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

Abstract

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 unoccupied states near the Fermi level.

Beryllium and Magnesium Metal Clusters: New Globally Stable Structures and G0W0 Calculations

“…A comparison of the G 0 W 0 @PBE IP values of the lowest-energy structures as computed in this work with the results reported in the literature is presented in Figure S10. In addition to the DFA-based Δ-SCF results, another set of G 0 W 0 (based on the LDA starting point) results as obtained by Zeng and He are presented. Although the overall trends in the two sets of G 0 W 0 results are the same, the IP values of Zeng and He are generally larger than ours.…”

“…The IP and EA properties are mostly obtained in terms of KS orbital energies and/or the Δ-SCF method − (i.e., the energy difference between the neutral and singly charged clusters). The GW method has been used to calculate the IPs of small Mg clusters and the lifetime of the Mg 40 cluster, but to the best of our knowledge, GW has not been used to compute the IPs and EAs of Be clusters. In this work, we will present systematic G 0 W 0 benchmark calculations for all the low-lying isomers of Be n and Mg n clusters.…”

Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

“…The immediate feature that stands out in Figure is a shift in the excitation peaks for the FLOSIC energies toward higher frequencies of about 1 eV with respect to the noncorrected case (larger gap), in line with the expected physical effect of SIE removal. , In contrast, it is interesting to note that the HOMO and LUMO canonical energies resulting from the self-consistent FLOSIC calculation (obtained directly as the eigenvalues of H KS ) are not largely affected, and give only slightly smaller gap (see Table ). In Perdew–Zunger (PZ), one can interpret the eigenvalues of the Lagrange multiplier matrix, Λ, utilized to solve the localization equations as the occupied orbital energies .…”