## 3 Results and Discussion
### Stabilization Effect of Additional Water on the Water Dissociation Reaction  
A final point needs to be addressed, i.e., the stability of the dissociation products, because the reverse reaction barriers tend to be low. A quantitative analysis is difficult because reaction barriers are difficult to evaluate in systems where there may be several reaction pathways. Nonetheless,we have attempted such analysis by calculating the water dissociation reaction barrier using a standard transition-state search algorithm [38; 39], in the presence of a varying amount of additional water molecules. In particular, we investigate the reaction mechanism involving MeOH assistance as discussed above, and compare that with the dissociation of pure H\({}_{2}\)O found previously [14]. Results are presented in Table 3 and Figure 4.  
In both cases--the MeOH assisted and pure H\({}_{2}\)O dissociation--it is obvious that increasing the number of water molecules decreases the forward reaction barrier for the individual reactions. This behavior has been analyzed in detail for the H\({}_{2}\)O case, where it was found that small water clusters form and are, in turn, responsible for decreasing the barrier [14]; we propose a similar mechanism in the presence of MeOH. However, more importantly, increasing the number of water molecules also increases the backward barrier, i.e., the barrier for the reverse reaction. In fact, in some cases (such as the pure water dissociation with only one H\({}_{2}\)O) the reverse barrier is so low that the product state cannot be considered stable at all and, even at low temperature, will recombine back into water molecules. It is thus the presence of additional water molecules that stabilizes the product state and makes the reaction observable. Note that experimentally, it is very difficult to determine the exact amount of water molecules inside the MOF pore and nearby the reaction site, but it is estimated based on isotherm measurements corrected to the higher temperature (180 \({}^{\circ}\)C), that 8 Torr of water result in at least 6 to 8 water molecules in the MOF unit cell (calculations based on the ideal gas law) [42]. In the previous section, comparison between pure water and water/alcohol mixtures was based on total energy calculations, providing good support for experimental observations. Calculating reaction barriers through transition-state searches becomes increasingly more complex in the presence of more water molecules (due to the vastly growing space of possible arrangements and reaction pathways) so that such calculations only provide upper limits for reaction barriers. Due to their  
Figure 4: Reaction barriers for the MeOH assisted and pure H\({}_{2}\)O dissociation in the presence of varying amounts of additional water molecules. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Water Systems** & **No. H\({}_{2}\)O** & \begin{tabular}{c} **Initial State** \\ **(eV)** \\ \end{tabular} & \begin{tabular}{c} **Transition** \\ **State (eV)** \\ \end{tabular} & \begin{tabular}{c} **Final State** \\ **(eV)** \\ \end{tabular} & \
\begin{tabular}{c} **Forward** \\ **Barrier (eV)** \\ \end{tabular} &
\begin{tabular}{c} **Backward** \\ **Barrier (eV)** \\ \end{tabular} \\ \hline \multirow{2}{*}{MeOH + H\({}_{2}\)O} & 1 & 0 & 1.607 & 1.386 & 1.607 & 0.220 \\  & 4 & 0 & 0.932 & 0.598 & 0.932 & 0.333 \\ \hline \multirow{4}{*}{H\({}_{2}\)O} & 1 & 0 & 1.085 & 1.054 & 1.085 & 0.031 \\  & 2 & 0 & 0.964 & 0.832 & 0.964 & 0.132 \\ \cline{1-1}  & 3 & 0 & 0.990 & 0.571 & 0.990 & 0.418 \\ \cline{1-1}  & 4 & 0 & 0.688 & 0.530 & 0.688 & 0.158 \\ \cline{1-1}  & 5 & 0 & 0.690 & 0.580 & 0.690 & 0.110 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reaction barriers for the MeOH assisted and pure H\({}_{2}\)O dissociation in the presence of varying amounts of additional water molecules. complexity and computer time needed, we only investigated a limited set. For instance, barriers for a MeOH/water mixture are only calculated for one and four water molecules.