Fig. 5: Calculated NPA charge distributions for Al₁₃ and B@Al₁₂.

a–d Natural population analysis (NPA) distributions for a Al₁₃⁻, b Al₁₃⁺, c B@Al₁₂⁻, and d B@Al₁₂⁺ for the optimized structures using PBE0 with 6-311+G(d) for Al₁₃⁻ and B@Al₁₂⁻ or with 6-311G(d) for Al₁₃⁺ and B@Al₁₂⁺. Along with the representative values, the charge amount is expressed by the color gradation: positive in red and negative in blue. The icosahedral I_h symmetries for Al₁₃⁻ and B@Al₁₂⁻ are lowered to C₁ for Al₁₃⁺ and C_i for B@Al₁₂⁺ owing to electron deficiency in the 2P shell. In general, a central Al/B atom is negatively charged, while the surface Al atoms are positively charged, with the exception of a top Al atom in the distorted Al₁₃⁺ in (b).