The Regioselectivity of Bingel–Hirsch Cycloadditions on Isolated Pentagon Rule Endohedral Metallofullerenes

In this work, the Bingel–Hirsch addition of diethylbromomalonate to all non‐equivalent bonds of Sc₃N@D_3h‐C₇₈ was studied using density functional theory calculations. The regioselectivities observed computationally allowed the proposal of a set of rules, the predictive aromaticity criteria (PAC), to identify the most reactive bonds of a given endohedral metallofullerene based on a simple evaluation of the cage structure. The predictions based on the PAC are fully confirmed by both the computational and experimental exploration of the Bingel–Hirsch reaction of Sc₃N@D_5h‐C_80, thus indicating that these rules are rather general and applicable to other isolated pentagon rule endohedral metallofullerenes.     

Synthesis and Electrochemical Studies of Bingel–Hirsch Derivatives of M3N@Ih‐C80 (M=Sc,Lu)

Bingel–Hirsch derivatives of the trimetallic nitride template endohedral metallofullerenes (TNT‐EMFs) Sc₃N@I_h‐C₈₀ and Lu₃N@I_h‐C₈₀ were prepared by reacting these compounds with 2‐bromodiethyl malonate, 2‐bromo‐1,3‐dipyrrolidin‐1‐ylpropane‐1,3‐dionate bromide, and 9‐bromo fluorene. The mono‐adducts were isolated and their ¹H NMR spectra showed that the addition occurred with high regioselectivity at the [6,6] bonds of the I_h‐C₈₀ fullerene cage. Electrochemical analysis showed that the reductive electrochemistry behavior of these derivatives is irreversible at a scan rate of 100 mV s^?1, which is comparable to the behavior of the pristine fullerene species. The first reduction potential of each derivative is either cathodically or anodically shifted by a different value, depending on the attached addend. Bis‐adducts containing EtOOC‐C‐COOEt and HC‐COOEt addends were isolated by HPLC and in the case of Sc₃N@I_h‐C₈₀ the first reduction potential exhibits a larger shift towards negative potentials when compared to the mono‐adduct. This observation is important for designing acceptor materials for the construction of bulk heterojunction (BHJ) organic solar cells, since the polyfunctionalization not only increases the solubility of the fullerene species but also offers a promising approach for bringing the LUMO energy levels closer for the donor and the acceptor materials.     

Full Exploration of the Diels–Alder Cycloaddition on Metallofullerenes M3N@C80 (M=Sc,Lu, Gd): The D5h versus Ih Isomer and the Influence of the Metal Cluster

In this work a detailed investigation of the exohedral reactivity of the most important and abundant endohedral metallofullerene (EMF) is provided, that is, Sc₃N@I_h‐C₈₀ and its D_5h counterpart Sc₃N@D_5h‐C₈₀, and the (bio)chemically relevant lutetium‐ and gadolinium‐based M₃N@I_h/D_5h‐C₈₀ EMFs (M=Sc, Lu, Gd). In particular, we analyze the thermodynamics and kinetics of the Diels–Alder cycloaddition of s‐cis‐1,3‐butadiene on all the different bonds of the I_h‐C₈₀ and D_5h‐C₈₀ cages and their endohedral derivatives. First, we discuss the thermodynamic and kinetic aspects of the cycloaddition reaction on the hollow fullerenes and the two isomers of Sc₃N@C₈₀. Afterwards, the effect of the nature of the metal nitride is analyzed in detail. In general, our BP86/TZP//BP86/DZP calculations indicate that [5,6] bonds are more reactive than [6,6] bonds for the two isomers. The [5,6] bond D _5h ‐b , which is the most similar to the unique [5,6] bond type in the icosahedral cage, I _h ‐a , is the most reactive bond in M₃N@D_5h‐C₈₀ regardless of M. Sc₃N@C₈₀ and Lu₃N@C₈₀ give similar results; the regioselectivity is, however, significantly reduced for the larger and more electropositive M=Gd, as previously found in similar metallofullerenes. Calculations also show that the D_5h isomer is more reactive from the kinetic point of view than the I_h one in all cases which is in good agreement with experiments.     

A Complete Guide on the Influence of Metal Clusters in the Diels–Alder Regioselectivity of Ih‐C80 Endohedral Metallofullerenes

The chemical functionalization of endohedral metallofullerenes (EMFs) has aroused considerable interest due to the possibility of synthesizing new species with potential applications in materials science and medicine. Experimental and theoretical studies on the reactivity of endohedral metallofullerenes are scarce. To improve our understanding of the endohedral metallofullerene reactivity, we have systematically studied with DFT methods the Diels–Alder cycloaddition between s‐cis‐1,3‐butadiene and practically all X@I_h‐C₈₀ EMFs synthesized to date: X=Sc₃N, Lu₃N, Y₃N, La₂, Y₃, Sc₃C₂, Sc₄C₂, Sc₃CH, Sc₃NC, Sc₄O₂ and Sc₄O₃. We have studied both the thermodynamic and kinetic regioselectivity, taking into account the free rotation of the metallic cluster inside the fullerene. This systematic study has been made possible through the use of the frozen cage model (FCM), a computationally cheap approach to accurately predicting the exohedral regioselectivity of cycloaddition reactions in EMFs. Our results show that the EMFs are less reactive than the hollow I_h‐C₈₀ cage. Except for the Y₃ cluster, the additions occur predominantly at the [5,6] bond. In many cases, however, a mixture of the two possible regioisomers is predicted. In general, [6,6] addition is favored in EMFs that have a larger charge transfer from the metal cluster to the cage or a voluminous metal cluster inside. The present guide represents the first complete and exhaustive investigation of the reactivity of I_h‐C₈₀‐based EMFs.     

Singly Bonded Monoadduct rather than Methanofullerene: Manipulating the Addition Pattern of Trimetallic Nitride Clusterfullerene through One Endohedral Metal Atom Substitution

Bingel–Hirsch reactions of trimetallic nitride clusterfullerenes (NCFs) generally yield methanofullerene (cyclopropane) adducts instead of singly bonded derivatives, which have been reported for monometallofullerenes. Herein, we report the synthesis and characterization of the Bingel–Hirsch derivative of a mixed metal nitride clusterfullerene (MMNCF) TiY₂N@I_h‐C₈₀. Surprisingly, in contrast to the reported Bingel–Hirsch cyclopropane adducts of the analogous NCF Y₃N@I_h‐C₈₀, the Bingel–Hirsch derivative of TiY₂N@I_h‐C₈₀ is the first singly bonded monoadduct (labeled as TiY₂N@C₈₀‐Mono) to be reported, which was determined unambiguously by single‐crystal X‐ray crystallography. Besides, the reactivity of TiY₂N@I_h‐C₈₀ was found to be significantly improved relative to that of Y₃N@I_h‐C₈₀. Upon substituting one endohedral yttrium (Y) atom of Y₃N@I_h‐C₈₀ with titanium (Ti), the Bingel–Hirsch derivative changes from the cyclopropane to the singly bonded monoadduct, revealing that not only the reactivity but also the addition pattern of NCFs can be manipulated simultaneously through one endohedral metal atom substitution.     

An Efficient Method to Separate Sc3N@C80 Ih and D5h Isomers and Sc3N@C78 by Selective Oxidation with Acetylferrocenium [Fe(COCH3C5H4)Cp]+

Based on the different oxidation potentials of endohedral fullerenes Sc₃N@C₈₀ I_h and D_5h and Sc₃N@C₇₈, an efficient and useful method that avoids HPLC has been developed for their separation. Selective chemical oxidation of the Sc₃N@D_5h‐C₈₀ isomer and Sc₃N@C₇₈ by using an acetylferrocenium salt [Fe(COCH₃C₅H₄)Cp]⁺ followed by column chromatographic separation and reduction with CH₃SNa resulted in the isolation of pure Sc₃N@I_h‐C₈₀, Sc₃N@C₇₈, and a mixture of Sc₃N@D_5h‐C₈₀ and Sc₃N@C₆₈.     

Isolation and Crystallographic Characterization of Two,Nonisolated Pentagon Endohedral Fullerenes: Ho3N@C2(22010)-C78 and Tb3N@C2(22010)-C78

Purified samples of Ho₃N@C₂(22010)-C₇₈ and Tb₃N@C₂(22010)-C₇₈ have been isolated by two distinct processes from the rich array of fullerenes and endohedral fullerenes present in carbon soot from graphite rods doped with Ho₂O₃ or Tb₄O₇. Crystallographic analysis of the endohedral fullerenes as cocrystals with Ni(OEP) (in which OEP is the dianion of octaethylporphyrin) shows that both molecules contain the chiral C₂(22010)-C₇₈ cage. This cage does not obey the isolated pentagon rule (IPR) but has two sites where two pentagons share a common C−C bond. These pentalene units bind two of the metal ions, whereas the third metal resides near a hexagon of the cage. Inside the cages, the Ho₃N or Tb₃N unit is planar. Ho₃N@C₂(22010)-C₇₈ and Tb₃N@C₂(22010)-C₇₈ use the same cage previously found for Gd₃N@C₂(22010)-C₇₈ rather than the IPR-obeying cage found in Sc₃N@D_3h-C₇₈.     

New Trifluoromethylated Derivatives of Metal Nitride Clusterfullerenes: Sc3N@Ih‐C80(CF3)14 and Sc3N@D5h‐C80(CF3)16

Trifluoromethylated derivatives of Sc₃N@I_h‐C₈₀ and Sc₃N@D_5h‐C₈₀ were synthesized by the reaction with CF₃I at 440 °C. HPLC separation of the mixture of Sc₃N@D_5h‐C₈₀(CF₃)_n derivatives resulted in isolation and X‐ray structure determination of Sc₃N@D_5h‐C₈₀(CF₃)₁₆, which represents a precursor of the known Sc₃N@D_5h‐C₈₀(CF₃)₁₈. Among the CF₃ derivatives of Sc₃N@I_h‐C₈₀, two new isomers of Sc₃N@I_h‐C₈₀(CF₃)₁₄ ( Sc‐14‐VI and Sc‐14‐VII ) were isolated by HPLC, and their molecular structures were determined by X‐ray diffraction, thus enabling a comprehensive comparison of altogether seven isomers. Two types of addition patterns with different orientations of the Sc₃N cluster relative to the I_h‐C₈₀ fullerene cage were established. In particular, Sc‐14‐VII represents a direct precursor of the known Sc₃N@I_h‐C₈₀(CF₃)₁₆‐ II . All molecular structures exhibit an ordered position of a Sc₃N cluster inside the fullerene C₈₀ cage.     

Blending Non‐Group‐3 Transition Metal and Rare‐Earth Metal into a C80 Fullerene Cage with D5h Symmetry

Rare‐earth metals have been mostly entrapped into fullerene cages to form endohedral clusterfullerenes, whereas non‐Group‐3 transition metals that can form clusterfullerenes are limited to titanium (Ti) and vanadium (V), and both are exclusively entrapped within an I_h‐C₈₀ cage. Non‐Group‐3 transition‐metal‐containing endohedral fullerenes based on a C₈₀ cage with D_5h symmetry, V_xSc_3?xN@D_5h‐C₈₀ (x=1, 2), have now been synthesized, which exhibit two variable cluster compositions. The molecular structure of VSc₂N@D_5h‐C₈₀ was unambiguously determined by X‐ray crystallography. According to a comparative study with the reported Ti‐ and V‐containing clusterfullerenes based on a I_h‐C₈₀ cage and the analogous D_5h‐C₈₀‐based metal nitride clusterfullerenes containing rare‐earth metals only, the decisive role of the non‐Group‐3 transition metal on the formation of the corresponding D_5h‐C₈₀‐based clusterfullerenes is unraveled.     

Crystallographic Evidence for Direct Metal–Metal Bonding in a Stable Open‐Shell La2@Ih‐C80 Derivative

Endohedral metallofullerenes (EMFs) have novel structures and properties that are closely associated with the internal metallic species. Benzyl radical additions have been previously shown to form closed‐shell adducts by attaching an odd number of addends to open‐shell EMFs (such as Sc₃C₂@I_h‐C₈₀) whereas an even number of groups are added to closed‐shell EMFs (for example Sc₃N@I_h‐C₈₀). Herein we report that benzyl radical addition to the closed‐shell La₂@I_h‐C₈₀ forms a stable, open‐shell monoadduct instead of the anticipated closed‐shell bisadduct. Single‐crystal X‐ray diffraction results show the formation of a stable radical species. In this species, the La?La distance is comparable to the theoretical value of a La?La covalent bond and is shorter than reported values for other La₂@I_h‐C₈₀ derivatives, providing unambiguous evidence for the formation of direct La?La bond.     

Preparation,Structural Determination,and Characterization of Electronic Properties of Bis‐silylated and Bis‐germylated Lu3N@Ih‐C80

Bis‐silylated and bis‐germylated derivatives of Lu₃N@I_h‐C₈₀ ( 3 , 4 , 5 ) were successfully synthesized by the photochemical addition of disiliranes 1 a , 1 b or digermirane 2 , and fully characterized by spectroscopic, electrochemical, and theoretical studies. Interestingly, digermirane 2 reacts more efficiently than disiliranes 1 a and 1 b because of its good electron‐donor properties and lower steric hindrance around the Ge?Ge bond. The 1,4‐adduct structures of 3 , 4 , 5 were unequivocally established by single‐crystal X‐ray crystallographic analyses. The electrochemical and theoretical studies reveal that the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the 1,4‐adducts are remarkably smaller than those of Lu₃N@I_h‐C₈₀, because the electron‐donating groups effectively raise the HOMO levels. It is also observed that germyl groups are slightly more electron‐donating than the silyl groups on the basis of the redox properties and the HOMO–LUMO energies of 4 and 5 . Bis‐silylation and bis‐germylation are effective and versatile methods for tuning the electronic characteristics of endohedral metallofullerenes.     

Preparation,Structural Determination,and Characterization of Electronic Properties of [5,6]‐ and [6,6]‐Carbosilylated Sc3N@Ih‐C80

Photochemical carbosilylation of Sc₃N@I_h ‐C₈₀ with silirane 1 afforded two corresponding [5,6]‐adducts, 2 and 3 , and a [6,6]‐adduct, 4 . The structural and electronic properties of these products were characterized by means of spectroscopic, electrochemical, and theoretical methods. The structure of 2 was disclosed by means of single‐crystal X‐ray crystallographic analysis. Thermal isomerization of 3 to 2 was observed, whereas that of 2 to 3 proceeded less efficiently at 100 °C. Upon heating under the same conditions, adduct 4 underwent facile decomposition to afford Sc₃N@I_h ‐C₈₀, or isomerized into small amounts of 2 and 3 . The relative stabilities of 2 , 3 , and 4 were rationalized through the results of theoretical calculations. In contrast, adducts 2 , 3 , and 4 were stable under the photolytic conditions employed for carbosilylation. The photochemical functionalization of Sc₃N@I_h ‐C₈₀ represents a convenient synthetic method to obtain thermally labile fullerene‐based products.     

Essential Factors for Control of the Equilibrium in the Reversible Rearrangement of M3N@Ih‐C80 Fulleropyrrolidines: Exohedral Functional Groups versus Endohedral Metal Clusters

The effects of exohedral moieties and endohedral metal clusters on the isomerization of M₃N@I_h‐C₈₀ products from the Prato reaction through [1,5]‐sigmatropic rearrangement were systematically investigated by using three types of fulleropyrrolidine derivatives and four different endohedral metal clusters. As a result, all types of derivatives provided the same ratios of the isomers for a given trimetallic nitride template (TNT) as the thermodynamic products, thus indicating that the size of the endohedral metal clusters inside C₈₀ was the single essential factor in determining the equilibrium between the [6,6]‐isomer (kinetic product) and the [5,6]‐isomer. In all the derivatives, the [6,6]‐ and [5,6]‐Prato adducts with larger metal clusters, such as Y₃N and Gd₃N, were equally stable, which is in good agreement with DFT calculations. The reaction rate of the rearrangement was dependent on both the substituent of exohedral functional groups and the endohedral metal‐cluster size. Further DFT calculations and ¹³C NMR spectroscopic studies were employed to rationalize the equilibrium in the rearrangement between the [6,6]‐ and [5,6]‐fulleropyrrolidines.     

Metal Nitride Cluster Fullerene M3N@C80 (M=Y,Sc) Based Dyads: Synthesis,and Electrochemical,Theoretical and Photophysical Studies

The first pyrrolidine and cyclopropane derivatives of the trimetallic nitride templated (TNT) endohedral metallofullerenes I_h‐Sc₃N@C₈₀ and I_h‐Y₃N@C₈₀ connected to an electron‐donor unit (i.e., tetrathiafulvalene, phthalocyanine or ferrocene) were successfully prepared by 1,3‐dipolar cycloaddition reactions of azomethine ylides and Bingel–Hirsch‐type reactions. Electrochemical studies confirmed the formation of the [6,6] regioisomers for the Y₃N@C₈₀‐based dyads and the [5,6] regioisomers in the case of Sc₃N@C₈₀‐based dyads. Similar to other TNT endohedral metallofullerene systems previously synthesized, irreversible reductive behavior was observed for the [6,6]‐Y₃N@C₈₀‐based dyads, whereas the [5,6]‐Sc₃N@C₈₀‐based dyads exhibited reversible reductive electrochemistry. Density functional calculations were also carried out on these dyads confirming the importance of these structures as electron transfer model systems. Furthermore, photophysical investigations on a ferrocenyl–Sc₃N@C₈₀‐fulleropyrrolidine dyad demonstrated the existence of a photoinduced electron‐transfer process that yields a radical ion pair with a lifetime three times longer than that obtained for the analogous C₆₀ dyad.     

Synchrotron Radiation for Structural Chemistry—Endohedral Natures of Metallofullerenes Found by Synchrotron Radiation Powder Method

The recent progress of the structural studies of endohedral metallofullerenes by the synchrotron radiation (SR) powder diffraction utilizing the maximum entropy method (MEM) is reviewed. Results of the endohedral metallofullerenes (Y@C₈₂, La@C₈₂, Sc@C₈₂, Sc₂@C₈₄, Sc₃@C₈₂, Sc₂@C₆₆, La₂@C₈₀ and Sc₂C₂@C₈₄) are given. The precise MEM charge densities of metallofullerenes presents the direct image of endohedral nature of metallofullerenes indicating the charge transfer from metal atoms to carbon cage, which governs the stability of the unique endohedral structures. The MEM/Rietveld method and SR powder method using imaging plate (IP), which are the crucial methods for data analysis and measurement in order to determine structure of fulleride, are also mentioned in some detail.     

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.     

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.     

Addition of S‐Heterocyclic Carbenes to Fullerenes: Formation and Characterization of Dithiomethano‐Bridged Derivatives

The reactions of novel S‐heterocyclic carbenes (SHCs), which were prepared by the cycloaddition of disilenes and digermenes to CS₂, with C₆₀ and Sc₃N@I_h‐C₈₀ afforded the corresponding methano‐bridged fullerenes. The [6,6]‐closed and [6,6]‐open structures were characterized for the SHC adducts of C₆₀ and Sc₃N@I_h‐C₈₀, respectively. These derivatives exhibited relatively low oxidation potentials, indicative of the electron‐donating effects of the SHC addends. The electronic properties of the SHC derivatives were clarified by the density functional theory calculations.     

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.     

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.