Systematic study of the effect of HSE functional internal parameters on the electronic structure and band gap of a representative set of metal oxides

The effect of the amount of Hartree–Fock mixing parameter (α) and of the screening parameter (w) defining the range separated HSE type hybrid functional is systematically studied for a series of seven metal oxides: TiO₂, ZrO₂, CuO₂, ZnO, MgO, SnO₂, and SrTiO₃. First, reliable band gap values were determined by comparing the optimal α reproducing the experiment with the inverse of the experimental dielectric constant. Then, the effect of the w in the HSE functional on the calculated band gap was explored in detail. Results evidence the existence of a virtually infinite number of combinations of the two parameters which are able to reproduce the experimental band gap, without a unique pair able to describe the full studied set of materials. Nevertheless, the results point out the possibility of describing the electronic structure of these materials through a functional including a screened HF exchange and an appropriate correlation contribution.