“…The electronic structure of a metal NP is strongly dependent on its size, especially at the nanoscale (Figure a). , Because of the electronic degeneracy in bulk metal, the electronic energy levels are compressed into bands according to the theory of energy band . In contrast to bulk metal, the electronic energy levels gradually become discrete and even behave as molecular orbitals, due to the confinement of electron wave functions within the dimensions of the particles when decreasing the size of metal particle to the nanoscale and atomic regimes, where a distinctive HOMO–LUMO gap and metallic-nonmetallic transition occur. ,, This phenomenon is called quantum size effects. ,,, The band gap between HOMO–LUMO can be approximately predicted by the Jellium model with eq : , E g = E f N 1 / 3 where N is the number of the atoms in the metal particle, E F the Fermi level energy, and E g the band gap energy, which approximates to the emission band in the photoluminescence spectrum from experiments. Hence, a shift in the fluorescence wavelength is well expected, along with the size modulation metal NPs, and one can also simply deduce the number of atoms of an unknown cluster from a simple photoluminescence spectrum with this formula.…”