Stability and Electronic Properties of Mixed Rare-Earth Tri-Metallofullerenes YxDy3-x@C80 (x = 1 or 2)

Tri-metallofullerenes, specifically M3@C80 where M denotes rare-earth metal elements, are molecules that possess intriguing magnetic properties. Typically, only one metal element is involved in a given tri-metallofullerene molecule. However, mixed tri-metallofullerenes, denoted as M1xM23-x@C80 (x = 1 or 2, M1 and M2 denote different metal elements), have not been previously discovered. The investigation of such mixed tri-metallofullerenes is of interest due to the potential introduction of distinct properties resulting from the interaction between different metal atoms. This paper presents the preparation and theoretical analysis of mixed rare-earth tri-metallofullerenes, specifically YxDy3−x@C80 (x = 1 or 2). Through chemical oxidation of the arc-discharge produced soot, the formation of tri-metallofullerene cations, namely Y2Dy@C80+ and YDy2@C80+ , has been observed. Density functional theory (DFT) calculations have revealed that the tri-metallofullerenes YxDy3−x@C80 (x = 1 or 2) exhibit a low oxidation potential, significantly lower than other fullerenes such as C60 and C70. This low oxidation potential can be attributed to the relatively high energy level of a singly occupied orbital. Additionally, the oxidized species demonstrate a large HOMO-LUMO gap similar to that of YxDy3−xN@C80, underscoring their high chemical stability. Theoretical investigations have uncovered the presence of a three-center two-electron metal–metal bond at the center of Y2DY@C80+ and YDy2@C80+ . This unique multi-center bond assists in alleviating the electrostatic repulsion between the metal ions, thereby contributing to the overall stability of the cations. These mixed rare-earth tri-metallofullerenes hold promise as potential candidates for single-molecule magnets.


Introduction
Fullerenes, which are carbon allotropes characterized by their cage-like structure, exhibit a notable structural feature of possessing a cavity with dimensions smaller than a nanometer.This inherent property allows for the accommodation of metal atoms within the internal space of the fullerene cages, leading to the creation of metallofullerenes.The synthesis, structures, and properties of metallofullerene molecules have undergone thorough examination [1][2][3][4][5][6][7].The incorporation of metal atoms or clusters enhances the optical, electrical, and magnetic properties of fullerene molecules, offering promising prospects for development in nonlinear optics, single-molecule magnets, fluorescent materials, and various other fields [8][9][10][11][12].In recent years, researchers have continuously expanded the types and forms of fullerenes by exploring new structures of metallofullerenes, which provides important inspiration for the development of novel molecular-based functional materials.
The internal cavity of a fullerene molecule typically falls within the sub-nanometer scale, capable of accommodating one, two, three, or more atoms [13][14][15][16][17][18][19].M@C 82 stands out as the most thoroughly examined mono-metallofullerene [20][21][22][23][24][25][26], primarily attributed to its remarkable production yield.The fullerene structure of M@C 82 can undergo functionalization, leading to the creation of various derivatives of metallofullerenes.An intriguing cationic mono-metallofullerene is Li@C + 60 .When compared to C 60 , Li@C + 60 demonstrates enhanced hydrogenation reactivity [27].The most-extensively studied di-metallofullerenes are M 2 @C 80 [28][29][30].Theoretical calculations for M 2 @C 80 indicate that lanthanide element dimers like La 2 and Ce 2 transfer six electrons to the carbon cage, resulting in the electron configuration of M 6+  2 @C 6- 80 .As the metal atom has contributed all its valence electrons, there is no metal-metal bond in M 2 @C 80 (M = La, Ce).On the other hand, lanthanide metal dimers, such as Gd 2 , Tb 2 , Dy 2 , and Er 2 , contribute five electrons to the carbon cage, forming the electron configuration of M 5+  2 @C 5- 80 , while retaining a metal bond occupied by a single electron.The neutral form of M 2 @C 80 (M = Gd, Tb, Dy, Er) is unstable due to the open-shell electronic structure of the outer carbon cage.However, covalent derivatization can stabilize these di-metallofullerenes.Of particular interest are the derivatives of Tb 2 @C 80 and Dy 2 @C 80 , which exhibit unique single-molecule magnet behavior [31].
In the case of metallofullerenes encapsulating three or more metal atoms, it is common to include one or more non-metal atoms within the fullerene cage.Examples include Sc 3 N@C 80 , VSc 2 N@C 80 , Sc 3 C 2 @C 80 , Sc 4 C 2 @C 80 , Ti 3 C 3 @C 80 , and Dy 3 C 2 @C 80 , etc. [19,[32][33][34][35][36].This is attributed to the significant Coulomb repulsion between the metal ions, which can be alleviated by the presence of non-metal atoms.Besides these cluster fullerenes, several reports have been published on tri-metallofullerenes without non-metal mediators, including Er 3 @C 74 , Y 3 @C 80 , Sm 3 @C 80 , Tm 3 @C 80 , and others [37][38][39][40][41][42].Popov et al. have postulated the presence of a pseudo atom at the core of the Y 3 @C 80 molecule, simulating the N atom in Y 3 N@C 80 [41].The interaction between the Y atoms and the pseudo atom mirrors that between the Y atoms and the N atom in Y 3 N@C 80 .Notably, the structure of Sm 3 @C 80 has been elucidated using single-crystal X-ray diffraction among these trimetallofullerenes [42].Recently, our group reported the successful extraction of Tm 3 @C 80 from arc-discharge-produced soot through chemical oxidation [43].Theoretical investigations have suggested the presence of a three-center two-electron metal-metal bonding in these tri-metallofullerenes.Moreover, larger tri-metallofullerenes have been identified in the gas phase via laser ablation [44][45][46][47].
To date, all the previously reported tri-metallofullerenes have exclusively utilized a single category of metal elements.The feasibility of encapsulating diverse metal atoms within the fullerene cage to generate tri-metallofullerenes with mixed elements remains uncertain.This study endeavors to investigate the synthesis of mixed rare-earth tri-metallofullerenes, specifically Y x Dy 3-x @C 80 (x = 1 or 2).DFT calculations have demonstrated their effectiveness in examining the structures and properties of metallofullerenes, establishing them as a reliable and robust method [10].In this work, we assess the stability and electronic characteristics of Y x Dy 3-x @C 80 (x = 1 or 2) through DFT calculations.

Results and Discussion
Following the arc-discharge process using a Y and Dy precursor mixture (with a molar ratio of Y:Dy = 2:1), we conducted the chemical oxidation of the resulting soot.Figure 1 displays the mass spectrum of the oxidized products.The most prominent peak corresponds to Y 3 @C 80 .Signals indicative of mixed rare-earth tri-metallofullerenes, specifically Y 2 Dy@C 80 and YDy 2 @C 80 , were also observed.This marks the first observation of the existence of mixed rare-earth tri-metallofullerenes.In this work, the mass spectra were measured in the positive mode.Typically, the peak intensity in the mass spectra may not accurately represent the yields of different metallofullerenes due to their varying ionization energies.However, in this study, the trimetallofullerenes (Y 3 @C 80 , Y 2 Dy@C 80 and YDy 2 @C 80 ) have very similar ionization energies, with calculations yielding values of 5.15, 5.14, and 5.13 eV, respectively.Consequently, based on the intensity of the mass peaks, the yields decrease in the following order: Y 3 @C 80 > Y 2 Dy@C 80 > YDy 2 @C 80 .Other peaks in the mass spectrum correspond to mono-metallofullerens M@C 2n and di-metallofullerenes M 2 @C 2n (M = Y or Dy).Fullerenes C 60 and C 70 were also produced in the arc-discharge process.However, their solubility in dichloromethane-the solvent used-is low.On the other hand, oxidized metallofullerenes readily dissolve in dichloromethane.As a result, the metallofullerenes were concentrated in the extract.Previous investigations have suggested that both Y 3 @C 80 and Tm 3 @C 80 share the same fullerene cage as Y 3 N@C 80 and Tm 3 N@C 80 , specifically the I h -symmetric C 80 cage [41,43].It should be noted that the symmetry of this fullerene is lowered to C 3v due to the Jahn-Teller symmetry reduction.The cage obtains its highest symmetry only when filled with metals [48].To ascertain whether Y 2 Dy@C 80 and YDy 2 @C 80 also adopt this particular fullerene cage, we conducted DFT calculations.Prior to this study, Popov et al. performed theoretical calculations to establish the energy order of C 6- 80 isomers [49].We considered the nine most stable C 6- 80 isomers as potential cages for encapsulating the Y and Dy atoms, forming Y 2 Dy@C 80 and YDy 2 @C 80 .Consequently, we obtained nine isomers for Y 2 Dy@C 80 and YDy 2 @C 80 .The relative energies, computed using the PBE0 functional, are presented in Tables 1 and 2. Our analysis reveals that the I h -symmetric cage corresponds to the lowest energy isomer for both Y 2 Dy@C 80 and YDy 2 @C 80 .Their molecular structures are depicted in Figure 2.  When encapsulating multiple metal atoms within a fullerene cage, it is often necessary to introduce one or two non-metal atoms between them to counteract the strong Coulomb repulsion.Examples of this phenomenon include Sc 3 C 2 @C 80 , Dy 3 C 2 @C 80 , and other cases [33,36,50].Theoretical confirmation exists showing that certain metal carbide cluster fullerenes, such as M x C y @C 2n , possess lower energy compared to their metallofullerene counterparts M x @C 2n+y .To assess the stability of Y 2 Dy@I h -C 80 (referred to as Y 2 Dy@C 80 hereafter) and Y 2 DyC 2 @C 78 , we also conducted energy calculations for Y 2 DyC 2 @C 78 .The computational results indicate that Y 2 DyC 2 @C 78 exhibits higher energy than Y 2 Dy@C 80 , as detailed in Table 3.Consequently, it can be concluded that Y 2 Dy@C 80 is thermodynamically more stable than its metallic carbon cluster counterpart, Y 2 DyC 2 @C 78 .A similar conclusion was drawn for YDy 2 @C 80 (Table 4).The stability of Y 2 Dy@C 80 and YDy 2 @C 80 was assessed by computing the binding energies (∆E b ) between the metal cluster and fullerene cage using hypothetical reactions (1) and ( 2).The definition of binding energy is as follows: ∆E b = E(fullerene) + E(metal cluster) − E(metallofullerene).Higher binding energy values indicate a greater stability of metallofullerenes.The binding energy calculated for Y 2 Dy@C 80 is 281 kcal/mol.On the other hand, the binding energy calculated for YDy 2 @C 80 is smaller, specifically 273 kcal/mol.The computed binding energy for Y 3 @C 80 is 289 kcal/mol.This sequence of the binding energy for Y 3 @C 80 , Y 2 Dy@C 80 , and YDy 2 @C 80 aligns with the order of their peak intensities in the mass spectrum.Consequently, it is reasonable to infer that the yield of tri-metallofullerenes is correlated with the binding energy.We have computed the van der Waals volume, which refers to the space enclosed within the isosurface with an electron density of 0.001 a.u., for C 80 , Y 3 @C 80 , Y 2 Dy@C 80 , and YDy 2 @C 80 .The obtained values are 820, 870, 875, and 876 Å 3 for C 80 , Y 3 @C 80 , Y 2 Dy@C 80 , and YDy 2 @C 80 , respectively.It is evident that the volume expands due to the incorporation of the metal cluster.The ionic radius of Dy 3+ (0.091 nm) is larger than that of Y 3+ (0.089 nm).According to the computed binding energies, it can be inferred that the Y 2 Dy cluster is better suited than the YDy 2 cluster for encapsulation within the C 80 cage.
For comparison, we also calculated the binding energy for Y 2 DyN@C 80 and YDy 2 N@C 80 , both of which are nitride clusterfullerenes known for their exceptional stability (reactions (3) and ( 4)).Previous studies have examined the stability of the nitride clusterfullerene M 3 N@C 80 for different metal atoms.These studies have revealed that certain rare-earth elements, such as La and Nd, are too large to fit within the I h -C 80 fullerene cage, while Dy and Y atoms possess suitable sizes.The computed binding energies for La 3 @C 80 and Nd 3 @C 80 are 217 and 237 kcal/mol, respectively, which are significantly lower than those of Y 3 @C 80 , Y 2 Dy@C 80 , and YDy 2 @C 80 .Signals corresponding to La 3 @C 80 and Nd 3 @C 80 were not detected in the oxidized products.We attribute this observation to the substantial size of the La and Nd atoms.Our calculations demonstrate that the binding energies of Y 2 DyN@C 80 and YDy 2 N@C 80 are 269 and 257 kcal/mol, respectively.The binding energies of Y 2 Dy@C 80 and YDy 2 @C 80 are higher than those of Y 2 DyN@C 80 and YDy 2 N@C 80 , indicating that Y 2 Dy@C 80 and YDy 2 @C 80 exhibit greater stability.It is important to note that the arc-discharge synthesis method involves conditions that are far from equilibrium.These conditions, referred to as non-equilibrium plasma by Osawa [51], prioritize structural and flux parameters over energy parameters.In previous studies, auxiliary parameters, such as activation energies and stochastic descriptors, have been utilized to predict the formation of fullerenes [52].In the case of Y 3 @C 80 , Y 2 Dy@C 80 , and YDy 2 @C 80 , the analysis based on stochastic descriptors may offer valuable insights.This aspect will be explored in our future research.
Chemical oxidation plays a crucial role in the extraction of Y 2 Dy@C 80 and YDy 2 @C 80 .Attempting direct extraction using conventional fullerene solvents such as toluene and CS 2 proved unsuccessful for these mixed rare-earth tri-metallofullerenes.This scenario echoes our earlier findings with Tm 3 @C 80 [43].The inference drawn is that Y 2 Dy@C 80 and YDy 2 @C 80 tend to undergo oxidation, and their resulting cations demonstrate chemical stability.Subsequently, we computed the ionization energy of Y 2 Dy@C 80 and YDy 2 @C 80 , and observed that they exhibit relatively low ionization energy values.Specifically, the ionization energy of Y 2 Dy@C 80 is 5.49 eV, while that of YDy 2 @C 80 is 5.47 eV.These values are significantly smaller than the calculated ionization energies of C 60 (7.76 eV) and C 70 (7.56eV).It has been reported that Li@C 60 can undergo oxidation to form Li@C + 60 , leading to the creation of various stable ionic compounds [53][54][55].Notably, the calculated ionization energy of Y 2 Dy@C 80 and YDy 2 @C 80 is comparable to that of Li@C 60 (5.73 eV), computed at the same level.Consequently, it can be inferred that Y 2 Dy@C 80 and YDy 2 @C 80 molecules may undergo chemical oxidation to produce their respective cations, namely Y 2 Dy@C + 80 and YDy 2 @C + 80 .Figure 2 presents the DFT-optimized structures of Y 2 Dy@C + 80 and YDy 2 @C + 80 .For comparison, the DFT-optimized structures of Y 2 DyN@C 80 and YDy 2 N@C 80 are also depicted in Figure 2. The comparison reveals that the structures of Y 2 Dy@C + 80 and YDy 2 @C + 80 closely resemble those of Y 2 DyN@C 80 and YDy 2 N@C 80 , respectively.The metal-metal distances are around 3.5 angstrom in these cations and neutral molecules.
The low ionization energy exhibited by Y 2 Dy@C 80 and YDy 2 @C 80 can be elucidated by examining the energy of molecular orbitals.We carried out calculations on the clusters of Y 2 Dy, YDy 2 , and the fullerene C 80 .Figure 3a displays the calculated molecular orbital diagrams.The LUMO/LUMO + 1/LUMO + 2 orbitals of the C 80 molecule are nearly degenerate, while there is a significantly large energy gap between LUMO + 2 and LUMO + 3.As a result, the C 80 cage has a preference to accept six electrons in order to achieve a stable electronic configuration.In the case of the Y 2 Dy and YDy 2 clusters, there are seven electrons with relatively high energy levels in the frontier molecular.Upon encapsulation of the metal cluster into the C 80 cage, six electrons are transferred to the LUMO/LUMO + 1/ LUMO + 2 orbitals of C 80 , leaving one unpaired electron on the metal cluster.In the case of the bare Y 2 Dy and YDy 2 clusters, there exist molecular orbitals that are associated with three-center two-electron bonding (encircled with dotted lines in Figure 3a).These specific molecular orbitals retain their bonding characteristics when the metal cluster is enclosed within C 80 due to their comparably low energy levels.2) decrease to 0.56, 0.62, and 0.75, respectively.This weakening of the metal atom bonding is a result of electron transfer from the metal cluster to the fullerene cage.At the same time, the repulsion between the metal ions becomes stronger in the metallofullerene compared to the bare metal cluster.A similar trend is observed for YDy 2 and YDy 2 @C 80 .In YDy 2 , the bond orders for Dy(1)-Dy(2), Dy(1)-Y, and Dy(2)-Y are 1.64, 1.94, and 1.94, respectively.These bond orders decrease to 0.54, 0.69, and 0.67 in YDy 2 @C 80 .
Figure 3b,c portray the calculated molecular orbitals for Y 2 Dy@C 80 and YDy 2 @C 80 .In both instances, the HOMO for the alpha spin possesses a relatively high energy level.Figure 3d displays the calculated spin density distribution for Y 2 Dy@C 80 and YDy 2 @C 80 .They exhibit a spatial distribution that is comparable to the alpha HOMO, signifying that the alpha HOMO primarily corresponds to the unpaired electron in the molecule.The high energy level of the alpha HOMO makes the molecule prone to oxidation into a cation.Upon careful analysis of the alpha HOMO's shape, it has been determined that it is a bonding orbital.The removal of an electron from this orbital would result in a reduction of the bonding strength between the metal atoms.Consequently, the cations Y 2 Dy@C + 80 and YDy 2 @C + 80 exhibit longer metal-metal distances compared to the neutral molecules Y 2 Dy@C 80 and YDy 2 @C 80 (Figure 2).
As previously mentioned, the molecular structures of Y 2 Dy@C + 80 and YDy 2 @C + 80 closely mirror those of Y 2 DyN@C 80 and YDy 2 N@C 80 , respectively.The metal-metal distances in Y 2 Dy@C + 80 and YDy 2 @C + 80 closely resemble those in Y 2 DyN@C 80 and YDy 2 N@C 80 .Our calculations further reveal that they share similar electronic structures.Figure 4a,b illustrate the molecular orbital energy diagrams for Y 2 Dy@C + 80 and Y 2 DyN@C 80 .Notably, the HOMO and LUMO of Y 2 Dy@C + 80 exhibit strikingly similar shapes to that of Y 2 DyN@C 80 .Meanwhile, the calculated HOMO-LUMO gap of Y 2 Dy@C + 80 (2.80 eV) is identical to that of Y 2 DyN@C 80 (2.80 eV).Among all the reported metallofullerenes, M 3 N@C 80 represents a type with a notably large HOMO-LUMO gap.DFT calculations in this study unveil that Y 2 Dy@C + 80 also possesses a substantial HOMO-LUMO gap, suggesting high stability for this cation.It is noteworthy that the neutral Y 2 Dy@C 80 exhibits a relatively small HOMO-LUMO gap (1.47 eV using the PBE0 functional, and 0.30 eV using the PBE functional), indicating its chemical reactivity.The significant increase in the HOMO-LUMO gap for Y 2 Dy@C + 80 enhances the chemical stability of Y 2 Dy@C 80 upon oxidation.It is noteworthy that the ELF distribution of Y 2 Dy@C + 80 closely resembles that of Y 2 DyN@C 80 (Figure 4c).In the case of Y 2 Dy@C + 80 , the ELF distribution at the molecular center indicates the presence of covalent bonding among the three metal atoms, specifically forming a three-center metal-metal bond.This bond corresponds to the HOMO-3 molecular orbital, as depicted in Figure 4a.For Y 2 DyN@C 80 , where the formal charge of the metal atom is +3, strong electrostatic repulsion exists between the metal ions.The central N 3-ion acts as a mediator, mitigating the repulsion between the metal ions.In the bare Y 2 Dy cluster, the bond lengths for Dy-Y(1), Dy-Y(2), and Y(1)-Y(2) are 3.21, 3.21, and 3.18 angstrom, respectively.However, in Y 2 Dy@C + 80 , the bond lengths for Dy-Y(1), Dy-Y(2), and Y(1)-Y(2) increase to 3.51, 3.51, and 3.51 angstrom, respectively, indicating strong repulsion between these metal ions.A similar trend is observed for YDy 2 and YDy 2 @C 80 .In YDy 2 , the bond lengths for Dy(1)-Dy(2), Dy(1)-Y, and Dy(2)-Y are 3.24, 3.21, and 3.21 angstrom, respectively.These bond lengths increase to 3.51, 3.49, and 3.50 angstrom in YDy 2 @C + 80 .In the case of Y 2 Dy@C + 80 , the three-center σ bond serves a role akin to that of the N 3-ion in Y 2 DyN@C 80 .The three-center σ bond can mitigate the repulsion between the metal ions and allows three metal atoms to be accommodated within the C 80 cage without the need for a nonmetal mediator.Thus, the three-center σ bond emerges as a crucial factor contributing to the stabilization of the tri-metallofullerene cation.Furthermore, our calculations indicate that the electronic structure of YDy 2 @C + 80 closely mirrors that of YDy 2 N@C 80 .They exhibit analogous frontier molecular orbitals and comparable ELF distribution at the molecular center (Figure 5).Consequently, the stability of YDy 2 @C + 80 can be elucidated in a manner similar to that of Y 2 Dy@C + 80 .The magnetic characteristics of rare-earth metallofullerenes are intriguing.Some of them are formed in high spin states [56,57].There have been reports highlighting the single-molecule magnet behavior of the clusterfullerenes Y 2 DyN@C 80 and YDy 2 N@C 80 [58].
Given that the cations Y 2 Dy@C + 80 and YDy 2 @C + 80 share similar geometrical and electronic structures with Y 2 DyN@C 80 and YDy 2 N@C 80 , respectively, these cations emerge as promising candidates for single-molecule magnets.Exploring the separation of these cations in future studies would constitute valuable and important research.

Experimental and Theoretical Methods
The metallofullerenes were synthesized using the arc-discharge technique.The anode was made of a carbon rod, while the cathode was a hollow carbon rod filled with a mixture of Y 2 O 3 , Dy 2 O 3 (molar ratio of Y:Dy = 2:1), and graphite powders.Prior to the discharge, the cathode was heated by connecting it to the anode and applying a current of 120 A for an hour under a dynamic vacuum.The actual arc-discharge process occurred at a current of 120 A in a 200 Torr helium environment, with a distance of approximately 1 cm between the anode and cathode.The raw soot generated from the arc was subjected to oxidation using AgSbF 6 in dichloromethane within a nitrogen-filled glove box for a duration of 24 h.Following the oxidation process, the solution was separated from the insoluble soot residue through centrifugation and filtration.No chromatographic purification was carried out.The sample was then analyzed using a mass spectrometer (AB SCIEX 5800 MALDI TOF/TOF, Toronto, Canada) to obtain a mass spectrum, with the analysis conducted in the positive mode without using any matrix.
We carried out DFT calculations to examine the structure and properties of the metallofullerenes.To optimize the structure and determine the molecule's energy, the PBE0 functional [59] was employed.The carbon and nitrogen atoms were treated using the 6-31G(d) basis set [60].The Y and Dy atoms were considered using the SDD pseudopotentials and the corresponding basis sets.The 6-311G(d) basis set was used for single-point energy calculations [61].To investigate the bonding properties of the molecules, the MULTIWFN program [62] was utilized to perform electron localization function (ELF) analysis [63] and Wiberg bond order analysis on a Lowdin orthogonalized basis.All DFT calculations were conducted using Gaussian16 version A03 [64].The visualization of the calculation results was accomplished using the Visual Molecular Dynamics (VMD, version 1.9.3) software [65].

Conclusions
We have conducted a comprehensive investigation into the stability and electronic properties of mixed rare-earth tri-metallofullerenes, specifically Y x Dy 3-x @C 80 (x = 1 or 2), through a combined experimental and theoretical study.Our findings indicate that the chemical oxidation of the arc-discharge produced soot can result in the formation of cations, namely Y 2 Dy@C + 80 and YDy 2 @C + 80 .Through DFT calculations, we have determined that the tri-metallofullerenes Y x Dy 3-x @C 80 (x = 1 or 2) possess a low oxidation potential, significantly lower than that of the other fullerenes like C 60 and C 70 .This low oxidation potential is attributed to the relatively high energy level of the singly occupied orbital alpha HOMO.Furthermore, the oxidized species exhibit a large HOMO-LUMO gap similar to that of Y x Dy 3-x N@C 80 , highlighting their high chemical stability.Theoretical studies have revealed the presence of a three-center two-electron metal-metal bond at the center of Y 2 Dy@C + 80 and YDy 2 @C + 80 .This unique multi-center bond helps alleviate the electrostatic repulsion between the metal ions, thus contributing to the overall stability of the cations.

Figure 1 .
Figure 1.(a) Mass spectrum for the oxidized metallofullerenes.The signals from Y 3 @C 80 , Y 2 Dy@C 80 and YDy 2 @C 80 are observed.(b) The experimental and calculated isotope distributions of the samples.

Figure 3 .
Figure 3. (a) The calculated molecular orbital energy level of C 80 compared to that of Y 2 Dy and YDy 2 clusters.The molecular orbitals corresponding to three-center two-electron metal-metal bonding in the clusters are encircled with dotted lines.The spatial distribution of the three-center two-electron metal-metal bonding orbital for the Y 2 Dy and YDy 2 clusters is shown.(b,c) The molecular orbital energy diagrams for Y 2 Dy@C 80 and YDy 2 @C 80 .(d) The calculated spin density distribution for Y 2 Dy@C 80 and YDy 2 @C 80 (isovalue = 0.0004).The bond lengths for Dy-Y(1), Dy-Y(2), and Y(1)-Y(2) in bare Y 2 Dy cluster are 3.21, 3.21, and 3.18 angstrom, respectively, which are much shorter than those in the metallofullerene Y 2 Dy@C 80 .We carried out a Wisberg bond order analysis for Y 2 Dy, YDy 2 , Y 2 Dy@C 80 , and YDy 2 @C 80 .In Y 2 Dy, the bond orders for Dy-Y(1), Dy-Y(2), and Y(1)-Y(2) are 1.76, 1.76, and 2.05, respectively, indicating a strong bonding interaction between the metal atoms.However, in Y 2 Dy@C 80 , the bond orders for Dy-Y(1), Dy-Y(2), and Y(1)-Y(2) decrease to 0.56, 0.62, and 0.75, respectively.This weakening of the metal atom bonding is a result of

Table 1 .
The calculated relative energy (kcal/mol) of Y 2 Dy@C 80 with different fullerene cages.The spiral number of the fullerene cage is included.

Table 3 .
The calculated relative energy (kcal/mol) of Y 2 Dy@I h -C 80 and Y 2 DyC 2 @C 78 with different fullerene cages.The spiral number of the fullerene cage is included.

Table 4 .
The calculated relative energy (kcal/mol) of YDy 2 @I h -C 80 and YDy 2 C 2 @C 78 with different fullerene cages.The spiral number of the fullerene cage is included.