Multiple configurations of the two excess $4f$ electrons on defective ${\text{CeO}}_2\left(111\right)$: Origin and implications

Density-functional theory calculations have been carried out to systematically study single surface oxygen vacancies on ${\text{CeO}}_2\left(111\right)$. It is surprisingly found that multiple structures with the two excess electrons localized at different positions can exist. We show that the origin of the multiconfigurations of $4f$ electrons is a result of geometric relaxation on the surface and strong localization characteristic of $4f$ electrons in ceria. The importance of $4f$ electron structures is also presented and discussed. These results may possess implications for our understanding of materials with $f$ electrons.

Figure 1

(Color online) (a) Calculated structure of ${\text{CeO}}_2\left(111\right)$ (top view, bond length in $\text{Å}$) and illustrations of the ${\text{CeO}}_2\left(111\right)$ containing single (b) top-surface and (c) subsurface O vacancies. The exposed ${\text{Ce}}_{7c}$ atoms are in white, ${\text{O}}_{3c}$ in red (dark gray), and ${\text{O}}_{4c}$ in blue (light gray). This notation is used throughout the paper. In (b) and (c), several exposed Ce atoms at the first-(1), second-(2), third-(3), and fourth-neighbor (4) positions with respect to the O vacancy $\left(v\right)$ are labeled. Red $V$ represents top-surface O vacancy and light-blue $V$ subsurface O vacancy.

Figure 2

(Color online) Calculated structures (top view) of the ${\text{CeO}}_2\left(111\right)$ surface containing single [(a)–(g)] top-surface and [(h)–(I)] subsurface O vacancy and the corresponding estimated vacancy formation energies $\left(E_{\text{vac}}\right)$. The isosurface $\left(0.05e/{\text{Å}}^3\right)$ of calculated spin charge densities are in dark blue. They are at two second-neighbor (a) ${\text{Ce}}^{3+}$, (b) first- and second-neighbor ${\text{Ce}}^{3+}$, (c) two first-neighbor ${\text{Ce}}^{3+}$, (d) first- and forth-neighbor ${\text{Ce}}^{3+}$, (e) first-neighbor ${\text{Ce}}^{3+}$ in the second Ce layer and second-neighbor ${\text{Ce}}^{3+}$, (f) first-neighbor ${\text{Ce}}^{3+}$ in the second Ce layer and first-neighbor ${\text{Ce}}^{3+}$, (g) first- and third-neighbor ${\text{Ce}}^{3+}$, with respect to the top-surface O vacancy; and (h) two second-neighbor ${\text{Ce}}^{3+}$, (i) separated first- and second-neighbor ${\text{Ce}}^{3+}$, first-neighbor ${\text{Ce}}^{3+}$ in the second Ce layer and (j) second-neighbor ${\text{Ce}}^{3+}$, (k) two first-neighbor ${\text{Ce}}^{3+}$, (l) first-neighbor ${\text{Ce}}^{3+}$ in the second Ce layer and first-neighbor ${\text{Ce}}^{3+}$, with respect to the subsurface O vacancy.

Figure 3

(Color online) Calculated structures (top view) of single ${\text{O}}_2$ molecule adsorbed at the ${\text{CeO}}_2\left(111\right)$ containing single (a) top- and (b) subsurface O vacancy and the estimated adsorption energies $\left(E_{\text{ad}}\right)$. The adsorbed ${\text{O}}_2$ is in orange.