Multi-center bonding and structural integrity in M₆M₈B₆₀ (M = Y, La, and Lu) metallo-borospherenes

Abstract

Recent experimental discoveries of metallo-borospherenes, La₃B₁₈⁻/Tb₃B₁₈⁻, revealed boron's capacity to form fullerene-like cage architectures, representing a significant advance in metallo-borospherene chemistry. Inspired by these findings, highly symmetric cage-like structures, M₆M₈B₆₀ (M = Y, La, and Lu), have been proposed via first-principles calculations, where metal atoms are embedded on the cage surface. The M₆M₈B₆₀ cage, unlike the La₃B₁₈⁻/Tb₃B₁₈⁻ clusters, are constructed via a mixed-unit, topology-driven strategy involving six M©B₈ and eight M©B₉ motifs. This design does not represent a simple size expansion from smaller boron cages, but instead establishes a new cage topology featuring a larger cavity, higher symmetry, and a highly delocalized multi-center bonding network. Binary system investigations further reveal negligible electronic overlap between neighboring M₆M₈B₆₀ units, confirming that each cluster can maintain its molecular integrity and exist as a stable, independent entity. Electronic structure analysis uncovers 111 uniformly distributed multi-center two-electron bonds, which underpin the exceptional stability and delocalized bonding characteristics of these metallo-borospherenes. Moreover, the robust cage of Y₆Y₈B₆₀ provides a versatile host for encapsulating various atoms and small molecules (Eu, CH₄, CO, H₂, and HF). Encapsulation of the Eu atom notably modulates the cage's properties, yielding the endohedral complex Eu@Y₆Y₈B₆₀ (Isomer I) with a magnetic moment of 7μ_B localized on the Eu center. The electrostatic interaction and weakly bound Eu–cage interaction highlight the tunable host–guest behavior of this system. These results expand the structural and electronic diversity of metallo-borospherenes and provide valuable insights into designing large, multifunctional boron-based nanocages with tailored electronic and magnetic properties.

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Introduction

Since the discovery of C₆₀ fullerene, low-dimensional carbon-based nanomaterials such as carbon nanotubes and graphene have become central topics in nanoscience. Boron, located adjacent to carbon in the periodic table, shares certain structural and bonding similarities with carbon. However, due to its electron-deficient nature, boron exhibits a rich variety of bonding motifs and can form stable covalent frameworks with unique geometries and properties, particularly in the form of clusters.

Extensive theoretical and experimental investigations have revealed that the structural evolution of bare boron clusters (B_n^−/0, n = 3–42)^1–9 followed a trend from planar or quasi-planar structures (n = 3–38, 41–42) to three-dimensional cage-like borospherenes (n = 39–40). Notably, the B₃₆ cluster, considered a precursor to borophene, has been successfully synthesized via atomic vapor deposition on Ag(111) substrates.^10–12 The B₄₀⁻ cluster, named “borospherene”, represented the first experimentally characterized all-boron fullerene.⁷ With increasing cluster size, core–shell-like borospherenes (e.g., B₄₆) and double-ring tubular structures (e.g., B₄₈, B₅₄, B₆₀, and B₆₂) have emerged, with the B₄₆ cluster being the smallest core–shell-like borospherene observed to date.^13,14

To overcome boron's intrinsic electron deficiency and further diversify boron-based nanostructures, transition metal (TM) doping has been proven to be an effective strategy. Several boron molecular wheels, including Co©B₈⁻, Ru©B₉⁻, Rh©B₉⁻, Ir©B₉⁻, Os©B₉⁻ and Y©B₁₁²⁻, have been proposed.^15–18 Notably, the planar structures with the highest coordination numbers reported to date were TaB₁₀⁻ and NbB₁₀⁻.^19,20 Beyond molecular wheels, various other nanostructures have also been proposed, encompassing half-sandwich,²¹ inverse sandwich,^22–25 drum-like structures^26,27 and the endohedral boron cages.^28–31 Among them, a new class of inverse-sandwich complexes, [La(η^x-B_x)La]⁻ (x = 7–9), have been characterized by photoelectron spectroscopy, in which the La 5dδ orbitals were stabilized through bonding with the π₂ orbitals of the B_x rings, forming a novel (d–p)δ bond that served as a crucial stabilizing factor for all three inverse-sandwich complexes.²⁵ Similar B₈ units were also found in the experimentally characterized expanded inverse-sandwich complexes La₂B₁₀⁻ and La₂B₁₁⁻.²⁴ The La₂B₁₀⁻ complex featured an off-plane B₂ unit attached to the B₈ ring, while La₂B₁₁⁻ incorporated an in-plane B₃ unit. Furthermore, the study confirmed that the largest monocyclic boron ring capable of forming an inverse-sandwich structure was the B₉ unit, offering new insights into the structural evolution of larger lanthanide boride clusters.

More recently, trihedral metallo-borospherenes, D_3h La₃B₁₈⁻ and D_3h Tb₃B₁₈⁻, have been both theoretically predicted and experimentally characterized, which underscored boron's capacity to form cage-like structures akin to fullerenes, holding great significance for the advancement of metallo-borospherene research.³² Subsequent theoretical investigations have further revealed a variety of lanthanide-doped boron clusters, including D_3h Be₃B₁₂^1+/2+, T_d La₄B₂₄, T_d La₄B₂₉^0/+/−, La@[La₅&B₃₀]^0/−/2− and B₂₀TM_n (TM = Sc, Y; n = 3, 4) structures, all exhibiting spherical aromaticity and good stability.^33–36

Despite the increasing diversity of metallo-borospherenes, most reported examples featured embedded or externally coordinated metal atoms. In contrast, large, hollow cage-like architectures remained rare. This gap motivated our current work. The experimental characterization of LaB₈ and LaB₉ structural units^24,25 prompted us to explore their assembly into large, cage-like metallo-borospherenes. Addressing this challenge, we report the hitherto unreported family of such clusters, M₆M₈B₆₀ (M = Y, La, and Lu), which exhibited remarkable size, symmetry, and thermodynamic stability. These structures featured a B₆₀ framework coordinated with fourteen metal atoms, comprising six equivalent B₈ rings and eight equivalent B₉ rings. Each ring hosted a metal center, forming six M©B₈ and eight M©B₉ structural units. Unlike previously reported boron-based clusters such as M₃B₁₈⁻ (M = La, Tb) and La₂B₁₀⁻,^32,37 the present M₆M₈B₆₀ systems were constructed via a mixed-unit, topology-driven strategy involving six M©B₈ and eight M©B₉ motifs. This design did not represent a simple size expansion from smaller boron cages but instead established a new cage topology featuring a larger cavity, higher symmetry, and a highly delocalized multi-center bonding network. Such characteristics provided a distinct structural platform for endohedral metallo-borospherenes that was fundamentally different from previously known systems. Importantly, structural motifs analogous to LaB₈ and LaB₉ have been experimentally identified in complexes such as [La(η⁹-B₉)La]⁻, La₂B₁₀⁻ and La₂B₁₁⁻,^24,25 lending strong experimental support to the plausibility of the M₆M₈B₆₀ (M = Y, La, and Lu) systems. Moreover, the robust, intrinsic cavity of the Y₆Y₈B₆₀ cluster enabled tunable host–guest chemistry, allowing the stable encapsulation of various atoms and small molecules (Eu, CH₄, CO, H₂, and HF).

Methods

Geometric optimizations were performed on the M₆M₈B₆₀ (M = Y, La, and Lu) structures using the PBE0 hybrid functional³⁸ in the Gaussian 16 package.³⁹ The boron atoms were described with the 6-311G(d) basis set, while the Y atoms were treated with the SDD basis set. The La and Lu atoms were described using the ECP48MWB and ECP60MWB pseudopotentials,^40,41 respectively. Subsequent vibrational frequency analyses at the same theoretical level confirmed the absence of imaginary frequencies, indicating that all optimized structures corresponded to local minima on the potential energy surface.

To assess the reliability of the computational results, supplementary calculations were performed using the PBE and TPSSh functionals⁴² to avoid potential bias from a single functional. The optimized geometries obtained with these functionals showed good consistency, with no significant structural differences observed, as summarized in Table S1. The PBE0 functional was selected as the primary computational method because it has been widely used and validated in previous studies on lanthanide-containing boron clusters,^34,43 and it also demonstrated good structural agreement across the systems examined in this work.

For the Eu@Y₆Y₈B₆₀ system, geometry optimizations were carried out at different spin multiplicities (2, 4, 6, 8, 10, and 12). The same functional and basis set as those for Y₆Y₈B₆₀ were employed, with the Eu atom described using the ECP28MWB basis set.^44,45 Frequency analysis again revealed no imaginary frequencies, confirming that all optimized structures represented local minima on the potential energy surface.

Ab initio molecular dynamics (AIMD) simulations were conducted using the DMol³ module in Materials Studio.⁴⁶ The simulations were performed in the NVT ensemble with a total duration of 10.0 ps and a time step of 1.0 fs. The temperature was controlled using the Nosé–Hoover chain (NH Chain) thermostat.⁴⁷

Furthermore, electronic properties—including electron density, density of states, molecular frontier orbitals, and adaptive natural density partitioning (AdNDP) analyses—were investigated using the Gaussian 16 package³⁹ using the same computational parameters as those applied in the geometry optimizations. The results were analysed using the Multiwfn program⁴⁸ and visualized with the VMD software.⁴⁹

Results and discussion

Configurations

Based on first-principles calculation, metallo-borospherenes M₆M₈B₆₀ (M = Y, La, and Lu) were constructed. After energy minimization, Y₆Y₈B₆₀, La₆La₈B₆₀ and Lu₆Lu₈B₆₀, with O_h, O and O_h symmetry, respectively, were found to adopt cage-like structures, as shown in Fig. 1. The M₆M₈B₆₀ (M = Y, La, and Lu) structures can be considered as consisting of a B₆₀ framework and fourteen metal atoms. To be more specific, the B₆₀ framework can be seen as the combination of six equivalent B₈ rings and eight equivalent B₉ rings. Each of these rings coordinated to a metal atom, resulting in six M©B₈ units and eight M©B₉ units. Additionally, each B₈ ring was surrounded by four B₉ rings, with two conjoined B rings sharing a B–B dumb-bell. Alternatively, the framework can also be described as each B₉ ring surrounded by three B₉ rings and three B₈ rings, with two conjoined B₉ rings sharing a B atom while two conjoined B₈ rings sharing a B–B dumb-bell.

Fig. 1 Optimized structures of O_h Y₆Y₈B₆₀ (a), O La₆La₈B₆₀ (b), and O_h Lu₆Lu₈B₆₀ (c). The B, Y, La and Lu atoms are colored in pink, cyan, cerulean and green, respectively.

The structural parameters of M₆M₈B₆₀ (M = Y, La, and Lu) obtained after energy minimization are listed in Table S1. The results indicated that although Y, La, and Lu atoms had the same effective number of valence electrons, their atomic radii differed significantly due to the lanthanide contraction effect, specifically in the order La (187.7 pm) > Y (180.1 pm) > Lu (173.4 pm). Owing to its larger radius, the La atom exhibited lower compatibility with the B₈ and B₉ rings in the structure, resulting in reduced symmetry.

The findings revealed two types of B–B bonds in the B₆₀ framework, with average bond lengths ranging from 1.614 Å to 1.746 Å. The shortest average bond length was slightly longer than that of typical B=B double bond (1.56 Å), while the longest average bond length was slightly longer than a typical B–B single bond (1.70 Å). Regarding interatomic metal distances, the average La^I ↔ La^II distance was approximately 5.028 Å, which was longer than the corresponding Lu^I ↔ Lu^II and Y^I ↔ Y^II distances by 0.339 Å and 0.299 Å, respectively. Meanwhile, the average La^II ↔ La^II distance was 5.977 Å, exceeding the Lu^II ↔ Lu^II and Y^II ↔ Y^II distances by 0.626 Å and 0.477 Å, respectively. These results indicated that the geometric structure of La₆La₈B₆₀ was more expanded compared to those of Y₆Y₈B₆₀ and Lu₆Lu₈B₆₀. Furthermore, the average binding energy per atom of Y₆Y₈B₆₀, La₆La₈B₆₀ and Lu₆Lu₈B₆₀ were calculated to be 5.858 eV per atom, 5.833 eV per atom and 5.782 eV per atom, respectively. These values were relatively close, suggesting their comparability in terms of energy. Based on the high similarity in geometric configuration and physical properties among these systems, Y₆Y₈B₆₀ was selected as a representative structure for further in-depth analysis.

Stability

To evaluate the thermodynamic stability of the M₆M₈B₆₀ (M = Y, La, and Lu) structures, ab initio molecular dynamics (AIMD) simulation was performed (Fig. 2 and S1–S6). The simulation was conducted using the NVT ensemble, with a total simulation time of 10.0 ps and a time step of 1.0 fs. The Nosé–Hoover chain (NH Chain) thermostat was employed to regulate the temperature during the NVT simulation. The temperature was gradually increased from 300 K to determine the maximum temperature at which the structure retained its stable configuration.

Fig. 2 AIMD simulations for the Y₆Y₈B₆₀ structure at 800 K and 900 K, with the total simulation time and time step of 10.0 ps and 1.0 fs, respectively.

The structural integrity of the Y₆Y₈B₆₀ structure was maintained at both 300 K and 600 K. At 800 K, approaching its thermodynamic stability limit, the total energy and temperature of the system reached equilibrium throughout the 10.0 ps simulation (Fig. S4). Moreover, the radial distribution function (RDF) of Y₆Y₈B₆₀ at 800 K revealed distinct Y–B and B–B peaks located at approximately 2.55 Å and 1.65 Å, respectively. These values aligned closely with the corresponding average distances in the initial structure—2.50 Å for Y–B and 1.61 Å for B–B—with deviations consistent with the expected thermal broadening effect (Fig. S5). Further quantitative analysis revealed that the Y₆Y₈B₆₀ structure exhibited an average root mean square deviation (RMSD) of 0.27 Å at 800 K, indicating that all atoms oscillated near their equilibrium positions (Fig. S6). However, when the temperature rose to 900 K, the topology of Y₆Y₈B₆₀ underwent significant distortion, and some surface Y©B₈ and Y©B₉ structural units were disrupted. Therefore, the Y₆Y₈B₆₀ structure remained stable up to approximately 800 K.

By comparison, the La₆La₈B₆₀ and Lu₆Lu₈B₆₀ structures demonstrated stability across 300, 600 and 900 K, maintaining their structural integrity up to 1300 K. The energy, radial distribution function (RDF), and root-mean-square deviation (RMSD) exhibited similar stable behavior for the Y₆Y₈B₆₀ cluster at 800 K, as depicted in Fig. S1–S6.

Afterwards, several isomers with low energy were selected and optimized during AIMD simulations to further evaluate the stability of the M₆M₈B₆₀ (M = Y, La, and Lu) structures (Fig. S7–S9). The energy differences (ΔE) between these optimized isomers and the target structure were calculated. The results revealed that the ΔE values were consistently positive, thereby indicating that the target configuration exhibited higher stability.

The investigation into the structural stability of M₆M₈B₆₀ (M = Y, La, and Lu) was extended to include their dimer systems. Four representative configurations of M₆M₈B₆₀ + M₆M₈B₆₀ (M = Y, La, and Lu) binary systems were constructed (Fig. 3, S11 and S13), and the variation of their binding energies with intermolecular distance was examined. Taking the Y₆Y₈B₆₀ structure as an example, the results revealed that in configurations (a)–(c), the binding energy decreased monotonically with increasing intermolecular distances, with no observable energy minimum (i.e., equilibrium binding position). This indicated the absence of an obvious stable equilibrium distance between the two molecules in these configurations, thereby precluding the formation of stable dimers. In contrast, configuration (d) exhibited a distinct equilibrium position in the binding energy curve, where the energy initially decreased, reached a minimum, and subsequently increased with increasing intermolecular distance. The results reflected a transition from the dominance of repulsive interactions to that of attractive interactions at a specific distance. The equilibrium intermolecular distance corresponding to this minimum was approximately 2.75 Å, confirming the feasibility of a stable dimer in this specific configuration.

Fig. 3 The average binding energy per atom (E_b) as a function of intermolecular distance for the Y₆Y₈B₆₀ + Y₆Y₈B₆₀ binary system. The four representative configurations (a–d) of Y₆Y₈B₆₀ binary systems were marked in the corresponding diagrams.

To gain deeper insight into the nature of the interactions, deformation electron density analyses (Fig. S10, S12 and S14) were performed at the equilibrium position and over a broader range (d = 2.75–4.75 Å). The results revealed negligible electron overlaps between adjacent Y₆Y₈B₆₀ units, thereby ruling out the possibility of covalent bonding or significant charge transfer. Even at the equilibrium distance (d = 2.75 Å), the charge density predominantly localized within each monomer. This key evidence excluded dominant chemical bonding mechanisms such as covalent or ionic interactions, indicating that the dimer formation was driven by a weak, non-chemical interaction. These findings further supported that Y₆Y₈B₆₀ can preserve its structural and electronic integrity as an independent molecular entity, reinforcing its potential as a stable building block for nanoscale assembly.

Electronic properties

To probe the electronic properties of the M₆M₈B₆₀ (M = Y, La, and Lu) structures, electron density analysis was performed (Fig. 4, S15 and S16), where blue and yellow indicated charge accumulation and depletion, respectively. Taking Y₆Y₈B₆₀ as an example, charge depletion was observed around the Y atoms, while significant charge accumulation was detected between the Y and B atoms within the Y©B₈ units. Concurrently, the coexistence of accumulation and depletion around the B atoms suggested the possible formation of multi-center two-electron bonds. Similar electronic features were observed in the La₆La₈B₆₀ and Lu₆Lu₈B₆₀ structures.

Fig. 4 Total electron density (a) and deformation electron density (b) of the Y₆Y₈B₆₀ structure, with an isosurface of 0.09 and 0.007 e Å⁻³, respectively. Blue corresponds to electron accumulation, whereas yellow areas indicate electron depletion.

The observed charge distribution can be attributed to a pronounced charge-transfer mechanism. For M₆M₈B₆₀ (M = Y, La, and Lu) systems, the rare-earth metal atoms (Y, La, and Lu) acted as effective electron donors to compensate for the intrinsic electron deficiency of the large boron cage. Hirshfeld population analysis indicated that each metal atom transferred approximately 0.57 e (Y), 0.55 e (La), and 0.59 e (Lu) to the B₆₀ framework. This substantial charge donation stabilized the delocalized bonding network of the cage and suppressed electronic instability that would otherwise arise in a pure B₆₀ structure.

To further clarify the electronic structure of the M₆M₈B₆₀ (M = Y, La, and Lu) system, the projected density of states (PDOS) and molecular frontier orbitals were computed, with the results presented in Fig. 5 and S17–S21, respectively. For the Y₆Y₈B₆₀ structure, the density of states (PDOS) was predominantly contributed by the hybridization of B 2s, 2p orbitals with Y 4d, 5s orbitals, exhibiting distinct orbital hybridization characteristics. The HOMO–LUMO gap of the Y₆Y₈B₆₀ structure was 0.86 eV. At both the HOMO and LUMO levels, the electronic states originated mainly from the hybridization of B 2p and Y 4d orbitals, and the corresponding molecular orbital clearly revealed features of p–d hybridization. Furthermore, below the HOMO level, the contribution from the B 2s orbitals gradually increased, while above the LUMO level, the contribution from the Y 5s orbitals became more pronounced. For La₆La₈B₆₀, the HOMO–LUMO gap was 0.89 eV, and its HOMO and LUMO orbitals exhibited hybridization characteristics like those of the Y₆Y₈B₆₀ structure. However, the Lu₆Lu₈B₆₀ structure had a HOMO–LUMO gap of 0.82 eV, with its frontier orbitals primarily formed by the hybridization of Lu 5d orbitals, reflecting the distinct electronic behaviour of the Lu element in the series.

Fig. 5 Total density of states (TDOS) and projected density of states (PDOS) of the Y₆Y₈B₆₀ structure. The HOMO (orange) and LUMO (purple) levels are shown by dashed lines.

Adaptive natural density partitioning (AdNDP) provided an effective approach for analysing the bonding characteristics of M₆M₈B₆₀ (M = Y, La, and Lu) systems (Fig. 6, S22 and S23). As illustrated in Fig. 6, for the Y₆Y₈B₆₀ structure, there were 111 multi-center two-electron bonds. Specifically, there were twenty-four 2c–2e B–B σ bonds with an occupancy number (ONs) of 1.81|e|, which were located at a shared B–B dumb-bell between two conjoined B rings. Additionally, there were forty-eight 3c–2e σ bonds, with high ONs ranging from 1.86|e| to 1.89|e|. Among them, twenty-four 3c–2e σ bonds occurred in a triangle composed of three B atoms, while the remaining twenty-four 3c–2e σ bonds were located at the Y©B₈ ring, forming a triangle consisting of B dumb-bell between two conjoined B rings and a Y atom. The twenty-four 4c–2e σ bonds with an ONs of 1.94|e| located on the 3B–1Y (B^I–B^II–B^I–Y^II) bonding in the Y©B₉ rings. There were six 9c–2e π bonds and eight 10c–2e σ bonds with high ONs of 1.97|e|, found between Y©B₈ units and Y©B₉ units, respectively. Besides, there was one 60c–2e σ bond with an ON of 2.00|e| involving sixty B atoms. Consequently, all 222 valence electrons of Y₆Y₈B₆₀ participated in bonding. A statistical table summarizing multi-center bonds has been added, including the number of bonds, bond types, and electron occupancy, as shown in Table S6. Similar bonding patterns were observed in La₆La₈B₆₀ and Lu₆Lu₈B₆₀ (Fig. S22 and S23). The structural similarity in bonding types among these three structures can be attributed to their identical number of effective valence electrons.

Fig. 6 Bonding pattern of the Y₆Y₈B₆₀ structure from AdNDP analysis. Corresponding ONs are listed.

Analysis of the bonding characteristics in the M₆M₈B₆₀ (M = Y, La, and Lu) systems revealed that the metal atoms were not merely adsorbed on the surface of the boron cage. Instead, the metal atoms were embedded near the centers of B₈ and B₉ rings, forming M©B₈ and M©B₉ motifs that were stabilized by three-center and four-center two-electron σ bonds, respectively, together with delocalized π interactions. These multi-center bonds strongly coupled the metal atoms to the boron framework, effectively preventing cage distortion or collapse.

Simulated IR, Raman and photoelectron spectroscopy

The infrared (IR) and Raman spectra of M₆M₈B₆₀ (M = Y, La, and Lu) were simulated, as shown in Fig. 7, to provide a theoretical foundation for their future spectroscopic characterization studies. Fig. S24–S29 further provided the vibration modes for the major peaks in the IR and Raman spectra. For Y₆Y₈B₆₀, strong IR active peaks were observed at 296.6, 344.1, 889.4, 1174.3, 1202.0 and 1283.6 cm⁻¹, while the Raman active vibration modes were observed at 60.0, 89.4, 110.7, 165.4 and 192.1 cm⁻¹. Notably, the 1283.6 cm⁻¹ IR peak also corresponded to the contraction modes of the B–B bonds and boron triangles (Fig. S24).

Fig. 7 Simulated IR and Raman spectra for M₆M₈B₆₀, as well as PES for M₆M₈B₆₀⁻ (M = Y, La, and Lu) structures. The full width at half maximum (FWHM) was set to 0.1 eV. For the Raman spectrum, the incident light and incident temperature were set to 488 nm and 300 K, respectively.

The IR and Raman spectra of O_h Lu₆Lu₈B₆₀ exhibited comparable characteristic peaks as O_h Y₆Y₈B₆₀. The IR active vibrations occurred at 286.5, 649.3, 879.8, 1204.1 and 1271.4 cm⁻¹. Additionally, four strong Raman active vibrations occurred at 74.7, 112.0, 140.0 and 177.4 cm⁻¹, in which the 74.7 cm⁻¹ Raman vibration peak primarily corresponded to the tension modes of the Lu atoms in Lu©B₉ units (Fig. S29).

The Raman spectrum of La₆La₈B₆₀ closely resembled those of Lu₆Lu₈B₆₀ and Y₆Y₈B₆₀, while its infrared spectrum differed significantly. There were four major Raman vibrations at 74.7, 128.0, 153.4, and 1233.7 cm⁻¹, as well as major IR vibrations at 1181.2, 1212.1 and 1236.7 cm⁻¹. Specifically, the 1236.7 cm⁻¹ IR peak corresponded to typical “radial breathing mode” (RBM) of cage-like complex (Fig. S26), and the 128.0 cm⁻¹ Raman peak also mainly corresponded to the contraction modes of the boron triangles (Fig. S27). Moreover, the lowest vibration frequency of the M₆M₈B₆₀ (M = Y, La, and Lu) was 57.6, 68.8 and 58.3 cm⁻¹, respectively, with no imaginary values, ensuring the kinetic stability of the structures. These simulated vibration spectra provided crucial reference data for the potential experimental characterization of these new metallo-borospherenes.

The combined IR and Raman spectra collectively verified the characteristic vibration modes of the boron cage framework. The observed peak shifts and intensity variations arising from different rare-earth elements can be principally ascribed to disparities in their atomic mass and ionic radius (La > Y > Lu). These variances further governed the bond lengths and strengths of the M–B (M = Y, La, and Lu) interactions, thereby dictating the molecular vibration frequencies and symmetry. Among these elements, La, with the largest ionic radius, induced the most pronounced structural perturbation. Moreover, the lowest vibration frequencies of M₆M₈B₆₀ (M = Y, La, and Lu) were identified as 57.6, 68.8, and 58.3 cm⁻¹, respectively, with no imaginary frequencies detected, affirming the favourable kinetic stability of such configurations. These simulated vibration spectra may serve as crucial benchmarks for the experimental characterization of emerging metallo-borospherenes.

Photoelectron spectroscopy (PES) was an essential analytical technique that investigated the elemental composition, chemical state, and electronic structure of materials by measuring the kinetic energy distribution of electrons ejected upon photon irradiation. It is particularly sensitive to surface electronic properties. Simulated PES can provide predictive insights for experimental measurements. The simulated PES of M₆M₈B₆₀⁻ (M = Y, La, and Lu) structures exhibited distinct characteristic peaks, which were expected to be readily identifiable in experimental spectra. The computed first vertical detachment energies (VDE₁) were 3.05 eV (Y₆Y₈B₆₀⁻), 2.25 eV (La₆La₈B₆₀⁻), and 3.20 eV (Lu₆Lu₈B₆₀⁻), respectively, corresponding to the energy difference between the anionic ground state and the neutral species at the anionic geometry. The first adiabatic detachment energies (ADE) were 2.86 eV (Y₆Y₈B₆₀⁻), 2.04 eV (La₆La₈B₆₀⁻), and 3.02 eV (Lu₆Lu₈B₆₀⁻), respectively, representing the energy difference between the anion and the neutral species at their respective potential energy minima. Compared to Y₆Y₈B₆₀⁻, the vertical detachment energy of La₆La₈B₆₀⁻ and Lu₆Lu₈B₆₀⁻ showed notable differences, particularly in the intensity and width of certain peaks. These distinctions likely stemmed from the differential modulation of the boron cage electronic structure by the respective rare-earth metals.

Endohedral metallo-borospherenes

M₆M₈B₆₀ (M = Y, La, and Lu) adopted hollow cage-like structures with diameters in the range of approximately 9.60–10.92 Å, 10.43–11.46 Å, and 9.21–10.68 Å for the Y-, La-, and Lu-based systems, respectively. These dimensions, which were significantly larger than both I_h-C₆₀ (∼7.1 Å) and I_h-C₈₀ (∼8.0 Å) fullerenes, endowed these clusters with the potential to encapsulate atoms or molecules, thereby offering a viable strategy for tuning their physical and chemical properties.

Taking Y₆Y₈B₆₀ as an example, the research revealed that the Y₆Y₈B₆₀ structure could effectively accommodate CH₄, CO, H₂, and HF molecules and Eu atom within the cavities, as shown in Fig. S30 and S31. Further geometric optimization revealed that the host framework of Y₆Y₈B₆₀ and the internal bond lengths of the encapsulated molecules underwent no significant changes after encapsulation (Fig. S30, S31 and Table S7), revealing that the possibility of cage-like Y₆Y₈B₆₀ could provide a stable and compatible environment for guest species.

Of particular interest was the magnetic behavior observed in Eu@Y₆Y₈B₆₀ systems. To determine the optimal embedding site for the Eu atom, three initial locations were considered within the Y₆Y₈B₆₀ cage: the cage center, near the Y©B₈ unit, and near the Y©B₉ unit. Corresponding initial configurations were constructed and subjected to geometry optimization under different spin multiplicities. The results indicated that the Eu atom initially placed near the Y©B₉ ring migrated toward the Y©B₈ ring, yielding only two stable isomers: isomer I, with Eu situated near the Y©B₈ ring at a distance of about 3.36 Å from the Y atom, and isomer II, where Eu was approximately located at the cage center, as shown in Fig. S31. Both isomers exhibited maximum stability at a spin multiplicity of 8, corresponding to a magnetic moment of 7μ_B.

Vibrational frequency analysis (Fig. S32) confirmed the kinetic stability of both isomers, with no imaginary frequencies observed. The computed frequency ranges were 42.4–1286.6 cm⁻¹ for Isomer I and 42.2–1271.5 cm⁻¹ for Isomer II. Total energy comparisons revealed that Isomer I was more stable than Isomer II by 2.51 eV. Furthermore, the encapsulation energy for Isomer I was calculated to be −4.28 eV, underscoring the favourable encapsulation of Eu atoms by the Y₆Y₈B₆₀ cage.

The thermodynamic stability of the Eu@Y₆Y₈B₆₀ (isomer I) system was assessed using ab initio molecular dynamics simulations (Fig. S33). Starting from 300 K and gradually increasing the temperature, the Eu@Y₆Y₈B₆₀ (isomer I) system was found to remain stable up to approximately 800 K. Furthermore, at 800 K, the evolution of temperature and energy over time confirmed that the system had reached equilibrium (Fig. S34). Upon further heating to 900 K, the isomer I system collapsed. These results demonstrated that the isomer I system possessed good thermodynamic stability at elevated temperatures, and Eu incorporation showed no adverse effect on the thermodynamic stability of the Y₆Y₈B₆₀ system.

Further Hirshfeld population analysis revealed that the Eu atom possessed a spin magnetic moment of approximately 6.98μ_B, while the contributions from Y and B atoms were negligible. Spin charge density analysis (Fig. 9a) further indicated significant electron localization at the Eu atom, suggesting that Eu served as the primary source of magnetism in the system. In addition, the projected density of states (PDOS) analysis of the Eu@Y₆Y₈B₆₀ system corroborated these findings. Specifically, Fig. 8(a) and (b) displayed the PDOS of Y and B atoms, respectively, showing nearly symmetric spin-up and spin-down distributions, which implied their minor contributions to the overall magnetism. In contrast, as shown in Fig. 8(c), the 4f orbitals of the Eu atom exhibited pronounced spin polarization with clear asymmetry between the spin-up and spin-down curves. These results collectively demonstrated that the magnetic moment in the Eu@Y₆Y₈B₆₀ system originated predominantly from the highly localized 4f electrons of the Eu atom.

Fig. 8 Projected density of states (PDOS) of the Eu@Y₆Y₈B₆₀ endohedral cluster (Isomer I), with a full width at half maximum (FWHM) of 0.10 eV. The Fermi level was set to 0 eV and indicated by a black dashed line. (a) PDOS of Y atoms in the Eu@Y₆Y₈B₆₀ cluster; (b) PDOS of B atoms in the Eu@Y₆Y₈B₆₀ cluster; and (c) PDOS of the Eu atom in the Eu@Y₆Y₈B₆₀ cluster.

Fig. 9 Electronic structure analysis of the Eu@Y₆Y₈B₆₀ system. (a) Spin charge density; and (b) Interaction Region Indicator (IRI) analysis. The isosurfaces of (a) and (b) were set at 0.02 e Å⁻³ and 0.5 e Å⁻³, respectively.

More importantly, projected density of states (PDOS) analysis indicated that within the energy range of Eu 4f orbitals, neither the B cage nor the Y atoms exhibited noticeable spin polarization, suggesting the absence of significant spin hybridization or strong exchange coupling. Furthermore, Hirshfeld population analysis showed that approximately 0.63e was transferred from Eu to the Y₆Y₈B₆₀ cage, indicating that the interaction may be primarily electrostatic in nature.

In addition, the Interaction Region Indicator (IRI) analysis was performed to visualize the interaction between Eu and the cage. The Interaction Region Indicator (IRI) is a real-space function defined by the electron density and its derivatives. It served as a powerful tool for visualizing and qualitatively characterizing various chemical interactions in molecular systems, including covalent bonds, hydrogen bonds, van der Waals forces, and steric repulsion. As shown in Fig. 9(b), the distinct green regions observed between them corresponded to weak interactions. Together, these results confirmed that Eu interacted with the Y₆Y₈B₆₀ framework mainly through electrostatic and weak interactions. These findings suggested that such systems held the potential for applications in magnetic storage and magnetic regulation, offering new insights for the design of functional nanomaterials.

Conclusions

In summary, a novel family of metallo-borospherenes, M₆M₈B₆₀ (M = Y, La, and Lu), have been theoretically predicted. These clusters exhibited high-symmetry cage-like frameworks composed of six equivalent M©B₈ and eight M©B₉ structural motifs, forming distinct M–B networks that differed from previously known metallo-borospherenes. The occurrence of La©B₈ and La©B₉ fragments in experimentally identified lanthanum–boron complexes (e.g., [La(η⁹-B₉)La]⁻, La₂B₁₀⁻, and La₂B₁₁⁻)^24,25 provided indirect but compelling evidence supporting the chemical feasibility of such large M–B assemblies. The structural stability of M₆M₈B₆₀ (M = Y, La, and Lu) was confirmed through a combination of AIMD simulations, vibration frequency analysis, and binary system investigations. In particular, the deformation electron density of the M₆M₈B₆₀ + M₆M₈B₆₀ systems exhibited negligible electronic overlap between adjacent monomers, indicating the absence of intercluster covalent bonding and confirming that each M₆M₈B₆₀ unit can maintain its molecular integrity as an independent entity. Electronic structure analysis further revealed a network of 111 multi-center two-electron (mc–2e) bonds across the entire framework, which underpinned their stability and represented a unique balance of electronic delocalization within this class of metallo-borospherenes. Simulated IR, Raman and PES spectra are provided as predictive references for future potential experimental identification. Moreover, the robust cage-like topology of Y₆Y₈B₆₀ allowed for the encapsulation of guest atoms or small molecules (Eu, CH₄, CO, H₂, and HF), offering tunable host–guest interactions that enabled tailored electronic and magnetic properties. Specifically, Eu encapsulation effectively tailored the electronic and magnetic properties, yielding the endohedral complex Eu@Y₆Y₈B₆₀ (Isomer I) with a magnetic moment of 7μ_B localized on the Eu atom. These findings enriched the structural diversity of metallo-borospherenes, highlighted their capacity to exist as stable, self-contained molecular units, and demonstrated their promise as multifunctional building blocks for nanoscale materials design and assembly.

Author contributions

Conceptualization, Hui-Yan Zhao and Ying Liu; writing – original draft, Yi-Sha Chen; writing – review & editing, Yi-Sha Chen, Jing-Jing Guo, Peng-Bo Liu, Hui-Yan Zhao, and Jing Wang; validation, Hui-Yan Zhao and Ying Liu; investigation, Hui-Yan Zhao and Ying Liu; methodology, Yi-Sha Chen, Hui-Yan Zhao and Ying Liu; funding acquisition, Yi-Sha Chen, Jing-Jing Guo, Peng-Bo Liu and Ying Liu.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). The configurations of AIMD simulation for M₆M₈B₆₀ (M=Y, La, Lu) structures at different temperatures; Energy, temperature, RDF and RMSD of M₆M₈B₆₀ (M=Y, La, Lu) structures varied with the simulation time during NVT molecular dynamics. The initial and optimized M₆M₈B₆₀ (M=Y, La, Lu) isomers; Deformation electron density of the M₆M₈B₆₀ (M=Y, La, Lu) binary systems; The average binding energy per atom (E_b) as a function of intermolecular distance for the M₆M₈B₆₀ (M=La, Lu) binary system; The electron density, molecular frontier orbitals, PDOS and AdNDP analysis of M₆M₈B₆₀ (M=La, Lu) structures; The molecular frontier orbitals of Y₆Y₈B₆₀ structure; Vibrational modes (IR and Raman) of M₆M₈B₆₀ (M=Y, La, Lu) structures. The optimized structure for Y₆Y₈B₆₀ after encapsulating atoms or small molecules; Raman spectra of the two isomers of Eu@Y₆Y₈B₆₀; The configurations of Eu@Y₆Y₈B₆₀ system after 10.0 ps AIMD simulations at different temperatures. Energy and temperature of Eu@Y₆Y₈B₆₀ varied with the simulation time during NVT molecular dynamics; Some typical average bond lengths, interatomic distances, symmetry and frequency for M₆M₈B₆₀ (M=Y, La, Lu) structures at different functionals; Hirshfeld population analysis results of the M₆M₈B₆₀ (M=Y, La, Lu) and Eu@Y₆Y₈B₆₀ systems; The bond types and electron occupancy of each multi-center bond of Y₆Y₈B₆₀ structure; The bonds lengths between atoms within molecules encapsulated in the Eu@Y₆Y₈B₆₀ system. Supplementary information is available. See DOI: https://doi.org/10.1039/d5nr05005g.

Acknowledgements

This work is funded by the National Natural Science Foundation of China (Grant Nos. 12174084 and 12404338), the Doctoral Research Start-up Foundation of Hebei Normal University (Grant Nos. L2023B08 and L2025B12), and the Innovation Funding Project for Doctoral Students of Hebei Province (Grant No. CXZZBS2025144).

References

1. A. P. Sergeeva, D. Y. Zubarev, H. J. Zhai, A. I. Boldyrev and L. S. Wang, J. Am. Chem. Soc., 2008, 130, 7244–7246.
2. H. J. Zhai, A. N. Alexandrova, K. A. Birch, A. I. Boldyrev and L. S. Wang, Angew. Chem., Int. Ed., 2003, 42, 6004–6008.
3. W. Huang, A. P. Sergeeva, H. J. Zhai, B. B. Averkiev, L. S. Wang and A. I. Boldyrev, Nat. Chem., 2010, 2, 202–206.
4. Q. Chen, T. T. Chen, H. R. Li, X. Y. Zhao, W. J. Chen, H. J. Zhai, S. D. Li and L. S. Wang, Nanoscale, 2019, 11, 9698–9704.
5. T. Jian, X. N. Chen, S. D. Li, A. I. Boldyrev, J. Li and L. S. Wang, Chem. Soc. Rev., 2019, 48, 3550–3591.
6. H. Bai, T. T. Chen, Q. Chen, X. Y. Zhao, Y. Y. Zhang, W. J. Chen, W. L. Li, L. F. Cheung, B. Bai, J. Cavanagh, W. Huang, S. D. Li, J. Li and L. S. Wang, Nanoscale, 2019, 11, 23286–23295.
7. H. J. Zhai, Y. F. Zhao, W. L. Li, Q. Chen, H. Bai, H. S. Hu, Z. A. Piazza, W. J. Tian, H. G. Lu, Y. B. Wu, Y. W. Mu, G. F. Wei, Z. P. Liu, J. Li, S. D. Li and L. S. Wang, Nat. Chem., 2014, 6, 727–731.
8. Q. Chen, W. L. Li, Y. F. Zhao, S. Y. Zhang, H. S. Hu, H. Bai, H. R. Li, W. J. Tian, H. G. Lu, H. J. Zhai, S. D. Li, J. Li and L. S. Wang, ACS Nano, 2015, 9, 754–760.
9. A. N. Alexandrova, A. I. Boldyrev, H. J. Zhai and L. S. Wang, Coord. Chem. Rev., 2006, 250, 2811–2866.
10. Z. A. Piazza, H. S. Hu, W. L. Li, Y. F. Zhao, J. Li and L. S. Wang, Nat. Commun., 2014, 5, 3113.
11. A. J. Mannix, X. F. Zhou, B. Kiraly, J. D. Wood, D. Alducin, B. D. Myers, X. Liu, B. L. Fisher, U. Santiago, J. R. Guest, M. J. Yacaman, A. Ponce, A. R. Oganov, M. C. Hersam and N. P. Guisinger, Science, 2015, 350, 1513–1516.
12. B. J. Feng, J. Zhang, Q. Zhong, W. B. Li, S. Li, H. Li, P. P. Cheng, S. Meng, L. Chen and K. H. Wu, Nat. Chem., 2016, 8, 563–568.
13. L. Sai, X. Wu, N. Gao, J. Zhao and R. B. King, Nanoscale, 2017, 9, 13905–13909.
14. L. Pei, Y. Y. Ma, M. Yan, M. Zhang, R. N. Yuan, Q. Chen, W. Y. Zan, Y. W. Mu and S. D. Li, Eur. J. Inorg. Chem., 2020, 2020, 3296–3301.
15. C. Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev and L. S. Wang, Angew. Chem., Int. Ed., 2011, 50, 9334–9337.
16. W. L. Li, C. Romanescu, T. R. Galeev, Z. A. Piazza, A. I. Boldyrev and L. S. Wang, J. Am. Chem. Soc., 2012, 134, 165–168.
17. R. Yu, S. Pan and Z. H. Cui, Front. Chem., 2021, 9, 751482.
18. X. R. Dong, J. X. Zhang, T. T. Chen, C. Q. Xu and J. Li, Inorg. Chem., 2024, 63, 6276–6284.
19. T. R. Galeev, C. Romanescu, W. L. Li, L. S. Wang and A. I. Boldyrev, Angew. Chem., Int. Ed., 2012, 51, 2101–2105.
20. S. Pan, S. Kar, R. Saha, E. Osorio, X. Zarate, L. Zhao, G. Merino and P. K. Chattaraj, Chem. – Eur. J., 2018, 24, 3590–3598.
21. M. X. Ren, S. Y. Jin, D. H. Wei, Y. Y. Jin, Y. H. Tian, C. Lu and G. L. Gutsev, Phys. Chem. Chem. Phys., 2019, 21, 21746–21752.
22. T. T. Chen, W. L. Li, W. J. Chen, J. Li and L. S. Wang, Chem. Commun., 2019, 55, 7864–7867.
23. Z. H. Cui, C. Chen, Q. Wang, L. L. Zhao, M. H. Wang and Y. H. Ding, New J. Chem., 2020, 44, 17705–17713.
24. Z. Y. Jiang, T. T. Chen, W. J. Chen, W. L. Li, J. Li and L. S. Wang, J. Phys. Chem. A, 2021, 125, 2622–2630.
25. T. T. Chen, W. L. Li, J. Li and L. S. Wang, Chem. Sci., 2019, 10, 2534–2542.
26. I. A. Popov, T. Jian, G. V. Lopez, A. I. Boldyrev and L. S. Wang, Nat. Commun., 2015, 6, 8654.
27. J. Wang, N. X. Zhang, C. Z. Wang, Q. Y. Wu, J. H. Lan, Z. F. Chai, C. M. Nie and W. Q. Shi, Phys. Chem. Chem. Phys., 2021, 23, 26967–26973.
28. J. Lv, Y. Wang, L. Zhang, H. Lin, J. Zhao and Y. Ma, Nanoscale, 2015, 7, 10482–10489.
29. J. Liu, Y. M. Zhang, C. Li, W. Jin, G. Lefkidis and W. Huebner, Phys. Rev. B, 2020, 102, 024416.
30. T. Zhang, M. Zhang, X. Q. Lu, Q. Q. Yan, X. N. Zhao and S. D. Li, Molecules, 2023, 28, 3892.
31. Q. Q. Yan, X. Zhao, T. Zhang and S. D. Li, ChemPhysChem, 2023, 24, e202200947.
32. T. T. Chen, W. L. Li, W. J. Chen, X. H. Yu, X. R. Dong, J. Li and L. S. Wang, Nat. Commun., 2020, 11, 2766.
33. X. Q. Lu, C. Y. Gao, Z. H. Wei and S. D. Li, J. Mol. Model., 2021, 27, 130.
34. M. Z. Ao, X. Q. Lu, Y. W. Mu, W. Y. Zan and S. D. Li, Phys. Chem. Chem. Phys., 2022, 24, 3918–3923.
35. L. J. Yan, J. Liu, J. M. Shao, Y. Z. Luo and W. Q. Shi, Results Phys., 2023, 44, 106162.
36. L. J. Yan, Inorg. Chem., 2022, 61, 10652–10660.
37. Z. Y. Jiang, T. T. Chen, W. J. Chen, W. L. Li, J. Li and L. S. Wang, J. Phys. Chem. A, 2021, 125, 2622–2630.
38. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158–6170.
39. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson and H. Nakatsuji. Gaussian 16, Revision C. 01.
40. M. Dolg, H. Stoll, A. Savin and H. Preuss, Theor. Chim. Acta, 1989, 75, 173–194.
41. M. Dolg, H. Stoll and H. Preuss, Theor. Chim. Acta, 1993, 85, 441–450.
42. J. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria, Phys. Rev. Lett., 2003, 91, 146401.
43. X. Y. Zhao, M. Yan, Z. H. Wei and S. D. Li, RSC Adv., 2020, 10, 34225–34230.
44. M. Dolg, H. Stoll and H. Preuss, J. Chem. Phys., 1989, 90, 1730–1734.
45. X. Y. Cao and M. Dolg, J. Chem. Phys., 2001, 115, 7348–7355.
46. B. Delley, J. Chem. Phys., 2000, 113, 7756–7764.
47. M. E. Tuckerman, Y. Liu, G. Ciccotti and G. J. Martyna, J. Chem. Phys., 2001, 115, 1678–1702.
48. T. Lu and F. Chen, J. Comput. Chem., 2012, 33, 580–592.
49. W. Humphrey, A. Dalke and K. Schulten, J. Mol. Graph., 1996, 14, 33–38.

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