Practical GW scheme for electronic structure of 3d-transition-metal monoxide anions: ScO−, TiO−, CuO−, and ZnO−

Abstract

The GW approximation to many-body perturbation theory is a reliable tool for describing charged electronic excitations, and it has been successfully applied to a wide range of extended systems for several decades using a plane-wave basis. However, the GW approximation has been used to test limited spectral properties of a limited set of finite systems (e.g., frontier orbital energies of closed-shell sp molecules) only for about a decade using a local-orbital basis. Here, we calculate the quasiparticle spectra of closed- and open-shell molecular anions with partially and completely filled 3d shells (shallow and deep 3d states, respectively), ScO−, TiO−, CuO−, and ZnO−, using various levels of GW theory, and compare them to experiments to evaluate the performance of the GW approximation on the electronic structure of small molecules containing 3d transition metals. We find that the G-only eigenvalue self-consistent GW scheme with W fixed to the PBE level (GnW0@PBE), which gives the best compromise between accuracy and efficiency for solids, also gives good results for both localized (d) and delocalized (sp) states of 3d-transition-metal oxide molecules. The success of GnW0@PBE in predicting electronic excitations in these systems reasonably well is likely due to the fortuitous cancellation effect between the overscreening of the Coulomb interaction by PBE and the underscreening by the neglect of vertex corrections. Together with the absence of the self-consistent field convergence error (e.g., spin contamination in open-shell systems) and the GW multisolution issue, the GnW0@PBE scheme gives the possibility to predict the electronic structure of complex real systems (e.g., molecule-solid and sp-d hybrid systems) accurately and efficiently.

Photoelectron spectra of early $3d$-transition metal dioxide cluster anions from $GW$ calculations

“…These findings are consistent with trends observed in Ref. 43. Finally, the Coulomb interaction terms were evaluated using the resolution-of-identity (RI) approximation.…”

“…As discussed in detail in Ref. 43, full frequency G 0 W 0 method leads to complicated self-energy pole structures, typically at nonfrontier orbitals, which results in multiple solutions of the quasiparticle equation and makes determining the correct and accurate quasiparticle energies difficult. This multisolution issue of G 0 W 0 is particularly prevalent in transition metal oxide systems with a PBE starting point.…”

“…As such, we checked the accuracy of our predictions for the quasiparticle energies by (i) also using the spectral-function method, which locates the quasiparticle peak with the highest weight in the spectral function, (ii) looking at the trends as a function of the basis set size and the amount of exact exchange, and (iii) by varying the parameters η and ∆ω, as recommended in Ref. 43.…”

“…For calculations performed with the G n W 0 and G n W n selfconsistency methods, we used the iterative scheme employed in MOLGW, described in Ref. 43, where the quasiparticle renormalization factor Z is set to Z = 1. In these calculations, we used a larger broadening parameter η = 0.01 Hartree for the self-energy poles (and accordingly, a larger frequency grid spacing of ∆ω = 0.01 Hartree) in order to avoid the oscillations typically observed in the quasiparticle energies of nonfrontier orbitals as a function of the iteration index.…”

“…Accordingly, there have been much fewer studies on the performance of the GW approximation for systems that contain transition metal elements. Motivated by this observation, here we continue with our recent benchmark studies 37,38,42,43 by focusing on the electronic structure of nega) Electronic mail: ogut@uic.edu. atively charged 3d-transition metal dioxide clusters TMO − 2 , for TM = Sc, Ti, V, Cr, and Mn.…”