Pros and cons of the time-dependent hybrid density functional approach for calculating the optical spectra of solids: a case study of CeO2

Abstract

The prediction of optical spectra of complex solids remains a great challenge for first-principles calculations due to the huge computational cost of the state-of-the-art many-body perturbation theory based GW-Bethe Salpeter equation (BSE) approach. An alternative method is the time-dependent density-functional theory (TDDFT) based on hybrid exchange–correlation functionals, which involves the essential ingredients of electron–hole interactions in its formalism in contrast to its local/semi-local functional counterparts. In this work, we investigate the optical absorption spectra of ceria (CeO₂), a prototypical lanthanide oxide with a 4f⁰ configuration, utilizing TDDFT based on four well-established hybrid functionals for ground state DFT calculations. All four functionals reproduce well the excitonic features of the experimental optical spectra, in spite of the significant differences in their band structures arising from different hybridization parameters (i.e. the fraction of the Hartree–Fock exchange and the screening parameter). It is demonstrated that the apparently weak dependence of the resulting optical spectra on the employed functionals is quite universal and applies to simple semiconductors such as Si and GaAs and insulator LiF as well. This study highlights the feasibility of TDDFT based on existing hybrids to describe optical spectra of solids, and also, points out the difficulty of obtaining accurate exciton binding energies using these hybrid functionals due to the strong functional dependence of quasi-particle band structures.