Correlation of the number of atoms, N, per cluster with emission energy. Emission energy decreases with increasing number of atoms. The correlation of emission energy with N is quantitatively fit with E_{fermi}/N^{1/3}, as predicted by the jellium model (, ). When N is equal to 1, the energy of valence electron is equal to Fermi energy because the valence electron is at the HOMO level. Emission energies of Au_{23} and Au_{31} exhibit slight deviations from the E_{fermi}/N^{1/3} scaling. Consistent with the narrow excitation and emission spectra, the potential confining the free electrons flattens slightly for Au_{23} and Au_{31}, with anharmonicity parameter U=0.033 (). The experimental values for the emission energies of Au_{3} (), Au_{28} ()and Au_{38} () are 3.66, 1.55, and 1.44 eV respectively (represented by ▲), which are all consistent with the observed scaling relations. Kubo’s predicted model E_{f}/N () and the square potential box model (6/5*E*_{f}/*N*^{2/3} () are also shown in the figure. Obviously these models can not accurately fit the emission energy scalings of the gold clusters.

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