# A Deeper Insight on the Stability of Water-Induced Reconstruction of Anatase (001) Surface
## 3 Results
The details and technicalities of the simulations can be found in a recent article that was mostly focussed on the study of the water structure [39];
* the contribution to the dispersion energy change due to the interaction between the adsorbed (and dissociated) water and the TiO\({}_{2}\) slab is measured from the ground states of the water reconstructed and the unreconstructed surfaces;
* the dispersion energy of one water molecule in bulk water is measured and averaged from BOMD of bulk water at room temperature; for this term we have obtained \(E^{d}_{H_{2}O}\approx-0.0245\pm 2*10^{-3}\)_Wy_;
* the contribution to the adsorption energy coming from the interaction between the slab and the bulk water above it is dominated by the medium-long range interactions and thus by the dispersion part of the energy. Using the above assumptions it can be shown [27] that the adsorption energy, appropriately corrected with the dispersion terms that should be present in bulk water, casts into:  
\[E^{d^{\prime}}=E^{a}+\Delta E^{d}_{slab-bulk\ water}-2E^{d}_{H_{2}O} \tag{4}\]  
with  
\[\Delta E^{d}_{slab-bulk\ water}=E^{d}_{(TiO_{2})-(n-2)(H_{2}O)_{m}}+E^{d}_{2 (H_{2}O)_{d}-(n-2)(H_{2}O)_{m}}-E^{d}_{(TiO_{2})-n(H_{2}O)_{m}} \tag{5}\]  
where \((H_{2}O)_{m(d)}\) stands for molecular (dissociated) water molecules and \(E^{d}_{(TiO_{2})-q(H_{2}O)_{m}}\), \(E^{d}_{2(H_{2}O)_{d}-p(H_{2}O)_{m}}\) are respectively the dispersion energy of the TiO\({}_{2}\) slab interacting with \(q\) water molecules in bulk water and the dispersion energy term of the two adsorbed and dissociated water molecules interacting with \(p\) water molecules in bulk water. On the basis of this simple model, we have calculated the dispersion corrected values of the average adsorption and surface energy for \((2 xn)\) reconstructed surfaces with \(n\) = 2-4 as listed in Table 2:  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surface Reconstruction** & \(E^{a}_{(2 xn)}\) **(eV)** & \(\gamma_{(2 xn)}\) **(J/m\({}^{2}\))** & \(\sigma_{xx}\) **(kbar)** & \(\sigma_{yy}\) **(kbar)** \\ \hline \((2\times 2)\) & \(-1.38\) & \(0.32\) & \(-12.38\) & \(-0.76\) \\ \((2\times 3)\) & \(-2.16\) & \(0.30\) & \(-17.06\) & \(1.71\) \\ \((2\times 4)\) & \(-2.61\) & \(0.37\) & \(-20.50\) & \(2.7\) \\ \((2\times 6)\) & \(-2.98\) & \(0.55\) & \(-25.29\) & \(The surface energy values corrected with the dispersion energy contribution from the bulk water show a new stability hierarchy where the second most stable surface reconstruction is the (2 \(\times\) 4) one instead of the (2 \(\times\) 2) one. Moreover, while the surface energy values increase with respect to the one in vacuum, the difference between (2 \(\times\) 3) and (2 \(\times\) 4) is reduced. At this point, we have employed the (2 \(\times\) 6) surface reconstruction in order to reproduce in a doubled supercell the (2 \(\times\) 3) surface reconstruction. We have attempted to obtain a spontaneous dissociative adsorption in the middle of the terrace so as to reproduce a (2 \(\times\) 3) periodicity and we have checked several different initial configurations. However we have only obtained molecular water adsorption on the terrace, as reported in Figure 3.