Empirical optimization of DFT  +  U and HSE for the band structure of ZnO

ZnO is a well-known wide band gap semiconductor with promising potential for applications in optoelectronics, transparent electronics, and spintronics. Computational simulations based on the density functional theory (DFT) play an important role in the research of ZnO, but the standard functionals, like Perdew-Burke-Erzenhof, result in largely underestimated values of the band gap and the binding energies of the Zn_3d electrons. Methods like DFT  +  U and hybrid functionals are meant to remedy the weaknesses of plain DFT. However, both methods are not parameter-free. Direct comparison with experimental data is the best way to optimize the computational parameters. X-ray photoemission spectroscopy (XPS) is commonly considered as a benchmark for the computed electronic densities of states. In this work, both DFT  +  U and HSE methods were parametrized to fit almost exactly the binding energies of electrons in ZnO obtained by XPS. The optimized parameterizations of DFT  +  U and HSE lead to significantly worse results in reproducing the ion-clamped static dielectric tensor, compared to standard high-level calculations, including GW, which in turn yield a perfect match for the dielectric tensor. The failure of our XPS-based optimization reveals the fact that XPS does not report the ground state electronic structure for ZnO and should not be used for benchmarking ground state electronic structure calculations.