Vertex effects in describing the ionization energies of the first-row transition-metal monoxide molecules.

ABSTRACT

The GW approximation is considered to be the simplest approximation within Hedin's formulation of many-body perturbation theory. It is expected that some of the deficiencies of the GW approximation can be overcome by adding the so-called vertex corrections. In this work, the recently implemented G0W0Γ0 (1) scheme, which incorporates the vertex effects by adding the full second-order self-energy correction to the GW self-energy, is applied to a set of first-row transition-metal monoxide (TMO) anions. Benchmark calculations show that results obtained by G0W0Γ0 (1) on top of the B3LYP hybrid functional starting point (SP) are in good agreement with experiment data, giving a mean absolute error of 0.13 eV for a testset comprising the ionization energies (IEs) of 27 outer valence molecular orbitals (MOs) from nine TMO anions. A systematic SP-dependence investigation by varying the ratio of the exact exchange (EXX) component in the PBE0-type SP reveals that, for G0W0Γ0 (1), the best accuracy is achieved with 20% EXX. Further error analysis in terms of the orbital symmetry characteristics (i.e., σ, π, or δ) in the testset indicates the best amount of EXX in the SP for G0W0Γ0 (1) calculations is independent of MO types, and this is in contrast with the situation in G0W0 calculations, where the best EXX ratio varies for different classes of MOs. Despite its success in describing the absolute IE values, we, however, found that G0W0Γ0 (1) faces difficulties in describing the energy separations between certain states of interest, worsening the already underestimated G0W0 predictions.