Computing relative stabilities of metallofullerenes by Gibbs energy treatments

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.

Two Metastable Endohedral Metallofullerenes Sc2C2@C1(39656)-C82 and Sc2C2@C1(51383)-C84: Direct-C2-Insertion Products from Their Most Stable Precursors

Endohedral metallofullerenes (EMFs) are sub-nano carbon materials with diverse applications, yet their formation mechanism, particularly for metastable isomers, remains ambiguous. The current theoretical methods focus mainly on the most stable isomers, leading to limited predictability of metastable ones due to their low stabilities and yields. Herein, we report the successful isolation and characterization of two metastable EMFs, Sc₂C₂@C₁(39656)-C₈₂ and Sc₂C₂@C₁(51383)-C₈₄, which violate the isolated pentagon rule (IPR). These two non-IPR EMFs exhibit a rare case of planar and pennant-like Sc₂C₂ clusters, which can be considered hybrids of the common butterfly-shaped and linear configurations. More importantly, the theoretical results reveal that despite being metastable, these two non-IPR EMFs survived as the products from their most stable precursors, Sc₂C₂@C_2v(5)-C₈₀ and Sc₂C₂@C_s(6)-C₈₂, via a C₂ insertion during the post-formation annealing stages. We propose a systematic theoretical method for predicting metastable EMFs during the post-formation stages. The unambiguous molecular-level structural evidence, combined with the theoretical calculation results, provides valuable insights into the formation mechanisms of EMFs, shedding light on the potential of post-formation mechanisms as a promising approach for EMF synthesis.

Carbene Addition Isomers of C70 formed in the Flame of Low-Pressure Combustion

In the flames during low-pressure combustion, not only a rich variety of fullerenes but also many reactive intermediates can be produced (e.g., carbene, CH₂) that are short-lived and cannot be stabilized directly under normal circumstances. These intermediates can be captured by fullerene carbon cages for stabilization. In this paper, three C₇₁H₂ isomers were synthesized in situ in low-pressure benzene-acetylene-oxygen diffusion flame combustion. The results, which were unambiguously characterized by single-crystal X-ray diffraction, show that the three isomers are carbene addition products of D_5h-C₇₀ on different sites. The relative energies and stability of different C₇₁H₂ isomers are revealed by Ultraviolet-Visible (UV-Vis) absorption spectroscopy, in combination with theoretical calculations, in this work. Both the in situ capture and theoretical study of these C₇₁H₂ isomers in low-pressure combustion will provide more information regarding carbene additions to other fullerenes or other carbon clusters at high temperatures.

Synthesis and Characterization of Two Isomers of Th@C82: Th@C2v(9)-C82 and Th@C2(5)-C82

Actinide endohedral fullerenes have demonstrated remarkably different physicochemical properties compared to their lanthanide analogues. In this work, two novel isomers of Th@C₈₂ were successfully synthesized, isolated, and fully characterized by mass spectrometry, X-ray single crystallography, UV-vis-NIR spectroscopy, Raman spectroscopy, and cyclic voltammetry. The molecular structures of the two isomers were determined unambiguously as Th@C_2v(9)-C₈₂ and Th@C₂(5)-C₈₂ by single-crystal X-ray diffraction analysis. Raman and UV-vis-NIR spectroscopies further confirm the assignment of the cage isomers. Electrochemical gaps suggest that both Th@C_2v(9)-C₈₂ and Th@C₂(5)-C₈₂ possess a stable closed-shell electronic structure. The computational results further confirm that Th@C_2v(9)-C₈₂ and Th@C₂(5)-C₈₂ exhibit a unique four-electron charge transfer from the metal to the carbon cage and are among the most abundant isomers of Th@C₈₂.

Discovery of Non-Isolated-Pentagon-Rule Fullerenes from Computational Characterization of U2O@C72

The reported actinide-based endohedral clusterfullerenes (ECFs) are rather scarce thus far. Though several members have been detected in mass spectra, their exact structures and properties mostly remain unclear. Herein, density functional theory calculations revealed that the U₂O@C₇₂ observed in recent experiments should be U₂O@D₂(10611)-C₇₂, U₂O@C₁(10610)-C₇₂, or U₂O@C_s(10616)-C₇₂. Featuring two pairs of fused pentagons, their outer cages all break the well-known isolated pentagon rule. U₂O@D₂(10611)-C₇₂ is the first clusterfullerene based on the D₂(10611)-C₇₂ cage, which only encapsulated dimetals (Sc₂, La₂, Ce₂, Pr₂) before. It is also the first time to reveal that C₁(10610)-C₇₂ and C_s(10616)-C₇₂ can serve as the parent cage of an endohedral fullerene. Interestingly, the three isomers could interconvert with each other via Stone-Wales transformation with one internal U atom dynamically changing its orientation according to the position of pentagon adjacencies. A common electronic structure of (U⁴⁺)₂(O)^2-@C₇₂^6- can be formally assigned to the three ECFs but with obvious covalent character for both U-O and U-C bonds. Their spatially extended U-5f orbitals substantially enhance the metal-cage interactions. Their various spectra were also simulated to assist future experiments. Moreover, our work shows that the careful choice of exchange-correlation functionals is rather critical for the structural characterization of ECFs.

Ho2O@D3(85)-C92: Highly Stretched Cluster Dictated by a Giant Cage and Unexplored Isomerization

For endohedral metallofullerenes (EMFs), it has been well established that the cage shape and size should match those of the endohedral cluster. As a result, sufficient cluster-cage interaction can be achieved, which is essential for mutual stabilization. Nevertheless, how a small endohedral cluster nests in a giant fullerene has been less explored. Herein, we report a pair of large oxide-cluster fullerene (OCF) isomers, denoted as Ho₂O@C₉₂-I and -II. Crystallographic studies reveal that major isomer-I possesses a D₃(85)-C₉₂ cage with a highly stretched Ho₂O cluster inside, which contributes to achieving regular metal-cage contacts. Density functional theory (DFT) computations also reveal the predominant abundance of the D₃(85) isomer relative to the other two possible minor species including C₁(67) and C₂(64) isomers. Moreover, electrochemical (EC) studies verify that the isomers exhibit almost identical redox behaviors, indicating their similar cage structures. On the basis of the remarkable topological similarity of D₃(85) and C₁(67) isomers, isomer-II is likely to be Ho₂O@C₁(67)-C₉₂, though it remains to be confirmed. Our studies thus provide new insights into the cage-cluster interplay and cage isomerization, both contributing to a better understanding of large EMFs.

U2O@C76: Non-Isolated-Pentagon-Rule Cages Prevail with the U2O Configuration Determined by Cage Shape and Dominated by Multicenter Bonds

Endohedral clusterfullerenes (ECFs) are fullerene cages with various metallic clusters trapped inside. So far, the actinide-based ECFs are rather scarce with their possible structures and chemistry remaining largely unexplored. Herein, density functional theory calculations characterized that the recently synthesized U₂O@C₇₆ could be U₂O@C_s(17 490)-C₇₆ or U₂O@C_2v(19 138)-C₇₆, whose cages have two or one pentagon adjacencies (PAs) and thus both violate the isolated pentagon rule (IPR). It is noteworthy that they are the first actinide-based ECFs bearing non-IPR outer cages. They are also the first C_s(17 490)- and C_2v(19 138)-C₇₆-based oxide ECFs. Moreover, U₂O@C_2v(19 138)-C₇₆ is the first example of a hexavalent metal cluster within the C_2v(19 138)-C₇₆ cage. Interestingly, although trapped by the two same-sized cages, the U₂O unit exhibits a bent and a perfect linear configuration, respectively, indicative of the crucial role of cage shape in steering the internal cluster configuration. Their electronic structures can be formally described as (U₂O)⁶⁺@C₇₆^6- with primary electrostatic attractions and secondary covalent interactions between cluster and cage. Significantly, bonding analyses reveal that the encaged U₂O moiety may only features two three-center, two-electron (3c-2e) U-O-U bonds with completely absent common two-center bonds.

Encapsulation of Monometal Uranium into Fullerenes C2n (2n = 70-74): Important Ionic U4+C2n4- Characters and Covalent U-Cage Bonding Interactions

By using density functional theory calculations combined with statistical thermodynamic analyses, the stabilization performance of a series of fullerene cages C_2n (2n = 70-74) via encapsulating monometal uranium was systematically and thoroughly investigated. Results indicate that fullerene cages D_5h(8149)-C₇₀ and D_3h(14246)-C₇₄ obeying the isolated pentagon rule and C₂(10612)-C₇₂ featured with one pentalene moiety were the most promising candidates to encage uranium. Subsequent Mulliken spin density distribution and frontier molecular orbital analyses suggest that four formal electron transfer occurs from monometal U to above the carbon cages. There also exists a high degree of covalent character between the atom U and fullerenes C_2n based on Mayer bond order and quantum theory of atoms in molecule (QTAIM) analyses, indicative of the cooperative stabilization by both ionic and covalent bonding interactions. In addition, investigations on the above-mentioned U@C_2n isomers and other favorable candidates (U@C_s(8094)-C₇₀, U@C₁(10610)-C₇₂, U@C₁(13393)-C₇₄, and U@C₁(14049)-C₇₄) reveal that these isomers could be closely linked via simple C₂ addition and Stone-Wales transformation. These results will provide a systematic understanding on U-based endohedral metallofullerenes (EMFs) and also might be helpful for further exploration of EMF growth mechanisms.

Ho2O@C84: Crystallographic Evidence Showing Linear Metallic Oxide Cluster Encapsulated in IPR Fullerene Cage of D2d(51591)-C84

Fullerene C₈₄ is the third-most-abundant species after C₆₀ and C₇₀. In the past decade, a variety of C₈₄-based clusterfullerenes have been well-studied experimentally, which otherwise do not include oxide clusterfullerenes (OCFs). In this work, we report a comprehensive inspection of Ho₂O@C₈₄, including its mass, spectroscopic, crystallographic, electrochemical (EC), and density functional theory (DFT) studies. Importantly, crystallographic data reveal an IPR cage of D_2d(51591)-C₈₄ with a linear endohedral Ho-O-Ho cluster, indicating that the compression effect of the C₈₄ cage is less pronounced compared to that of a smaller cage. The experimentally observed structure is confirmed by DFT computations, which also verify its superior stability. Further studies suggest that Ho₂O@C₈₄ has reduced EC and HOMO-LUMO gaps compared to those of empty species, again demonstrating the effect of cluster encapsulation.

Synthesis and Structural Studies of Two Paramagnetic Metallofullerenes with Isomeric C72 Cage

We synthesized and isolated two paramagnetic metallofullerenes of La@C₇₂ and Y@C₇₂ with different fullerene cages, which were characterized by electron paramagnetic resonance (EPR) spectroscopy and theoretical calculations. DFT calculations disclosed two possible isomers of La/Y@C₇₂ with C₇₂- C₂ and C₇₂- C_2v cages, both of which have similar thermodynamic stability and one pair of fused pentagons. Their paramagnetic properties were then studied by EPR spectroscopy, and the obtained EPR signals were analyzed with very different hyperfine coupling constants, revealing distinct electron spin distributions for these two species. Furthermore, the experimental coupling constants were compared with those of calculated coupling constants, and comparison results revealed that the produced La@C₇₂ has a C₇₂- C_2v cage and Y@C₇₂ has a C₇₂- C₂ cage. These studies illustrate that the electron spin can be used as a probe to identify metallofullerene structure due to the susceptibility of spin-metal couplings. The successful isolation and characterizations of La@C₇₂ and Y@C₇₂ with such a small C₇₂ cage reveal their stability that is important for application as paramagnetic molecule materials.

Crystallographic characterization of Y2C2n (2n = 82, 88–94): direct Y–Y bonding and cage-dependent cluster evolution

The long-sought Y–Y bonding is experimentally observed in organometallic complexes for the first time by encapsulation inside the hollow cavity of C_3v(8)-C₈₂ and C_s(6)-C₈₂ fullerene cages.

Th-Based Endohedral Metallofullerenes: Anomalous Metal Position and Significant Metal-Cage Covalent Interactions with the Involvement of Th 5f Orbitals

Endohedral metallofullerenes (EMFs) containing actinides are rather intriguing due to potential 5f-orbital participation in the metal-metal or metal-cage bonding. In this work, density functional theory calculations first characterized the structure of recently synthesized ThC₇₄ as Th@ D_{3 h}(14246)-C₇₄. We found that the thorium atom adopts an unusual off-axis position inside cage due to small metal ion size and the requirement of large coordination number, which phenomenon was further extended to other Th-based EMFs. Significantly, besides the strong metal-cage electrostatic attractions, topological and orbital analysis revealed that all the investigated Th-based EMFs exhibit obvious covalent interactions between metal and cage with substantial contribution from the Th 5f orbitals. The encapsulation by fullerenes is thus proposed as a practical pathway toward the f-orbital covalency for thorium. Interestingly, the anomalous internal position of Th led to a novel three-dimensional metal trajectory at elevated temperatures in the D_{3 h}-C₇₄ cavity, as elucidated by the static computations and molecular dynamic simulations.

La–La bonded dimetallofullerenes [La2@C2n]−: species for stabilizing C2n (2n = 92–96) besides La2C2@C2n

Theoretical investigations suggest that carbon cages C_2n could be captured as both electron reduced [La₂@C_2n]⁻ with La–La bonding and pristine La₂C₂@C_2n forms.

Eu@C72: Computed Comparable Populations of Two Non-IPR Isomers

Relative concentrations of six isomeric Eu@C 72 -one based on the IPR C 72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon-pentagon junction (symmetries C 2 and C 2 v ), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon-pentagon fusions-are DFT computed using the Gibbs energy in a broad temperature interval. It is shown that the two non-IPR isomers with one pentagon-pentagon junction prevail at any relevant temperature and exhibit comparable populations. The IPR-satisfying structure is disfavored by both energy and entropy.

Single crystal structures and theoretical calculations of uranium endohedral metallofullerenes (U@C2n , 2n = 74, 82) show cage isomer dependent oxidation states for U

First X-ray structures and metal oxidation state dependence on cage isomerism for U-EMFs.

Charge transfer is a general phenomenon observed for all endohedral mono-metallofullerenes. Since the detection of the first endohedral metallofullerene (EMF), La@C₈₂, in 1991, it has always been observed that the oxidation state of a given encapsulated metal is always the same, regardless of the cage size. No crystallographic data exist for any early actinide endohedrals and little is known about the oxidation states for the few compounds that have been reported. Here we report the X-ray structures of three uranium metallofullerenes, U@D_3h-C₇₄, U@C₂(5)-C₈₂ and U@C_2v(9)-C₈₂, and provide theoretical evidence for cage isomer dependent charge transfer states for U. Results from DFT calculations show that U@D_3h-C₇₄ and U@C₂(5)-C₈₂ have tetravalent electronic configurations corresponding to U⁴⁺@D_3h-C₇₄^4– and U⁴⁺@C₂(5)-C₈₂^4–. Surprisingly, the isomeric U@C_2v(9)-C₈₂ has a trivalent electronic configuration corresponding to U³⁺@C_2v(9)-C₈₂^3–. These are the first X-ray crystallographic structures of uranium EMFs and this is first observation of metal oxidation state dependence on carbon cage isomerism for mono-EMFs.

La3N@C92: An Endohedral Metallofullerene Governed by Kinetic Factors?

Different structures have been proposed so far for the C92 isomer that encapsulates M3N (M = La, Ce, Pr). We show here that the electrochemical properties of the predicted most abundant (thermodynamic) isomer for La3N@C92 does not agree with experiment. After a systematic search within the huge number of possible C92 isomers, we propose other candidates with larger electrochemical gaps for La3N@C92 before its structure could be finally determined by X-ray crystallography. We do not discard that the thermodynamic isomer could be detected in future experiments though.

Sc3N@Cs(39715)–C82: a missing isomer linked to Sc3N@C2v(39718)–C82 by a single step Stone–Wales transformation

Density functional theory combined with statistical mechanics calculations indicate that Sc₃N@C_2v(39718)–C₈₂ and Sc₃N@C_s(39715)–C₈₂ linked by a single Stone–Wales transformation can be obtained at the fullerene formation temperature region.

Tuning metal cluster catalytic activity with morphology and composition: a DFT study of O2 dissociation at the global minimum of PtmPdn (m + n = 5) clusters

The catalytic property for O₂ dissociation of the pure Pt₅ cluster can be further improved by introducing the Pd atoms based on the morphology and composition.

Sc2O@C(2v)(5)-C80: Dimetallic Oxide Cluster Inside a C80 Fullerene Cage

A new oxide cluster fullerene, Sc2O@C(2v)(5)-C80, has been isolated and characterized by mass spectrometry, UV-vis-NIR absorption spectroscopy, cyclic voltammetry, (45)Sc NMR, DFT calculations, and single crystal X-ray diffraction. The crystallographic analysis unambiguously elucidated that the cage symmetry was assigned to C(2v)(5)-C80 and suggests that the Sc2O cluster is ordered inside the cage. The crystallographic data further reveals that the Sc1-O-Sc2 angle is much larger than that found in Sc2O@T(d)(19151)-C76 but almost comparable to that in Sc2O@Cs(6)-C82, suggesting that the endohedral Sc2O unit is flexible and can display large variation in the Sc-O-Sc angle, which depends on the size and shape of the cage. Computational studies show that there is a formal transfer of four electrons from the Sc2O unit to the C80 cage, i.e., (Sc2O)(4+)@(C80)(4-), and the HOMO and LUMO are mainly localized on the C80 framework. Moreover, thermal and entropic effects are seen to be relevant in the isomer selection. Comparative studies between the recently reported Sc2C2@C(2v)(5)-C80 and Sc2O@C(2v)(5)-C80 reveal that, despite their close structural resemblance, subtle differences exist on the crystal structures, and the clusters exert notable impact on their spectroscopic properties as well as interactions between the clusters and corresponding cages.

Different Factors Govern Chlorination and Encapsulation in Fullerenes: The Case of C66

C66 is one of the smallest fullerenes that is able to encapsulate more than one metal atom, as in Sc2@C66, as well as to get chlorinated at a low level, C66Cl10 or C66Cl6. We show here, with the help of computations at density functional theory level, that these two means of obtaining derivatives of non-isolated pentagon rule fullerenes are dictated by different factors. Chlorination takes place at temperatures lower than 2000 K, once the neutral fullerenes are formed. Encapsulation is, however, mainly governed by the charge transfer, although the Sc···Sc distance is also playing a role in the stability of Sc2@C66.

Theoretical Insight into the Ambiguous Endohedral Metallofullerene Er3C74: Covalent Interactions among Three Lanthanide Atoms

All of C74-based endohedral metallofullerenes (EMFs) are found to be monometallofullerenes with the same D3h(14246)-C74 cage so far. An opening question is whether other C74 cages could survive during the production of some novel C74-EMFs. Theoretically, we studied the trimetallic endohedral fullerene Er3C74, the existence of which had been proven without any further characterizations. Two thermodynamically stable Er3C74 isomers were obtained, both of which could be expressed as Er3@C74, meaning that previously synthesized Er3C74 is indeed an endohedral trierbium fullerene. Besides the isomer with well-known D3h(14246)-C74 cage which obeys isolated pentagon rule (IPR), another one possesses the C1(13771)-C74 cage with two adjacent pentagons. Notably, it is the first time an endohedral metallofullerene containing the C1(13771)-C74 cage has been reported. Frontier orbitals analysis, bonding analysis in terms of quantum theory of atoms-in-molecule (QTAIM) and Mayer bond order, together with two-dimensional maps of electron localization function (ELF) and Laplacian of electron density of Er3@D3h(14246)-C74 and Er3@C1(13771)-C74 show obvious covalent interactions not only between metallic atoms and carbon cage but also among three erbium atoms. Finally, simulated IR spectra of Er3@D3h(14246)-C74 and Er3@C1(13771)-C74 were simulated, which should be useful to distinguish those two isomers.

Sc2O@Td 19151)-C76 : hindered cluster motion inside a tetrahedral carbon cage probed by crystallographic and computational studies

A new cluster fullerene, Sc2 O@Td (19151)-C76 , has been isolated and characterized by mass spectrometry, UV/Vis/NIR absorption, (45) Sc NMR spectroscopy, cyclic voltammetry, and single-crystal X-ray diffraction. The crystallographic analysis unambiguously assigned the cage structure as Td (19151)-C76 , which is the first tetrahedral fullerene cage characterized by single-crystal X-ray diffraction. This study also demonstrated that the Sc2 O cluster has a much smaller ScOSc angle than that of Sc2 O@Cs (6)-C82 and the Sc2 O unit is fully ordered inside the Td (19151)-C76 cage. Computational studies further revealed that the cluster motion of the Sc2 O is more restrained in the Td (19151)-C76 cage than that in the Cs (6)-C82 cage. These results suggest that cage size affects not only the shapes but also the cluster motion inside fullerene cages.

Theoretical study on experimentally detected Sc2S@C84

Sc(2)S@C(84) has recently been detected but not structurally characterized.1 Density functional theory calculations on C(84) and Sc(2)S@C(84) show that the favored isomer of Sc(2)S@C84 shares the same parent cage as Sc(2)C2@C(84), whereas Sc(2)S@C(84):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 Sc(2)S@C(84):51575 is favored when the temperature exceeds 2,800 K and it can transform into the most favorable isomer Sc(2)S@C(84):51591. Molecular orbital analysis indicates that both Sc(2)S and Sc(2)C(2) formally transfer four electrons to the cage, and quantum theory of atoms in molecules analysis demonstrates that there is a covalent interaction between Sc(2)S and C(84):51591. The IR spectra of Sc(2)S@C(84) are provided to aid future structural identification.

Small endohedral metallofullerenes: exploration of the structure and growth mechanism in the Ti@C2n (2n = 26-50) family

Analysis of the structure and the bottom-up growth mechanism in the family of small endohedral metallofullerenes Ti@C_2n (2n = 26–50).

The formation of the smallest fullerene, C₂₈, was recently reported using gas phase experiments combined with high-resolution FT-ICR mass spectrometry. An internally located group IV metal stabilizes the highly strained non-IPR C₂₈ cage by charge transfer (IPR = isolated pentagon rule). Ti@C₄₄ also appeared as a prominent peak in the mass spectra, and U@C₂₈ was demonstrated to form by a bottom-up growth mechanism. We report here a computational analysis using standard DFT calculations and Car–Parrinello MD simulations for the family of the titled compounds, aiming to identify the optimal cage for each endohedral fullerene and to unravel key aspects of the intriguing growth mechanisms of fullerenes. We show that all the optimal isomers from C₂₆ to C₅₀ are linked by a simple C₂ insertion, with the exception of a few carbon cages that require an additional C₂ rearrangement. The ingestion of a C₂ unit is always an exergonic/exothermic process that can occur through a rather simple mechanism, with the most energetically demanding step corresponding to the closure of the carbon cage. The large formation abundance observed in mass spectra for Ti@C₂₈ and Ti@C₄₄ can be explained by the special electronic properties of these cages and their higher relative stabilities with respect to C₂ reactivity. We further verify that extrusion of C atoms from an already closed fullerene is much more energetically demanding than forming the fullerene by a bottom-up mechanism. Independent of the formation mechanism, the present investigations strongly support that, among all the possible isomers, the most stable, smaller non-IPR carbon cages are formed, a conclusion that is also valid for medium and large cages.

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@Td(19151)-C76 which satisfies the isolated-pentagon rule (IPR) possesses the lowest energy, followed by three non-IPR structures (Sc2S@C2v(19138)-C76, Sc2S@Cs(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@Td(19151)-C76, Sc2S@C2v(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 (13)C NMR spectra of those three stable structures are introduced to assist experimental identification and characterization in future.

Stability computations for isomers of La@C(n) (n = 72, 74, 76)

Density-functional theory calculations are presented for low-energy La@C₇₂, La@C₇₄ and La@C₇₆ isomers with IPR (isolated pentagon rule) and non-IPR cages. The relative isomeric production yields at high temperatures are evaluated using the calculated terms, and the relationships to observations are discussed.

C₇₄ endohedral metallofullerenes violating the isolated pentagon rule: a density functional theory study

Precise studies on M(2)@C(74) (M = Sc, La) series by means of DFT methods have disclosed that certain non-IPR isomers are more stable than the IPR structure. M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74), both of which have two pentagon adjacencies (PA), present excellent thermodynamic stability with very small energy differences. Statistical mechanics calculations on the M(2)@C(74) series reveal that M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74) are quite favoured by entropy effects below 3000 K. Sc(2)@C(74) and La(2)@C(74) series are found to have similar electronic transfer but different electronic structures due to the distinct properties of scandium and lanthanum elements according to Natural Bond Orbital (NBO) analysis in conjunction with orbital interaction diagrams. Investigations of bonding energies reflect quite different influences of the two types of metal atoms to C(74) metallo-fullerenes. Further examinations on C(74) metallo-fullerenes uncover significant stabilization effects of metal atoms acting on PA fragments. Geometrical structures of certain non-IPR cages (from C(72) to C(76)), which exhibit splendid stabilities when encapsulating metallo-clusters, are found to be related by Stone-Wales transformation and C(2) addition. Furthermore, IR spectra and (13)C NMR spectra of M(2)@C(2)(13295)-C(74) and M(2)@C(2)(13333)-C(74) have been simulated to assist further experimental characterization.

The smallest stable fullerene, M@C28 (m = Ti, Zr, U): stabilization and growth from carbon vapor

The smallest fullerene to form in condensing carbon vapor has received considerable interest since the discovery of Buckminsterfullerene, C(60). Smaller fullerenes remain a largely unexplored class of all-carbon molecules that are predicted to exhibit fascinating properties due to the large degree of curvature and resulting highly pyramidalized carbon atoms in their structures. However, that curvature also renders the smallest fullerenes highly reactive, making them difficult to detect experimentally. Gas-phase attempts to investigate the smallest fullerene by stabilization through cage encapsulation of a metal have been hindered by the complexity of mass spectra that result from vaporization experiments which include non-fullerene clusters, empty cages, and metallofullerenes. We use high-resolution FT-ICR mass spectrometry to overcome that problem and investigate formation of the smallest fullerene by use of a pulsed laser vaporization cluster source. Here, we report that the C(28) fullerene stabilized by encapsulation with an appropriate metal forms directly from carbon vapor as the smallest fullerene under our conditions. Its stabilization is investigated, and we show that M@C(28) is formed by a bottom-up growth mechanism and is a precursor to larger metallofullerenes. In fact, it appears that the encapsulating metal species may catalyze or nucleate endohedral fullerene formation.