Ln₃@C₈₀⁺ (Ln = lanthanide): a new class of stable metallofullerene cations with multicenter metal–metal bonding in the sub-nanometer confined space

Abstract

Among the large number of members in the metallofullerene family, the nitride clusterfullerene M₃N@C₈₀ (M = trivalent metal) is a special one with extraordinarily high stability. It is generally thought that the molecule would be unstable without the nitrogen ion N³⁻ in the center of the M₃ moiety, because N³⁻ can compensate for the Coulomb repulsion between the metal ions M³⁺. Indeed, the tri-metallofullerenes Ln₃@C₈₀ (Ln = trivalent lanthanide) are missing in the family of metallofullerenes to date. In this paper, we provide new insights into the stability of Ln₃@C₈₀ by a combined experimental and theoretical study. Density functional calculations demonstrate that Ln₃@C₈₀ are thermodynamically stable molecules. However, their small HOMO–LUMO gaps can induce severe kinetic instability. Meanwhile, Ln₃@C₈₀ has the smallest ionization energy among the metallofullerene molecules reported so far. Experimental and theoretical studies prove that the Ln₃@C₈₀ molecules can be greatly stabilized by chemical oxidation, because the Ln₃@C₈₀⁺ cation has a large HOMO–LUMO gap comparable to that of Ln₃N@C₈₀. Furthermore, Ln₃@C₈₀⁺ and Ln₃N@C₈₀ have similar molecular geometries and electronic structures. There is a three-center two-electron σ bond in the center of the Ln₃ cluster in Ln₃@C₈₀⁺. This special metal–metal bond significantly compensates for the electrostatic repulsion between the Ln ions and thus stabilizes the cation Ln₃@C₈₀⁺. In previous studies, there are very few examples of metallofullerene cations, because most of the metallofullerene cations are highly unstable. This study provides a strategy for obtaining a new class of stable metallofullerene cations, which can be used to construct a variety of novel ionic compounds Ln₃@C₈₀⁺X⁻.

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1 Introduction

As unique core–shell structured clusters, endohedral metallofullerenes (EMFs) have been intensively investigated due to their tunable physicochemical properties. In recent decades, a variety of metallofullerenes, such as mono-metallofullerenes (M@C_2n), di-metallofullerenes (M₂@C_2n) and endohedral clusterfullerenes (M_xA_y@C_2n (A = nonmetal element)), have been synthesized and theoretically investigated.^1–4 Among these metallofullerenes, the C₈₀-containing ones are attractive compounds, not only because of the high symmetry of I_h-C₈₀ but also for its ability to accommodate two metal atoms or a mixed metal/nonmetal cluster.^5–13

On one hand, the outer C₈₀ fullerene cage provides a sub-nanometer confined space to capture and stabilize the originally unstable cluster with novel chemical bonding types. For instance, a two-center one-electron metal–metal bond has been discovered in M₂@C₈₀ (M = Y or lanthanides).^14–17 The radical bridge between the two metals is well-protected by the fullerene cage, and it leads to strong magnetic exchange coupling between lanthanide ions in Ln₂@C₈₀.¹⁸ On the other hand, electron transfer from the encapsulated metal species to the outer C₈₀ cage results in a strong Coulomb repulsion between the highly charged metal ions. Although the fullerene cage restricts the dissociation of the encapsulated metal cluster, the metal atoms still tend to be as far from each other as possible. When three or more metal atoms are encapsulated in the fullerene cage, introducing one or more non-metal atoms is usually necessary to partially compensate for the Coulomb repulsion between the metal atoms. One typical example is the nitride clusterfullerene M₃N@C₈₀, which can be described as (M³⁺)₃N³⁻@C₈₀⁶⁻.¹⁹

In contrast to the well-studied nitride clusterfullerene M₃N@C₈₀ (M = trivalent metal), much less is known about the corresponding tri-metallofullerene M₃@C₈₀. Although the synthesis of Tb₃C₈₀ has been reported previously,²⁰ it is not clear whether Tb₃C₈₀ is the conventional metallofullerene Tb₃@C₈₀ or carbide clusterfullerene Tb₃C₂@C₇₈. A theoretical study on Y₃@C₈₀ suggests that Y₃@C₈₀ is more stable than Y₃C₂@C₇₈ and that Y₃@C₈₀ mimics Y₃N@C₈₀ with a pseudoatom instead of the nitrogen atom in the center of the molecule.²¹ Shi and coworkers have reported the crystal structure characterization of Sm₃@I_h-C₈₀.²² It should be noted that the oxidation state of Sm in the metallofullerene is +2, which is different from that of the metals in M₃N@C₈₀. Thus, the Sm element cannot form a nitride clusterfullerene. Other reports on metallofullerenes containing three metal atoms include the synthesis of Er₃C₇₄ ²³ and Dy₃C₉₈.²⁴ The bonding character of the Er₃ cluster in C₇₄ has been studied theoretically.²⁵ The metallofullerenes mentioned above were produced by vaporizing metal/graphite composite rods with a Krätschmer–Huffman fullerene generator. Tri-metallofullerenes with larger sizes were observed in the gas phase by the method of laser ablation.^26–29

For the lanthanide elements that can form nitride clusterfullerenes (such as Gd, Dy, Er, Tm, Lu, etc.), it is still an open question whether they can form tri-metallofullerenes Ln₃@C₈₀. If the formation of Ln₃@C₈₀ is possible, several questions would be raised: (i) which lanthanide elements prefer to form stable tri-metallofullerenes Ln₃@C₈₀? (ii) How the electronic and chemical properties of Ln₃@C₈₀ are affected by different lanthanide metal atoms? (iii) How to stabilize or capture such Ln₃@C₈₀ molecules? To address these issues, we conducted a theoretical investigation on Ln₃@C₈₀ (Ln = La, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu) by employing density functional theory (DFT) calculations. The molecular structures, stabilities, electronic properties and bonding features of Ln₃@C₈₀ were investigated. DFT calculations reveal that the Ln₃@C₈₀ compounds have small ionization energies and that they are prone to lose an electron to form a stable cation. We have obtained the cation Ln₃@C₈₀⁺ in experiments through the chemical oxidation of Ln₃@C₈₀. In the research field of metallofullerenes, most studies were conducted on neutral metallofullerene molecules. The knowledge on metallofullerene cations is very limited, because most of them are not stable. The only example of a stable metallofullerene cation reported so far is [Li@C₆₀]⁺. It can be used to construct a variety of ionic compounds [Li@C₆₀]⁺X⁻ (X = SbCl₆, PF₆, etc.), which have unique structures and fascinating properties.^30–33 The tri-metallofullerenes Ln₃@C₈₀⁺ reported in this paper represent a new class of stable metallofullerene cations with unique metal–metal bonding features.

2 Methods

2.1 Computational details

Previous studies have demonstrated that density functional calculations using PBE³⁴ and PBE0 ³⁵ functionals can give reasonable results on the geometries and energies of metallofullerenes.^{9,15,21,36–38} In this study, the geometrical structures of Ln₃@C₈₀ (Ln = La, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu) and their cations were optimized using the PBE and PBE0 functionals. It should be noted that some of these molecules contain a partially-filled 4f-shell. It is difficult to treat such electronic configurations by single-determinant DFT calculations. Considering that the 4f electrons of lanthanide atoms are usually not involved in the chemical bonding of metallofullerenes, we employed ECPnMWB (n is the number of core electrons) with 4f-in-core effective core potentials and the corresponding valence basis sets for the lanthanide atoms. In a recent work by Popov and coworkers,³⁹ the results of DFT calculations on Dy₃C₂@C₈₀ with a similar 4f-in-core treatment are consistent with the experimental results, confirming the reliability of such a calculation method.

For geometry optimization, the 6-31G(d) basis set⁴⁰ was used for the carbon atom. For single-point energy calculations, the extended basis set 6-311G(d)⁴¹ was used instead. Vibrational frequency analyses were performed on the optimized structures to ensure that they are local minima on the energy potential surface. To investigate the bonding nature of the Ln₃@I_h-C₈₀ molecules, the Mayer bond order (MBO),⁴² multicenter bond order (MCBO)⁴³ and electron localization function (ELF)⁴⁴ were examined using the MULTIWFN 3.7 program.⁴⁵ All the DFT calculations in this study were carried out using the Gaussian 16 Rev. A03 package.⁴⁶ The calculated results were visualized using visual molecular dynamics (VMD).⁴⁷

2.2 Experimental section

Trimetallofullerene Tm₃@C₈₀ was prepared by using the arc-discharge method. A hollow graphite rod filled with a mixture of Tm₂O₃ and graphite powder (molar ratio of Tm : C = 1 : 15) was used as the anode, and a pure graphite rod was used as the cathode. The arc discharge was performed at a current of 100 A under a He atmosphere (200 Torr). The arc-produced raw soot was oxidized by AgSbF₆ in dichloromethane (DCM) in a nitrogen-filled glove box for 24 h. After the oxidation reaction, the solution was separated from the insoluble soot residue by centrifugation. The resulting dark-brown solution was filtered through a membrane filter (pore diameter = 0.22 μm), and it was vacuum-evaporated to remove the solvent. Then the solid was dissolved in a mixed solvent of toluene and acetonitrile (1 : 1). The composition of the solution was characterized by using laser desorption ionization time of flight (LDI-TOF) mass spectrometry (AB Sciex 5800 mass spectrometer).

3 Results and discussion

3.1 Stability of Ln@C₈₀

For C₈₀-based clusterfullerenes containing three metal atoms, such as M₃N@C₈₀,¹⁹ M₃C₂@C₈₀,^39,48 Sc₃CH@C₈₀ ¹⁰ and Ti₃C₃@C₈₀,⁴⁹ it is generally accepted that the encapsulated cluster transfers six electrons to the fullerene cage. On the other hand, for trimetallofullerenes without any non-metal mediator, such as Y₃@C₈₀ ²¹ and Er₃@C₇₄,²⁵ the inner metal atoms are also thought to donate six electrons in total to the outer cage. Therefore, the stability of these metallofullerenes is related to the stability of the fullerene cage in the hexaanionic state C_2n⁶⁻.

In a previous study by Popov and coworkers, the relative energy of C₈₀⁶⁻ isomers has been calculated theoretically.³⁶ In order to determine which isomer is most preferable in energy for encapsulation of three lanthanide atoms to form Ln₃@C₈₀, we used the nine lowest energy isomers of C₈₀⁶⁻ as the candidates for the host fullerene cage. Three lanthanide atoms were encapsulated in these fullerene cages to form nine isomers of Ln₃@C₈₀. The calculated relative energies based on PBE and PBE0 functionals are summarized in Table S1.† It can be found that Ln₃@C₈₀ based on I_h and D_5h cage structures are the two lowest energy isomers. In this work, Tm₃@C₈₀ was selected as a representative compound for further discussion. The relative energies and HOMO–LUMO gaps of Tm₃@C₈₀ isomers are listed in Table 1. It is found that the most stable isomer of Tm₃@C₈₀ is Tm₃@I_h (31 924)-C₈₀, which is more stable than the others by at least 13 kcal mol⁻¹. The second most stable isomer is Tm₃@D_5h (31 923)-C₈₀. The stability order of Tm₃@C₈₀ is similar to that of Tm₃N@C₈₀.⁵⁰ Further theoretical studies in this work were conducted on the most stable isomer, i.e. Tm₃@I_h-C₈₀.

Table 1 Relative energies (ΔE, in kcal mol⁻¹) and HOMO–LUMO gaps (H–L gap, in eV) of Tm₃C₈₀ molecules calculated using PBE0 and PBE functionals (6-31G(d) and ECP58MWB basis sets are used for C and Tm atoms, respectively)

Tm3C80 (spiral number)	PBE0		PBE
	ΔE	H–L gap	ΔE	H–L gap
a HOMO–LUMO gap for α spin orbitals. b HOMO–LUMO gap for β spin orbitals.
Tm3@Ih (31 924)-C80	0.00	1.50^a/2.70^b	0.00	0.28^a/1.43^b
Tm3@D5h (31 923)-C80	14.08	0.28^a/1.43^b	13.32	0.28^a/1.38^b
Tm3@C2v (31 922)-C80	23.89	1.41^a/1.59^b	21.65	0.47^a/0.59^b
Tm3@C2v (31 920)-C80	37.40	0.95^a/1.54^b	34.54	0.09^a/0.52^b
Tm3@C1 (28 319)-C80	41.63	1.19^a/1.81^b	36.56	0.32^a/0.78^b
Tm3@C1 (28 324)-C80	42.91	1.56^a/1.44^b	38.98	0.52^a/0.40^b
Tm3@C1 (28 325)-C80	31.18	1.34^a/2.30^b	29.62	0.27^a/1.16^b
Tm3@C2 (29 591)-C80	36.42	1.40^a/2.49^b	35.20	0.24^a/1.38^b
Tm3@C1 (31 876)-C80	38.68	1.60^a/1.25^b	34.04	0.59^a/0.30^b

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It is known that some metal carbide clusterfullerenes M_xC_y@C_2n are lower in energy as compared with their metallofullerene form M_x@C_2n+y.^48,51–54 To compare the stability of Tm₃@I_h-C₈₀ and Tm₃C₂@C₇₈, we also performed calculations on Tm₃C₂@C₇₈. The calculated results reveal that Tm₃C₂@C₇₈ has a higher energy than Tm₃@I_h-C₈₀ (see Table S2†). Therefore, it can be concluded that Tm₃@I_h-C₈₀ is thermodynamically more stable than its carbide form.

In previous studies, the stability of the nitride clusterfullerene M₃N@C₈₀ for various metals has been investigated.^36,55,56 It has been found that some lanthanide atoms such as La and Nd are too large to be encapsulated in the I_h-C₈₀ fullerene cage. For the metallofullerene Ln₃@I_h-C₈₀, the size of the encapsulated atom may have a similar effect on the stability of the metallofullerene. In this work, the stability of Ln₃@I_h-C₈₀ for various lanthanide elements was evaluated by calculating the following energetic parameters. The first one is the formation energy (ΔE_f), which was calculated based on the hypothetical reaction (1). In addition, we also calculated the binding energy (ΔE_b) and the encapsulation energy (ΔE_encap) based on hypothetical reactions (2) and (3). Previous studies have demonstrated that large binding energy and encapsulation energy values suggest high stability of metallofullerenes.⁵⁷ Meanwhile, the cluster formation energy (ΔE_cluster) based on reaction (4) could be obtained by subtracting the binding energies (ΔE_b) from the encapsulation energies (ΔE_encap).

3M + 80C → M₃@C₈₀ ΔE_f (1)

M₃ + C₈₀ → M₃@C₈₀ ΔE_b (2)

3M + C₈₀ → M₃@C₈₀ ΔE_encap (3)

3M → M₃ ΔE_cluster (4)

According to the calculation results (Fig. 1a–c), the values of the formation energy, the binding energy and the encapsulation energy become more negative from early lanthanide elements to late lanthanide elements. This trend is consistent with the decreasing order of the ionic radius of lanthanide elements. Therefore, the encapsulation of three lanthanide atoms with smaller sizes in I_h-C₈₀ is more favorable in energy than the encapsulation of lanthanide atoms with larger sizes such as La and Nd, which is similar to the case of M₃N@C₈₀. Among all these compounds, Tm₃@I_h-C₈₀ has the largest binding energy and encapsulation energy, indicating that the formation of Tm₃@I_h-C₈₀ is more favorable than other Ln₃@I_h-C₈₀ compounds. The binding energy has been used to interpret the stability of metallofullerenes.^36,57 For the lanthanide elements with a relatively small ionic radius such as Tm and Lu, their nitride clusterfullerenes Ln₃N@C₈₀ can be produced in high yields experimentally. We calculated the binding energies of Ln₃N@C₈₀ (Ln = La, Gd, Tm, Lu) and compared them with that of Ln₃@C₈₀ (Fig. 1b). It is found that the binding energies of Ln₃@I_h-C₈₀ compounds are larger than those of Ln₃N@I_h-C₈₀, implying that it is possible to obtain the metallofullerenes Ln₃@I_h-C₈₀ in experiments.

Fig. 1 The calculated (a) formation energies (ΔE_f), (b) binding energies (ΔE_b), and (c) encapsulation energies (ΔE_encap) of Ln₃@I_h-C₈₀ (Ln = La, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu) and (d) the metal cluster formation energies (ΔE_cluster) using the PBE functional.

Fig. 1d shows the metal cluster formation energy (ΔE_cluster) for various lanthanide metals. It can be seen that ΔE_cluster becomes less negative on going from early lanthanide elements to late lanthanide elements. Although the cluster formation energy for Tm is the smallest among the metal elements, the encapsulation energy for Tm₃@I_h-C₈₀ is the largest due to a strong interaction between the Tm₃ cluster and the I_h-C₈₀ fullerene cage. Therefore, the interaction between the Ln₃ metal cluster and the fullerene cage contributes significantly to the driving force for the formation of Ln₃@I_h-C₈₀ compounds.

3.2 Geometric structures of Ln₃@I_h-C₈₀

Fig. 2 and Fig. S1† show the optimized structures of Ln₃@I_h-C₈₀ (Ln = La, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu) using PBE and PBE0 functionals, respectively. The encapsulated triangular metal cluster deforms the carbon cage and further causes symmetry reduction of the molecule. The structures of the Ln₃ cluster with the coordinated fullerene fragments are displayed in the figure for clarity. The Ln–Ln bond lengths of Ln₃@I_h-C₈₀ in the ground states are summarized in Table 2. In most cases, the Ln–Ln distance is longer than that of a typical Ln–Ln single bond. When La₃ and Nd₃ clusters are encapsulated in I_h-C₈₀, each metal atom coordinates with a hexagonal carbon ring of the cage. The La or Nd metal atoms almost form an equilateral triangle with metal–metal distances of 3.274 Å–3.277 Å and 3.494 Å–3.499 Å in the case of La and Nd, respectively. As for the encapsulated Gd₃ and Tb₃ clusters, each metal atom is located near the junctions of three hexagons (penalene). In the case of Dy₃@C₈₀, three Dy atoms are non-equivalent. One Dy atom resides under a hexagonal ring, and the other two Dy atoms are located near the junctions of two hexagons (naphthalene). The Dy atoms in Dy₃@C₈₀ form an isosceles triangle with Dy–Dy distances of 3.437/3.470/3.470 Å, which are longer than the Dy–Dy distances in Dy₃C₂@C₈₀ (3.440/3.382/3.408 Å).³⁹ For the Ho₃, Er₃ and Tm₃ clusters, the metal atoms are situated at the junctions of one pentagon and two hexagons (acenaphthylene) as shown in the figure. In the situation of Lu₃@C₈₀, the three Lu atoms of the Lu₃ cluster show different characteristics. One Lu atom resides under a hexagon, and the other two Lu atoms are near the “naphthalene” and “acenaphthylene” fragments, respectively.

Fig. 2 The upper part shows the front view and side view of the optimized geometric structures of Ln₃@I_h-C₈₀ (Ln = La, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu) using the PBE functional. The lower part shows the coordinated environments of the Ln₃ clusters inside the fullerene cage.

Table 2 Calculated relative energies (RE, in kcal mol⁻¹), Ln–Ln bond lengths (in Å), the Mayer bond order between the metal and the carbon atoms in Ln₃@I_h-C₈₀ and spin population of the metal cluster

Ln3@C80	RE (in kcal mol^−1)		Ln–Ln (in Å)				Mayer bond order				Spin population of the metal cluster
Metal atom	Doublet	Quartet	1	2	3	Average	Ln3	Ln(1)	Ln(2)	Ln(3)
La	0	6.28	3.269	3.277	3.272	3.273	5.006	1.658	1.673	1.676	1.045
Nd	0	7.94	3.499	3.499	3.494	3.496	5.565	1.856	1.851	1.857	0.624
Gd	0	10.20	3.490	3.481	3.273	3.415	4.815	1.624	1.602	1.589	0.556
Tb	0	13.34	3.433	3.473	3.472	3.459	4.531	1.495	1.545	1.492	0.542
Dy	0	16.00	3.437	3.470	3.470	3.459	4.423	1.448	1.511	1.465	0.570
Ho	0	6.18	3.448	3.454	3.451	3.451	4.320	1.443	1.437	1.440	0.521
Er	0	21.53	3.437	3.465	3.434	3.445	4.054	1.361	1.375	1.318	0.697
Tm	0	23.32	3.443	3.466	3.457	3.455	4.219	1.425	1.402	1.392	0.576
Lu	0	28.47	3.319	3.568	3.575	3.487	4.263	1.314	1.311	1.638	0.636

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3.3 Electronic structure and bonding feature of Ln₃@I_h-C₈₀

The relative energies of Ln₃@I_h-C₈₀ with different spin multiplicities are summarized in Table 2 and S3.† The calculations reveal that all the compounds have doublet ground states. The unpaired spin density distributions for the ground states of Ln₃@I_h-C₈₀ compounds calculated using the PBE functional are shown in Fig. 3. The unpaired electron in La₃@I_h-C₈₀ is mostly localized on the La₃ cluster, corresponding to a singly occupied three-center π bonding orbital. For the other Ln₃@I_h-C₈₀ compounds, unpaired electron distributions both on the inner metal cluster moiety and on the fullerene cage can be observed. The calculated spin populations of the metal clusters are listed in Table 2. The La₃ cluster has a spin population of 1.045, while the spin population for other clusters is in the range of 0.5–0.7.

Fig. 3 The calculated spin density distributions of Ln₃@I_h-C₈₀ (isovalue = 0.001).

The neutral I_h-C₈₀ molecule has almost degenerate LUMO/LUMO+1/LUMO+2 orbitals and a significantly large LUMO+2–LUMO+3 energy gap. Hence, the I_h-C₈₀ cage prefers to accept six electrons to form a stable electronic configuration. Fig. 4 shows the energy levels of the canonical molecular orbitals (CMOs) for Ln₃ units and empty I_h-C₈₀. There are seven electrons that have close energy levels in the frontier molecular orbitals of the metal cluster. When the metal cluster is encapsulated into the I_h-C₈₀ cage, six electrons are transferred to the LUMO/LUMO+1/LUMO+2 orbitals of I_h-C₈₀, and one unpaired electron is left on the metal cluster. The energy level of this singly occupied orbital is close to that of the LUMO+3 of I_h-C₈₀, resulting in a narrow HOMO–LUMO gap of Ln₃@C₈₀. The electronic configuration of Ln₃@C₈₀ can be described as Ln₃⁶⁺@C₈₀⁶⁻. The unpaired electron in Ln₃@C₈₀ occupies a molecular orbital with a relatively high energy. Consequently, the Ln₃@C₈₀ molecules have small ionization energies. Our DFT calculations reveal that the ionization energies of Ln₃@C₈₀ are in the range of 5.22–5.65 eV (Table S4†), which are much smaller than the calculated ionization energies of C₆₀ (7.76 eV), C₇₀ (7.56 eV) and Ln₃N@C₈₀ (around 6.79 eV). It has been reported that Li@C₆₀ can be oxidized to Li@C₆₀⁺ and that it can form a variety of stable ionic compounds.^30–32 The calculated ionization energy of Tm₃@C₈₀ (5.50 eV) is smaller than that of Li@C₆₀ (5.73 eV). Therefore, it can be deduced that the Tm₃@C₈₀ molecule could be oxidized chemically to its cation Tm₃@C₈₀⁺.

Fig. 4 The calculated canonical molecular orbital (CMO) energy level of I_h-C₈₀ compared to those of Nd₃, Gd₃, Tm₃ and Lu₃ clusters in their ground states. The occupied and unoccupied molecular orbitals are denoted in black and blue lines, respectively. The CMOs corresponding to 3c-2e metal–metal bonding in Ln₃ clusters are encircled with orange dotted lines. As an example, the spatial distribution of the 3c-2e metal–metal bonding orbital for Nd₃ is shown in the bottom left corner of the figure.

For bare Ln₃ clusters, there are molecular orbitals that correspond to three-center two-electron (3c-2e) bonding (encircled with orange dotted lines in Fig. 4). Because of the relatively low energy of these molecular orbitals, the 3c-2e bonding is preserved after the metal cluster is encapsulated in I_h-C₈₀. This is confirmed by examining the spatial distribution of molecular orbitals for Ln₃@C₈₀. As an example, the molecular orbital corresponding to 3c-2e bonding in Tm₃@C₈₀ is shown in Fig. 5a. ELF analysis also reveals that there exists three-center metal–metal bonding in Tm₃@C₈₀ (Fig. 5b). We found that the ELF for the encapsulated Tm₃ cluster is very different from the ELF for the bare Tm₃ cluster. In the case of the bare Tm₃ cluster, Tm–Tm bonding is observed at the edge rather than in the center of the cluster (Fig. 5b). Therefore, the bonding feature of the Tm₃ cluster is changed after being encaged in the sub-nanometer confined space of I_h-C₈₀. Moreover, our calculations reveal that the bonding feature of other Ln₃ clusters undergoes similar changes in I_h-C₈₀.

Fig. 5 (a) The molecular orbital energy diagram of the Tm₃@I_h-C₈₀ molecule. The energy levels of the occupied and unoccupied CMOs are denoted in black and blue, respectively. The HOMO of Tm₃@I_h-C₈₀ corresponds to a singly occupied π bonding orbital and the HOMO−5 corresponds to the 3c-2e metal–metal bonding orbital. (b) Color filled two-dimensional ELF maps of the metal cluster plane for Tm₃@I_h-C₈₀ (upper part) and the bare Tm₃ cluster (lower part).

3.4 Chemical oxidation of Tm₃@C₈₀

As we discussed above, Tm₃@C₈₀ has large encapsulation and binding energies, implying that it is possible to obtain Tm₃@C₈₀ in experiments. Therefore, we performed arc-discharge synthesis of Tm-metallofullerenes. It has been reported that AgSbF₆ can be used to oxidize metallofullerenes into their cations.⁵⁸ Considering that Tm₃@C₈₀ has a small ionization energy, we treated the arc-discharge produced soot with AgSbF₆ in DCM. As a result, some Tm-metallofullerenes were oxidized into cations and they were solubilized in the solvent. Then, the solvent was evaporated and the resultant solid was redissolved in a mixture of toluene and acetonitrile (1 : 1). The mass spectrum of the solution (Fig. 6a) confirms that Tm₃@C₈₀ has been extracted from the raw soot. We ascribed the signal of Tm₃@C₈₀ to its cation, because no signal of Tm₃@C₈₀ was observed without using AgSbF₆.

Fig. 6 (a) The experimental LDI-TOF mass spectrum of Tm₃@C₈₀⁺ as well as the measured and calculated isotope distributions of the corresponding sample. (b) Three-dimensional ELF isosurface and color filled two-dimensional ELF maps of the metal cluster plane for the Tm₃@I_h-C₈₀ cation (left) and Tm₃N@I_h-C₈₀ molecule (right). (c and d) The molecular orbital energy diagrams of the Tm₃@I_h-C₈₀ cation and Tm₃N@I_h-C₈₀. The energy levels of the occupied and unoccupied CMOs are denoted in black and blue, respectively.

The structure and electronic properties of the Tm₃@C₈₀ cation were studied using DFT calculations. Since the Tm₃ cluster may have different orientations inside the fullerene cage, we calculated the energies of different conformations of Tm₃@C₈₀⁺. Their relative energies and geometrical parameters are listed in Table S6.†Fig. 6b shows the most stable structure of Tm₃@C₈₀⁺ and the ELF distribution. The Tm–Tm distance in Tm₃@C₈₀⁺ is in the range of 3.511–3.529 Å, which is longer than that in neutral Tm₃@C₈₀ (3.443 Å on average). Accordingly, the distance between the Tm atoms and the C₈₀ cage gets shorter, leading to a stronger interaction between the Tm atoms and the fullerene cage. The total Mayer bond order between the Tm₃ cluster and the C₈₀ cage increases from 4.219 to 4.777 after oxidation. As shown in Fig. 5a, the HOMO of Tm₃@C₈₀ corresponds to a singly occupied π bonding orbital. The removal of the electron in this orbital weakens the bonding between the Tm atoms. We examined the multi-center bond order (MCBO) for the Tm₃ cluster in Tm₃@C₈₀ and Tm₃@C₈₀⁺. The MCBO index between the three Tm atoms in Tm₃@C₈₀ is 0.344, while that in Tm₃@C₈₀⁺ is 0.331, indicating that the three-center bond between Tm atoms in Tm₃@C₈₀ is stronger than that in Tm₃@C₈₀⁺. Both the MCBO indices for the Tm₃ cluster in Tm₃@C₈₀ and Tm₃@C₈₀⁺ are larger than that of the bare Tm₃ cluster (0.294). It should be noted that the average oxidation state of the Tm atom increases from +2 to +7/3 after oxidation of Tm₃@C₈₀. This change leads to a stronger electrostatic repulsion between the Tm ions inside the fullerene cage. In this situation, the cation Tm₃@C₈₀⁺ can still survive because the 3c-2e bonding between the Tm ions significantly compensates for the repulsion effect. As shown in Fig. 6b, the ELF distribution of Tm₃@C₈₀⁺ reveals that there exists three-center bonding between the Tm ions. Fig. 6c shows the molecular orbitals of Tm₃@C₈₀⁺. It can be seen that the molecular orbital HOMO−3 corresponds to a three-center σ bond.

It is known that Tm₃N@C₈₀ is a clusterfullerene with high stability. In this study, we found that both the molecular geometry and the electronic structure of Tm₃@C₈₀⁺ resemble that of Tm₃N@C₈₀. The Tm–Tm distance in Tm₃@C₈₀⁺ (3.511–3.529 Å) is very close to that in Tm₃N@C₈₀ (around 3.55 Å). Meanwhile, the ELF distribution of Tm₃@C₈₀⁺ is also similar to that of Tm₃N@C₈₀ (Fig. 6b). In the case of Tm₃N@C₈₀, the formal charge of the Tm atom is +3, and there is a strong electrostatic repulsion between the Tm³⁺ ions. The central N³⁻ ion serves as a mediator and it reduces the repulsion between the Tm³⁺ ions. In the case of Tm₃@C₈₀⁺, the three-center σ bond plays a similar role to the N³⁻ ion in Tm₃N@C₈₀. As a result, three Tm ions can be accommodated inside the C₈₀ cage without a nonmetal mediator. Therefore, the three-center σ bond is a critical factor that stabilizes the tri-metallofullerene cation. Furthermore, we found that Tm₃@C₈₀⁺ and Tm₃N@C₈₀ have similar Frontier molecular orbitals. The energy diagrams and spatial distributions of the frontier molecular orbitals of Tm₃@C₈₀⁺ and Tm₃N@C₈₀ are shown in Fig. 6c and d. It can be seen that the molecular orbitals including the LUMO, HOMO and HOMO−1 for Tm₃@C₈₀⁺ and Tm₃N@C₈₀ are very similar in shape. Meanwhile, the calculated HOMO–LUMO gap of Tm₃@C₈₀⁺ (1.46 eV) using the PBE functional is close to that of Tm₃N@C₈₀ (1.58 eV). Among all the reported metallofullerenes, M₃N@C₈₀ is a kind of metallofullerenes that have large HOMO–LUMO gaps. DFT calculations in this work reveal that Tm₃@C₈₀⁺ also has a large HOMO–LUMO gap, implying that this cation has high stability. It should be noted that the neutral Tm₃@C₈₀ has a rather small HOMO–LUMO gap (0.28 eV), indicating that it is a chemically reactive molecule. Because Tm₃@C₈₀⁺ has a much larger HOMO–LUMO gap, the chemical stability of Tm₃@C₈₀ can be enhanced greatly upon oxidation. The change in the HOMO–LUMO gap explains the following facts: (1) the neutral Tm₃@C₈₀ is not observed in the extract of raw soot by using conventional fullerene solvents such as toluene and xylene; (2) Tm₃@C₈₀ can be chemically oxidized to a stable cation Tm₃@C₈₀⁺. Besides Tm₃@C₈₀⁺, tri-metallofullerene cations containing other metals such as Er₃@C₈₀⁺ and Dy₃@C₈₀⁺ can also be obtained through a similar oxidation method (Fig. S2†).

4 Conclusions

DFT calculations demonstrated that tri-metallofullerenes Ln₃@C₈₀ are thermodynamically stable molecules. The binding energy of Ln₃@C₈₀ is larger than that of the nitride clusterfullerene Ln₃N@C₈₀, revealing that encapsulation of a Ln₃ cluster in C₈₀ is favorable in energy. DFT calculations also revealed that Ln₃@C₈₀ has the smallest ionization energy among the metallofullerene molecules reported so far. We used AgSbF₆ to oxidize the arc-discharge-produced soot containing Tm₃@C₈₀ and obtained the cation Tm₃@C₈₀⁺. We found that both the molecular geometry and the electronic structure of Tm₃@C₈₀⁺ resemble that of Tm₃N@C₈₀. In particular, both of them have large HOMO–LUMO gaps, implying that Tm₃@C₈₀⁺ has high stability as Tm₃N@C₈₀ does. There is a three-center two-electron σ bond in the center of the Tm₃ cluster in Tm₃@C₈₀⁺. This special metal–metal bond compensates for the electrostatic repulsion between the Tm ions and thus greatly stabilizes the cation Tm₃@C₈₀⁺. The metallofullerene cations Ln₃@C₈₀⁺ can be used as building blocks to construct a variety of novel ionic compounds Ln₃@C₈₀⁺X⁻ in future studies.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We are grateful for the support from the Outstanding Innovative Talents Cultivation Funded Programs 2021 of Renmin University of China, the Beijing Municipal Natural Science Foundation (grant no. 2212030), and the National Natural Science Foundation of China (grant no. 22175199). Resources supporting this work were provided by the Public Computing Cloud Platform of Renmin University of China.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Additional calculation results and molecular coordinates. See DOI: https://doi.org/10.1039/d2qi00051b

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