Nonclassical fullerenes with a heptagon violating the pentagon adjacency penalty rule

Nonclassical fullerenes with heptagon(s) and their derivatives have attracted increasing attention, and the studies on them are performing to enrich the chemistry of carbon. Density functional theory calculations are performed on nonclassical fullerenes C_n (n = 46, 48, 50, and 52) to give insight into their structures and stability. The calculated results demonstrate that the classical isomers generally satisfy the pentagon adjacency penalty rule. However, the nonclassical isomers with a heptagon are more energetically favorable than the classical ones with the same number of pentagon–pentagon bonds (B₅₅ bonds), and many of them are even more stable than some classical isomers with fewer B₅₅ bonds. The nonclassical isomers with the lowest energy are higher in energy than the classical ones with the lowest energy, because they have more B₅₅ bonds. Generally, the HOMO–LUMO gaps of the former are larger than those of the latter. The sphericity and asphericity are unable to rationalize the unique stability of the nonclassical fullerenes with a heptagon. The pyramidization angles of the vertices shared by two pentagons and one heptagon are smaller than those of the vertices shared by two pentagons and one hexagon. It is concluded that the strain in the fused pentagons can be released by the adjacent heptagons partly, and consequently, it is a common phenomenon for nonclassical fullerenes to violate the pentagon adjacent penalty rule. These findings are heuristic and conducive to search energetically favorable isomers of C_n, especially as n is 62, 64, 66, and 68, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C<Subscript>60</Subscript>

Kekulé count is not as useful in predicting the thermodynamic stability of fullerenes as it is for benzenoid hydrocarbons. For example, the Kekulé count of the icosahedral C₆₀, the most stable fullerene molecule, is surpassed by its 20 fullerene isomers (Austin et al. in Chem Phys Lett 228:478–484, 1994). This article investigates the role of Clar number in predicting the stability of fullerenes from Clar’s ideas in benzenoids. We find that the experimentally characterized fullerenes attain the maximum Clar numbers among their fullerene isomers. Our computations show that among the 18 fullerene isomers of C₆₀ achieving the maximum Clar number (8), the icosahedral C₆₀ has the largest Kekulé count. Hence, for fullerene isomers of C₆₀, a combination of Clar number and Kekulé count predicts the most stable isomer.     

Further test of the isolated pentagon rule: Thermodynamic and kinetic stabilities of C84 fullerene isomers

Thermodynamic and kinetic stabilities of 73 C₈₄ fullerene isomers were estimated from the MM3 heats of formation and the recently defined bond resonance energies (BREs), respectively. The BRE represents the contribution of a given π bond in a molecule to the topological resonance energy (TRE). All π bonds shared by two pentagons turned out to be highly reactive without exceptions. C₈₄ fullerene isomers with such π bonds must be incapable of survival during harsh synthetic processes. Thus, the isolated pentagon rule (IPR) proved to be applicable to such large fullerene cages. For sufficiently large fullerenes like C₈₄, some isolated-pentagon isomers are also predicted to be very unstable with highly antiaromatic π bonds. © 1996 by John Wiley & Sons, Inc.     

The Most Stable Isomers of Giant Fullerenes C102 and C104 Captured as Chlorides,C102(603)Cl18/20 and C104(234)Cl16/18/20/22

The chlorination of HPLC fractions with pristine giant fullerenes, C₁₀₂ and C₁₀₄, followed by X‐ray crystallographic study of chlorides, C₁₀₂(603)Cl_18/20 and C₁₀₄(234)Cl_16–22, confirmed the presence of the most stable IPR (IPR=Isolated Pentagon Rule) isomers, C₁₀₂(603) and C₁₀₄(234), in the fullerene soot. The discussion concerns the chlorination patterns of polychlorides and relative stability of pristine isomers of C₁₀₂ and C₁₀₄ fullerenes.     

New C70(CF3) n isomers (n = 12, 14, 16). Realkylation and addend rearrangements

New isomers of trifluoromethyl derivatives of [70]fullerene, C₇₀(CF₃)₁₂ (one isomer), C₇₀(CF₃)₁₄ (three isomers), and C₇₀(CF₃)₁₆ (one isomer) were synthesized, chromatographically isolated, and characterized by single-crystal X-ray analysis. Three of the five new isomers were obtained by annealing a mixture of higher trifluoromethyl derivatives (realkylation*). Trifluoromethylation of two individual C₇₀(CF₃)₁₂ isomers revealed rearrangements of CF₃ groups on the fullerene sphere along with the direct addition to the double bonds. The relative energies of the isomers were calculated using the density functional theory.     

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.     

From C58 to C62 and back: Stability,structural similarity,and ring current

An increasing number of observations show that non‐classical isomers may play an important role in the formation of fullerenes and their exo‐ and endo‐derivatives. A quantum‐mechanical study of all classical isomers of C₅₈, C₆₀, and C₆₂, and all non‐classical isomers with at most one square or heptagonal face, was carried out. Calculations at the B3LYP/6‐31G* level show that the favored isomers of C₅₈, C₆₀, and C₆₂ have closely related structures and suggest plausible inter‐conversion and growth pathways among low‐energy isomers. Similarity of the favored structures is reinforced by comparison of calculated ring currents induced on faces of these polyhedral cages by radial external magnetic fields, implying patterns of magnetic response similar to those of the stable, isolated‐pentagon C₆₀ molecule. © 2016 Wiley Periodicals, Inc.     

Towards the selective formation of specific isomers of fullerenes: T - and p-dependence in the yield of various isomers of fullerenes C60–C84

Systematic fractional change in the yield of various isomers of fullerenes was revealed to strongly depend on temperature of a buffer gas. A new kinetic consideration is proposed for understanding the observed temperature- and pressure-dependence of yield of fullerenes. The model consists of three competitive reactions in consideration of plausible behaviors of a precursor, (1) decomposition into smaller fragments, (2) isomerization leading to formation of a stable fullerene cage, and (3) growth into a larger carbon cluster. Arrhenius activation energy of formation of stable fullerenes was determined to be 0.8 eV for both C₆₀ and C₇₀, while a higher energy of 2.0?3.3 eV for seven different isomers of higher fullerenes ranging from C₇₆ to C₈₄. Correlation in the activation energy is noted for a series of higher fullerenes with different sizes, suggesting the existence of a specific precursor in their formation processes.     

Separation and identification of fullerenes by liquid chromatography

Summary The separation of fullerenes with a monomeric octadecylsilica bonded phase using n-hexane or toluene/methanol mobile phase systems is described. Analytical and preparative separations, incorporating on-line UV/VIS spectral measurements, confirmed the existence of large fullerenes such as C₇₆, C₇₈ and C₈₄. However, isomers of C₇₈ and C₈₄ were not conclusively found.     

Generating functions for the cage isomers of the C20n icosahedral fullerenes

The number of isomeric cages for the C_20n icosahedral fullerenes (Goldberg polyhedra), is given by the coefficient ofn ^–s in the expansion of the Dirichlet generating function (s)L[s, x(3)].When this coefficient is even, the cages occur as chiral pairs of point symmetry I; when odd, there is one structural isomer of point symmetry I _h , and the other isomers, if any, occur as chiral pairs. Asymptotic estimates are given for the number of isomers of each type.     

Synthetic Approaches toward Molecular and Polymeric Carbon Allotropes

Life on earth is based on compounds that have carbon frames and backbones. Today, chemists have added to the world of biomolecules and biopolymers approximately 10⁷ different synthetic molecules and polymers, the structures of which also depend on the formation of strong, stable carbon–carbon bonds. Although the stability of carbon–carbon bonds has been recognized for more than a century, the two natural modifications graphite and diamond were, until recently, the only allotropic forms of carbon on earth that were available in macroscopic quantities and were structurally well characterized. With the synthesis of macroscopic quantities of buckminsterfullerene (C₆₀) and the higher fullerenes (C₇₀, C₇₆, C₇₈, etc.) and the exploration of the fascinating properties of these all-carbon spheres, this situation has completely changed. In the coming decades, the design, preparation, and study of novel molecular and polymeric allotropic forms of carbon will be a central topic in chemistry. Research in this area will dramatically advance the fundamental knowledge on carbon-based matter and, as already illustrated by the ongoing work on C₆₀, generate unprecedented technological perspectives. This review surveys synthetic organic-chemical approaches toward the preparation and study of all-carbon molecules and polymers that differ from the familiar networks of graphite and diamond as well as from the fullerenes. We will also discuss the ongoing research on fullerenes with a particular focus on the synthetic approaches to these all-carbon spheres and their transition metal complexes.     

Deformation and thermodynamic instability of a C84 fullerene cage

Quantum chemical calculations of electronic and geometric structures were performed for molecules of 24 isomers of C₈₄ fullerenes obeying the isolated pentagons rule. The reasons for the instability of isomers not obtained experimentally were established, and the possibility of obtaining some of them was proven. It was shown that the deformation of hexagons and pentagons is the most important geometric parameter directly connected with the thermodynamic instability of fullerenes having closed shells, reflecting the local strain of the molecules.     

Cationic Closo Carboranes—Promising Weakly Coordinating Ions

The unexplored carbon rich cationic closo carboranes, C₃B_n?3H_n⁺¹ (n=5, 6, 7, 10, 12) are investigated theoretically. The position isomers were calculated at the B3LYP/6‐31G* level, and the charge distribution in the cluster is estimated by NBO analysis. The criterion of ring‐cap orbital overlap compatibility along with the number of B? C, C? C, and B? B bonds help in explaining the stability order in each category. The most stable isomer is the one with maximum ring‐cap orbital overlap and largest number of B? C bonds. The order of relative stability among the trigonal bipyramid is 1c > 1b > 1a ′, where the stability is proportional to the number of CH caps over the small three‐membered ring. The C₃B₃H₆⁺ isomer with the one allyl C3 group ( 2b ) is more favorable than the one with a cyclopropenyl group ( 2a ). Among the C₃B₄H₇⁺ isomers the stability order is 3e > 3d > 3c > 3b > 3a , which mostly depends on the ring‐cap orbital overlap. In the bicapped square antiprism (4) where there is large number of isomers, the order follows the rule of ring cap compatibility and the number of B? C bonds. The order of 5e > 5d > 5c > 5b > 5a obtained from the calculations is in perfect agreement with the above sited rules. Equations (1) – (5) devised for estimating the stability of isomers of C₃B_n?3H_n⁺ indicate an increase in stability with cage size. The mono‐positive charge of the isomers is distributed throughout the cage, making them suitable candidates as weakly electrophillic cations. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1542–1551, 2001     

Structural connectivity and formation mechanism of monometallic cluster fullerenes YCN@Cn (n = 68–84)

Excited by the recently experimental reports of monometallic cluster fullerenes, we examined the electronic and geometrical properties of monometallic cluster fullerenes YCN@C_n with size from C₆₈ to C₈₄ by density functional theory and statistical thermodynamic calculations. The calculations demonstrate that the thermodynamically favored isomers of YCN@C_n are in good agreement with available experimental results. Morphology analysis shows that the lowest‐energy YCN@C_n species are structurally connected by C₂ insertion/extrusion and Stone–Wales rotation, which can be promoted under high temperature; enthalpy–entropy interplay can change the relative abundances of low‐energy isomers significantly at high temperature. All the results suggest that there is a structural evolution among these metallic cluster fullerenes in discharge condition, and thus, can rationalize their structural diversity in the soot and partly disclose their formation mechanism. The geometrical structures, electronic properties of these endohedral fullerene were discussed in detail.     

Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

To gain insight into the structures and stability of F₄F₆ polyhedrons formed by squares and hexagons, a density functional theory study was performed on all isomers of F₄F₆ polyhedrons with sizes from 8 to 60. The calculated results demonstrate that the six squares tend to isolate from each other, i.e. these F₄F₆ polyhedrons obey the isolated square rule. Those isomers with fewer B₄₄ bonds (square-square adjacencies) are more stable than those with more B₄₄ bonds, i.e. they obey square adjacency penalty rule. Both of the two rules in F₄F₆ polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F₅F₆ fullerenes and can be used to screen the lowest energy isomers of F₄F₆ polyhedrons as IPR and PAPR do in classic fullerenes. Structural analysis demonstrates that the pyramidalization of carbon atoms at the square-square adjacencies determines the stability of corresponding structures. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported from Southwest University, China (Grant No. SWNUB2005002) and Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment within Ministry of Education, Chongqing University (Grant No. KLVF-2007-5)     

The effects of atom pyramidalization and square distribution on the stability of F4F6‐(BN)n polyhedrons

The structures and stability of F₄F₆‐(BN)_n polyhedrons (n = 20–30) with the alternation of B and N atoms were studied with DFT method. The calculation results reveal that the atoms at square–square fusions with large pyramidalization angles are remarkably extruded out of the surfaces of (BN)_n polyhedrons. The energetically favorable isomers do not contain square–square bonds and the energies of those isomers containing square–square bonds increase with the number of square–square bonds linearly, demonstrating that the energetically favorable structures of F₄F₆‐(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The atom pyramidalization determines the stability of the isomers. The binding energy is fitted to the numbers of vertices formed from different faces and a model is proposed to predict the relative stability of these polyhedral molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum-Chemical Simulation of New Hybrid Nanostructures: Small Fullerenes C20 and C28 in Single-Walled Boron-Nitrogen Nanotubes

A quantum-chemical simulation of new hybrid nanostructures consisting of regular chains of the small fullerenes C₂₀ and C₂₈ encapsulated into the bulk of achiral zigzag single-walled boron-nitrogen nanotubes [(C₂₀,C₂₈)@BN-NT]. The electronic properties and the nature of interatomic bonds in these nanostructures are analyzed as a function of the fullerene and the distances between fullerenes in the chain and between fullerenes and tube walls. The electronic characteristics of hybrid nanostructures are compared with those of "isolated" fullerenes and nanotubes, and (C20,C28) + BN-NT structures simulating fullerene adsorption on tube surface as the initial stage of (C₂₀,C₂₈)@BN-NT formation.     

First Isomers of Pristine C104 Fullerene Structurally Confirmed as Chlorides,C104(258)Cl16 and C104(812)Cl24

Isolation and characterization of very large fullerenes is hampered by a drastic decrease of their content in fullerene soot with increasing fullerene size and a simultaneous increase of the number of possible IPR (Isolated Pentagon Rule) isomers. In the present work, fractions containing mixtures of C₁₀₂ and C₁₀₄ were isolated in very small quantities (several dozens of micrograms) by multi‐step recycling HPLC from an arc‐discharge fullerene soot. Two such fractions were used for chlorination with a VCl₄/SbCl₅ mixture in glass ampoules at 350–360 °C. The resulting chlorides were investigated by single‐crystal X‐ray diffraction using synchrotron radiation. By this means, two IPR isomers of C₁₀₄, numbers 258 and 812 (of 823 topologically possible isomers), have been confirmed for the first time as chlorides, C₁‐C₁₀₄(258)Cl₁₆ and D₂‐C₁₀₄(812)Cl₂₄, respectively, while an admixture of C₂‐C₁₀₄(811)Cl₂₄ was assumed to be present in the latter chloride. DFT calculations showed that pristine C₁₀₄(812) belongs to rather stable C₁₀₄ cages, whereas C₁₀₄(258) is much less stable.     

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.