Theoretical study of complexes of closo-borane, alane, and gallane anions with cations of light metals inside and outside of icosahedral clusters [A₁₂H₁₂^2-] (A = B, Al, and Ga)

Systematic B3LYP/6-31G* and B3LYP/6-311+G* calculations have been performed for families of closo-borane, alane, and gallane clusters consisting of A₁₂H₁₂^2- (A = B, Al, and Ga) cages with endohedral or exohedral Lⁿ⁺ metal cations (Lⁿ⁺ = Li⁺, Na⁺, Cu⁺, Be²⁺, Mg²⁺, Zn²⁺, Al⁺, Al³⁺, Ga⁺, and Ga³⁺). Exohedral structure 1, with tridentate cation coordination at an icosahedron face, is a global minimum for most species; bidentate coordination (structure 2) is the transition state for cation migration around the dianion exterior. Migrational barriers (h_migr), which range from 3 to 5 kcal/mol for monocations and 10-15 kcal/mol for dications, increase with increased cation charge and increased cationic radius. Lⁿ⁺@B₁₂H₁₂^2- (Lⁿ⁺ = Li⁺, Be²⁺,Na⁺, Mg²⁺, Al³⁺), Lⁿ⁺@Al₁₂H₁₂^2-(Lⁿ⁺ = Li⁺, Na⁺, Mg²⁺, Al⁺), and Lⁿ⁺Ga₁₂H₁₂^2- (Lⁿ⁺ = Li⁺, Na⁺, Mg²⁺, Ga³⁺) endohedral clusters, with their cations located at the A₁₂H₁₂^2- cage centers, are local I_h minima (3). Endohedral-exohedral isomer relative energies, E_rel(3/1), which are very high for the boranes, decrease rapidly down the borane-alane-gallane group and decrease along the He-Li⁺-Be²⁺-B³⁺ and Ne-Na⁺-Mg²⁺-Al³⁺ isoelectronic series. Endohedral isomers of gallane clusters with heavy multicharged cations are predicted to be most favorable in energy. Two types of transition structures for a 3 → 1 endohedral-exohedral rearrangement exist: cation exit through an edge and Lⁿ⁺ exit via a ruptured pentagonal "neck" of the cage. Li⁺ and Be²⁺ borane salts prefer the former pathway, whereas Li⁺, Na⁺, and Mg²⁺ alane and gallane salts favor the latter mechanism. Cation exit barriers, h_rear, range from ∼15-55 kcal/mol and in an isoelectronic series decrease with increasing cation charge and increasing atomic mass. Endohedral Lⁿ⁺@A₁₂H₁₂^2- clusters show significant charge transfer from the anion to the cation; the hydrogen shell [H]₁₂ donates electrons to Lⁿ⁺ via the internal [A]₁₂ shell, which in many cases serves as an electron "conductor".