Spherical trihedral metallo-borospherenes

The discovery of borospherenes unveiled the capacity of boron to form fullerene-like cage structures. While fullerenes are known to entrap metal atoms to form endohedral metallofullerenes, few metal atoms have been observed to be part of the fullerene cages. Here we report the observation of a class of remarkable metallo-borospherenes, where metal atoms are integral parts of the cage surface. We have produced La3B18– and Tb3B18– and probed their structures and bonding using photoelectron spectroscopy and theoretical calculations. Global minimum searches revealed that the most stable structures of Ln3B18– are hollow cages with D3h symmetry. The B18-framework in the Ln3B18– cages can be viewed as consisting of two triangular B6 motifs connected by three B2 units, forming three shared B10 rings which are coordinated to the three Ln atoms on the cage surface. These metallo-borospherenes represent a new class of unusual geometry that has not been observed in chemistry heretofore.

T he electron deficiency of boron often leads to electron delocalization and the violation of the octet rule in boron compounds and three-dimensional (3D) cage units in different bulk boron allotropes [1][2][3] . Because of the strong boron-boron bonding, there were speculations about the formation of boron nanotubes composed of a triangular boron lattice 4,5 , after the discovery of carbon nanotubes. The triangular boron lattice can be viewed as a graphene-like sheet with the filling of a boron atom in each B 6 hexagon. Further theoretical calculations revealed, however, that triangular lattices with hexagonal vacancies were more stable and more suitable to construct boron nanotubes 6,7 . In the meantime, combined spectroscopic and theoretical studies have shown that size-selected boron clusters all have 2D structures with delocalized multi-center bonding within the cluster plane [8][9][10][11] . The discovery of the hexagonal 2D B 36 clusters provided the first experimental evidence of the viability of atom-thin boron nanostructures with hexagonal vacancies, named as borophene akin to graphene 12 . Borophenes have been recently synthesized using atomic vapor deposition on Ag(111) substrates 13,14 , forming a new class of synthetic 2D nanomaterials 15 . The analogy between nanostructures made of boron and carbon has been further extended when the B 40 and B 39clusters were found to have global minimum cage structures 16,17 , i.e. borospherenes analogous to the fullerenes. Fullerenes are known to form endohedral metallofullerenes for alkali, alkali earth, lanthanide, and actinide elements 18,19 , albeit not for transitions metals. Heterofullerenes in which one carbon atom is substituted by a transition metal atom have been observed in the gas phase, but the metal substitution induces large local structural distortions and such heterofullerenes have not been synthesized in the bulk [20][21][22] . The first cage cluster made of multiple metal atoms and carbons was proposed to be Ti 8 C 12 + (metallocarbohedrene) 23 . However, subsequent theoretical calculations showed that the metallocarbohedrene is not stable and the global minimum of Ti 8 C 12 + consisted of a tetrahedral, closepacked Ti 8 clusters coordinated by six C 2 units on the cluster surface 24 . In the present article, we report the first observation of a class of metallo-borospherenes, hollow cage clusters consisting of three lanthanide (Ln) atoms and 18 boron atoms (Ln 3 B 18 -).
Transition-metal-doped boron clusters were first found to form aromatic borometallic molecular wheels, M©B n − (n = 8-10) 25,26 , as well as metal-centered nanotubular structures 27 . More interestingly, it has been shown that transition metals can be an integral part of larger 2D boron clusters 28 , leading to the possibility of metallo-borophenes 29 . Lanthanide-doped boron clusters, however, have been found recently to form very different structures, due to both charge transfer interactions and strong (d-p)π bonding 30 . For example, lanthanide-doped boron clusters do not form similar borometallic molecular wheels as the transition metals. Instead, they form inverse-sandwich-type structures for Ln 2 B nclusters (n = 7-9) 31,32 . The most recent study indicates that the inverse-sandwich structure may extend to form lanthanide-boron nanowires 33 .
Here we report a joint photoelectron spectroscopy (PES) and quantum chemistry study of two tri-lanthanide-doped B 18 clusters (La 3 B 18and Tb 3 B 18 -), which are found to possess unprecedented D 3h cage structures with the Ln atoms being integral parts of the cage surface. These D 3h metallo-borospherenes belong to an unusual class of geometry known as spherical trihedron. The B 18 framework consists of two B 6 triangles connected by three B 2 units, forming three shared B 10 rings. The high stability of the spherical trihedral structures is derived from the strong interactions between the Ln atoms and the B 10 rings via charge transfer interactions and d-p covalent bonding. Theoretical calculations show that the entire series of lanthanide elements (Ln = La-Lu) can form spherical trihedral Ln 3 B 18 -metallo-borospherenes with tunable magnetic properties, making them a fascinating series of building blocks for new types of magnetic materials.

Results and discussion
Photoelectron spectroscopy. The PE spectrum at 193 nm was first measured for the La 3 B 18cluster (Fig. 1a), which was found to exhibit a relatively simple pattern compared with that of the recently reported La 3 B 14cluster 33 . This observation suggested that La 3 B 18should possess a highly symmetric structure. Subsequently, we also obtained the spectrum of a late-Ln cluster Tb 3 B 18 - (Fig. 2a) and observed a spectral pattern, exhibiting some similarities to that of La 3 B 18and suggesting that these two Lndoped boron clusters should have similar structures and chemical bonding. The well-resolved PES features of the Ln 3 B 18clusters serve as electronic fingerprints to allow analyses of their structures and chemical bonding by comparing with theoretical calculations, as shown in Figs. 1b, 2b, and Supplementary Tables S1 and S2 for Ln = La and Tb, respectively.
The spectrum of La 3 B 18displayed five well-resolved bands labeled as X, A, B, C, and D (Fig. 1a). The X band yielded the first vertical detachment energy (VDE) of 2.97 eV for La 3 B 18 -. The adiabatic detachment energy (ADE) for band X was evaluated from its onset to be 2.80 eV, which also represents the electron affinity (EA) of neutral La 3 B 18 . The higher binding energy bands (A, B, C, and D) correspond to detachment transitions to the excited states of neutral La 3 B 18 . The A band at 3.64 eV was broad and not well resolved at 193 nm, but it was slightly better resolved in the 266 nm spectrum ( Supplementary Fig. 1). This broad spectral feature could be due to geometry changes upon electron detachment or overlapping detachment transitions. Band B at 4.01 eV is sharper compared with band A (Fig. 1a). An intense and sharp band C at 4.43 eV was clearly resolved in the 193 nm ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-16532-x spectrum. Following a large energy gap, a broad band (D) was observed above~5.5 eV. Due to the poor signal-to-noise ratio, band D was tentatively assigned for the sake of discussion. The PE spectrum of Tb 3 B 18showed five well-resolved peaks assigned as X, A, B, C, D (Fig. 2a). The X band gave rise to a VDE of 3.26 eV for Tb 3 B 18and an ADE of 3.13 eV, which is also the EA of neutral Tb 3 B 18 . Band A was observed at a VDE of 3.84 eV, followed by three closely-lying bands (B, C, D). Band B at 4.28 eV and band C at 4.52 eV were relatively weak and closely spaced, whereas band D at 4.77 eV was much more intense. Beyond 5 eV, the signal-to-noise ratio was poor and no obvious spectral bands were observed. Band E close to the threshold at a VDE of 6.2 eV was tentatively labeled. The overall spectral pattern for Tb 3 B 18exhibits some similarity to that of La 3 B 18 -. In particular, the strong X and D bands in Tb 3 B 18are similar to the strong X and C bands in La 3 B 18 -. There is a large energy gap on the high binding energy side in both spectra. Similar spectral patterns could be an indication of similar structures, as have been observed for a series of dilanthanide clusters (Ln 2 B 8 -) 31 .
Global minimum structural searches. The low-lying isomers within 55 kcal mol −1 of the global minimum at the levels of PBE/ TZP and PBE0/TZP are presented in Supplementary Fig. 2. The global minimum of La 3 B 18is a hollow cage with a closed-shell ground state ( 1 A 1 ) and D 3h symmetry. This is a hetero-metalloborospherene, in which the three La atoms are integral parts of the cage surface, as shown in Fig. 3. All the other low-lying isomers are low-symmetry 3D structures, many of which are distorted cages. The highly symmetric global minimum D 3h metalloborospherene exhibits overwhelming stability relative to the other low-lying isomers: it is more stable than the nearest isomer with C s symmetry by~19 kcal mol −1 at the PBE/TZP and PBE0/TZP levels of theory. The B 18 framework in the La 3 B 18cage can be viewed as consisting of two B 6 triangles linked together at their three corners by three B 2 units, creating three shared B 10 rings along the C 3 axis. The three La atoms are coordinated by the three B 10 rings, giving rise to the closed cage structure. The La 3 B 18metallo-borospherene has an oblate shape with a diameter of 4.62 Å along the C 3 axis (between the two B 6 triangles) and 5.09 Å encompassed by the three equatorial La atoms. The relevant bond lengths of the La 3 B 18metallo-borospherene are shown in Supplementary Fig. 3a.
The hollow cage structure of La 3 B 18was totally unexpected and the geometry is highly unusual. To further examine its stability and robustness, we performed ab initio molecular dynamics (AIMD) simulations at different temperatures, 300, 500, 700, and 1000 K (see Supplementary Fig. 4). We found that even at 1000 K the La 3 B 18metallo-borospherene is dynamically stable for the 13 ps duration of the simulations. At 1000 K, the structure displayed a root-mean-square-deviation of 0.199 Å and a maximum bond length deviation of 0.260 Å during the simulations.
The similarity in their PE spectra suggested that the global minima of Tb 3 B 18and La 3 B 18should be similar. Because of the localized and nonbonding nature of the 4f orbitals in Tb, we optimized the D 3h structure for Tb 3 B 18using the 4f-in-core pseudopotential 34 . The structural parameters of the Tb 3 B 18metallo-borospherene are similar to those for La 3 B 18 -(Supplementary Fig. 3), except that the Tb-B and B-B bond lengths are all slightly shorter due to the smaller atomic radius of Tb as a result of the lanthanide contraction. Because of the use of the 4fin-core pseudopotential, the spin state of the Tb 3 B 18metalloborospherene was not determined from the geometry optimization. We performed broken symmetry calculations and compared the relative energies between the ferromagnetic and antiferromagnetic couplings of the 4f electrons, as shown in Supplementary Table 3 for Tb 3 B 18 -, as well as for Pr 3 B 18 -. The relative energies due to the inter-atomic spin couplings of the unpaired 4f electrons are relatively small, although the high spin ferromagnetic coupling seems to give the lowest energy in both cases. Hence, the spin multiplicity of the Tb 3 B 18metallo-borospherene should be 19 (with 18 unpaired 4f electrons).   Table 4), slightly underestimated relative to the experimental data of 3.13/3.26 eV probably due to the use of the 4f-in-core approximation as well as the incomplete account of electron correlations. Nevertheless, the theoretical results by not considering the 4f electrons and detachment channels are still in very good agreement with the experimental data, as can be seen in Fig. 2  To understand the stability of these remarkable cage structures, we carried out fragment MO analyses by first considering the construction of the B 18 framework in two different pathways and then its bonding with the three La atoms, as schematically shown in Fig. 5. Figure 5a shows one possible path to construct the B 18 framework by the fusion of three B 10 rings. Four of the boron atoms in each B 10 ring are shared with the other B 10 rings, which each coordinate to a La atom to form three shared La©B 10 units. This hypothetical formation pathway of La 3 B 18can be expressed by the following steps: The energetics were calculated from single-point energy differences of the reactants and products, using the geometries directly taken from the optimized La 3 B 18cage at the PBE/TZP level of theory. The interactions between the B 18 framework and the three La atoms are extremely strong (steps 2 and 3), which underlies the stability of the La 3 B 18cage. It should be noted that in platonic solids four surfaces are the minimum number to form a 3D object, i.e., the tetrahedron. However, Fig. 5a shows that three La©B 10 surfaces are fused together to form the D 3h La 3 B 18cage. This is because the La©B 10 surface is curved. It turns out that the Ln 3 B 18metallo-borospherenes belong to a class of geometry mathematically known as n-gonal hosohedron, which is basically a tessellation of lunes on a spherical surface, such that each lune shares the same two vertices. Thus, the D 3h La 3 B 18cage is a trigonal hosohedron, also known as spherical trihedron, where the two vertices consist of the triangular B 6 units. To the best of our knowledge, such a geometry has not been observed in any cluster or molecular systems heretofore.    Figure 5b shows another pathway to construct the La 3 B 18cage, in which the B 18 framework is formed by two triangular B 6 motifs linked by three B 2 bridges, such that three B 10 rings are created. This hypothetical pathway can be represented by the following steps: The interactions between the B 18 framework and the three La atoms to form the La 3 B 18cage are represented by steps 2/3 or 6/7 with an estimated binding energy of 724.6 kcal mol -1 , i.e., 241.5 kcal mol −1 for the binding energy between each La atom and the B 10 ring. This huge La-B 10 binding energy underlies the extraordinary stability of the La 3 B 18metallo-borospherene. Compared with the pathway in Fig. 5a, the pathway in Fig. 5b is more favorable energetically since each step is exothermic. We should emphasize, though, that these exercises provide different views of the unprecedented hollow cage structures. The two pathways to construct the La 3 B 18cage depicted in Fig. 5 certainly do not represent the mechanisms about how it is formed.
The nature of the bonding between B 18 and the La atoms. Since the global minimum of B 18 is a planar structure 36 , the stabilization of the 3D B 18 framework is entirely due to its strong bonding with the three La atoms, as discussed above. We have analyzed the nature of the La-B 10 bonding in the La 3 B 18metalloborospherene using several different methods. The MO energylevel diagram and the relevant MOs of La 3 B 18derived from the La 3and B 18 moieties are shown in Fig. 4. The 5e′′, 9e′, and 1a 1 ′′ MOs of La 3 B 18 -(red-colored) represent the bonding orbitals between the three La atoms and the B 18 moiety, mainly corresponding to the interactions between the irreducible representations, 4e′′, 6e′, and 1a 1 ′′ on the B 18 moiety and 6e′′, 12e′, and 2a 1 ′′ on the La 3moiety (the red highlighted MOs). Supplementary Table S5 gives the compositions of the 5e′′, 9e′, and 1a 1 ′′ MOs, which are dominated by contributions from the B 18 moiety. Hence, there is a strong charge transfer from La to B 18 , resulting in a closed-shell La 3 B 18with a large HOMO-LUMO gap of 1.51 eV computed at the PBE/TZP level. The La atoms are in their favorite +III oxidation state in La 3 B 18 -, which can be viewed approximately as (La 3+ ) 3 [B 18 10-]. As shown in Fig. 4, the 6e′′, 12e′, and 2a 1 ′′ irreducible representations on the La 3moiety are of La 5d characters, while the 4e′′, 6e′, and 1a 1 ′′ irreducible representations on the B 18 framework are of B 2p characters. Hence, the 5e′′, 9e′, and 1a 1 ′′ MOs also represent significant La 5d and B 18 2p covalent bonding. It is the strong covalent and ionic bonding between the La atoms and the B 10 rings that gives rise to the extraordinary stability of the La 3 B 18cage structure. These bonding characteristics are found in all lanthanide boride compounds due to the low electronegativity of the lanthanide elements and their diffuse 5d orbitals 37 .
The La-B 10 interactions can be further characterized using the EDA-NOCV method with B 18 (…6a 1 ′ 2 1a 1 ′′ 0 6e′ 0 4e′′ 0 ) and La 3 -(…6e′′ 4 2a 1 ′′ 2 12e′ 4 ) fragments, a powerful energy decomposition tool to give insight into chemical bonding 38 . We analyzed the B 18 …La 3interaction by the decomposition of the orbital terms into pairwise contributions, as shown in Supplementary Fig. 6. There are three major terms ΔE 1 , ΔE 2 , and ΔE 3 associated with the deformation densities Δρ 1 , Δρ 3 , and Δρ 3 , respectively. The remaining terms contribute <10% to the total orbital interactions. The color code of the deformation densities indicates the direction of the charge flow from red → blue. It is interesting to see that the 1a 1 ′′ orbital of La 3 B 18 -, which is analogous to the (d-p)δ bonding MO in the Ln 2 B 8inverse sandwich complexes 31,32 , contributes significantly (25.7% from the EDA-NOCV analyses, Supplementary Fig. 6) to the stability of the orbital interaction. The other two stronger Δρ 2 (34.8%) and Δρ 3 (28.9%) deformation densities correspond to the degenerate 9e′ and 5e′′ MOs, respectively. The direction of the charge flow is from the La 3to the B 18 moiety, consistent with the fragment MO analyses discussed above (Fig. 4).
We further analyzed the chemical bonding in the La 3 B 18metallo-borospherene using the adaptive natural density partitioning (AdNDP) approach 39 , as shown in Fig. 6. The first row displays nine localized two-center two-electron (2c-2e) σ bonds formed within the three B 2 units and between the B 2 units and the three apexes of the two B 6 triangles. The second row reveals the delocalized bonds in the B 6 triangles, with four three-center twoelectron (3c-2e) σ bonds within each B 6 unit. The multi-center 12c-2e and 18c-2e delocalized bonds can be viewed as π bonds within the B 6 units. The third row represents totally delocalized σ and π bonds within the B 18 framework. The last row shows five totally delocalized 21c-2e bonds between the La atoms and the B 18 framework, corresponding to the 5e′′, 9e′, and 1a 1 ′′ MOs in Fig. 4. We also found that the La 3 B 18metallo-borospherene possesses both 3D aromaticity with calculated nucleusindependent chemical shifts (NICS) 40  We also performed bond-order index analyses for the B-B and La-B interactions, as presented in Supplementary Table 7. The B 2 bridges have shorter bond lengths and higher bond orders than those of the B 6 triangles. In terms of the La-B interactions, the distances and bond order indices are similar to those in the lanthanide-boron complexes reported previously [30][31][32][33] .
A new class of spherical trihedron metallo-borospherenes. The discoveries of the La 3 B 18and Tb 3 B 18metallo-borospherenes suggest that other lanthanide elements could also form similar structures because of the similarity in the chemical properties of the whole series of lanthanides. We have calculated the D 3h cage structures for all the lanthanide elements, Ln 3 B 18 -(Ln = Ce-Lu). The coordinates obtained at the PBE0 level are given as Supplementary Data 1, whereas those of La 3 B 18and La 3 B 18 are provided in Supplementary Table 8. All these structures are indeed minima on their potential energy surfaces. Hence, we conclude that there indeed exist a whole class of Ln 3 B 18metalloborospherenes. While borospherenes have not been observed beyond the B 40 cluster 42 , the unique bonding characteristics between lanthanide and boron suggest that other lanthanide metallo-borospherenes with different sizes and Ln x B ystoichiometries may exist. Recent studies of transition-metal borides showed that the metal-boron interactions have major influences on their magnetic properties 43,44 . Hence, the understanding of Ln-B interactions in the metallo-borospherene systems may provide insights for the design of lanthanide borides with tunable magnetic or catalytic properties.
In conclusion, we report the observation of the first trilanthanide-doped boron cage clusters (metallo-borospherenes), in which the metal atoms are integral parts of the cage surface. Photoelectron spectra of two representative systems, Ln 3 B 18 -(Ln = La, Tb), show similar and relatively simple spectral patterns, suggesting that they have similar highly symmetric structures. Theoretical calculations reveal that the Ln 3 B 18anions have cagelike structures with D 3h symmetry: two planar B 6 triangular units linked by three B 2 bridges to form the B 18 framework consisting of three shared B 10 rings coordinated to the three Ln atoms. Strong ionic and covalent chemical bonding is found between the Ln atoms and the B 18 framework. The extraordinary stabilities of the metallo-borospherenes are understood by various theoretical analyses. La 3 B 18is found to have a closed-shell electron configuration with a large HOMO-LUMO gap and possesses 3D aromaticity. The Ln 3 B 18cage complexes are expected to exist for all lanthanide elements, suggesting the possibility that there may exist a large class of lanthanide metallo-borospherenes with different Ln/B stoichiometries and tunable properties.

Methods
Experimental details. The experiments were carried out using a magnetic-bottle PES apparatus equipped with a laser vaporization supersonic cluster source, details of which have been published elsewhere 11 . The La 3 B 18and Tb 3 B 18clusters were produced by laser vaporization of a La/ 11 B or Tb/ 11 B mixed target, respectively. The laser-induced plasma was cooled by a He carrier gas seeded with 5% Ar, initiating nucleation between the boron and lanthanide atoms. The nascent clusters were entrained in the carrier gas and underwent a supersonic expansion. Negatively-charged clusters were extracted from the collimated cluster beam and analyzed by a time-of-flight mass spectrometer. Both pure (B n -) and mixed (Ln x B y -) clusters were produced from the cluster source. The La 3 B 18and Tb 3 B 18clusters of current interest were mass-selected and photodetached by the 193 nm (6.424 eV) radiation from an ArF excimer laser or the fourth harmonics from a Nd: YAG laser (266 nm, 4.661 eV). Photoelectrons were collected and analyzed in a 3.5m-long electron flight tube at nearly 100% efficiency. The photoelectron spectra were calibrated by the known transitions of Auand Bi -. The resolution of the PES apparatus (ΔKE/KE) was around 2.5%, that is, about 25 meV for photoelectrons with 1 eV kinetic energy (KE).
Computational methods. Unbiased global-minimum structural searches for the La 3 B 18cluster were performed using the TGMin 2.0 code 45  ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-16532-x the global minimum, which was significantly lower in energy in comparison to the next lowest-lying isomer ( Supplementary Fig. 2). To confirm the stability of the global minimum, we conducted another 500 structural searches, using the D 3h cage as the seed structure. No structures with lower energies were found. All the local minima were verified via harmonic vibrational frequency calculations. The frozencore approximation was employed for the inner shells of [1s 2 ] for B and [1s 2 −4d 10 ] for the La atoms. The zero-order regular approximation 49 was applied, to account for the scalar relativistic effects. Low-lying isomers were subsequently optimized using the PBE and PBE0 density functionals 50 along with the TZP basis sets. Born-Oppenheimer molecular dynamic simulations were further carried out on La 3 B 18for 13 ps using the CP2K code 51 at different temperatures, from 300 to 1000 K ( Supplementary Fig. 4). To minimize the 4f-electron induced complexity (i.e. spin multiplicity) and considering the negligible geometry change due to the occupations of the localized 4f orbitals (radial-density maximum probability radii <0.5 Å), we used the 4f-in-core pseudopotentials 34 for the lanthanide elements to optimize the geometric parameters in the other Ln 3 B 18 -(Ln = Ce-Lu) species. The simulation of the PE spectra was done using the ΔSCF-TDDFT method 52 with the SAOP exchange-correlation functional 53 to account for the long-range interactions. The ground state adiabatic and vertical detachment energies were calculated at the DFT levels, as well as the more accurate DLPNO-CCSD(T) level 54 with the Def2-TZVP basis sets 55 and the Def2-TZVPP pseudopotential for La 34 , utilizing the AutoAux generation procedure 55 . We also used the 4f-in-core pseudopotential 34 for the simulation of the PE spectrum of Tb 3 B 18without consideration of the 4f electron detachment channels. Previous studies showed that such detachment channels carried very low detachment cross sections at the low detachment photon energies used and the main PES features of Ln-B binary clusters were dominated by MOs with Ln sd or B sp characters [31][32][33] . Chemical bonding and electronic structure analyses were carried out by canonical molecular orbital (MO) theory and the semi-localized AdNDP method 39 . We also performed calculations using the energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) approach 38 to quantitatively elucidate the bonding mechanisms between the B 18 and La 3moieties. The bond order indexes of different interatomic interactions were calculated using the Mayer 56 , Gopinathan-Jug (G-J) 57 , and Nalewajski-Mrozek schemes 58 .

Data availability
The data that support the findings of this study are available within the article and the associated Supplementary information. Any other data are available from the corresponding authors upon request.