Strucutres and Stabilities
With inspiration from the previously reported D3h La3B18− and D3h La3B20− [24, 26] which possess two equivalent eclipsed B6 triangles interconnected by three B2 units on the cage surface and three deca-coordinate La centers in three conjoined η10-B10 rings, we manually constructed the perfect tetrahedral cage-like Td La4B24 (1) with four equivalent interconnected B6 triangles on the cage surface and four nona-coordinate La centers in four conjoined η9-B9 rings (Fig. 1) Encouragingly, extensive GM searches show that, being overwhelmingly more stable than other low-lying isomers, La4B24 (1, 1A1) is the well-defined GM of the neutral (Fig. S1) with the lowest vibrational frequency of υmin = 119.87 cm− 1 at PBE0. It is 0.79 eV more stable than the second lowest-lying isomer Cs La4B24 with a B2 core and 1.23 eV more stable than the third lowest-lying isomer Cs La4B24 with a B3 core at CCSD(T) level, respectively (Fig. S1). The triplet cage-like C1 La4B24 (3A) slightly distorted due to Jahn-Teller effect appears to be much less stable than the Td GM (by 1.28 eV) at PBE0 (Fig. S1). La4B24 (1) possesses the B-B bond length of rB−B = 1.57 Å between the interconnected B6 triangles, B-B bond length of r′B−B = 1.66 Å within the central B3 triangles in B6 triangular motifs, and average La–B coordination bond length of rLa−B = 2.75 Å between La atoms and their η9-B9 ligands. The large calcualted HOMO–LUMO gap of ΔEgap = 2.35 eV at PBE0 well supports its high chemical stability. Cage-like La4B24 (1) appears to be the first metallo-borospherene possessing the same tetrahedral symmetry as its carbon fullerene counterpart − the experimentally observed quintet Td C28 (5A1) [29]. Extensive molecular dynamics simulations
indicate that La4B24 (1) is also highly dynamically stable, with the small calculated average root-mean-square-deviations of RMSD = 0.13 Å and maximum bond length deviations of MAXD = 0.43 Å at 1000 K, respectively (Fig. 2). Detailed NBO analyses show that the La centers in La4B24 (1) possess the natural atomic charge of qLa = + 1.49 |e| and electronic configuration of La[Xe]4f0.165d1.326s0.09, indicating that La donates its 6s2 electron almost completely to the surrounding B9 ligand in La4B24 (1) while accepting partial valence electron (~ 0.32 |e|) from the boron ligand in its partially occupied 5d orbitals via p→d back donations. Bond order analyses show that the La centers in La4B24 (1) possess the total Wiberg bond order of WBILa=2.79 and average La–B bond order of WBILa−−B=0.26, evidencing the formation of effective La–B coordination interactions in the complex.
The high-symmetry tetrahedral Td La4[B@B4@B24] (2) (2A2) was achieved by encapsulating a B-centered tetrahedral Td B@B4 core inside cage-like La4B24 (1), forming a perfect tetrahedral core-shell lanthanide boride complex with a tetra-coordinate B at the cage center (Fig. 1). Surprisingly and intriguingly, extensive DFT calculations indicate that, with a singly occupied non-degenerate highest occupied α-orbital (a2), the doublet La4[B@B4@B24] (2) well retains its identical tetrahedral Td symmetry during full structural optimizations. As the most stable isomer obtained, it lies 0.79 eV lower than the second lowest-lying isomer C1 La4B29 (2A) (Fig. S2). The tetrahedral B@B4 core and La4B24 (1) shell turn out to match both geometrically and electronically in La4[B@B4@B24] (2) which has the lowest vibrational frequency of υmin = 128.94 cm− 1 and α-HOMO-LUMO gap of △Egap=2.23 eV. Detaching one election from or attaching one electron to La4[B@B4@B24] (2) results in the perfect singlet Td La4[B@B4@B24]+ (3, 1A1) and Td La4[B@B4@B24]− (4, 1A1) which also appear to be the well-defined GMs of the systems lying 0.79 eV and 0.69 eV lower than the second lowest-lying core-shell Cs La4B29+ and C1 La4B29− at PBE0, respectively (Fig. S3 and Fig. S4). La4[B@B4@B24]+/− (3/4) possess the large HOMO-LUMO gaps of △Egap = 2.84/2.21 eV and lowest vibrational frequencies of υmin = 125.50/131.35 cm− 1. The La4[B@B4@B24]0/+/− (2/3/4) core-shell complex series in a 1 + 4 + 28 structural motif possess the B-B bond lengths of rB−B=1.65/1.64/1.66 Å between the central B atom and inner tetrahedron (Bi)4, B-B distances of rB−B=1.73/1.73/1.73 Å between the inner tetrahedron (Bi)4 and outer tetrahedron (Bo)24, and the La–B distances of rLa−−B=2.88/2.93/2.85 Å between the B atom at the center and La atoms on the outer shell. They can thus be viewed as the first bi-shell metallo-borospherenes with the B center encapsulated in an inner tetrahedron (Bi)4 and an outer tetrahedron La4(Bo)24. Similar to the previously reported endohedral metallosilicon fullerenes Td M4@Si28 (M = Al and Ga) which follow the structural motif of 4 + 28 [28], core-shell La4[B@B4@B24]0/+/− (2/3/4) in the structural motif of 1 + 4 + 28 possess the same tetrahedral symmetry as their carbon fullerene counterpart Td C28 [29]. These core-shell complexes also appear to be highly dynamically stable, as exemplified in Fig. 2 for La4[B@B4@B24]− (4) which has the small calculated average RMSD = 0.13 Å and MAXD = 0.41 Å at 1000 K, respectively.
The behavior of the central B atom in these core-shell complexes appears to be especially interesting. Detailed NBO analyses indcate that the central B in La4[B@B4@B24]0/+/− (2/3/4) possesses the natural atomic charge of qB=-1.00/-1.05/-1.00 |e|, electronic configurations of B[He]2s0.512p3.48/B[He]2s0.522p3.52/B[He]2s0.522p3.52, and total Wiberger bond orders of WBIB = 3.71/3.71/3.71, respectively. The central B atom thus carries approximately a unitary negative charge of qB≈-1.0 |e| in these complexes regardless of the charge states of the systems, resulting in a B− monoanion at the cage center which is isovalent with a neutral C atom. The negatively charged tetra-coordinate B− center in 2, 3, 4 is thus a boron analog of the tetrahedral C in Td CH4, indicating the B−~C analogy [44] in these B-centered core-shell complexes.
Bonding analyses
To better interpret the high stabilities of these Td lanthanide boride complexes, we performed detailed AdNDP bonding analyses on the closed-shell La4B24 (1) and La4[B@B4@B24]+ (3) to recover both the localized and delocalized bonds of the systems. As shown in Fig. 3(a), La4B24 (1) possesses 6 2c-2e B-B σ bonds with the occupation number of ON = 1.88 |e| between the four inter-connected B6 triangles on the cage surface and 16 3c-2e σ bonds with ON = 1.91 |e| on four equivalent B6 triangular motifs, forming the σ skeleton of the cage-like system. As expected from chemical intuition, there exist 4 equivalent 6c–2e π bonds with ON = 1.91 over the four interconnected B6 triangles. The remaining 16 delocalized bonds are mainly responsible for the La–B9 coordination interactions in the complex, including 12 equivalent 5c-2e La–B4 (d-p) σ bonds with ON = 1.72 and 4 equivalent 10c-2e La–B9 (d-p) δ bond with ON = 1.62 evenly distributed over four La@B9 nonagons on the cage surface. Such a bonding pattern renders spherical aromaticity to cage-like La4B24 (1), as evidenced by the calculated negative nucleus-independent chemical shift (NICS) [45] values of NICS = − 31.69 ppm at the cage center and NICS = − 33.41 ppm 1.0 Å above the cage center along the C2 molecular axes.
Figure 3(b) indicates that the core-shell La4[B@B4@B24]+ (3) well inherits the main bonding elements of La4B24 (1), with the 6 2c-2e B-B σ bonds, 16 3c-2e σ bonds, 12 5c-2e La–B4 (d-p) σ bonds, and 4 10c-2e La-B9 (d-p) δ bonds remaining basically unchanged. The main difference occurs at the 4 2c-2e B-B σ-bonds in the B@B4 core beween the central B atom and (Bi)4 inner tetrahedron and 4 7c-2e B6(π)-B(p) σ interactions between the four Bi atoms in the inner shell and four capping B6 triangles in the outer shell in the first row and 3 29c-2e π-p σ bonds totally delocalized on the core-shell B29 framework ([B@B4@B24]) in the fourth row. Interestingly, similar to La4B24 (1), La4[B@B4@B24]0/+/− (2/3/4) possess the negative calculated NICS values of NICS=-33.92/-43.18/-28.19 ppm 1.0 Å above the B center along the C2 molecular axes, respectively, indicating that these core-shell borospherenes are also spherically aromatic in nature. The 12 5c-2e La–B4 (d-p) σ and 4 10c-2e La–B9 (d-p) δ coordination bonds in La4B24 (1) and La4[B@B4@B24]+(3) play a vital role in stabilizing these perfect tetrahedral lanthanide boride complexes.
IR, Raman, and UV-Vis/PES Spectral Simulations
The IR, Raman, and UV-Vis spectra of La4B24 (1) and IR, Raman, and PES spectra of La4[B@B4@B24]− (4) are computationally simulated in Fig. 4 to facilitate their future characterizations. Td La4B24 (1) possesses highly simplified IR and Raman spectra due to its high symmetry, including four sharp IR peaks at 215(t2), 239(t2), 810(t2) and 1036 (t2) cm− 1 and eight active Raman vibrations at 137 (a1), 239(t2), 391(a1), 473(a1), 1036(t2), 1065(a1), 1257(t2) and 1267(a1) cm−1, respectively. Detailed vibrational analyses indicate that the symmetrical vibrations at 137 cm−1 (a1) and 391 cm−1 (a1) represent typical radial breathing modes (RBMs) of the cage-like complex which can be used to characterize single-walled hollow boron nanostructures [46]. The strong UV bands around 323, 341, 376, 436 and 459 nm originate from electronic transitions from deep inner shells of the neutral to its high-lying unoccupied molecular orbitals, while the weak broad bands around 490, 526, 625 and 772 nm mainly involve electronic excitations from the occupied frontier orbitals around the HOMO (t2) of the neutral. As shown in Fig. 4(b), La4[B@B4@B24]− (4) exhibits similar IR and Raman spectral features to La4B24 (1), with the strongest IR vibration at 258 cm−1 (t2) and typical RBM vibrations at 153 cm−1 (a1) and 448 (a1) cm−1. The calculated PES spectrum of La4[B@B4@B24]− (4) exhibits major spectral features at 2.08, 3.51, 3.75, 4.31, and 5.18 eV which correspond to vertical electronic transitions from the ground state of the anion (1A1) to the ground state (2A2) and excited states (2T1, 2T2, 2T2, 2T2) of the neutral at the ground-state geometry of the anion, respectively.