# A Deeper Insight on the Stability of Water-Induced Reconstruction of Anatase (001) Surface
## 4 Discussion  
Two main results of the previous section are worth to be analyzed and discussed: first the stability hierarchy between the three WIR surface geometries that have been considered, namely (2 \(\times\) 2), (2 \(\times\) 3), and (2 \(\times\) 4), is changed when the missing part of the dispersion energy, the one that is typically due to the bulk water above the surface, is included. Hence, the results obtained in vacuum might change in bulk water as evidenced by the change of the positions in the stability hierarchy between (2 \(\times\) 2) and (2 \(\times\) 4): In bulk water, indeed, the (2 \(\times\) 4) surface is more stable than the (2 \(\times\) 2) that, on the contrary, appears to be more stable in vacuum. This behavior is related to the different values measured for the \(\Delta E_{slab-bulk\_water}^{d}\) energy data shown in Table 2: the dispersion energy change, due to the interaction with the bulk water, between the reconstructed and the unreconstructed surfaces increases with the surface area (also this term per unit area increases with the area as well). Then, according to the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Surface Reconstruction** & \(\Delta E_{slab-bulk\_water}^{d}\) **(eV)** & \(E^{a^{\prime}}\) **(eV)** & \(\gamma^{\prime}\) **(J/m2)** \\ \hline (2 \(\times\) 2) & \(-\)0.0302 & \(-\)1.06 & 0.51 \\ (2 \(\times\) 3) & 0.0057 & \(-\)1.82 & 0.42 \\ (2 \(\times\) 4) & 0.0476 & \(-\)2.25 & 0.47 \\ (2 \(\times\) 6) & 0.1355 & \(-\)2.58 & 0.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average adsorption and surface energy values corrected with the dispersion energy contribution from bulk water. Figure 3: Initial (**a**) and final (**b**) adsorption configurations of one water molecule on adsorption sites at the middle of the terrace in a (2 \(\times\) 6) reconstructed surface. Red: Oxygen; Grey: Titanium, white: Hydrogen. The adsorption is molecular. Equation (4), the dispersion energy of bulk water \(E_{H_{2}O}^{d}\) contributes to lower the adsorption energy. The surface energy is obtained from the corrected values of the average adsorption energy by dividing for the surface area and this reduces the positive correction term (that lowers the absolute value of the adsorption energy) at larger extent in larger areas. In other words, the correction per unit area is greater for (2 \(\times\) 2) than for (2 \(\times\) 4) thus resulting in the inversion of stability. It is interesting to note that the correction due to the dispersion energy results in closer surface energy values between (2 \(\times\) 3) and (2 \(\times\) 4). Moreover, the evidence that the adsorption in the (2 \(\times\) 6) reconstructed surface is molecular also in the middle of the terrace, evidence that we have got after various attempts to obtain a dissociative adsorption, indicates that the (2 \(\times\) 3) reconstruction should be, most probably, thermally activated because we expects the existence of an energy barrier for a further dissociative adsorption along [100] as soon as the ridge is already formed. Lastly, because the adsorption on the (2 \(\times\) 3) and (2 \(\times\) 4) water reconstructed surfaces is molecular [27], it is plausible that in bulk water the hierarchy could be further changed if one takes into account the molecular adsorption energy occurring on the available sites. Indeed also molecular adsorption events might release some energy per unit area due to the small, but not negligible, surface relaxation. For this reason we have sampled all the possible adsorption sites on the  
The adsorption energy values shown in Table 3 are larger for (2 \(\times\) 4) than for (2 \(\times\) 3) and this is consistent with the lower residual stress found in (2 \(\times\) 3). This circumstance, anyway, tells us that the surface relaxation induced by molecular adsorption onto (2 \(\times\) 4) should be larger than the one occurring on (2 \(\times\) 3).