We have calculated molecular geometries, HOMO-LUMO gaps, Fermi levels and vibrational frequencies for the σ-linear, σ-bent and π-coordinated [Au₂₀-C₆₀-Au₂₀]ⁿ⁻ (n = 0–3) complexes using the density functional B3LYP method and LANL2DZ basis sets. Our calculations showed that the σ-bent η^1(b)-[Au_20-C_60-Au₂₀]³⁻ complex is the global minimum structure with Au-C distances of 2.27 and 2.97 Å, respectively. The C₆₀ calculated bouncing frequencies for the [Au₂₀-C₆₀-Au₂₀]ⁿ⁻ (n = 0–3) complexes appear at 18–60 cm⁻¹ and compare well with the experimental value of 40 cm⁻¹. The calculations of Mulliken charges indicate that the electrostatic interaction of the C₆₀ⁿ⁻ ions with the Au₂₀ clusters plays a major role in the stability and electron-conducting properties of the [Au₂₀-C₆₀-Au₂₀]ⁿ⁻ (n = 0–3) complexes. The orbital analysis and calculated Fermi levels of the complexes indicate that the neutrally-charged singlet [Au₂₀-C₆₀-Au₂₀] complexes have the HOMO-1 and LUMO+1 delocalized orbitals with Fermi levels at −5.18 eV that line up with the free C₆₀ Fermi level.

我们使用以下公式计算了σ线性，σ弯曲和π坐标[Au ₂₀ -C ₆₀ -Au ₂₀ ] ^{n −}（n =  0–3）配合物的分子几何结构，HOMO-LUMO间隙，费米能级和振动频率。密度泛函B3LYP方法和LANL2DZ基集。我们的计算表明，σ弯曲η1 ^（b） -[Au _20- C _60- Au ₂₀ ] ^3-复合物是全局最小结构，Au-C距离分别为2.27和2.97Å。C ₆₀为[Au ₂₀ -C ₆₀ -Au ₂₀ ]计算的弹跳频率^{n −}（ n =  0–3）络合物出现在18–60 cm ^-1处，并与40 cm ^-1的实验值很好地比较。Mulliken电荷的计算表明，C ₆₀ ^n-离子与Au ₂₀团簇的静电相互作用在[Au ₂₀ -C ₆₀ -Au ₂₀ ] ^n-（n = 0–3）复合体。配合物的轨道分析和计算的费米能级表明，中性带电单峰[Au ₂₀ -C ₆₀ -Au ₂₀]配合物具有HOMO-1和LUMO + 1离域轨道，费米能级为-5.18 eV，与自由C ₆₀费米能级一致。