Structures, stabilities, and ionization potentials of dodecahedrane endohedral complexes

The equilibrium geometries and frequencies of endohedral complexes between H, He, Ne, Ar, Li, Li⁺, Be, Be⁺, Be²⁺, Na, Na⁺, Mg, Mg⁺, and Mg²⁺ and dodecahedrane (XΓ₂₀H₂₀) were computed at B3LYP/6-311+G(d,p). The majority have I_h minima; the exceptions, XΓ₂₀H₂₀ (X = Be, Be⁺, Be²⁺), have C_5v symmetry with X localized against an inner cage face. Cage C-C bonds shorten slightly (<0.01 Å) and cage C-H bonds lengthen slightly (≤0.02 Å) in the series: M²⁺Γ₂₀H₂₀ → M⁺Γ₂₀H₂₀ → MΓ₂₀H₂₀ (M = Li, Na, Be, Mg). These subtle changes in dodecahedrane geometry are due to donation of electron density from the encapsulated metal atom into the C-C bonding and C-H antibonding endohedral complex HOMO, which has a structure closely resembling the LUMO (A_1g) of dodecahedrane. The zero point-corrected inclusion energies of Li⁺Γ₂₀H₂₀ (I_h; -12.7 kcal/mol), Be⁺Γ₂₀H₂₀ (C_5v; - 1.3 kcal/mol), Be²⁺Γ₂₀H₂₀ (C_5v; -236.3 kcal/mol) and Mg²⁺Γ₂₀H₂₀ (I_h; -118.0 kcal/mol) are exothermic relative to their isolated components. However, all the endohedral dodecahedrane complexes are higher in energy than their corresponding exohedral isomers. Endohedral He and Li⁺ chemical shifts are 0.9 and 1.9 ppm, respectively. MΓ₂₀H₂₀ (M = Li, Na, Be, Mg) species possess lower first ionization potentials than the Cs atom (3.9 eV) and, therefore, are "superalkalis". Removal of dodecahedrane hydrogens can increase endohedral complex stability significantly. Thus, endohedral beryllium in the beryllocene complex, BeΓ₂₀H₁₀ (D_5d) is 75.3 kcal/mol more stable than its isolated components, in contrast with BeΓ₂₀H₂₀ which is unstable by 127.7 kcal/mol. Dodecahedrane, HeΓ₂₀H₂₀ and Li⁺Γ₂₀H₂₀ B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) absolute energies did not change significantly (<0.31 kcal/mol) when computed using either a pruned (75,302) or pruned (99,590) integration grid; with the addition of zero point energy the maximum deviation was less than 0.53 kcal/mol.