and understanding the relative stability of exohedral fullerenes is an important aspect of fullerene chemistry, since the experimentally formed structures do not generally follow the rules that govern addition reactions or the making of pristine fullerenes. First-principles theoretical calculations are of limited applicability due to the large number of possible isomeric forms, for example, more than 50 billion for C₆₀X₈. Here we propose a simple model, exclusively based on topological arguments, that allows one to predict the relative stability of exohedral fullerenes without the need for electronic structure calculations or geometry optimizations. The model incorporates the effects of π delocalization, cage strain, and steric hindrance. We show that the subtle interplay between these three factors is responsible for (i) the formation of non-IPR (isolated pentagon rule) exohedral fullerenes in contrast with their pristine fullerene counterparts, (ii) the appearance of more pentagon-pentagon adjacencies than predicted by the PAPR (pentagon-adjacency penalty rule), (iii) the changes in regioisomer stability due to the chemical nature of the addends, and (iv) the variations in fullerene cage stability with the progressive addition of chemical species.

Structural interconnections and the role of heptagonal rings in endohedral trimetallic nitride template fullerenes

Recent experiments indicate that fullerene isomers outside the classical definition can also encapsulate metallic atoms or clusters to form endohedral metallofullerenes. Our systematic study using DFT calculations, suggests that many heptagon-including nonclassical trimetallic nitride template fullerenes are similar in stability to their classical counterparts, and that conversion between low-energy nonclassical and classical parent cages via Endo-Kroto insertion/extrusion of C2 units and Stone-Wales isomerization may facilitate the formation of endohedral trimetallic nitride fullerenes. Close structural connections are found between favored isomers of trimetallic nitride template fullerenes from C78 to C82 . It appears that the lower symmetry and local deformations associated with introduction of a heptagonal ring favor encapsulation of intrinsically less symmetrical mixed metal nitride clusters. © 2016 Wiley Periodicals, Inc.

Isolation and Crystallographic Characterization of La2C2@Cs(574)-C102 and La2C2@C2(816)-C104: Evidence for the Top-Down Formation Mechanism of Fullerenes

Tubular higher fullerenes are prototypes of finite-length end-capped carbon nanotubes (CNTs) whose structures can be accurately characterized by single-crystal X-ray diffraction crystallography. We present here the isolation and crystallographic characterization of two unprecedented higher fullerenes stabilized by the encapsulation of a La2C2 cluster, namely, La2C2@Cs(574)-C102, which has a perfect tubular cage corresponding to a short (10, 0) zigzag carbon nanotube, and La2C2@C2(816)-C104 which has a defective cage with a pyracylene motif inserting into the cage waist. Both cages provide sufficient spaces for the large La2C2 cluster to adopt a stretched and nearly planar configuration, departing from the common butterfly-like configuration which has been frequently observed in midsized carbide metallofullerenes (e.g., Sc2C2@C80-84), to achieve strong metal-cage interactions. More meaningfully, our crystallographic results demonstrate that the defective cage of C2(816)-C104 is a starting point to form the other three tubular cages known so far, i.e., D5(450)-C100, Cs(574)-C102, and D3d(822)-C104, presenting evidence for the top-down formation mechanism of fullerenes. The fact that only the large La2C2 cluster has been found in giant fullerene cages (C>100) and the small clusters M2C2 (M = Sc, Y, Er, etc.) are present in midsized fullerenes (C80-C86) indicates that geometrical matching between the cluster and the cage, which ensures strong metal-cage interactions, is an important factor controlling the stability of the resultant metallofullerenes, in addition to charge transfer.

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.

C100 is Converted into C94 Cl22 by Three Chlorination-Promoted C2 Losses under Formation and Elimination of Cage Heptagons

Chlorination of the C100 (18) fullerene with a mixture of VCl4 and SbCl5 gives rise to branched skeletal transformations affording non-classical (NC) C94 (NC1)Cl22 with one heptagon in the carbon cage together with the previously reported C96 (NC3)Cl20 with three heptagons. The three-step pathway to C94 (NC1)Cl22 starts with two successive C2 losses of 5:6 CC bonds to give two cage heptagons, whereas the third C2 loss of the 5:5 CC bond from a pentalene fragment eliminates one of the heptagons. Quantum-chemical calculations demonstrate that the two unusual skeletal transformations-creation of a heptagon in C96 (NC3)Cl20 through a Stone-Wales rearrangement and the presently reported elimination of a heptagon through C2 loss-are both characterized by relatively low activation energy.

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.