## 2 Reaction Mechanisms and Kinetics of Electrocatalytic Nitrate Reduction
### DFT Calculation as an Advanced Tool for eNO\({}_{3}\)R
#### 2.2.5 Analyzing Experimental Data vs. DFT for Nitrate Reduction  
The comparison between experimental data and DFT-based simulations reveals notable discrepancies in the detailed energetics of intermediate steps within eNO\({}_{3}\)R. Regarding that, [PERSON] et al. [73] reported that product selectivity and Faradaic efficiencies (FE) for N\({}_{2}\)O, NH\({}_{3}\), and H\({}_{2}\) obtained from a nanostructured Ag electrode in phosphate-buffered saline (PBS) show distinct potential windows, where NH\({}_{3}\) production becomes dominant at lower potentials, and N\({}_{2}\)O prevails at higher potentials. This experimental observation aligns with predictions from DFT-based microkinetic simulations, as shown in Figure 8a,b, which highlight potential-dependent shifts in selectivity. However, discrepancies in the energetics of intermediate steps arise; while DFT predicts the RDS for NH\({}_{3}\) production as the electrochemical protonation of H\({}^{*}\)NOH, experimental results indicate deviations in the exact potential for product transitions. Similarly, the competition between NH\({}_{2}\)OH and NH\({}_{3}\) production is captured by DFT, though slight variations in NH\({}_{2}\)OH suppression onset are noted experimentally [73]. Despite these differences, microkinetic modeling plays a crucial role in bridging the gap between theory and experiment. As shown by [PERSON] et al. [74] who compared experimental observations with model predictions to elucidate nitrate reduction reaction (NRA) dynamics on transition metal surfaces (Figure 8c,d). The experimental  
Figure 7: (**a**) The differences between the limiting potentials for the eNO\({}_{3}\)R and HER, i.e., U\({}_{\text{L}}\)(eNO\({}_{3}\)R) – U\({}_{\text{L}}\)(H\({}_{2}\)), are plotted against the limiting potentials for the eNO\({}_{3}\)R, U\({}_{\text{L}}\)(eNO\({}_{3}\)R), for different transition metals. U\({}_{\text{L}}\)(eNO\({}_{3}\)R) – U\({}_{\text{L}}\)(H\({}_{2}\)) shows the trend in selectivity for the eNO\({}_{3}\)R over the HER, and U\({}_{\text{L}}\)(eNO\({}_{3}\)R) reflects the trend in eNO\({}_{3}\)R activity. The most promising catalysts lie in the upper-right corner of the plot [66]. (**b**) Gibbs free energy diagram of the hydrogen evolution reaction (HER) on the TM\({}_{2}\)/N\({}_{6}-\) G (TM = Sc to Zn) surface [68].  
rate-order profiles exhibited a potential-dependent peak, characteristic of a competitive Langmuir-Hinshelwood mechanism, indicating interdependence between H* and nitrate adsorption. By calibrating a microkinetic model to incorporate the rate-limiting steps of nitrate reduction and hydrogen evolution kinetics, they achieved agreement between experimental and modeled nitrate rate orders by adjusting thermodynamic parameters (\(\Delta\)G\({}_{\text{H*}}\)-\(\Delta\)G\({}_{\text{NO}_{3}}\)-). The model effectively captured observed trends, including shifts in peak rate order and mass transfer limitations, reinforcing its validity and providing key insights into the competitive adsorption and reaction kinetics across various transition metal catalysts [74]. Furthermore, the integration of machine learning and Artificial Intelligence techniques holds significant potential to further facilitate these modeling efforts by optimizing parameter selection and improving predictive accuracy. This will be explored in the next section.