Orbital Localization-Driven Disruption of Peripheral Bonding in Valence-Isoelectronic B₁₂^- Clusters

We present a systematic theoretical study of a valence-isoelectronic substitution series based on the quasi-planar B₁₂^- cluster, elucidating the effects of heavier Group 13 dopants (Al, Ga, and In) on its geometric and electronic structure. Unbiased global minimum (GM) searches using the Coalescence Kick (CK) algorithm across doublet and quartet spin states identify the most stable structures of B₁₂^-, AlB₁₁^-, GaB₁₁^-, InB₁₁^-, Al₂B₁₀^-, Ga₂B₁₀^-, AlGaB₁₀^-, GaInB₁₀^-, and Al₃B₉^- clusters. Relative energetics of GMs and low-lying isomers are obtained at the DLPNO-CCSD(T)/aug-cc-pVTZ//U-TPSSh-D4/def2-TZVPD level. Our results show that the B₁₂^--like motif persists up to two substitutions (Al₂B₁₀^-, Ga₂B₁₀^-) and in the mixed-metal composition (AlGaB₁₀^-), where dopants occupy peripheral sites and preserve strong localized two-centertwo-electron (2c-2e) σ bonding. Adaptive Natural Density Partitioning (AdNDP) analysis reveals that localization of a single unpaired electron (1c-1e) in an s-type orbital on the dopant atom replaces the fully delocalized π-bonding orbital of the parent cluster. This localization induces substantial geometric puckering while retaining the peripheral 2c-2e σ framework and, qualitatively, the B₁₂^--like core. In contrast, when orbital localization progresses to formation of an s-type lone pair (1c-2e) on one Al atom in Al₃B₉^-, the valence-isoelectronic principle breaks down, leading to rupture of the peripheral bonding network and a transition to a three-dimensional structure. Similarly, incorporation of a single In atom causes pronounced deviation from the parent B₁₂^- geometry in both InB₁₁^- and GaInB₁₀^-, driven by analogous 1c-2e lone-pair formation on the substituted atom arising from the enhanced s-orbital stabilization and increased s-p splitting.