# Water on Actinide Dioxide Surfaces: A Review of Recent Progress
## 2 Oxygen Vacancies on AnO\({}_{2}\) Surfaces  
The effect of oxygen vacancies is crucial for understanding the reactivity of AnO\({}_{2}\) surfaces as radiation damage can lead to the formation of vacancies on these surfaces. Indeed, studies of the reactivity of H\({}_{2}\)O on UO\({}_{2}\) surfaces indicate weak reactivity on stoichiometric UO\({}_{2}\) (111) surface, while dissociative adsorption and hydrogen (H\({}_{2}\)) formation upon reduction of the surfaces with oxygen vacancies [45, 46]. Similarly, oxygen vacancies have been demonstrated to have a strong impact on the surface chemistry of transition metal and lanthanide oxides, as evidenced by the catalytic properties of CeO\({}_{2}\), a close sibling of AnO\({}_{2}\) sharing the crystal structure and oxidation states [38]. The formation of an oxygen vacancy in CeO\({}_{2}\) leaves two excess electrons in the host material, which localize at two 4\(f\) orbitals of Ce sites, reducing them to Ce\({}^{3+}\)[47]. The formation of Ce\({}^{3+}\) has been demonstrated to alter the reactivity of CeO\({}_{2}\) (111) surface, such as the activation of the acetaldehyde for coupling reactions [48]. The integrated experimental and theoretical efforts have made great progress in understanding its surface reactivity and reaction mechanism. In this section, we will illustrate the progress for the AnO\({}_{2}\) systems.  
\begin{table}
\begin{tabular}{c c c c} \hline
**References** & **Methods** & \(\Upsilon_{\text{(111)}}\) & \(\Upsilon_{\text{(110)}}\) & \(\Upsilon_{\text{(100)}}\) \\ \hline [PERSON] et al. [2] & GGA & 0.59–0.33 & 1.01–0.83 & 1.21–1.07 \\ \hline [PERSON] et al. [37] & GGA + \(U\) & & & \\  & (\(U\) = 4 eV) & 0.78 & 1.05 & 1.47 \\ \hline [PERSON] et al. [40] & Hybrid functional & 0.94 & - & - \\ \hline [PERSON] et al. [41] & GGA & 0.888 & - & - \\ \hline [PERSON] et al. [42] & GGA + \(U\) & 0.76–0.78 & - & - \\ \hline [PERSON] et al. [22] & GGA + \(U\) & 0.71 & 1.08 & 1.49 \\ \hline [PERSON] et al. [43] & GGA + \(U\) & 0.73 & 1.16 & 1.46 \\ \hline [PERSON] et al. [20] & GGA + \(U\) & 0.48 & 0.77 & 1.25 \\ \hline [PERSON] et al. [25] & Ionic shell model & 1.064 & 1.561 & - \\ \hline [PERSON] et al. [27] & Born model & 1.27 & 2.0 & 2.72 \\ \hline [PERSON] et al. [29] & Pair potentials & 1.29 & 2.04 & 2.45 \\ \hline [PERSON] et al. [30] & Ionic crystal & 1.24 & - & 2.22 \\ \hline [PERSON] et al. [31] & Tight-binding & 1.07 & 1.72 & 2.03 \\ \hline [PERSON] et al. [32] & Born-Mayer model & 1.030 & - & - \\ \hline [PERSON] et al. [26] & Thermodynamic & 0.95 & 1.266 & 1.333 \\ \hline [PERSON] et al. [33] & Pair potentials & 1.14 & - & 1.60 \\ \hline \end{tabular}
\end{table}
Table 2: UO\({}_{2}\) surface energies in units of J/m\({}^{2}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**References** & **Methods** & \(\Upsilon_{\text{(111)}}\) & \(\Upsilon_{\text{(110)}}\) & \(\Upsilon_{\text{(100)}}\) \\ \hline [PERSON] et al. [44] & LDA/GGA + \(U\) & 0.72–1.04 & 1.20–1.44 & 1.52–1.84 \\ [PERSON] et al. [28] & DFT & GGA + \(U\) & 0.72–0.74 & 1.10–1.13 & 1.64–1.69 \\  & (\(U\) = 3.3 eV) & 0.74 & 1.15 & 1.76 \\ [PERSON] et al. [37] & GGA + \(U\) & & & \\  & (\(U\) = 4 eV) & & & \\ \hline \end{tabular}
\end{table}
Table 3: PuO\({}_{2}\) surface energies in units of J/m\({}^{2}\).