## 2 Reaction Mechanisms and Kinetics of Electrocatalytic Nitrate Reduction
### DFT Calculation as an Advanced Tool for eNO\({}_{3}\)R  
In recent years, significant advancements have been made in using Density Functional Theory (DFT) to simulate the mechanisms of nitrate reduction, providing new insights into this process. DFT calculations have revealed critical details about the adsorption energies of various nitrogen species (e.g., NO\({}_{3}^{-}\), NO\({}_{2}^{-}\), NO, N\({}_{2}\), etc.), which are necessary for assessing the catalytic activity of different materials. The adsorption of nitrates plays a crucial role in electrocatalytic processes as it represents the first step. Employing DFT calculation, it  
Figure 3: The proposed direct electron reduction and indirect adsorbed hydrogen reduction in nitrate electroreduction.  
has been demonstrated that NO\({}_{3}^{-}\) can be adsorbed on the active site via chemisorption (2O and 1 O patterns) or physisorption (Figure 4) [50].  
Furthermore, the presence of oxygen species at the catalytic sites is significant because it can facilitate this bond-breaking process, making it easier for the subsequent steps of nitrate reduction to occur. The subsequent steps of the mechanism following nitrate adsorption are generally exothermic, indicating the presence of multiple rate-determining steps within the process [51]. DFT, in conjunction with the use of descriptors, has proven instrumental in predicting novel materials by identifying specific RDS, as illustrated in Table 2.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Electrode Materials** & **Free Energy Diagram** & **Rate Determining Steps** & **Refs.** \\ \hline Cu catalyst anchored on porous N-doped carbon. (Cu\(-\)NC) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pathways and limiting steps for novel categories synthesizing electrode materials for eNO\({}_{3}\)R using DFT calculations.  
Figure 4: Three possible configurations for the adsorption of NO\({}_{3}^{-}\).  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Electrode Materials** & **Free Energy Diagram** & **Rate Determining Steps** & **Refs.** \\ \hline Au (111) (in yellow), Au (331) (in blue), Pd modified Au(331) (in red). & \(\mathrm{NO_{7}^{-}(ads)\to NO_{2}^{-}(ads)+O_{(ads)}}\) & \(\mathrm{NO_{7}^{-}(ads)\to NO_{2}^{-}(ads)+O_{(ads)}}\) \\ Au (111) (in yellow), Au (331) (in blue), Pd modified Au(331) (in red). & \(\mathrm{NO_{7}^{-}(ads)\to NO_{(ads)}+O_{(ads)}}\) & [55] \\ Au (111) (1.74 eV) & Au (331) (0.83 eV) & \\ Au (331) (0.23 eV) & Pd-Au (331) (0.23 eV) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._This approach offers deeper insights into the selective catalytic reduction mechanisms of nitrates into gaseous nitrogen or ammonium. Similar advancements have been observed in hydrogen evolution reactions (HER), highlighting the competitive nature of these processes with eNO\({}_{3}\)R. Furthermore, the integration of artificial intelligence (AI) and machine learning (ML) provides a promising avenue for predicting catalytic performance and significantly reducing the computational demands of DFT, thereby accelerating material discovery and optimization.