Performance of the G₀W₀ Method in Predicting the Electronic Gap of TiO₂ Nanoparticles

Using a relativistic all-electron description and numerical atomic-centered orbital basis set, the performance of the G₀W₀ method on the electronic band gap of (TiO₂)_n nanoparticles (n = 1-20) is investigated. Results are presented for G₀W₀ on top of hybrid (PBE0 and a modified version with 12.5% of Fock exchange) functionals. The underestimation of the electronic band gap from Kohn-Sham orbital energies is corrected by the quasiparticle energies from the G₀W₀ method, which are consistent with the variational ΔSCF approach. A clear correlation between both methods exists regardless of the hybrid functional employed. In addition, the vertical ionization potential and electron affinity from quasiparticle energies show a systematic correlation with the ΔSCF calculated values. On the other hand, the shape of the nanoparticles promotes some deviations on the electronic band gap. In conclusion, this study shows the following: (i) A systematic correlation exists between band gaps, ionization potentials, and electron affinities of TiO₂ nanoparticles as predicted from variational ΔSCF and G₀W₀ methods. (ii) The G₀W₀ approach can be successfully used to study the electronic band gap of realistic size nanoparticles at an affordable computational cost with a ΔSCF accuracy giving results that are directly related with those from photoemission spectroscopy. (iii) The quasiparticle energies are explicitly required to shed light on the photocatalytic properties of TiO₂. (iv) The G₀W₀ approach emerges as an accurate method to investigate the photocatalytic properties of both nanoparticles and extended semiconductors.