Hybrid-DFT+V$_w$ method for accurate band structure of correlated transition metal compounds: the case of cerium dioxide

Hybrid functionals' non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a know drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT+V$_w$ method [V. Iv{\'a}dy, et al., Phys. Rev. B 90, 035146 (2014)]. Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT+V$_w$ functional can be determined from approximate quasi-particle spectra. The proposed technique leads to a reduction of self-interaction and provides improved description for both $s$ / $p$ and $d$ / $f$-electrons of the simulated system. The performance of our charge self-consistent method is illustrated on the electronic structure calculation of cerium dioxide where good agreement with both quasi-particle and experimental spectra is achieved.