Organometallic complexes play a crucial role in catalysis, energy and medicine nowadays. Stabilities of organometallic complexes have been commonly determined by Effective Atomic Number (EAN) rule (i.e., 18-electron rule) proposed in the 1920s, that the effective atomic number of the central metal atom surrounded by ligands is numerically equal to the atomic number of the noble-gas element found in the same period as the metal1. EAN rule is based on valence electron count of the central metal atom instead of the non-metal ligand, and is applicable for a majority of organometallic complexes. In particular, metal carbido complexes bearing single-carbon-atom ligand such as the active site of nitrogenase (Fe7MoS9C) provide ideal models of adsorbed carbon atoms in heterogeneous catalysis, and have been attracting enormous interests during the past few decades2,3,4,5,6,7,8,9,10. Unlike the traditional multinuclear organometallic complexes, for metal carbido complexes the single-carbon-atom ligand becomes the center and bonds with 1 to 6 metals, thus the EAN rule is inapplicable due to the complicated coordination nature of the ligands especially the central single-carbon-atom ligand2,3,4,5,6,7,8,9,10. Hence, it is desirable to establish a new rule governing the stabilities of metal carbido complexes. For binuclear metal carbido complexes containing a carbido bridge such as LnM = C = MLn and LnM ≡ C-M’Ln, the central μ2-carbido ligand adopts an eight-electron configuration4,5. However, upon increasing the number of metals coordinated with the central single-carbon-atom ligand to three, the central μ3-carbido ligand does not always follow the eight-electron configuration6,7,8. Furthermore, in the metal carbido complexes bearing μ5- and μ6-carbido ligands, the central carbon atom is regarded as a hypervalency carbon due to the formation of more than four metal-carbon bonds9,10. Therefore, due to the diversity of the coordination numbers of the central single-carbon-atom ligand, it is difficult to establish a general rule for the conventional metal carbido complexes.

As the simplest metal carbido complexes with the ligands being only carbon atoms, trimetallic μ3-carbido clusterfullerenes (μ3-CCFs) featuring confinement of a single-carbon-atom ligand within carbon cage was found in 2014 (ref. 11). Due to electron transfer from the encapsulated metal carbido cluster to the outer carbon cage, μ3-CCFs exhibit intriguing electronic properties and promising applications in spintronics and high-density storage devices inaccessible by the conventional metal carbido complexes11,12,13,14,15,16,17,18,19. TiLu2C@Ih(7)-C80 is the first μ3-CCF isolated in 2014, in which a Ti=C double bond was identified by single-crystal X-ray diffraction11. Later on, a few Ti-based μ3-CCFs were isolated, including TiM2C@Ih(7)-C80 (M = Sc, Y, Nd, Gd, Tb, Dy, Er)11,12,13,14,15,16, TiM2C@D5h(6)-C80 (M = Sc, Dy)12,13, and TiSc2C@C78 (ref. 13), among which only TiSc2C@Ih(7)-C80, TiDy2C@Ih(7)-C80 and TiTb2C@Ih(7)-C80 were crystallographically determined. More recently, another non-rare earth (non-RE) metal, the actinide metal uranium (U), was also reported to form μ3-CCF USc2C@Ih(7)-C80, in which the U metal exhibits a formal valence state of +4 and bonds with the central μ3-carbido ligand via a U = C double bond as well17,18. Different to the well-known trimetallic nitride clusterfullerenes (NCFs) M3N@C2n bearing primarily RE metals with +3 valence states (M3+) and M-N single bonds20,21, in μ3-CCFs the valence state of the non-RE metal changes to +4 as the result of formation of M = C (M = Ti, U) double bond, while the RE metals keep the +3 valence states and M-N single bonds11,12,13,14,15,16,17,18,19. Hence, μ3-CCFs offer a unique platform stabilizing μ3-carbido ligand which bonds with metals via multiple bonds. Although a number of μ3-CCFs have been isolated, only few were crystallographically characterized, and the reported non-RE metals within μ3-CCFs are quite limited to Ti and U. This limitation is because the formation prerequisite of μ3-CCF is unclear. Therefore, it is highly desired to explore new μ3-CCFs based on other non-RE metals and to establish a general rule elucidating stabilization of the μ3-carbido ligand within it.

Herein, we synthesized and isolated three vanadium(V)-based μ3-CCFs, including VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, among them the latter two represent the first crystallographically determined non-Ih-symmetry μ3-CCFs. The common feature of their molecular structures is the existence of V = C double bond along with Sc-C single bonds. Their electronic structures were investigated by density functional theory (DFT) calculations, unraveling high valence state of V (+4). Combining all reported sixteen μ3-CCFs, we further carried out a systematic DFT study on their stabilities, and proposed a supplemental Octet Rule based on valence electron count of the central ligand to account for stabilization of the metal carbido cluster within μ3-CCF. This rule is also applicable for NCF VSc2N@C80 and the conventional binuclear metal carbido complexes containing a carbido bridge such as LnM = C=MLn and LnM ≡ C-M’Ln, thus offers a general rule determining the stabilities of μ3-CCFs and guides the exploration of μ3-CCFs or even other metal carbido complexes.


Syntheses and Isolation of VSc2C@C80 (I, II) and VSc2C@C78

V-based μ3-CCFs, including two isomers of VSc2C@C80 (labeled as I, II) and VSc2C@C78 were synthesized by Krätschmer-Huffman direct current (DC) arc discharge method19. Graphite rods packed with a mixture of Sc2O3, VC and graphite powder with a molar ratio of 0.5:1:15 were vaporized in the arcing chamber under a 200 mbar helium atmosphere. The obtained soot was then extracted with carbon disulfide (CS2), followed by four-step high-performance liquid chromatography (HPLC) isolations supplemented by laser desorption time-of-flight mass spectroscopic (LD-TOF MS) analysis. In the first step, fractions A and B both contain the same MS signal peak at M/Z = 1113 (Supplementary Fig. 1 and Table 1), which is assigned to VSc2C@C80. Since the retention times of fractions A and B are quite different, the two VSc2C@C80 molecules detected in these two fractions are isomers with different cage isomeric structures. The first isomer VSc2C@C80 (I) has been isolated from fraction A and identified as VSc2C@Ih(7)-C80 very recently (Supplementary Fig. 2)19, therefore the second isomer isolated from fractions B after four-step HPLC separation is labeled as VSc2C@C80 (II) (Supplementary Fig. 3). Besides, another V-μ3-CCF with a MS signal peak at M/Z = 1089 is also isolated from fraction C (Supplementary Fig. 4), which is assigned to VSc2C@C78.

The high purities of the isolated VSc2C@C80 (II) and VSc2C@C78 are verified by the single peaks observed by HPLC (Fig. 1a) and single mass peaks in their LD-TOF MS spectra (Fig. 1b). Furthermore, the isotopic distributions of VSc2C@C80 (II) and VSc2C@C78 agree well with the calculated ones, confirming their proposed chemical formulae. Interestingly, the analogous V-based μ3-CCF V2ScC@C80 and Sc-only μ3-CCF Sc3C@C80 are not detected, and this phenomenon is distinctly different from the case of the reported V-based NCFs for which both VSc2N@C80 and V2ScN@C80 were synthesized along with Sc3N@C8022,23. The difference between V-based μ3-CCFs and NCFs suggests the unique formation prerequisite of μ3-CCF as discussed in details below.

Fig. 1: The purity examination of VSc2C@C80 (II) and VSc2C@C78.
figure 1

a HPLC chromatograms and b LD-TOF mass spectra of VSc2C@C80 (II) and VSc2C@C78. (column: Buckyprep, eluent: toluene, flow rate: 5 mL.min−1, injection volume: 5 mL, temperature: 40 °C).

X-ray crystallographic structures of VSc2C@D 5h(6)-C80 and VSc2C@D 3h(5)-C78

To determine the molecular structures of VSc2C@C80 (II) and VSc2C@C78, we used decapyrrylcorannulene (DPC) as a host to co-crystallize them24,25,26,27,28. Black single co-crystals were both obtained and used for single-crystal X-ray diffraction study, accomplishing unambiguous determination of their molecular structures as VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 (see Supplementary Tables 24 for the detailed crystallographic data and discussion). Figure 2a, b exhibit the molecular structures of these two μ3-CCFs together with DPC molecules within VSc2C@D5h(6)-C80·2(DPC)·4(C7H8) and VSc2C2@D3h(5)-C78·2(DPC)·4(C7H8) co-crystals, revealing that the DPC molecules adopt V-shape configuration and embrace two fullerene molecules. Such a stoichiometric ratio of 1:2 is quite different from the 1:1 ratio in the co-crystals of endohedral fullerenes with the commonly used NiII(OEP) (OEP = octaethylporphyrin) host, suggesting their difference in host-guest interactions29,30,31,32,33. To date, all crystallographically determined μ3-CCFs, including TiM2C@Ih(7)-C80 (M = Sc13, Tb14, Dy16, Lu11), USc2C@Ih(7)-C80 (ref. 18), and VSc2C@Ih(7)-C80 (ref. 19), are based on Ih(7)-C80 cage. Although non-Ih-symmetry cages such as TiSc2C@D5h(6)-C80, TiDy2C@D5h(6)-C80 and TiSc2C@D3h(5)-C78 have been isolated, none of them were crystallographically characterized12,13. Therefore, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 represent the first non-Ih-symmetry μ3-CCFs with the molecular structures unambiguously determined by X-ray crystallography.

Fig. 2: X-ray structures of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78.
figure 2

Drawings of the crystallographically determined structures of VSc2C@D5h(6)-C80·2(DPC) (a) and VSc2C@D3h(5)-C78·2(DPC) (b). The positions of the major cluster sites with respect to the nearest carbon atoms of cage within VSc2C@D5h(6)-C80 (c) and VSc2C@D3h(5)-C78 (d). Only one orientation of the fullerene cage together with the major site of VSc2C cluster is given for clarity. Solvent molecules, the minor cage and minor metal positions are omitted for clarity. Gray: C; Blue: Sc; Green: V; Pink: N.

The fullerene cages of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are disordered in two orientations. Similar to the cases of VSc2C@Ih(7)-C80 and other EMFs19,34, the encapsulated V/Sc atoms within VSc2C cluster exhibit obvious disorders due to the thermal vibration, whereas the central carbon atoms are fully ordered. Although the encapsulated VSc2C clusters within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are both disordered in four orientations, V and Sc atoms can be distinguished according to a comparison of the R1/wR2 values obtained from different conformations of the encapsulated VSc2C cluster combined with DFT calculations (see Supplementary Tables 5, 6 and Figs. 5–7 for details). Close-up views of the molecular structures of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 with only major orientation of the fullerene cage and the major site of VSc2C cluster are shown in Fig. 2c, d and Supplementary Fig. 8. For VSc2C@D5h(6)-C80, the V atom lies at the pentagon-hexagon conjunction, while the two Sc atoms are beneath the pentagon-hexagon-hexagon conjunctions. Upon decreasing the cage size to D3h(5)-C78, V atom is beneath the hexagon-hexagon-hexagon conjunction and two Sc atoms both reside under the center of hexagon. Despite of the difference on the locations of metal atoms, the VSc2C clusters within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 both keep the planar triangle geometry since the sum of metal-carbon-metal angles is close to 360°. This feature resembles those of VSc2C@Ih(7)-C80 (ref. 19) and other crystallographically determined MSc2C@Ih(7)-C80 (M = Ti13, U18) μ3-CCFs.

The crystallographic characterizations of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 facilitate analyses of V-C and Sc-C bonding natures. As illustrated in Fig. 2c,d, the lengths of V-C bond within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are 1.885(6) Å and 1.867(8) Å, respectively, which are comparable to that within VSc2C@Ih(7)-C80 (1.877(5) Å)19 and thus can be assigned to V = C double bond. Interestingly, this feature differs from those of VSc2N@Ih(7)-C80 and VSc2N@D5h(6)-C80 NCFs in which V-N single bonds exist instead22,23. On the other hand, the lengths of Sc-C bonds in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are respectively 2.078(6)/2.186(5) Å and 2.054(10)/2.055(9) Å (Supplementary Table 7), which are very close to those observed in MSc2C@Ih(7)-C80 (M = V19, Ti13, U18), indicating that the two Sc–C bonds are single bonds. Notably, the metal-to-carbon distances in VSc2C@D5h(6)-C80 and VSc2C@Ih(7)-C80 are all slightly larger than that in VSc2C@D3h(5)-C78, suggesting stretching of VSc2C cluster along with the cage expansion from C78 to C80. The V-C and Sc-C bonding features observed in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 as well as VSc2C@Ih(7)-C80 highly resemble those in the reported μ3-CCFs TiM2C@Ih(7)-C80 (M = Sc13, Tb14, Dy16, Lu11) and USc2C@Ih(7)-C80 (ref. 18), indicating the considerable structural similarity among μ3-CCFs in terms of the existence of one double bond between the non-RE metal and the central carbon atom along with two RE metal-C single bonds. This stimulates us to propose a stabilization mechanism of μ3-CCF as discussed below.

DFT calculations of electronic configurations of VSc2C@D 5h(6)-C80 and VSc2C@D 3h(5)-C78

To investigate the electronic structures of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 including the valence states of the encapsulated V atom and the interaction between V and C atoms, we carried out DFT calculations with the Vienna Ab-initio Simulation Package (VASP) at generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) levels35. According to DFT optimized molecular structures (Supplementary Fig. 9), the V-C bond lengths within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are 1.850 Å and 1.810 Å, respectively, while the Sc-C distances are 2.15/2.15 Å and 2.20/2.22 Å. These theoretical predictions agree well with the crystallographical results discussed above. To explore electronic structures of the VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, we calculated the spin-resolved molecular levels and plot the spatial distributions of several frontier molecular orbitals (Supplementary Fig. 10). It is clear that two molecules possess the spin-polarized ground states. Most frontier molecular orbitals are delocalized on the whole carbon cages, while there are also some localized molecular orbitals, mainly contributed by the inner VSc2C cluster. For example, for the spin-up electrons, the single occupied molecular orbitals (SOMO-1) of VSc2C@D5h(6)-C80 and SOMO-3 of VSc2C@D3h(5)-C78 mainly localized around the V atom, according to the percentage of the V occupations in the majority-orbital composition. These results imply that there is one unpaired electron for V atom in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, leading to the doublet ground states. The total magnetic moments of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 are predicted to be about 1.02 and 0.98 µB, respectively. Figure 3a illustrates the spin-density spatial distributions of two molecules. Clearly, the spin-density mainly localized around the V atom, indicating that the V atom contributes mainly to the total magnetic moment. The atomic magnetic moment of V atom is about 1.15 and 1.05 µB in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, respectively. Note that, in these two molecules the V atom antiferromagnetically couples with the neighboring C atom. The calculated partial density of states (DOS) for the V atom’s spin-split d orbitals of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 display different distributions for the majority and minority electrons (Supplementary Fig. 11). The molecular magnetic moments with one unpaired electron are mainly contributed by the \({3d}_{{z}^{2}}\) orbitals of the V atom. At the same time, the \({3d}_{{xy}}\) and \({3d}_{{yz}}\) orbitals give the non-negligible contributions to total magnetic moments of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, respectively. The electron configuration of the V atom is [Ar]3d34s2, and one unpaired electron means the loss of four valence electrons from the V atom, resulting in a valence state of V4+ within both μ3-CCFs.

Fig. 3: Electronic structures and relative total energies of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78.
figure 3

a Spin density distribution of VSc2C@D5h(6)-C80 (left) and VSc2C@D3h(5)-C78 (right) with an isovalue of 0.002. Yellow: V; Pink: Sc; Blue: C. b Schematic diagram for electronic localized functions (ELF) maps of VSc2C@D5h(6)-C80 (left) and VSc2C@D3h(5)-C78 (right) acting on the plane of the entrapped clusters. Red: V; Pink: Sc; Gray: C. c The relative total energies (ΔE, eV) of MSc2C@C2n (M = V, Ti, U, 2n = 78, 80) μ3-CCFs with different electronic configurations of MSc2C cluster.

The V-C bonding type within VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 can be analyzed by the electronic localized function (ELF) maps, shown in Fig. 3b. Obviously, the interactions between V and C atoms are similar for two molecules. The visible electronic distributions are found on V atom, implying covalent interactions between V and C atoms. This is similar to the case of VSc2C@Ih(7)-C80 (ref. 19). Note that the electronic distribution on the V atom in VSc2C@D5h(6)-C80 is slightly less than that in VSc2C@D3h(5)-C78. This observation is consistent with their difference on the predicted V-C distances (1.850 and 1.810 Å in VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, respectively). The different electronic distributions in these two molecules can be understood by the analysis of the Bader charges, since the electronic transfer from the V atom to the outer cage within VSc2C@D5h(6)-C80 (1.33 e) is larger than that within VSc2C@D3h(5)-C78 (1.30 e). Combining the analyses of the spin density, the frontier molecular orbitals, partial density of states, and ELF maps, a + 4 formal valence state of the encapsulated V and covalent interactions for V = C double bonds are revealed for both VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 μ3-CCFs. Noteworthy, The proposed V4+ configuration within VSc2C@Ih(7)-C80 and VSc2C@D5h(6)-C80 μ3-C-CFs is obviously different to the V3+ state within the reported VSc2N@Ih(7)-C80 and VSc2N@D5h(6)-C80 NCFs22,23. Hence, the valence state of V can be steered via simply altering the non-metal atom within the encapsulated metal cluster.

Supplemental Octet Rule for μ3-carbido ligand in μ3-CCFs

Due to the multihapto nature of the carbon cage, EAN rule is inapplicable for μ3-CCFs. To understand the peculiar formation of the μ3-carbido ligand in μ3-CCFs, we carried out a systematic DFT study on the stabilities of VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 with different electronic configurations based on M = C/M-C bonds with M4+/M3+ valence states, combined with those of the reported MSc2C@Ih(7)-C80 (M=Ti, U) μ3-CCFs as the representative members based on other non-rare earth metals of Ti, U. As seen from Fig. 3c, clearly [V4+(Sc3+)2C4-]6+@[Ih(7)-C80]6-, [V4+(Sc3+)2C4-]6+@[D5h(6)-C80]6- and [V4+(Sc3+)2C4-]6+@[D3h(5)-C78]6- based on M4+ = C4- double bond are the most stable configurations with the lowest total energies (see also Supplementary Table 8). Altering the M4+ = C4- double bond to M4+-C4- single bond/M3+ = C3- double bond/M3+-C3- single bond results in increased total energies and consequently less stable configurations. Similar results are obtained for MSc2C@Ih(7)-C80 (M = Ti, U) μ3-CCFs. Therefore, for MSc2C@C2n (M = V, Ti, U; 2n = 80, 78) μ3-CCFs, M4+/Sc3+ cations and the central C4− anion are needed, affording one M = C double bond along with two Sc-C single bonds. The entire MSc2C cluster then transfers six electrons to the outer fullerene cage, enabling stable μ3-CCF molecule. In this way, the central C4- anion exhibits an eight-electron configuration. So far, there are sixteen μ3-CCFs in total have been reported, we further calculated the relative energies of the other eleven μ3-CCFs with different configurations. We find that, similar to the cases of MSc2C@C2n (M = V, Ti, U, 2n = 78, 80), the configuration bearing a central carbon with an eight-electron configuration is the most stable structure for all μ3-CCFs (Supplementary Table 9). Based on these results, we propose a supplemental Octet Rule, that the central μ3-carbido ligand prefers to have eight electrons in the valence shell so as to be stabilized in μ3-CCF. In fact, the classic Octet Rule proposed by Lewis in 1916 has been commonly used for covalent compounds36,37, but never been used for metal carbido complexes. In this work, we manage to extend it to μ3-CCFs as a special type of metal carbido complexes, and succeed in interpreting the peculiar formation of the μ3-carbido ligand within μ3-CCFs. Noteworthy, this supplemental Octet Rule is also applicable for the conventional binuclear metal carbido complexes containing a carbido bridge such as LnM = C = MLn and LnM ≡ C-M’Ln, but it is not always valid for μ3-carbido ligand within the conventional trinuclear metal carbido complexes4,5,6,7,8. Furtheromore, in the metal carbido complexes bearing μ5- and μ6-carbido ligands, this Rule is not applicable any more because the central carbon atom is coordinated with more than four metals and thus is a hypervalency carbon9,10. For the well-known metal carbido complex Fe7MoS9C as the active site of nitrogenase, although a central C4- anion also exists, it violates the supplemental Octet Rule because the central C4- anion bonds with six iron atoms to form a Fe6C core2,38.

According to this supplemental Octet Rule, the necessity of involving a four-valency non-RE metal for the formation of MSc2C@C2n μ3-CCFs can be easily understood, since a M4+ cation is demanded to accomplish M = C double bond whereas +4 valence state is generally not preferable for the RE metals39. This also accounts for the absence of Sc-only μ3-CCF Sc3C@C80 under our synthesis condition, which is theoretically predicted very recently as an unstable free radical with one unpaired electron on the cage derived from the formal five-electron transfer40, since Sc4+ cation is hardly accessible. Interestingly, once the one deficient electron in the outer cage of unstable Sc3C@C80 is compensated by encapsulating one hydrogen atom, Sc3CH@C80 with an electronic configuration of [(Sc3+)3C4-H+]6+@[C80]6- forms and the supplemental Octet Rule is also satisfied for the central C4- anion41,42. Likewise, V2ScC@C80 based on two V4+ cations would violate the Octet Rule and thus seems also impossible. Therefore, this supplemental Octet Rule may be used as a simple guide for design of μ3-CCFs, offering opportunity to encapsulate other non-rare earth metals into fullerene cage.

It is intriguing to examine the applicability of this supplemental Octet Rule in other types of clusterfullerenes. VSc2N@Ih(7)-C80 NCF as an analogous V-containing trimetallic clusterfullerene is considered. Interestingly, upon changing the central non-metal atom from carbon to nitrogen, [V3+(Sc3+)2N3-]6+@[Ih(7)-C80]6- based on V3+-N3- single bond becomes the most stable configuration (see Supplementary Table 10), as experimentally confirmed22. Since N atom has five valence electrons, upon formation of VSc2N@Ih(7)-C80 NCF, V3+/Sc3+ cations along with three V-N/Sc-N single bonds exist, rendering an eight-electron configuration for the central N3- anion as well. Therefore, this supplemental Octet Rule is also applicable for NCF.

Electronic properties of VSc2C@D 5h(6)-C80 and VSc2C@D 3h(5)-C78

In order to probe the effect of the central nonmetal atom (C/N) on the electronic properties of μ3-CCF and NCF, we carried out UV-vis-NIR spectroscopic and electrochemical characterizations. Figure 4a compares the UV-vis−NIR absorption spectra of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 dissolved in toluene (see Supplementary Fig. 12 and Table 11 for their characteristic absorption data along with analogous μ3-CCFs and NCFs). VSc2C@D5h(6)-C80 exhibits a broad absorption peak at 447 nm and a minor shoulder peak at 383 nm, and the overall spectral feature looks similar to that of VSc2N@D5h(6)-C80 but quite different from that of VSc2C@Ih(7)-C8022,23. This is understandable since the outer fullerene cages of VSc2C@D5h(6)-C80 and VSc2N@D5h(6)-C80 are same while π − π* transitions of the fullerene cage predominantly determines the electronic absorptions of EMFs34. For VSc2C@D3h(5)-C78, two intense absorption peaks at 462 and 581 nm are observed, resembling Sc3N@D3h(5)-C78 despite of some shifts of the absorption peaks due to the discrepancy on the encapsulated cluster. According to the absorption spectral onsets of 1490 and 1430 nm for VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, their optical bandgaps (ΔEgap, optical) are determined to be 0.83 and 0.87 eV, respectively, which are comparable to that of VSc2C@Ih(7)-C80 (0.88 eV)19.

Fig. 4: Electronic properties of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78.
figure 4

a UV-vis−NIR spectra of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 dissolved in toluene. Insets: Photographs of their corresponding solutions in toluene. b Cyclic voltammograms of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 in o-DCB solution with ferrocene (Fc) as the internal standard under different scan regions. Scan rate: 100 mV/s, TBAPF6 as supporting electrolyte. The half-wave potentials (E1/2) of each redox step are marked with a solid dot to aid comparison. The asterisk labels the oxidation and reduction peaks of ferrocene.

Although few D5h(6)-C80- and D3h(5)-C78-based μ3-CCFs like TiSc2C@D5h(6)-C80, TiDy2C@D5h(6)-C80 and TiSc2C@D3h(5)-C78 were isolated before, their electrochemical properties have never been investigated yet. Figure 4b presents cyclic voltammograms of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 measured in o-dichlorobenzene (o-DCB) with tetrabutylammonium hexafluorophosphate (TBAPF6) as supporting electrolyte (see Supplementary Fig. 13 for cyclic voltammograms in different scanning regions), and their characteristic redox potentials along with the analogous NCFs are summarized in Supplementary Table 12. For VSc2C@D3h(5)-C78, two reversible oxidation steps with half-wave potentials (E1/2) at 0.14 and 0.69 V in the anodic region are observed, and the first oxidation potential is more negative than that measured for Sc3N@D3h(5)-C78 while the second one is close to that of Sc3N@D3h(5)-C78 (ref. 40). In the cathodic region, VSc2C@D3h(5)-C78 shows quite different reductive behavior compared to Sc3N@D3h(5)-C78 in terms of number of the reduction steps: VSc2C@D3h(5)-C78 exhibits two irreversible reduction steps and two reversible reduction steps, while there are only two irreversible reduction steps for Sc3N@D3h(5)-C78 (ref. 43). In particular, the first reduction potential (redE1) of VSc2C@D3h(5)-C78 is positively shifted by 650 mV relative to that of Sc3N@D3h(5)-C78. The more positive redE1 and more negative first oxidation potential (oxE1) of VSc2C@D3h(5)-C78 result in a much smaller electrochemical gap (1.05 eV) than that of Sc3N@D3h(5)-C78 (1.77 eV). Similar phenomenon is observed for VSc2C@D5h(6)-C80, which exhibits two reversible oxidation steps with E1/2 at 0.30 and 0.66 V and three reversible reduction steps with E1/2 at −0.70, −1.31, and −2.16 V. The oxE1 and oxE2 values are both more negative than those of VSc2C@Ih(7)-C80 and VSc2N@D5h(6)-C80. In addition, the reductive behavior of VSc2C@D5h(6)-C80 is more different with VSc2N@D5h(6)-C80 which shows four reversible reduction steps instead, and the electrochemical gap of VSc2C@D5h(6)-C80 (1.00 eV) is smaller than that of VSc2N@D5h(6)-C80 (1.20 eV)23. Therefore, the encapsulated cluster especially the central nonmetal atom affects sensitively the electronic properties of the trimetallic clusterfullerene.


In summary, three V-based μ3-CCFs, namely VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78, are successfully synthesized and isolated, among them the latter two represent the first crystallographically determined non-Ih-symmetry μ3-CCFs. Their molecular structures are determined unambiguously by single-crystal X-ray diffraction, revealing the existence of V = C double bonds and high valence state of V (+4). This differs from those of VSc2N@Ih(7)-C80 and VSc2N@D5h(6)-C80 NCFs in which V-N single bonds and V3+ valence state exist. The encapsulated cluster especially the central nonmetal atom affects sensitively the electronic properties of μ3-CCF and NCF trimetallic clusterfullerenes. On the basis of a systematic DFT study on the stabilities of all reported sixteen μ3-CCFs, a supplemental Octet Rule is proposed, that the central μ3-carbido ligand prefers to have eight electrons in the valence shell so as to be stabilized in μ3-CCF. The applicability of this supplemental Octet Rule in other types of clusterfullerenes is exemplified by VSc2N@Ih(7)-C80 NCF. By applying the classic Octet Rule to μ3-CCFs as the simplest metal carbido complexes, we establish a rule beyond the EAN rule commonly used during the past century, offering new insight into the stability criteria of multinuclear clusterfullerenes containing single-atom-ligand.


Synthesis and isolation of VSc2C@I h(7)-C80, VSc2C@D 5h(6)-C80 and VSc2C@D 3h(5)-C78

VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 were synthesized in a Krätschmer-Huffman generator by vaporizing composite graphite rods containing a mixture of Sc2O3, VC and graphite powder (the molar ratio of Sc:V:C = 1:1:15) as the raw material with the addition of 200 mbar He. The produced soot was collected and Soxhlet-extracted by CS2 for 24 h. The resulting brown-yellow solution was distilled to remove CS2, and then immediately redissolved in toluene and subsequently passed through a 0.2 μm Telflon filter (Sartorius AG, Germany) for HPLC separation. I VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 were isolated by three/four-step HPLC (LC-9104, Japan Analytical Industry) as described in details in Supplementary Figs. 14. The relative abundance of the products is shown in the Supplementary Table 1. The purity of the isolated VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 were checked by HPLC and LD-TOF MS (Biflex III, Bruker Daltonics Inc., Germany).

Spectroscopic and electrochemical study

UV-vis−NIR spectra of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 dissolved in toluene were recorded on a UV−vis−NIR 3600 spectrometer (Shimadzu, Japan) using a quartz cell of 1 mm layer thickness and 1 nm resolution. Electrochemical study of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 were performed in o-dichlorobenzene (o-DCB, anhydrous, 99%, Aldrich). The supporting electrolyte was tetrabutylamonium hexafluorophosphate (TBAPF6, puriss. electrochemical grade, Fluka) which was dried under pressure at 340 K for 24 h and stored in glovebox prior to use. Cyclic voltammogram experiments were performed with a CHI 660D potentiostat (CHI Instrument, USA) at room temperature. A standard three-electrode arrangement of a platinum (Pt) disc as working electrode, a platinum wire as counter electrode, and a silver wire as an auxiliary electrode was used. In a comparison experiment, ferrocene (Fc) was added as the internal standard and all potentials are referred to Fc/Fc+ couple.

X-ray crystallographic study

Crystal growths of VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78 were accomplished by slow evaporation from mixed solutions of purified sample and DPC in toluene, and small black crystals suitable for X-ray crystallographic study were obtained after two weeks. The crystallographic characterization was performed in beamline station BL17B at Shanghai Synchrotron Radiation Facility. The structure was refined using all data (based on F2) by SHELXL 2015 (ref. 44) within OLEX2 (ref. 45). A summary of the crystallographic data is listed in Supplementary Table 2. The ORTEP-style illustration with probability ellipsoids and notes on CheckCif file B-level alerts are shown in Supplementary Fig. 14 and Supplementary Table 13.


In our calculations, the geometrical structures and electronic properties were explored by performing spin-polarized density functional theory (DFT) methods implemented in the Vienna Ab-initio Simulation Package (VASP). The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form was adopted to describe the exchange and correlation energy35. The energy cutoff of 400 eV was selected for the plane wave expansion and an automatic k-point mesh (1 × 1 × 1) was generated with a Gamma-centered grid.