Structural properties and quasiparticle band structure of zirconia

We report ab initio calculations of the structural and quasiparticle properties of ${\mathrm{ZrO}}_2$, otherwise known as zirconia. The plane-wave pseudopotential method is used to compute the structural properties of the cubic, tetragonal, and monoclinic phases of zirconia. Oxygen vacancies in the cubic phase are also studied using a supercell approach. The structural parameters, including all internal degrees of freedom of all phases, are relaxed. Excellent agreement is achieved with experiment and with other ab initio calculations available. We compute the quasiparticle band gaps within Hedin’s $\mathrm{GW}$ approximation using the method of Hybertsen and Louie, and confirm that the quasiparticle approach can be successfully applied to transition-metal oxides if the core-valence overlap is small. We predict the fundamental gap of pure cubic, tetragonal, and monoclinic zirconia to be 5.55 eV, 6.40 eV, and 5.42 eV, respectively. Within the $\mathrm{GW}$ approximation, the oxygen vacancy state in the cubic phase is found to be nondegenerate, fully occupied, and well separated from the valence and conduction bands, positioned 2.1 eV below the conduction band edge.