# A Deeper Insight on the Stability of Water-Induced Reconstruction of Anatase (001) Surface
## 2 Methods  
All the calculations have been performed in the context of state of the art DFT with plane waves basis for both the electron density and wave-functions and periodic boundary conditions (PBCs). We have employed ultrasoft pseudopotentials [28] and the generalized gradient approximation (GGA) as implemented by the Perdew-Burke-Ernzerhof (PBE) scheme [29]. This computational approach has been already successfully employed in the previous literature revealing that PBE is the best GGA exchange-correlation scheme for the TiO\({}_{2}\)-water system [30]. Some technical aspects are worth to be mentioned such as the energy cutoff values employed for the wave functions and the electron density (60 Ry and 600 Ry respectively) and the threshold values employed for convergence of the atomistic optimization procedure, namely \(10^{-4}\) Ry / Bohr for residual forces and \(10^{-8}\) Ry for the total energy. It is important to evidence the necessity to add a dispersion correction term to the total energy in order to represent correctly the water-surface interaction. Generally speaking, this term is always expected to improve the energetics even though its inclusion causes a slight shortening of bond lengths and lattice constants [31; 32] that, however, remain within the DFT-PBE error bar. In the particular case of the TiO\({}_{2}\)-water system, we have recently shown that the inclusion of the dispersion term is mandatory to get a reliable description of the adsorption and the surface energy values for the reconstructed surface. For all these reasons, we have included in the Hamiltonian a dispersion energy term by employing the well known Grimme-D2 correction [33]. Special mention deserves to be devoted to the well known self-interaction problem affecting standard DFT resulting in a wrong description of the electron localization of 3d orbitals. This inaccurate description affects the electronic properties of the system and should be taken into account especially for transition metals such as Ti. A common method to correct the self-interaction error is the so called DFT+U scheme where the orbital occupancy is forced to integer values by the inclusion of the Hubbard term in the Hamiltonian [20]. However we have shown that, concerning the present system, the inclusion of the Hubbard term does not affect the energetic properties we are interested in because these properties, depending on the difference between the energy values obtained from different configurations (see below), are rather insensitive to the inclusion of the Hubbard term [27]. For this reason the Hubbard term has not been included in our model. Further details of the adopted computational scheme, together with the comparison of the bulk anatase properties obtained with the present scheme and other ones from the previous literature, can be found in a recent article [27]. The anatase (001) surface has been modeled through a slab geometry with the surface orthogonal to the z axis. The anatase bulk crystal was cleaved to expose the (001) surface and then relaxed. The slab contains four layers that provide an adequate geometry to describe in a correct way the relaxation  
Figure 2: The water induced (2 \(\times\) 4) reconstruction occurring in a 4 \(\times\) 4 supercell: **(a)** Side view, **(b)** top view. In the top view, the periodical arrangement of the hydrogen bonds along the ridge are evidenced with the arrow indicating the OH direction of the hydroxyl aligned along [100]. Red: Oxygen; Grey: Titanium, white **(a)** or cyan **(b)**: Hydrogen. pattern of the topmost layers in a real surface [23; 25; 32; 34]. Moreover the supercell size along the z-axis has been chosen to have a \(\sim\)40 A-thick vacuum region in order to avoid artifacts due to the PBCs. An important choice is to keep fixed just the atoms belonging to bottom-most layer in order to reproduce the bulk atomic positions. Indeed, the less rigorous choice, adopted by many authors, of keeping fixed two bottom layers does not guarantee the correct relaxation patten in the slab [27].