Double Aromaticity and Inverse-Sandwich Structures in Double-Lanthanide-Doped Boron Clusters: Excitation from f-Electrons to d-Electrons

To elucidate the size-dependent formation mechanism of inverse-sandwich structures in double-lanthanide-doped boron clusters, we systematically investigated the geometric and electronic properties of M₂B₁₀^- (M = La, Ce, Pr, and Nd) clusters through density functional theory calculations. Theoretical optimizations reveal that all studied systems adopt inverse-sandwich configurations with two lanthanide atoms sandwiching a B₉ ring at <i>n</i> = 9. Theoretical binding energies (BEs) show excellent agreement with experimental values (BEs < 5 eV), providing the robust validation of the predicted inverse-sandwich configurations. Adaptive natural density partitioning (AdNDP) analysis uncovers a unique bonding mechanism involving f → d electronic excitation in lanthanides, which facilitates the formation of directional d-p δ bonds between metal centers and the boron framework. This electron redistribution simultaneously satisfies the Hückel 4<i>n</i> + 2 rule for both σ- and π-aromaticity, establishing the first example of double aromaticity in lanthanide-doped clusters. The excitation-induced electronic configuration (f + d - 1) dictates the ground-state spin multiplicity while reducing metal-boron binding energy. This energy penalty explains the structural transition from inverse-sandwich to conventional geometries at <i>n</i> = 10, as evidenced by comparative studies on La₂B₁₀^-. Our findings establish <i>n</i> = 9 as the critical size limit for inverse-sandwich stability in double-lanthanide systems and propose a general electronic design rule for tailoring aromaticity in heavy metal-doped clusters.