Cage-like La₄B₂₄ and Core-Shell La₄B₂₉^0/+/- : 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 T_d La₄B₂₄ (1) and core-shell T_d La₄B₂₉ (2), T_d La₄B₂₉⁺ (3), and T_d La₄B₂₉^- (4) which all possess the same geometrical symmetry as their carbon fullerene counterpart T_d 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 T_d 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 T_d CH₄ (B^- ~ C). Detailed orbital and bonding analyses indicate that these T_d 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.