The amplitude of the odd-even variation in binding energy is calculated for cationic gold clusters, ${\text{Au}}_n^{+},n=8-26$, extracted from experimental literature data. The data are found to agree fairly well with a simple Fermi gas estimate. Motivated by this, the canonical ensemble free energies are calculated for a ladder spectrum. Experimentally observed differences in ground state dissociation free energies between species with odd and even numbers of valence electrons reaches the high temperature limit at temperatures significantly below values corresponding to the HOMO-LUMO gap. Remarkably, the asymptotic high temperature limit does not correspond to the complete disappearance of the zero temperature free energy difference. Likewise, the amount of electronically excited states are significantly higher than a simple estimate based on the Boltzmann factor of the gap energy, having implications for threshold ionization yields.

计算阳离子金簇的结合能的奇偶变化幅度， ${\text{金}}_{ñ}^{+}，ñ=8--26$，从实验文献数据中提取。发现该数据与简单的费米气体估算值非常吻合。以此为动力，计算出了梯形谱的正则合奏自由能。实验观察到，奇数和偶数价电子的物种之间的基态解离自由能差异在温度大大低于对应于HOMO-LUMO间隙的温度下达到了高温极限。值得注意的是，渐进高温极限并不对应于零温度自由能差的完全消失。同样，电子激发态的数量明显高于基于能隙的玻尔兹曼因子的简单估计，这对阈值电离产率有影响。