Perfect Spherical Tetrahedral Metallo-Borospherene Ta4B18 as a Superatom Following the 18-Electron Rule.

Cage-like metallo-borospherenes exhibit unique structures and bonding. Inspired by the newly reported smallest spherical trihedral metallo-borospherene D 3h Ta3B12 - (1), which contains two equivalent B3 triangles interconnected by three B2 units on the cage surface, we present herein a first-principles theory prediction of the perfect spherical tetrahedral metallo-borospherene T d Ta4B18 (2), which possesses four equivalent B3 triangles interconnected by six B atoms, with four equivalent nonacoordinate Ta centers in four η9-B9 rings as integrated parts of the cage surface. As the well-defined global minimum of the neutral, Ta4B18 (2) possesses four 10c-2e B9(π)-Ta(dσ) and eight 10c-2e B9(π)-Ta(dδ) coordination bonds evenly distributed over four Ta-centered Ta@B9 nonagons, with the remaining 18 valence electrons in nine 22c-2e totally delocalized bonds following the 18-electron principle (1S21P61D10) of a superatom. Such a bonding pattern renders spherical aromaticity to the tetrahedral complex, which can be used as building blocks to form the face-centered cubic crystal Ta4B15 (3). The IR, Raman, and UV-vis spectra of Ta4B18 (2) are theoretically simulated to facilitate its future experimental characterizations.

Introduction

Boron as a prototypical electron-deficient element exhibits unique structures and bonding in bulk allotropes, polyhedral molecules, and gas-phase clusters.[1−3] Combined photoelectron spectroscopy (PES) and first-principles theory investigations in the past two decades have unveiled a rich landscape for size-selected boron clusters (B–/0) from planar or quasi-planar species (n = 3–38, 41, and 42) to cage-like borospherenes (C3/C2 B39– and D2d B40–/0) featuring delocalized multicenter two-electron (mc-2e) σ and π bonds, with B39– being the only boron cluster monoanion possessing a cage-like global minimum (GM).[2−9] Seashell-like C2 B28–/0 and Cs B29– were later observed in PES measurements as minor isomers coexisting with their quasi-planar GM counterparts.[7,8] Endohedral M@B40 (Ca, Sr, Sc, Y, and La) and exohedral M&B40 (M = Be and Mg) metallo-borospherenes were proposed in theory shortly after the discovery of D2d B40–/0.[10,11] Endohedral D2 Ta@B22– and D2d U@B40 were predicted to be superatoms following the 18-electron rule and 32-electron principle, respectively.[12,13] Other cage-like B clusters (n = 20, 30, 38, 40, 50, and 60) and related Ti-doped species have also been predicted in theory.[14,15] Joint ion-mobility measurements and density functional theory (DFT) investigations indicated that B+ boron cluster monocations possess double-ring tubular structures in the size range between n = 16 and 25.[16] Extensive GM searches and DFT calculations showed that B46 is the smallest core–shell boron cluster with a B4 core at the center (B4@B42), while B48, B54, B60, and B62 are the first bilayer boron clusters predicted to date.[17,18] Encouragingly, bilayer B48–/0 has been very recently confirmed in gas-phase PES measurements, revealing a new structural domain in boron nanoclusters and nanomaterials.[19]

Transition metal-doping generates interesting structures and bonding in boron clusters. Typical examples include the experimentally confirmed monometal-centered boron wheels M@B (Co@B8–, Ru@B9–, and Ta@B10–), double-ring tubular boron drums M@B– (Mn@B16–, Co@B16–, Rh@B18–, and Ta@B20–), and di-metal-doped inverse-sandwich D6h Ta2&B6–/0.[20−26] Di-La-doped inverse-sandwich-type mono-decker La2B– (n = 7–9)[27,28] and tri-La-doped inverse triple-decker La3B14– were also observed in PES experiments.[29] Double-ring tubular C2h La2B20 (La2[B2@B18) was predicted to be a molecular rotor with fluxional bonds at room temperature.[30] The first tri-La-doped spherical trihedral metallo-borospherene D3h La3B18– with three decacoordinate La centers as integral parts of the cage surface has been discovered recently in a combined experimental and theoretical investigation.[31] The first core–shell spherical trihedral metallo-borospherene D3h La3B20– (La3[B2@B18]−) with a B2 core was predicted shortly after.[32] The smallest tri-Ta-doped spherical trihedral metallo-borospherene D3h Ta3B12– (1) has been very recently predicted by our group, which consists of two eclipsed B3 triangles on the top and bottom interconnected by three B2 units on the waist.[33] However, there have been no experimental or theoretical evidence reported on tetra-Ta-doped boron clusters to date. Tetra-metal-doped endohedral metallo-silicon fullerenes Td M4Si28 (M = Al and Ga) have been theoretically proposed to possess the same tetrahedral symmetry as their fullerene counterpart Td C28.[34,35] It is natural to ask at the current stage what GM structures the smallest tetra-Ta-doped boron fullerenes may have and if perfect spherical tetrahedral metallo-borospherenes are favored in thermodynamics over their alternative counterparts.

Based on extensive GM searches and first-principles theory calculations, we predict herein the perfect spherical tetrahedral metallo-borospherene Td Ta4B18 (2), which possesses four equivalent B3 triangles at four corners interconnected by six B atoms on the edges, with four equivalent nonacoordinate Ta centers in four η9-B9 rings as integral parts of the cage surface, in the same tetrahedral symmetry as its fullerene counterpart Td C28.[35] The spherically aromatic Ta4B18 (2) possesses one 10c-2e B9(π)–Ta(dσ) bond and two 10c-2e B9(π)–Ta(dδ) coordination bonds over each Ta@B9 nonagon, with the remaining 18 valence electrons in nine 22c-2e bonds following the 18-electron rule (1S21P61D10). Ta4B18 (2) can be used as building blocks to form the face-centered three-dimensional (3D) Ta4B15 (3), which is metallic in nature.

Results and Discussion

Structures and Stabilities

Inspired by the newly reported smallest tri-metal-doped spherical trihedral metallo-borospherene D3h Ta3B12– (1),[33] which contains two equivalent B3 triangles interconnected by three B2 units on the waist, with three octacoordinate Ta centers as integral parts of the cage surface, we manually designed the tetra-metal-doped perfect spherical tetrahedral metallo-borospherene Td Ta4B18 (2) (1A1), which possesses four equivalent B3 triangles interconnected by six B atoms on the edges, with four nonacoordinate Ta centers in four η9-B9 rings as integrating parts of the cage surface (Figure ). Interestingly and encouragingly, extensive TGMin GM searches[36,37] show that Ta4B18 (2) is the well-defined GM of the neutral complex lying 1.04 eV lower than the second lowest-lying isomer Cs Ta4B18 (1A′) at the CCSD(T)[38−40] level. All the other low-lying cage-like isomers appear to be at least 1.07 eV less stable than the GM in thermodynamics (Figure S1). The first slightly distorted triplet D2 Ta4B18 (3B2) is found to lie 1.08 eV higher than the Td GM at CCSD(T). A similar situation exists in Nb4B18 for which the perfect tetrahedral Td Nb4B18 also appears to be the well-defined GM of the neutral (Figure and Figure S2). Ta4B18 (2) possesses the optimized B–B bond lengths of rB–B = 1.56 between the B3 triangles at the corners and bridging B atoms on the edges, r′B–B = 1.69 Å within the B3 triangles, and an average Ta–B coordination bond length of rTa–B = 2.35 Å between Ta atoms and their η9-B9 ligands. The large energy gaps between the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ΔEgap = 2.63 and 2.60 eV calculated for Td Ta4B18 and Td Nb4B18, respectively, well support their high chemical stabilities, similar to the situations observed in cage-like D2d B40 and C3/C2 B39–.[4,5]

Figure 1

Optimized structures of Ta3B12– (1), Ta4B18 (2), and 3D Ta4B15 crystal (3), with bond lengths indicated in Å in 1 and 2 at the PBE0 level.

Figure 2

Five lowest-lying isomers of (a) Ta4B18 and (b) Nb4B18 with the relative energies indicated in eV at the CCSD(T) level.

Extensive molecular dynamics (MD) simulations indicate that Ta4B18 (2) is also highly dynamically stable, as evidenced by its small calculated average root-mean-square-deviation of RMSD = 0.12 Å and a maximum bond length deviation of MAXD = 0.41 Å at 1500 K (Figure S3a). Similarly, Td Nb4B18 possesses a small calculated average root-mean-square-deviation of RMSD = 0.12 Å and a maximum bond length deviation of MAXD = 0.36 Å at 1200 K (Figure S3b). These highly stable tetra-Ta-doped spherical tetrahedral metallo-borospherenes possess the same tetrahedral symmetry as their carbon fullerene counterpart Td C28.[35]Td Ta4B18 (2) can be further self-assembled into the face-centered crystal Ta4B15 (3) (P-43m) in which each face-centering B atom is shared by two neighboring cubic unit cells, as shown in Figure . Ta4B15 (3) possesses the optimized lattice parameters of a = b = c = 5.77 Å at the PBE level,[42] with both the B–B and B–Ta distances remaining basically unchanged compared to the corresponding bond length values in Td Ta4B18 (2). The face-centering B atoms in Ta4B15 (3) are tetrahedrally coordinated, forming tetrahedral B(B)4 local structures with a B–B bond length of 1.57 Å. The calculated band structures of Ta4B15 (3) indicate that the face-centered 3D crystal is metallic in nature (Figure S4). Its projected density of states (PDOS) shows that both the B-2p orbitals and the Ta-5d orbitals contribute to the calculated PDOS near the Fermi level, with the former making major contributions to the PDOS above the Fermi level while the latter dominating the PDOS below the Fermi level.

Natural Bonding Orbital and Bonding Pattern Analyses

The high stability of Td Ta4B18 (2) originates from its unique structural and bonding patterns. Detailed natural bonding orbital (NBO) analyses show that the four equivalent nonacoordinate Ta atoms in Ta4B18 (2) possess the natural atomic charges of qTa = +0.94 |e|, electronic configurations of Ta[Xe]6s0.235d3.74, total Wiberg bond indexes of WBITa = 5.22, and Ta–B coordination bond orders of WBITa–B = 0.41–0.45 (Ta–B interactions within the quasi-planar Ta@B9), indicating that each Ta atom donates its 6s2 electrons almost completely to the η9-B9 ligands while in return accepts roughly one electron (≈0.74 |e|) in its partially filled 5d orbitals from the surrounding B9 ligand via effective B(2p) → Ta(5d) backdonations. Such Ta–B coordination interactions appear to be comparable with those in the previously reported D3h Ta3B12–, which has the Ta–B coordination bond order of WBITa–B = 0.50–0.53 (Ta–B interactions within the Ta@B8 octagonal pyramids).[33]

Detailed adaptive natural density partitioning (AdNDP)[43,44] bonding analyses shown in Figure unveil both the localized and delocalized bonds of the system. Td Ta4B18 (2) possesses 12 equivalent 2c-2e B–B σ bonds between four B3 triangles at the corners and six bridging B atoms on the edges and four equivalent 3c-2e σ bonds on four B3 triangles in the first row and 12 10c-2e B9–Ta coordination bonds evenly distributed on four equivalent Ta@B9 nonagonal faces, including four equivalent 10c-2e B9(π)–Ta(dσ) bonds in the first row and eight 10c-2e B9(π)–Ta(dδ) bonds in the second row. There exist thus one 10c-2e B9(π)–Ta(dσ) bond and two 10c-2e B9(π)–Ta(dδ) bonds over each Ta@B9 nonagon, forming a local 6-π aromatic system over each quasi-planar Ta@B9 unit to help stabilize the tetrahedral complex, similar to the situation in the experimentally observed aromatic inverse sandwich La2B8.[27] The remaining 18 valence electrons occupy nine totally delocalized 22c-2e bonds in the third row, including one 22c-2e S-type bond, three 22c-2e P-type bonds, and five 22c-2e D-type bonds. The nine 22c-2e bonds well correspond to the superatomic electronic configuration (1S21P61D10) of Td Ta4B18 (2) depicted in Figure S5. As shown in Figure S6, Td Nb4B18 exhibits a similar bonding pattern. Such bonding patterns render spherical aromaticity to both Td Ta4B18 (2) and Td Nb4B18, as evidenced by the calculated large negative nucleus-independent chemical shift[45,46] values of NICS = −141.9 and −124.9 ppm at their cage centers, respectively.

Figure 3

AdNDP bonding patterns of Td Ta4B18 (2), with the occupation numbers (ONs) indicated.

The spherical aromatic nature of Td Ta4B18 (2) is further evidenced by its iso-chemical shielding surfaces (ICSSs)[47,48] depicted in Figure a based on the calculated NICS-ZZ components, where the z axis is parallel to a C3 molecular axis of the system to show the chemical shielding around the Ta@B9 nonagon on the top, in comparison with the corresponding calculated ICSSs of benzene C6H6 in the C6 direction (Figure b). The areas highlighted in yellow inside the Ta4B18 tetrahedron and within about 1.0 A above the Ta centers in radial directions belong to chemical shielding regions with negative NICS-ZZ values, showing that the main aromatic contribution originates from Ta(5d)–B(2p) coordination interactions between the Ta centers and B9 ligands. The chemical deshielding areas with positive NICS-ZZ values highlighted in green are located outside the Ta@B9 nonagons in tangential directions. Interestingly, as clearly shown in Figure , the ICSSs of Td Ta4B18 (2) appears to be similar to those of benzene D6h C6H6 in radial directions, well demonstrating the aromatic nature of the spherical tetrahedral complex.

Figure 4

Comparison between the calculated iso-chemical shielding surfaces (ICSSs) of (a) Ta4B18 (2) and (b) D6h C6H6, with the corresponding NICS-ZZ components indicated. The C3 axis of Ta4B18 (2) and the C6 axis of C6H6 are designated as the z axis in the vertical direction. Yellow regions stand for chemical shielding areas, while green areas represent chemical deshielding regions.

Simulated IR, Raman, and UV–Vis Spectra

The infrared (IR), Raman, and UV–vis spectra of Td Ta4B18 (2) and Td Nb4B18 are computationally simulated in Figure and Figure S7 to facilitate their spectral characterizations. As shown in Figure , Ta4B18 (2) possesses four sharp IR peaks at 161(t2), 310(t2), 659(t2), and 1082(t2) cm–1 and five major Raman active vibrations at 329(e), 467(t2), 622(a1), 999(e), and 1236(a1) cm–1. The weak Raman peak at 223(a1) cm–1 and strongest Raman peak at 622(a1) cm–1 correspond to typical “radial breathing modes” (RBMs) of the cage-like structure, which can be used to characterize single-walled hollow boron nanostructures.[49] The simulated UV–vis spectrum of Ta4B18 (2) with 150 excited states included in the calculations exhibits strong absorption peaks at 294, 393, and 409 nm, which mainly originate from electron transitions from the deep inner shells to the highly unoccupied molecular orbitals of Ta4B18 (2). Td Nb4B18 exhibits similar spectral features to Ta4B18 (2) (Figure S7).

Figure 5

Simulated (a) IR, (b) Raman, and (c) UV–vis spectra of Td Ta4B18 (2) at the PBE0 level.

Conclusions

Based on extensive GM searches and first-principles theory calculations, we have proposed in this work the perfect spherical tetrahedral metallo-borospherenes Td Ta4B18 (2) and Td Nb4B18, which possess the same tetrahedral symmetry as their carbon fullerene counterpart Td C28. Td M4B18 (M = Ta and Nb) appears to be spherically aromatic in nature, with 18 valence electrons occupying nine 22c-2e totally delocalized bonds following the superatomic electronic configuration of 1S21P61D10. Such highly stable spherically aromatic metallo-borospherene clusters may be synthesized and characterized in gas phases by laser ablations of Ta–B or Nb–B binary targets.[19−29,31] As the smallest tetra-metal-doped metallo-borospherenes reported to date, they are possible to be self-assembled to form novel 3D boron nanostructures.

Theoretical Procedure

Extensive GM searches on Ta4B18 and Nb4B18 were performed using the Tsinghua Global Minimum (TGMin) package,[36,37] in conjunction with manual structural constructions based on the smallest metallo-borospherene D3h Ta3B12– (1).[33] More than 1500 singlet or triplet stationary points were explored for each cluster at the PBE/DZVP level.[42] Low-lying isomers were then fully optimized at the PBE0[41] level with the 6-31+G* basis set[50] for B and the Stuttgart (2f1g) pseudopotential[51,52] for Ta and Nb using the Gaussian-16 program suite,[53] with vibrational frequencies checked to make sure that all isomers reported are true minima. The 10 lowest-lying isomers were subsequently reoptimized using the PBE0 functional with the aug-cc-pVTZ basis set[54,55] for B and the Stuttgart (2f1g) pseudopotential for Ta and Nb. Relative energies for the five lowest-lying isomers were further refined for Ta4B18 using the more accurate coupled cluster method with triple excitations CCSD(T)[38−40] implemented in Molpro[56] with the basis set of 6-31G(d) for B and the Stuttgart (2f1g) pseudopotential for Ta. The calculations on the 3D Ta3B15 crystal (3) were performed using the Vienna ab initio simulation package (VASP)[57,58] within the framework of the projector-augmented wave (PAW) pseudopotential method[59,60] and PBE generalized gradient approximation (GGA).[42,61] Natural bonding orbital analyses were performed using the NBO 6.0 program.[62] Nucleus-independent chemical shifts (NICS)[45,46] were calculated at the cage centers to assess the spherical aromaticity of tetrahedral metallo-borospherenes. The iso-chemical shielding surfaces (ICSSs)[47,48] were generated with the Multiwfn 3.7 code.[63] Chemical bonding was analyzed using the adaptive natural density partitioning (AdNDP) method,[43,43] which has been successfully applied to various organic and inorganic species.[2−10,18,19] Molecular dynamics (MD) simulations were carried out on Td Ta4B18 for 30 ps using a CP2K software suite.[64] The iso-surface maps of various orbitals and the iso-chemical shielding surfaces (ICSSs) were realized using the visual molecular dynamics (VMD) software.[65]