Quantum Chemical Insight of the Dimetallic Sulfide Endohedral Fullerene Sc2S@C70: Does It Possess the Conventional D5h Cage?

Like C₆₀, C₇₀ is one of the most representative fullerenes in fullerene science. Even though there are 8149 C₇₀ isomers, only two of them have been found before: the conventional D_5h and an isolated pentagon rule (IPR)‐violating C_2v(7854). Through the use of quantum chemical methods, we report a new unconventional C₇₀ isomer, C₂(7892), which survives in the form of dimetallic sulfide endohedral fullerene Sc₂S@C₇₀. Compared with the IPR‐obeying C₇₀ and the C_2v(7854) fullerene with three pairs of pentagon adjacencies, the C₂(7892) cage violates the isolated pentagon rule and has two pairs of pentagon adjacencies. In Sc₂S@C₂(7892)‐C₇₀, two scandium atoms coordinate with two pentalene motifs, respectively, presenting two equivalent Sc? S bonds. The strong coordination interaction, along with the electron transfer from the Sc₂S cluster to the fullerene cage, results in the stabilization of the non‐IPR endohedral fullerene. The electronic structure of Sc₂S@C₇₀ can be formally described as [Sc₂S]⁴⁺@[C₇₀]^4?; however, a substantial overlap between the metallic orbitals and cage orbitals has also been found. Electrochemical properties and electronic absorption, infrared, and ¹³C NMR spectra of Sc₂S@C₇₀ have been calculated theoretically.     

Theoretical Study on Experimentally Detected Sc2S@C84

Sc₂S@C₈₄ has recently been detected but not structurally characterized. 1 Density functional theory calculations on C₈₄ and Sc₂S@C₈₄ show that the favored isomer of Sc₂S@C₈₄ shares the same parent cage as Sc₂C₂@C₈₄, whereas Sc₂S@C₈₄:51383, which violates the isolated‐pentagon rule, is the second lowest energy isomer with the widest HOMO–LUMO gap and shows high kinetic stability. The analysis shows that Sc₂S@C₈₄:51575 is favored when the temperature exceeds 2 800 K and it can transform into the most favorable isomer Sc₂S@C₈₄:51591. Molecular orbital analysis indicates that both Sc₂S and Sc₂C₂ formally transfer four electrons to the cage, and quantum theory of atoms in molecules analysis demonstrates that there is a covalent interaction between Sc₂S and C₈₄:51591. The IR spectra of Sc₂S@C₈₄ are provided to aid future structural identification.     

Dimetallic sulfide endohedral metallofullerene Sc2S@C76: Density functional theory characterization

In terms of density functional theory combined with statistic mechanics computations, we investigated a dimetallic sulfide endohedral fullerene Sc₂S@C₇₆ which has been synthesized without any characterization in experiments. Our theoretical study reveals that Sc₂S@T_d(19151)‐C₇₆ which satisfies the isolated‐pentagon rule (IPR) possesses the lowest energy, followed by three non‐IPR structures (Sc₂S@C_2v(19138)‐C₇₆, Sc₂S@C_s (17490)‐C₇₆, and Sc₂S@C₁(17459)‐C₇₆). To clarify the relative stabilities of those isomers at high temperatures, enthalpy–entropy interplay has been taken into consideration. Calculation results indicate that three species Sc₂S@T_d(19151)‐C₇₆, Sc₂S@C_2v(19138)‐C₇₆, and Sc₂S@C₁(17459)‐C₇₆ have noticeable molar fractions at the fullerene‐formation temperature region (500–3000K), and the Sc₂S@C₁(17459)‐C₇₆ with one pentagon pair becomes the most predominant isomer above 1800 K, suggesting that the unexpected non‐IPR structure is thermodynamically favorable at elevated temperatures. In addition, the structural characteristics, electron features, UV‐vis‐NIR adsorptions, and ¹³C NMR spectra of those three stable structures are introduced to assist experimental identification and characterization in future. © 2014 Wiley Periodicals, Inc.     

La2@Cs(17 490)‐C76: A New Non‐IPR Dimetallic Metallofullerene Featuring Unexpectedly Weak Metal–Pentalene Interactions

Although all the pure‐carbon fullerene isomers above C₆₀ reported to date comply with the isolated pentagon rule (IPR), non‐IPR structures, which are expected to have different properties from those of IPR species, are obtainable either by exohedral modification or by endohedral atom doping. This report describes the isolation and characterization of a new endohedral metallofullerene (EMF), La₂@C₇₆, which has a non‐IPR fullerene cage. The X‐ray crystallographic result for the La₂@C₇₆/[Ni^II(OEP)] (OEP=octaethylporphyrin) cocrystal unambiguously elucidated the C_s(17 490)‐C₇₆ cage structure, which contains two adjacent pentagon pairs. Surprisingly, multiple metal sites were distinguished from the X‐ray data, which implies dynamic behavior for the two La³⁺ cations inside the cage. This dynamic behavior was also corroborated by variable‐temperature ¹³⁹ La NMR spectroscopy. This phenomenon conflicts with the widely accepted idea that the metal cations in non‐IPR EMFs invariably coordinate strongly with the negatively charged fused‐pentagon carbons, thereby providing new insights into modern coordination chemistry. Furthermore, our electrochemical and computational studies reveal that La₂@C_s(17 490)‐C₇₆ has a larger HOMO–LUMO gap than other dilanthanum‐EMFs with IPR cage structures, such as La₂@D_3h(5)‐C₇₈ and La₂@I_h(7)‐C₈₀, which implies that IPR is no longer a strict rule for EMFs.     

Calculated relative yields for Sc2S@C82 and Y2S@C82

The paper reports computations for a newly observed class of the mixed, sulfur-containing X₂S@C₈₂ metallofullerenes, namely for X = Sc and Y, based on encapsulation into the C _s and C_3v ?C₈₂ isolated pentagon rule cages. Their structural, vibrational, and energetic characteristics from the density-functional-theory calculations with the standard 6-31G* and LanL2DZ basis sets are used for the evaluations of the relative production yields. The encapsulation Gibbs energy terms from the partition functions combined with the observed saturated metal pressures are employed. A model scheme is used dealing with the XS template gas-phase presence. The computations predict that Sc₂S@C₈₂ should be produced in considerably larger amounts than Y₂S@C₈₂ which is in agreement with available observations. The yield order originates in the fact that both energetics and saturated metal pressure favor Sc over Y.     

The Driving Force of Photoinduced Charge Separation in Metal‐Cluster‐Encapsulated Triphenylamine‐[80]fullerenes

Understanding photoinduced charge separation in fullerene‐based dye‐sensitized solar cells is crucial for the development of photovoltaic devices. We investigate here how the driving force of the charge separation process in conjugates of M@C₈₀ (M=Sc₃N, Sc₃CH, Sc₃NC, Sc₄O₂, and Sc₄O₃) with triphenylamine (TPA) depends on the nature of the metal cluster. Both singlet and triplet excited‐state electron‐transfer reactions are considered. These results based on TD‐DFT calculations demonstrate that the driving force of charge separation in TPA‐M@C₈₀ can be tuned well by varying the structure of the metal cluster encapsulated inside the fullerene cage.     

Isolated pentagon rule violating endohedral metallofullerenes explained using the Hückel rule: A statistical mechanical study of the C84 Isomeric Set

Fullerenes and their structure and stability have been a major topic of discussion and research since their discovery nearly 30 years ago. The isolated pentagon rule (IPR) has long served as a guideline for predicting the most stable fullerene cages. More recently, endohedral metallofullerenes have been discovered that violate the IPR. This article presents a systematic, temperature dependent, statistical thermodynamic study of the 24 possible IPR isomers of C₈₄ as well as two of the experimentally known non‐IPR isomers (51365 and 51383), at several different charges (0, ?2, ?4, and ?6). From the results of this study, we conclude that the Hückel rule is a valid simpler explanation for the stability of fused pentagons in endohedral metallofullerenes. © 2014 Wiley Periodicals, Inc.     

The First Experimentally Confirmed Isolated Pentagon Rule (IPR) Isomers of Higher Fullerene C98 Captured as Chlorides,C98(248)Cl22 and C98(116)Cl20

High‐temperature chlorination of pristine C₉₈ fullerene isomers separated by HPLC from the fullerene soot afforded crystals of C₉₈Cl₂₂ and C₉₈Cl₂₀. An X‐ray structure elucidation revealed, respectively, the presence of carbon cages of the most stable C₂‐C₉₈(248) and rather unstable C₁‐C₉₈(116), which represent the first isolated pentagon rule (IPR) isomers of fullerene C₉₈ confirmed experimentally. The chlorination patterns of the chlorides are discussed in terms of the formation of isolated C=C bonds and aromatic substructures on the fullerene cages.     

Chlorination of IPR C100 Fullerene Affords Unconventional C96Cl20 with a Nonclassical Cage Containing Three Heptagons

Chlorination of C₁₀₀ fullerene with a mixture of VCl₄ and SbCl₅ afforded C₉₆Cl₂₀ with a strongly unconventional structure. In contrast to the classical fullerenes containing only hexagonal and pentagonal rings, the C₉₆ cage contains three heptagonal rings and, therefore, should be classified as a fullerene with a nonclassical cage (NCC). There are several types of pentagon fusions in the C₉₆ cage including pentagon pairs and pentagon triples. The three‐step pathway from isolated‐pentagon‐rule (IPR) C₁₀₀ to C₉₆(NCC‐3hp) includes two C₂ losses, which create two cage heptagons, and one Stone–Wales rotation under formation of the third heptagon. Structural reconstruction established C₁₀₀ isomer no. 18 from 450 topologically possible IPR isomers as the starting C₁₀₀ fullerene. Until now, no pristine C₁₀₀ isomers have been confirmed based on the experimental results.     

Bingel–Hirsch Addition on Endohedral Metallofullerenes: Kinetic Versus Thermodynamic Control

An extensive theoretical study of the Bingel–Hirsch addition of bromomalonate on scandium nitride endohedral fullerenes has been carried out. The prototypical and highly symmetrical Sc₃N@I_h‐C₈₀, with a structure that satisfies the isolated pentagon rule (IPR), and the non‐IPR Sc₃N@D₃(6140)‐C₆₈ fullerene show analogous reaction paths despite the distinct topology of the carbon networks and different rotation freedom of the internal nitride cluster. For the two metallofullerenes, our results predict that the reaction takes place under kinetic control yielding open‐cage fulleroids on [6,6] bonds, which is in good agreement with experimental data. The theoretical studies also show that predicting the reactivity of endohedral metallofullerenes is not straightforward and often an accurate analysis of the potential energy surface is required.     

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.     

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)Cl_28/30 compounds, respectively, which retain their IPR cage connectivities. In contrast, isomer C_2v‐C₁₀₀(417) gives C_s‐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)Cl_18/22 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.     

Unusual Chlorination Patterns of Three IPR Isomers of C88 Fullerene in C88(7)Cl12/24, C88(17)Cl22, and C88(33)Cl12/14

High‐temperature chlorination of three IPR isomers of fullerene C₈₈, C₂‐C₈₈(7), C_s‐C₈₈(17), and C₂‐C₈₈(33), resulted in the isolation and X‐ray structural characterization of C₈₈(7)Cl₁₂, C₈₈(7)Cl₂₄, C₈₈(17)Cl₂₂, and C₈₈(33)Cl_12/14. Chlorination patterns of C₈₈(7) and C₈₈(33) isomers are unusual in that one or more pentagons remain free from chlorination while some other pentagons are occupied by two or three Cl atoms. The addition patterns of the isolated chlorides are discussed in terms of the distribution of twelve pentagons on the carbon cages and the formation of stabilizing isolated C=C bonds and benzenoid rings.     

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.     

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.     

C68 Fullerene Isomers,Anions, and their Metallofullerenes: Charge‐Stabilizing Different Isomers

The complete set of 6332 classical isomers of the fullerene C₆₈ as well as several non‐classical isomers is investigated by PM3, and the data for some of the more stable isomers are refined by the DFT‐based methods HCTH and B3LYP. C₂:0112 possesses the lowest energy of all the neutral isomers and it prevails in a wide range of temperatures. Among the fullerene ions modeled, C₆₈^2?, C₆₈^4? and C₆₈^6?, the isomers C₆₈^2?(C_s:0064), C₆₈^4?(C_2v:0008), and C₆₈^6?(D₃:0009) respectively, are predicted to be the most stable. This reveals that the pentagon adjacency penalty rule (PAPR) does not necessarily apply to the charged fullerene cages. The vertical electron affinities of the neutral C_s:0064, C_2v:0008, and D₃:0009 isomers are 3.41, 3.29, and 3.10 eV, respectively, suggesting that they are good electron acceptors. The predicted complexation energy, that is, the adiabatic binding energy between the cage and encapsulated cluster, of Sc₂C₂@C₆₈(C_2v:0008) is ?6.95 eV, thus greatly releasing the strain of its parent fullerene (C_2v:0008). Essentially, C₆₈ fullerene isomers are charge‐stabilized. Thus, inducing charge facilitates the isolation of the different isomers. Further investigations show that the steric effect of the encaged cluster should also be an important factor to stabilize the C₆₈ fullerenes effectively.     

The saturated hydrides of C<Subscript>60</Subscript>:F<Subscript>5</Subscript>F<Subscript>6</Subscript> PK F<Subscript>5</Subscript>F<Subscript>7</Subscript> isomers

The carbon cages composed of pentagons and heptagons (F₅F₇ isomers) are the analogs of fullerenes composed of pentagons and hexagons (F₅F₆ isomers). To provide insight into the structures and stability of the hydrides of F₅F₆ and F₅F₇ isomers, systematical density functional theory calculations are performed on all the 1,812 F₅F₆–C₆₀H₆₀ and 56 F₅F₇–C₆₀H₆₀. The calculated results demonstrate that the isomer with lowest/highest energy has most/fewest fused pentagons for both F₅F₆ and F₅F₇ hydrides and the stability of these hydrides increase with the number of fused pentagons roughly. The lowest energy F₅F₆–C₆₀H₆₀ and F₅F₇–C₆₀H₆₀ are 237.1 and 152.5 kcal/mol lower in energy than the isolated pentagon rule (IPR) C₆₀H₆₀, respectively; however, these two parent cages are 529.6 and 660.0 kcal/mol higher in energy than the IPR C₆₀. The calculations suggest that heptagon-containing cages, not only those violating the IPR can be the candidate cages for fullerene derivatives and the possible repulsion between the added atoms may play an important role in determining the structures and stability of the hydrides of carbon cages.     

Diels–Alder Reaction on Free C68 Fullerene and Endohedral Sc3N@C68 Fullerene Violating the Isolated Pentagon Rule: Importance of Pentagon Adjacency

The reaction mechanism and regioselectivity of the Diels–Alder reactions of C₆₈ and Sc₃N@C₆₈, which violate the isolated pentagon rule, were studied with density functional theory calculations. For C₆₈, the [5,5] bond is the most favored thermodynamically, whereas the cycloaddition on the [5,6] bond has the lowest activation energy. Upon encapsulation of the metallic cluster, the exohedral reactivity of Sc₃N@C₆₈ is reduced remarkably owing to charge transfer from the cluster to the fullerene cage. The [5,5] bond becomes the most reactive site thermodynamically and kinetically. The bonds around the pentagon adjacency show the highest chemical reactivity, which demonstrates the importance of pentagon adjacency. Furthermore, the viability of Diels–Alder cycloadditions of several dienes and Sc₃N@C₆₈ was examined theoretically. o‐Quinodimethane is predicted to react with Sc₃N@C₆₈ easily, which implies the possibility of using Diels–Alder cycloaddition to functionalize Sc₃N@C₆₈.     

Synthesis and Isolation of the Titanium–Scandium Endohedral Fullerenes—Sc2TiC@Ih‐C80, Sc2TiC@D5h‐C80 and Sc2TiC2@Ih‐C80: Metal Size Tuning of the TiIV/TiIII Redox Potentials

The formation of endohedral metallofullerenes (EMFs) in an electric arc is reported for the mixed‐metal Sc–Ti system utilizing methane as a reactive gas. Comparison of these results with those from the Sc/CH₄ and Ti/CH₄ systems as well as syntheses without methane revealed a strong mutual influence of all key components on the product distribution. Whereas a methane atmosphere alone suppresses the formation of empty cage fullerenes, the Ti/CH₄ system forms mainly empty cage fullerenes. In contrast, the main fullerene products in the Sc/CH₄ system are Sc₄C₂@C₈₀ (the most abundant EMF from this synthesis), Sc₃C₂@C₈₀, isomers of Sc₂C₂@C₈₂, and the family Sc₂C_{2 n} (2 n=74, 76, 82, 86, 90, etc.), as well as Sc₃CH@C₈₀. The Sc–Ti/CH₄ system produces the mixed‐metal Sc₂TiC@C_{2 n} (2 n=68, 78, 80) and Sc₂TiC₂@C_{2 n} (2 n=80) clusterfullerene families. The molecular structures of the new, transition‐metal‐containing endohedral fullerenes, Sc₂TiC@I_h‐C₈₀, Sc₂TiC@D_5h‐C₈₀, and Sc₂TiC₂@I_h‐C₈₀, were characterized by NMR spectroscopy. The structure of Sc₂TiC@I_h‐C₈₀ was also determined by single‐crystal X‐ray diffraction, which demonstrated the presence of a short Ti=C double bond. Both Sc₂TiC‐ and Sc₂TiC₂‐containing clusterfullerenes have Ti‐localized LUMOs. Encapsulation of the redox‐active Ti ion inside the fullerene cage enables analysis of the cluster–cage strain in the endohedral fullerenes through electrochemical measurements.     

Assigning the major isomers of fullerene C88 by theoretical 13C NMR spectra

The IPR isomers of fullerene C₈₈ have been studied using density functional theory. Structures of all C₈₈ isomers with non-zero HOMO–LUMO gaps were optimized at the B3LYP/STO-3G level. Those isomers having energies lower than 25 kcal/mol were subjected to geometry optimization using the 6-31G basis set. Isomer 17 has the lowest energy, followed by 7 and 33. All three isomers have large HOMO–LUMO gaps. ¹³C NMR chemical shifts were obtained employing the GIAO method. The comparison between predicted and measured NMR spectra strongly supports the observed C₈₈-1(C_s) as isomer 17, and isomers C₈₈-2(C₂) and C₈₈-3(C₂) as 7 and 33, respectively.