GW approximation for open-shell molecules: a first-principles study

A prerequisite to characterize magnetic materials is the capability to describe systems containing unpaired electrons. In this study, we benchmark the one-shot GW (G ₀ W ₀) on top of different unrestricted mean-field solutions for open-shell molecules using Dunning's correlation-consistent basis sets expanded in terms of Gaussian functions. We find that the G ₀ W ₀ correction to hybrid functionals provides reasonably accurate results for the ionization energies of open-shell systems when compared to those obtained from high-level ab initio methods. Moreover, the quality of the G ₀ W ₀ exchange–correlation approximation is evaluated by the discrepancy between the ionization energy of the neutral molecules and the electron affinity of the corresponding cations. Furthermore, we assess the capability of the GW to reproduce the correct energy ordering of molecular spin–orbitals. To such an aim, we thoroughly discuss three open-shell molecules CN, NH₂, and O₂, for which approximate functionals fail to correctly capture the single-electron spectrum. Particularly, we demonstrate that the overestimation of the exchange energy in the studied spin–orbitals is reduced by the GW dynamic correlation term, restoring the molecular orbital ordering. Interestingly, we find that deviations of the exchange and correlation energies, in comparison with our ab initio reference, can be very different for molecular orbitals with different symmetry, e.g. σ and π-type orbitals. (paper)