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Scaling of the self-energy correction to the HOMO-LUMO gap with magnesium cluster size and its potential for extrapolating to larger magnesium clusters

This paper presents a computational method for the estimation of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of metallic nano-clusters using efficient density functional computations with the high accuracy of the GW method. Electronic structures of magnesium nano-clusters Mgn (n = 1–22, 25, 30, 35, and 40) are computed using the density functional theory (DFT) and the quasiparticle GW method. It is found that the energy difference between the DFT and GW results, defined as the scissors operator or correction, is only dependent on the cluster size and independent of the electronic shell filling effect. The scissors operators of HOMOs and LUMOs of metallic clusters can thus be fitted by using simple power functions of the cluster size n. Therefore, the HOMOs and LUMOs of metallic clusters can be efficiently calculated using DFT with a modification of scissors operators. The scissors operators are also demonstrated to be applicable to occupied and unoc...