# Water on Actinide Dioxide Surfaces: A Review of Recent Progress
## 1 Introduction
This work is not a complete review of all the efforts in the field, but rather we focus on the recent relevant progress in hope that this review can encourage broader interests and further studies on the surface chemistry of AnO\({}_{2}\). Bulk AnO\({}_{2}\) from the elements Th through Cf has been observed to crystalize in a fluorite structure, as shown in Figure 1[6]. In this structure, each actinide atom is eight-fold coordinated, and the oxygen atom is four-fold coordinated. Each actinide atom is formally in the +4 oxidation state, and the oxygen atoms are in the \(-2\) state. The properties of actinide materials are closely dependent on the contraction and stabilization of 5\(f\) orbitals traversing the actinide series. For example, the lattice constant of bulk AnO\({}_{2}\) shows a monotonic decrease from ThO\({}_{2}\) to CfO\({}_{2}\), however, it deviates from the trend at CmO\({}_{2}\) as a result of orbital mixing and covalency between the metal 5\(f\) and the oxygen 2\(p\) orbitals. This increased orbital mixing can be tracked down to the proximity in energy between those two orbital manifolds and is now referred to as energy-driven covalency in the literature [21]. The surface properties (surface energy, reconstruction, reactivity, and so on) of AnO\({}_{2}\) are highly dependent on the surface geometry. The top and side views of the low indexed (111), (110), and (100) surfaces of AnO\({}_{2}\) are shown in Figure 2. Along the (111) direction, the surface consists of alternating oxygen and actinide layers with a tri-layer structure (O-An-O). Each tri-layer has a net dipole moment of zero in the direction perpendicular to the surface [22], and the most stable surface is terminated by an oxygen layer. Along the (110) direction, a series of neutral AnO\({}_{2}\) planes are found; therefore,  
Figure 1: Unit cell of fluorite AnO\({}_{2}\). The blue and red atoms correspond to the actinide and oxygen atoms, respectively. the surface is nonpolar. Along the (100) direction, AnO\({}_{2}\) consists of alternating oxygen and actinide layers with the sequence of -O\({}_{2}\)-An-O\({}_{2}\)-An-O\({}_{2}\)-. Cleaving the crystal perpendicular to the (100) direction yields a polar surface with a net dipole moment, which is inherently unstable. A nonpolar stable surface is achieved by the removal of half of the oxygen atoms from the surface. This reconstruction leads to a slab-type unit cell of the form O-An-O\({}_{2}\)-(An-O\({}_{2}\))\({}_{n}\)-An-O\({}_{2}\)-An-O, as shown in Figure 2. The surface that contains 50% oxygen vacancies on the topmost oxygen layer has been observed for UO\({}_{2}\) (100) [23; 24]. Calculated surface energies of AnO\({}_{2}\) have been reported in several papers, particularly for ThO\({}_{2}\), UO\({}_{2}\), and PuO\({}_{2}\). Tables 1-3 summarize the surface energies for the low indexed (111), (110), and (100) surfaces, comparing the different reports that employed DFT and those that relied on other classical models [25; 26; 27; 28; 29; 30; 31; 32; 33]. It is seen that DFT calculations give rise to smaller surface energies than the classical models for ThO\({}_{2}\), UO\({}_{2}\), and PuO\({}_{2}\) surfaces. A variation in the surface energies is also observed for DFT calculations owing to the use of different level of theory and parameters in the calculations. Despite the variation in the calculated surface energies, all these calculations predict the (111) surface to have the lowest surface energy, hence being the most stable surface for AnO\({}_{2}\). Therefore, nanocrystals of AnO\({}_{2}\) are expected to be mostly terminated by the (111) surface and grow in octahedral shape, according to the Wulff constructions [34]. The relative stability of surfaces can be modified through the selective adsorption of organic ligands on different surfaces, which is key for the controlled synthesis of nanocrystals with different morphologies [35; 36].