Cage-like La4B24 and Core-Shell La4B290/+/− : perfect spherically aromatic tetrahedral metallo-borospherenes

Cage-like and core-shell metallo-borospherenes exhibit interesting structures and bonding. Based on extensive global searches and first-principles theory calculations, we predict herein the perfect tetrahedral cage-like Td La4B24 (1) and core-shell Td La4B29 (2), Td La4B29+ (3), and Td La4B29− (4) which all possess the same geometrical symmetry as their carbon fullerene counterpart Td C28, with four equivalent interconnected B6 triangles on the cage surface and four nona-coordinate La centers in four conjoined η9-B9 rings. In these tetra-La-doped boron complexes, La4[B@B4@B24]0/+/− (2/3/4) in the structural motif of 1 + 4 + 28 contain a B-centered tetrahedral Td B@B4 core in a La-decorated tetrahedral La4B24 shell, with the negatively charged tetra-coordinate B− at the center being the boron analog of tetrahedral C in Td CH4 (B− ~ C). Detailed orbital and bonding analyses indicate that these Td lanthanide boride complexes are spherically aromatic in nature with a universal La--B9 (d-p) σ and (d-p) δ coordination bonding pattern. The IR, Raman, and UV-Vis or photoelectron spectra of these novel metallo-borospherenes are computationally simulated to facilitate their spectral characterizations. Graphical abstract Graphical abstract


Introduction
Boron as a prototypical electron-deficient element possesses a rich chemistry next only to carbon in the periodical table. It exhibits a strong propensity to form multi-center-two-electron (mc-2e) bonds in both bulk allotropes and polyhedral molecules [1,2]. Persistent joint photoelectron spectroscopy (PES) and first-principles theory investigations in the past two decades have unveiled a rich landscape for size-selected boron clusters (B n ) which are all characterized with delocalized multicenter bonding [2][3][4][5][6]. Seashell-like borospherenes C 2 B 28 − and C s B 29 − were late observed in PES measurements as minor isomers competing with their quasi-planar global minimum (GM) counterparts [7,8]. Endohedral M@B 40 (M = Ca, Sr) and exohedral M&B 40 (M = Be, Mg) metalloborospherenes were predicted in theory shortly after the discovery of D 2d B 40 −/0 [9]. Endohedral metallo-borospherenes D 2 Ta@B 22 − and D 2d U@B 40 were proposed to be superatoms matching the 18-electron rule and 32-electron principles, respectively [10,11]. Joint ion-mobility measurements and density functional theory (DFT) investigations indicated that boron cluster monocations (B n + ) possess doublering tubular geometries in the size range between n = 16-25 [12]. Extensive GM searches showed that complicated structural competitions exist in medium-sized B n clusters, with B 46 being the smallest core-shell boron cluster (B 4 @B 42 ) and B 48 , B 54 , B 60 , and B 62 being the first bilayer boron clusters predicted to date [13,14]. inter-connected B 6 triangles on the cage surface and four nona-coordinate La centers in four equivalent conjoined η 9 -B 9 nonagonal ligands, presenting the first metalloborobspherene counterparts of the experimentally observed tetrahedral carbon fullerene T d C 28 [29]. More intriguingly, La 4 [B@B 4 @B 24 ] 0/+/− (2/3/4) in the structural pattern of 1 + 4 + 28 possess a tetra-coordinate B center encapsulated in an inner tetrahedron (B i ) 4 and an outer tetrahedron La 4 (B o ) 24 . These high-symmetry lanthanide boride complexes turn out to be spherically aromatic in nature with a universal La-B 9 (pd) σ and (p-d) δ coordination bonding pattern.  [31] and TPSSh [32] levels with the basis set of 6-311 + G(d) [33] for B and Stuttgart relativistic small-core pseudopotential for La [34,35] using the Gaussian 09 program suite [36], with the vibrational frequencies checked to make sure all the obtained structures are true minima on the potential surfaces. . Relative energies of the three lowest-lying isomers were further refined for La 4 B 24 and La 4 B 29 + at the coupled cluster CCSD(T)/6-31G(d) level [37][38][39] implemented in MOLPRO [40] at PBE0 geometries. Chemical bonding analyses were performed for La 4 B 24 (1) and La 4 [B@B 4 @B 24 ] + (3) using the adaptive natural density partitioning (AdNDP) approach [41] at the PBE0 level. Natural bonding orbital (NBO) analyses were achieved using the NBO 6.0 program [42]. Born-Oppenheimer molecular dynamics (BOMD) simulations were carried out on La 4 B 24 (1), La 4 B 29 (2), La 4 B 29 + (3), and La 4 B 29 − (4) for 30 ps at 300 K and 1000 K using the CP2K code [43].

Strucutres and stabilities
With inspiration from the previously reported D 3h La 3 (1) with four equivalent interconnected B 6 triangles on the cage surface and four nonacoordinate La centers in four conjoined η 9 -B 9 rings ( Fig.1) Encouragingly, extensive GM searches show that, being overwhelmingly more stable than other low-lying isomers, La 4 B 24 (1, 1 A 1 ) is the well-defined GM of the neutral (Fig. S1) with the lowest vibrational frequency of υ min = 119.87 cm −1 at PBE0. It is 0.79 eV more stable than the second lowestlying isomer C s La 4 B 24 with a B 2 core and 1.23 eV more stable than the third lowest-lying isomer C s La 4 B 24 with a B 3 core at CCSD(T) level, respectively (Fig. S1). The triplet cage-like C 1 La 4 B 24 ( 3 A) slightly distorted due to Jahn-Teller effect appears to be much less stable than the T d GM (by 1.28 eV) at PBE0 (Fig. S1).  (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 αorbital (a 2 ), the doublet La 4 [B@B 4 @B 24 ] (2) well retains its identical tetrahedral T d symmetry during full structural optimizations. As the most stable isomer obtained, it lies 0.79 eV lower than the second lowest-lying isomer C 1 La 4 B 29 ( 2 A) (Fig. S2). The tetrahedral B@B 4 core and La 4 B 24 (1) shell turn out to match both geometrically and electronically in La 4 [B@B 4 @B 24 ] (2) which has the lowest vibrational frequency of υ min = 128.94 cm −1 and α-HOMO-LUMO gap of ΔE gap = 2.23 eV. Detaching one election from or attaching one electron to La 4 [B@B 4 @B 24 ] (2) results in the perfect s i n g l e t T d L a 4 [ B @ B 4 @ B 2 4 ] + ( 3 , 1 A 1 ) a n d T d La 4 [B@B 4 @B 24 ] − (4, 1 A 1 ) 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 C s La 4 B 29 + and C 1 La 4 B 29 − at PBE0, respectively ( Fig. S3 and Fig. S4).  4 and an outer tetrahedron La 4 (B o ) 24 . Similar to the previously reported endohedral metallosilicon fullerenes T d M 4 @Si 28 (M = Al and Ga) which follow the structural motif of 4 + 28 [28], core-shell La 4 [B@B 4 @B 24 ] 0/+/− (2/3/4) in the structural motif of 1 + 4 + 28 possess the same tetrahedral symmetry as their carbon fullerene counterpart T d C 28 [29]. These core-shell complexes also appear to be highly dynamically stable, as exemplified in Fig. 2 [44] in these B-centered coreshell complexes. The tetrahedral T d B − @B 4 unit in La 4 [B@B 4 @B 24 ] 0/+/− (2/3/4) appears to have the same symmetry as the well-known tetrahedral T d BH 4 − (which is isovalent with T d CH 4 [44]), in obvious contrast to the experimentally observed planar C 2v B 5 − in gas phase [2,3] due to effective B(p)-B 6 (π) σ interactions between the B − @B 4 core and T d B 24 outer shell (as detailed below).

Bonding analyses
To better interpret the high stabilities of these T d lanthanide boride complexes, we performed detailed AdNDP bonding analyses on the closed-shell La 4 B 24 (1) and La 4 [B@B 4 @B 24 ] + (3) to recover both the localized and delocalized bonds of the systems. As shown in Fig. 3(a),

Conclusions
Perfect tetrahedral cage-like La 4 B 24 (1) and core-shell La 4 B 29 0/+/− (2/3/4) with spherical aromaticity have been predicted in this work at first-principles theory level to be the first metallo-borospherenes reported to date possessing the same tetrahedral symmetry as their carbon fullerene counterpart T d C 28 . The tetrahedral B@B 4 core and tetrahedral La 4 B 24 (1) shell match both geometrically and electronically in the La 4 B 29 0/+/− (2/3/4) series. Such species could be synthesized and characterized in gas phases using a La-B binary target in PES experiments. [21][22][23][24] These high-symmetry lanthanide boride complexes and their chemically modified derivatives may serve as building blocks to form various nanoclusters and nanomaterials with novel electronic, magnetic, and optical properties.
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