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16 November 2025

Spherical Trihedral Metallo-Borospherene with Asymmetric Triangles in Boron Framework

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,
,
and
1
College of Electronics & Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China
2
Hefei National Research Center for Physical Sciences at the Microscale, State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
*
Authors to whom correspondence should be addressed.
Nanomaterials2025, 15(22), 1728;https://doi.org/10.3390/nano15221728 
(registering DOI)
This article belongs to the Special Issue Theoretical Calculation Study of Nanomaterials: 2nd Edition
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Abstract

The recent discovery of spherical trihedral metallo-borospherenes Ln3B18− (Ln = La, Tb) represents the onset of an unprecedented class of boron-metal binary nanomaterials, where heterogeneous La or Tb atoms, alongside B atoms, constitute integral components of the outer cage surface. Here, C3v A1-Sc3B16+ is theoretically predicted as the global minimum by the particle swarm optimization (PSO) algorithm, and its B16-framework comprises unequal B6 and B7 triangles, connected by three B atoms between the vertexes of the B6 triangle and the interval edges of the B7 triangle. This arrangement forms three equivalent η7-B7 rings, each centered with a Sc atom. The cage surface of the second low-lying A2 isomer features an asymmetric triangle of B3 and B7, along with three B2-linked units. This configuration gives rise to three equivalent octacoordinated Sc atoms, each centered within η8-B8 rings. These two cationic isomers have been proven to be very stable in kinetics and thermodynamics. Our findings regarding unequal boron triangles and smaller odd-coordinated rings in the B-framework enrich the geometric patterns of trihedral metallo-borospherenes.

1. Introduction

It is widely acknowledged that carbon’s bonding properties exhibit various forms of sp3, sp2, and sp bonding, resulting in a wide variety of nanostructures. As the left neighbor of carbon in the periodic table, boron shares similarities in bonding variability and can rival carbon in generating nanostructural analogs. Typical examples include the two-dimensional (2D) graphene [], stripped from layered graphite, while borophene lacks a large, blocky layered counterpart; experimental synthesis has successfully yielded various structural motifs depending on the substrate []. Moreover, corresponding to the structure of bilayer graphene, bilayer borophenes have been obtained experimentally on Cu(111) or Ag(111) substrates, respectively [,]. In the case of clusters, the resemblances between them are more obvious. As a counterpart to C60 [], all-boron fullerene D2d B40−/0, which is known as borospherenes, has been confirmed experimentally and theoretically []. Notably akin to the first axial chiral fullerene D2 C76 [], the first axial chiral borospherene C3/C2 B39− is characterized through photoelectron spectroscopy (PES) measurements []. In contrast to the endohedral metallofullerenes M@C60 (M = La, Li, Er, Dy, Gd, Ca, Nd, Y) [,,], the endohedral metallo-borospherenes of M@B40 (Ca, Sr) and M@B40 (M = Sc, Y, La) are theoretically devised [,]. Another remarkable property of C60 is its ability to encapsulate small molecules, while B40−/0 has been demonstrated to accommodate H2, HF, and H2O within its cage []. All this indicates the emergence of a new field of scientific research, parallel to that of carbon fullerenes.
With four valence orbitals but only three valence electrons (2s22p1), boron is a prototypical electron-deficient element. A common strategy to compensate for this deficiency is to introduce electron-rich heteroatoms into boron-based materials, yielding unique properties and attractive chemical bonds [,,]. This principle is clearly exemplified in free-standing, graphene-like borophene. Although inherently unstable, it can be effectively stabilized by the strategic insertion of elements such as Fe, Cr, Ti, Hf, V, Nb, and Ta [,,,]. This approach also enables the formation of diverse structural motifs in transition-metal-doped boron clusters, including half-sandwich structures (PrB7−, CoB12−, and RhB12−) [,], inverse-sandwich complexes (Ta2B6−/0, Pr2B8−, and La2Bn− (n = 7–9)) [,], inverse triple decker La3B14− [], boron molecular wheels MBn− (CoB8−, RuB9−, TaB10− and NbB10−) [,], double-ring tubular boron drums MBn− (MnB16−, CoB16−, RhB18−, and TaB20−) [,,,], and spherical trihedral metallo-borospherenes Ln3B18− (Ln = La, Tb) [], etc. Among them, the geometry of D3h Ln3B18− stands out as a pioneering discovery in chemistry. This structure features a B18 framework comprising two equivalent B6 triangles, interconnected by three B2 units, forming three conjoined B10 rings centered by Ln atoms. Since then, a series of similar derivatives have been rationally designed, including the spherical tetrahedral metallo-borospherene Ta4B18 [], the expanded spherical trihedral metallo-borospherenes TM3B15 (TM = Zr, Hf; q = −1, 0, +1) [], and Ta3B12−, which exhibits σ + π + δ triple aromaticity [], etc. These derivatives have a common feature, that is, the B-skeletons are concentrated on B6 or B3 triangles. Furthermore, a large B7 triangle motif has been identified in TM3/4B20 (TM = Sc, Y) []. However, the trihedral metallo-borospherenes structure incorporating other boron motifs remains scarce.
In this work, we successfully designed a novel type of spherical trihedral metallo-borospherenes, namely C3v A1- and A2-Sc3B16+ clusters. They both possess an asymmetric B16 framework constructed from different regular boron triangles (B6/B7 or B3/B7 motifs), along with boron linkers, forming three equivalent η7-B7 and η8-B8 rings, respectively. The three Sc atoms were selected as the coordinating centers due to their optimal size match with the boron rings and their shared group with La in the periodic table. These two isomers are located through the particle swarm optimization (PSO) searches. Their high stability is evidenced by the lowest relative energy and substantial energy gaps, along with the geometries retained at 1200K, as demonstrated by molecular dynamics (MD) simulations, etc. Additionally, the simulated Infrared (IR) and Raman spectra are provided to facilitate future experiments.

2. Materials and Methods

The entire computational procedure comprises three sequential steps. First, a structural search was conducted using the PSO algorithm as implemented in the CALYPSO 6.0 (Crystal structure AnaLYsis by Particle Swarm Optimization) package []. The key parameters configured for this search included: atomic species and their quantities, minimum interatomic distance constraint (DistanceOfIon), population size (PopSize), maximum number of steps (MaxStep), particle swarm ratio (PsoRatio), as well as electron count (Nelect), which determines the charge state of the system. Among them, the PsoRatio parameter governs structural diversity and is typically set to 0.60 to achieve optimal results. The search completed 100 generations, with 30 low-lying isomers identified in each cycle, and ultimately yielded approximately 2500 trial structures for each charged state of Sc3B16 (cationic, neutral, and anionic), all optimized at the PBE/6-31+G(d) level of theory. Then, the initially obtained low-lying isomers are fully re-optimized using the Gaussian 16 program suite [], employing combinations of the PBE0 [] or TPSSh [] functionals and the basis set of Stuttgart relativistic small-core pseudopotential for Sc atoms and 6-311+G(d) for B atoms, which are usually adopted for boron-based clusters [,,]. Frequency calculations give no imaginary values for all selected isomers, indicating they are true minima on the potential surfaces. The last step involves higher-level energy refinement, where relative energies are recalculated using the more accurate coupled-cluster method with triple excitations, CCSD(T) [], at PBE0-optimized geometries. In addition, to examine their thermal stability, Born-Oppenheimer molecular dynamics (BOMD) simulations are performed using QUANTUM ESPRESSO 7.3 [] for 20 ps at the temperatures of 300 K, 1200 K, and 1500 K. MOs and spectra are visualized using Multiwfn_3.8 [].

3. Results

3.1. Structures and Stability

Considering the boron framework motifs (B6, B3, and B7 triangles) present in the known spherical trihedral metallo-borospherene, we manually construct two types of asymmetric boron frameworks. These are obtained by combining B6 and B7 triangles, or B3 and B7 triangles, and the connectors adopt three boron atoms or three B2 units, respectively. Aligned with its high stability, a spherical trihedral metallo-borospherene should inherently have an advantage in energy compared to other low-lying isomers. To achieve this objective, we adjust various parameters, including the charges of whole systems, the sizes and configurations of boron skeletons, the types and number of doped heteroatoms, etc. Encouragingly, extensive global minimum (GM) searches of Sc3B16+ successfully yielded two unique structural motifs, both possessing C3v symmetry, which were assigned as the lowest-lying isomers A1 and A2 depicted in Figure 1. As expected, A1 possesses the B6 and B7 triangles, as well as the three linked boron atoms form three equivalent conjoined η7-B7 rings, centered with three Sc atoms. A2 isomer has three equivalent conjoined η8-B8 rings, each with an octacoordinated Sc atom at the center.
Figure 1. Geometries, symmetries, and electronic states of the two low-lying isomers of Sc3B16+, both of which exhibit a spherical trihedral metallo-borospherene structure. Color code: Sc (white), B (pink), the linking B atoms (green), and the boron rings (yellow).
The confirmation of these two structures as the most stable isomers is further supported by the relative energies presented in Figure 2, which displays the first twelve low-energy isomers ranked according to their relatively elevated energies at the PBE0 level of calculation. The relative energy of A2 is 0.42/0.25/0.15 eV higher than that of A1 isomer calculated by PBE0 (left), TPSSh (middle), and CCSD(T) (right) levels, respectively. In the subsequent low-energy isomers, some (e.g., A3, A4, and A5) lose the equivalent conjoined rings on their cage surfaces, whereas others, notably A6 or A11 isomers, exhibit relatively high symmetry of C2v, with the relative energies as high as 0.74/0.45/0.50 eV and 1.07/0.87/0.78 eV, respectively. Such large relative energies indicate markedly reduced stability compared to A1 and A2. Therefore, none of these isomers corresponds to the structural type we anticipated. Simultaneously, we assess the charge impact on the stability of these two structures, as illustrated in Figure S1i,ii. Regardless of whether they are in a neutral or anionic state, the desired spherical trihedral metallo-borospherene no longer exhibits the lowest energy. It is 0.71/0.88/0.86 and /0.75/1.06/1.00 eV higher in energy than the lowest-lying isomer B1 in its neutral state, and 0.68/0.79/0.77 and /1.38/1.58/1.68 eV higher in energy than C1 in the anionic state at the calculation of PBE0, TPSSh, and CCSD(T) levels, respectively. Consequently, they also do not possess the high stability characteristic of spherical trihedral metallo-borospherene and thus fall outside the primary concerns of this work.
Figure 2. Geometries, symmetries, and relative energies (in eV) of low-lying Sc3B16+ isomers, computed at the PBE0/TPSSh/CCSD(T)//B/6-311+G(d)/Sc/SDD levels. All isomers are labeled (A1, A2, A3, …,) in order of increasing PBE0 relative energy.
As we already know, vibrational analysis can be used to evaluate the stability of nanoclusters: real frequencies indicate stability, while imaginary frequencies denote instability. All of the presented structures have real frequencies, suggesting their high stability and realizability. To judge the stability of small molecules, Hoffmann et al. have proposed more accurate criteria, in which the true value of the smallest vibrational frequency should be reasonably large, 100 cm−1 or more []. The lowest vibrational frequency of A1 and A2 isomers is 246 or 248 cm−1, respectively, which are sufficient to meet the stability criterion and indicate their good dynamical stability. The neutral counterparts exhibit frequencies of 90 and 93 cm−1, while the anionic counterparts display frequencies of 121 and 166 cm−1, respectively, significantly smaller than those of A1 and A2, indicating their lower stability compared to the corresponding cationic states. Furthermore, the energy gap (Egap), defined as the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), i.e., E(LUMO) − E(HOMO), is another useful measure for assessing the kinetic stability of small clusters. A significant energy gap correlates with a heightened energy demand for electron excitation. The calculated Egap of both are 2.33 and 2.55 eV, respectively, potentially indicating high stability. As for their neutral and anionic counterparts with spherical trihedral metallo-borospherene structures, the gaps are smaller, where the neutral isomers B3 and B4 have gaps of 1.60 and 1.55 eV, and the anionic isomers C5 or C6 have gaps of 1.68 and 1.36 eV at PBE0 levels, respectively, all suggesting lower stability.
We additionally investigate the thermal stabilities of A1 and A2 isomers by BOMD, a method allowing for the analysis of stability through tracking changes in total energy, motion trajectory, and structure across various temperatures over a period of time. At the temperature of 300 K, the two lowest-lying isomers retain their integrity, with no collapse in geometry observed. Specifically, over a period of 20 ps with a time step of 1 fs, there is no significant distortion in the positions of three Sc atoms and the shapes of B16-frameworks. As shown in Figure 3a,b, the total potential energies for these two cage-like isomers exhibit minimal variation, approximately 0.05 eV/atom (blue lines), a slight fluctuation around a certain constant magnitude. At the same time, the average root mean square deviations (RMSD) are also small, with 0.076 Å for the A1 isomer and 0.078 Å for the A2 isomer (red lines). Even at 1200 K, the basic structural patterns of both isomers can be maintained, with RMSD of 0.161 and 0.130 Å, respectively. When the two isomers are in neutral or anionic states, their RMSD shows significant distortions and they even transform into another geometry as depicted in Figure S2. Actually, at a higher temperature of 1500 K, the geometry of cationic A1 isomer can still be retained with an RMSD of 0.171 Å. Conversely, the cationic A2 isomer experiences significant variation with an RMSD of 1.021 Å, swiftly transitioning to another geometry as shown in Figure S3. This result underscores the superior stability of the cationic A1 isomer over A2, which is fully consistent with the computed relative energies. Specifically, the A1 isomer is more stable than A2 by 0.42 eV (PBE0), 0.25 eV (TPSSh), and 0.15 eV (CCSD(T)), respectively. These findings collectively establish A1 as a more promising candidate for synthesis than the A2 isomer.
Figure 3. BOMD trajectory and RMSD of C3v Sc3B16+ obtained for a time of 20 ps at 300 K for (a) A1-Sc3B16+, RMSD = 0.076 Å (on average); (b) A2-Sc3B16+, RMSD = 0.078 Å (on average); and at 1200 K for (c) A1-Sc3B16+, RMSD = 0.161 Å (on average); (d) A2-Sc3B16+, RMSD = 0.130 Å (on average).

3.2. Bonding Pattern Analyses

Obviously, the C3v A1- and A2-Sc3B16+ isomers, featuring spherical trihedral metallo-borospherene structures, exhibit higher stability than the other low-energy isomers, as determined by the above energy calculations and stability analysis. Regardless of its charge state (neutral, anionic, or cationic), the most stable isomer of B16 is invariably either a quasi-planar structure or a double ring structure that competes with a planar structure [,,]. To elucidate the origin of the high stability in these two configurations, their bonding natures are analyzed. Generally, the B–B bonds on the periphery are localized two-center–two-electron (2c–2e) σ bonds, while the delocalized multi-center–two-electron (nc–2e) σ and π bonds occur within the interior or throughout the entire skeleton.
As shown in Figure 4, the C3v A1 isomer has three 2c–2e B–B σ bonds, connecting the three linked B atoms with the three apexes of the B6 triangle, each with an occupation number (ON) of 1.77 |e|. The σ–skeleton of the cage-like surface also includes thirteen delocalized 3c–2e B–B σ bonds, of which four reside in the B6 triangle, six in the B7 triangle, and three between the linked B atoms and the B7 triangle. The ON falls within the range of 1.80~1.89 |e|. The multi-center 13c–2e and 16c–2e B–B delocalized bonds, which span the B6 and the B7 units, can be viewed as π or σ bonds, respectively. The subsequent bonds in the second row represent totally delocalized π bonds and σ bonds of the B16 framework. The remaining five totally delocalized 19c–2e Sc–B bonds exist between the three Sc atoms and the B16 framework. Despite the different geometry with the A1 isomer, the bonding pattern of the C3v A2 isomer is nearly identical to that of the A1 isomer, with the main discrepancy being the distributions of skeleton bonds and ONs: specifically, three 2c–2e and thirteen 3c–2e B–B σ for A1, versus six 2c–2e and ten 3c–2e B–B σ for A2. The significant differences in ON values are primarily due to delocalized bonds within the boron framework, arising from variations in geometric patterns in B16.
Figure 4. AdNDP bonding patterns of C3v (a) A1-Sc3B16+ and (b) A2-Sc3B16+ at PBE0 level.

3.3. Aromaticity

For spherical clusters, the nucleus-independent chemical shift (NICS) is often used to assess aromaticity, a concept first proposed by von Schleyer in 1966 to characterize the aromaticity of organic compounds [,]. It can be obtained by introducing a virtual atom (ghost atom) Bq at an arbitrarily selected location, where negative NICS indicates aromaticity and positive NICS indicates antiaromaticity. To vividly demonstrate chemical shielding, we have computed the magnetic shielding tensor at evenly distributed grid points surrounding the system and generated specific tensor components as iso-chemical shielding surfaces (ICSSs) [,]. Based on the calculated NICS-ZZ components, a three-dimensional isosurface map is plotted to demonstrate the chemical shielding shown in Figure 5, with the z direction aligned parallel to the C3 molecular axis. The chemical shielding area of A1-Sc3B16+ is divided into two parts by the Sc3 plane (Figure 5a). At the side of the B7 triangle, the chemical shielding area with negative NICS-ZZ values extends from the interior to a vertical interval of about 1.0 Å above the B7 triangle, highlighted in green, while the chemical de-shielding regions with positive NICS-ZZ values are horizontally surrounding around the B7 triangle, with the color of blue and the shape of a belt-like. At the B6 triangle side, the chemical de-shielding region is intermittently distributed, failing to fully enclose the B6 triangle horizontally, indicating relatively weaker local aromaticity. In brief, the most stable isomer of Sc3B16+ is partially aromatic. The second low-lying isomer A2-Sc3B16+, which is with the combination of B3 and B7 triangles on the cage surface, also possesses a local aromaticity as shown in Figure 5b. Despite the disparity in geometries, A1- and A2-Sc3B16+ exhibit similar aromaticity, probably because both of them have a nearly circular B7 triangle. From the top view, their ICSSs’ behaviors closely resemble that of typical aromatic benzene C6H6 (Figure 5c), confirming the aromatic character. It is worth noting that the side view reveals a distinct separation of the blue-marked chemical de-shielding region, clearly different from benzene and other spherical trihedral metallo-borospherenes, such as D3h Ta3B12− [], Td Ta4B18 [], D3h La@[La5&B30] [], etc. The possible cause is asymmetric triangles within the boron skeleton. Hence, the isoelectronic D3h Sc3B152− with two symmetrical triangular B6 triangles is calculated, and the chemical deshielding region shows an intermittent distribution, yet from the side it appears as a continuous band (Figure S4).
Figure 5. Calculated ICSSs (isovalue: ±2 ppm) of C3v Sc3B16+ with (a) A1 and (b) A2 geometric structures, and (c) D6h C6H6, all of which have the corresponding NICS-ZZ components indicated. The C3 axis of A1 and A2 isomers around their two triangles of B7 and B6, or B7 and B3, and the C6 axis of C6H6 is designated as the z axis in the vertical direction. The chemical shielding and de-shielding areas are indicated in green or blue, respectively.

3.4. Simulated IR and Raman Spectra

To facilitate the experimental characterizations in the future, the IR and Raman spectra of C3v A1- and A2-Sc3B16+ are computationally simulated at the PBE0/6-311+G(d) level. Since the calculated harmonic frequencies systematically overestimate experimental values, a standard scaling procedure (νscaled = Scaling Factor × νcalculated) was applied [,]. The spectra in Figure 6 were consequently generated by scaling the raw frequencies with a factor of 0.958, as recommended by the authoritative NIST Computational Chemistry Comparison and Benchmark Database (CCCBDB) []. As shown, the lowest-lying isomer exhibits five major asymmetrical IR vibrations at 315, 460, 793, 1022, and 1058 cm−1, and five symmetrical Raman vibrations at 479, 593, 908, 1022, 1058 cm−1, as well as numerous relatively weak Raman spectral features within the range of 237~419 cm−1. Detailed vibrational analyses reveal that the two symmetrical vibrations at 257 and 593 cm−1 represent typical radial breathing modes (RBMs) of three Sc atoms and the B16-framework on the cage-like surface, respectively. Such RBM spectral features are distinctive, much as they are in characterizing single-walled hollow boron nanostructures []. As for the A2 isomer, the IR peaks mainly occur at 238, 295, 394, 437, 512, 1099, and 1210 cm−1. The Raman-active vibrations include two major peaks at 573 and 1265 cm−1, along with a series of minor vibrations at 246, 276, 746, 787, 1013, 1081, and 1099 cm−1, etc. Among them, the two Raman vibrations at 246 and 573 cm−1 are identified as its RBMs. Despite both A1- and A2-Sc3B16+ having C3v cage-like structures, geometric differences significantly influence their spectral characteristics and allow for distinction through these analytical methods.
Figure 6. Simulated IR and Raman spectra of C3v (a) A1-Sc3B16+ and (b) A2-Sc3B16+ at PBE0/6-311+G(d) level (units: cm−1; scaling factors of 0.958).

4. Conclusions

In this work, we design a new type of spherical trihedral metallo-borospherene A1-and A2-Sc3B16+, which is typically characterized by the combinations of asymmetric B6 and B7 triangles, or B3 and B7 triangles, as well as boron units, in the outer B16-framework. The two envisaged geometries were identified as the lowest-lying isomers by the PSO algorithm, as well as by PBE0, TPSSh, and CCSD(T) calculations, which consistently show that these structures possess the lowest relative energies. Their high stability is confirmed by the facts of real frequencies, especially the minimum vibrational frequencies with large values of 246 and 248 cm−1, and the geometries maintained at 1200 K. By adjusting the boron framework with asymmetric triangles, it is possible to introduce novel electronic, magnetic, and optical properties to spherical trihedral metallo-borospherene nanoclusters, thereby extending their applications.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/nano15221728/s1. Figure S1: Geometries, symmetries and relative energies of the low-lying isomers of neutral and anionic Sc3B16; Figure S2: RMSD of C3v Sc3B16 in neutral (a,b) and anionic (c,d) states obtained for a time of 20 ps at the temperatures of 1200 K; Figure S3: BOMD trajectory and RMSD of C3v A1- and A2-Sc3B16+ obtained for a time of 20 ps at the temperatures of 1500 K; Figure S4: Calculated ICSSs of (a) C3v Sc3B152− and (b) D6h C6H6; Table S1: Cartesian coordinates of the first six low-lying isomers of Sc3B16+ at PBE0/6-311+G(d) level.

Author Contributions

Conceptualization, Q.X.; methodology, validation, formal analysis, S.L. and Q.L.; investigation, Q.X. and S.L.; resources, Q.L.; data curation, Q.X. and S.L.; writing—original draft preparation, Q.X.; writing—review and editing, visualization, supervision, project administration, funding acquisition, W.W. and L.Y. All authors have read and agreed to the published version of the manuscript.

Funding

The research was supported by the Guangdong Basic and Applied Basic Research Foundation [No. 2023A1515012286].

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Synthesis, Crystal Structure and Thermoelectric Properties of the Type-I Clathrate Sn38Sb8I8
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