Extracting Features of Active Transition Metal Electrodes for NO Electroreduction with Catalytic Matrices

Electrocatalytic reduction of oxidized nitrogen compounds (NOx) promises to help rebalance the nitrogen cycle. It is widely accepted that nitrate reduction to NH4+/NH3 involves NO as an intermediate, and NO hydrogenation is the potential-limiting step of NO reduction. Whether *NO hydrogenates to *NHO or *NOH is still a matter of debate, which makes it difficult to optimize catalysts for NOx electroreduction. Here, “catalytic matrices” are used to swiftly extract features of active transition metal catalysts for NO electroreduction. The matrices show that active catalysts statistically stabilize *NHO over *NOH and have undercoordinated sites. Besides, square-symmetry active sites with Cu and other elements may prove active for NO electroreduction. Finally, multivariate regressions are able to reproduce the main features found by the matrices, which opens the door for more sophisticated machine-learning studies. In sum, catalytic matrices may ease the analysis of complex electrocatalytic reactions on multifaceted materials.


INTRODUCTION
Nitrogen is the most abundant element in the Earth's atmosphere, and various N-containing compounds are created and consumed in nature as part of a dynamic but delicate environmental equilibrium known as the nitrogen cycle. In a well-balanced nitrogen cycle, several biogeochemical processes successively transform atmospheric N 2 into NH 4 + , NO 2 − , and NO 3 − and back to N 2 . Specifically, nitrogen fixation in the soil in the form of NH 3 /NH 4 + originates from organic matter in decomposition, bacteria, and plants. In addition, natural nitrification processes occur in the soil that transform ammonia into nitrite and nitrate, and then denitrification bacteria or plants reduce the latter and release N 2 back to the atmosphere, closing the cycle. 1,2 Importantly, the Haber-Bosch synthesis (N 2 + 3H 2 → 2NH 3 ), 3,4 provided the basis for the massive production of synthetic fertilizers, which ultimately facilitated an unprecedented growth of the human population. 5 The Haber-Bosch synthesis is among the most energy-intensive industrial processes, requiring active Fe-based catalysts and high temperatures and pressures (400−500°C, 100−300 bar), 6 and the H 2 needed for the reaction is usually obtained from fossil fuels via steam reforming of natural gas. 7−9 Apart from that, the widespread use of fertilizers causes the excessive release of nitrate to the soil, which resulted in a tremendous imbalance of the nitrogen cycle. 10,11 In fact, ground and surface waters currently display alarming concentrations of nitrate and nitrite, which have presumably created dead zones in coastal areas 12 and may lead to severe health issues. 13,14 Denitrification of NO x compounds in electrolyzers is a promising strategy to help rebalance the nitrogen cycle. Indeed, N 2 , N 2 O, NH 3 , and NH 2 OH under mild operating conditions can be produced using electricity from renewable sources. 15,16 However, numerous challenges hamper the design of efficient and selective electrocatalysts made upon abundant elements. One such challenge is the elaboration of a comprehensive reaction mechanism that incorporates factors such as pH, applied potential, and structural sensitivity.
It is widely accepted that during NO 3 − reduction to NH 3 / NH 4 + , NO is formed. 17 Besides, NO hydrogenation is the potential-limiting step of NO reduction and is key to regulating the selectivity of NO x electroreduction. 17−20 Importantly, it is not yet obvious when *NO hydrogenation leads to *NHO or *NOH and various opinions are found in the literature. For example, using DFT calculations and classification methods, Wan et al. investigated the NO x reduction selectivity and activity of a series of metal electrodes. 21 They found that various Cu facets are selective to NH 3 by virtue of their moderate adsorption energies of *NO and *H. They further suggested *NHO as a hydrogenation intermediate for Ag and Au, whereas *NOH is formed on Cu. Moreover, Casey-Stevens et al. 18 explored possible mechanisms toward the formation of NH 4 + , NH 3 OH + , and N 2 O from NO electroreduction on various transition metal electrodes using DFT calculations. They found that *NOH formation is the potential-limiting step for NH 4 + production on Cu(111), Rh(111), and Pd(111), while for Ag(111) and Au(111) it is *NHO formation.
Clayborne et al. 20 combined ground-state and transitionstate DFT calculations to inspect *NO electroreduction on Pt(111). They concluded that the path leading to NH 3 /NH 4 + at low coverage of *NO involves *NOH. This adsorbate is also kinetically favored on Pt(100), as suggested by the agreement between the simulated and experimental reductive stripping voltammetry of NO. 22 Katsounaros et al. 19 combined experiments and DFT calculations to investigate the structuresensitive electroreduction of NO on Pt. They showed that Pt(111) and Pt(100) exhibit different behavior: at low coverage (0.25 ML *NO), Pt(111) hydrogenates *NO to *NOH. When the *NO coverage is 0.50 ML, *NO is initially reduced to *NHO, and then to *NOH. On Pt(100), at high *NO coverage (0.50 ML *NO), one-half of the *NO is hydrogenated to *NOH, and the other half to *NHO.
In perspective, all these observations suggest that *NO hydrogenation to *NOH or *NHO depends not only on the type of metal but also on additional factors such as the geometry of the surface sites and their availability. Hence, a fair question is whether the structural sensitivity of active NO electroreduction catalysts can be established in simple terms. To address this point, here we present "catalytic matrices", which help to rapidly examine the structure-sensitive activity and selectivity trends for electrocatalytic *NO hydrogenation on six active sites of various surfaces of nine transition metals. Catalytic matrices enable a statistical treatment of the trends that leads to qualitative and quantitative conclusions. In particular, the matrices show that active catalysts for *NO electroreduction ought to contain undercoordinated Cu sites, and active alloys may be formed that contain square-symmetry sites. Finally, we supplement our study by showing that the matrices are more descriptive than adsorption-energy scaling relations and that multivariate regressions can reproduce their main features, which opens the door for future studies with more advanced machine learning techniques.
The DFT calculations were carried out with the VASP code. 23 The Perdew−Burke−Ernzerhof (PBE) exchangecorrelation functional 24 was chosen because it accurately describes the three series of transition metals 25,26 and their low Miller index surfaces. 27 The valence electron density was expanded using a plane-wave basis set with a cutoff of 450 eV for the kinetic energy. The effect of the atomic cores on the valence electron density was incorporated by means of the projector augmented-wave method. 28 The Methfessel-Paxton approach 29 was used to smear the Fermi level with k B T = 0.2 eV, always extrapolating the total energies to 0 K upon convergence. The calculations were spin unrestricted for Co and Ni slabs and gas-phase NO. The numerical integration in the reciprocal space was carried out using Monkhorst−Pack 30 grids of special k-points. To avoid spurious electrostatic interactions between periodically repeated slabs, periodic images in the vertical direction were separated by more than 15 Å of vacuum and dipole corrections were also applied. The conjugate gradient algorithm was used for the geometry optimizations, with iterations performed until the maximal force on all atoms was below 0.05 eV Å −1 . The adsorbates, adatom islands, and the top two metal layers of the slabs were relaxed in all directions, while the bottom layers were fixed at the bulk equilibrium distances to provide an adequate environment below the surface region. Boxes of 9 × 10 × 11 Å 3 were used to calculate O 2 , H 2 , H 2 O, N 2 , NH 3 , and NO, considering the Γ-point only, using Gaussian smearing and k B T = 0.001 eV, with further extrapolation to 0 K.
The Gibbs free energy difference for the considered elementary steps (ΔG) was approximated as ΔG ≈ ΔE DFT + ΔZPE − TΔS + ΔE solvation , where ΔE DFT is the PBE-calculated energy difference, ΔZPE is the zero-point energy change, and TΔS is the corresponding entropy change at 298.15 K. For gasphase molecules the total entropies were obtained from thermodynamic tables, 31 and their free energies were corrected semiempirically (more details on this procedure are available in section S1), 32−35 while for adsorbates ΔS only includes vibrational entropies. ΔE solvation is the contribution of solventadsorbate interactions to the free energy, which we evaluated using four different solvation approaches, see sections S1 and S2. The results in the figures and tables below are from an approach combining microsolvation 36 and implicit solvation. 37 Finally, the energetics of proton−electron pairs was described by means of the computational hydrogen electrode, which seizes the equilibrium in solution between those and gaseous hydrogen. 38

RESULTS AND DISCUSSION
Electrocatalytic hydrogenation of *NO in acid media involves a proton−electron transfer and two possible products can be formed:  Table 1 is a structure-sensitive matrix for the selectivity of *NO hydrogenation on late transition metal surfaces. The matrix shows on a per metal and facet basis the cases where *NOH, *NHO or both are the most stable products of *NO hydrogenation. Since the accuracy of DFT-PBE calculations is around ±0.1 eV, we consider *NOH and *NHO to be similarly stable when: abs(ΔG NHO − ΔG NOH ) < 0.1 eV. In such case, both hydrogenated intermediates are likely to be formed and transition-state searches are advisable. 20 We note that Table 1 contains data with a mixed solvation approach 36 and analogous tables for data in a vacuum and with the remaining solvation methods are reported in Tables S2−S5.
The selectivity matrix can be analyzed in terms of its rows (metals) and columns (active sites), such that it is both material-and structure-sensitive. According to the rows, *NHO dominates on Cu, Ag, and Au (group 11 of the periodic table). *NOH or both are common on Ni, Pd, and Pt (group 10). On Co, Rh, and Ir (group 9) the most common product is again *NHO, particularly when the adsorption sites are undercoordinated and/or have square symmetry. In turn, the columns of the selectivity matrix indicate a clear difference among (111) terraces and the other surface sites: most facets are statistically inclined toward *NHO except for (111) terraces. This means that Cu, Ag, Au, and Pd polycrystalline electrodes would be well represented by the (111)  For comparison, the selectivity trends are presented in Figure 2 as a parity plot. In it, the adsorption energies of the two competing adsorbates of *NO hydrogenation are plotted as a scaling relation. 39 Data points above the parity line (where ΔG NHO = ΔG NOH ) represent sites inclined to produce *NOH, and the opposite is true for sites producing *NHO. The selectivity matrix in Table 1 is more illustrative of the trends, as it shows that transition metals within a given group of the periodic table and also certain active sites tend to behave similarly. The difficulties extracting overall features from a large data set comprising numerous facets by means of scaling relations is exemplified in section S8, where a comprehensive analysis is provided. Our conclusion is that a matrix representation of the trends is, in this case, a more efficient way of condensing and analyzing large amounts of data. Table 2 summarizes the percentage of cases where *NOH, *NHO, or both, are the most stable intermediates. In general, *NHO seems to be the main product across the different surface sites among the nine metals analyzed here. In fact, nearly two-thirds of the active sites are predicted to produce *NHO from *NO hydrogenation. However, Table 2 shows that the selectivity varies from one group of the periodic table to another: *NHO formation is favored by Cu, Ag, Au (group 11), and Co, Rh, and Ir (group 9), while Ni, Pd, and Pt (group 10) have mixed selectivity or are inclined toward *NOH.
We note in passing that the results in Tables 1, 2, and S2−S8 stress the importance of accounting for solvent-adsorbate interactions but show that the different methods provide  Table 1. Structure-Sensitive Selectivity Matrix for *NO Hydrogenation on Transition Metals a a cn: coordination number of the active sites. Color code: blue for *NOH, red for *NHO; light blue/red indicates both adsorbates might be formed but with a slight tendency toward *NOH/*NHO, such that abs(ΔG NHO − ΔG NOH ) < 0.1 eV. similar conclusions. However, the choice of solvation method has proved crucial in quantitative analyses aimed at comparing with experiments, such as the assessment of catalytic pathways and onset potentials for other reactions. 36,40−42 Often, the potential-limiting step of NO reduction to NH 4 + and hydroxylamine on transition metals is the hydrogenation of *NO to *NHO or *NOH. 18−20 Thus, this step may as well be important for the activity and dictates the onset potential of the overall NO reduction reaction. While the equilibrium potential for NO reduction to NH 4 + is as high as 0.84 V vs RHE (reversible hydrogen electrode; hereon the potentials are reported in that scale), the onset potentials of transition metals are usually in the range of 0.0 to 0.3 V. [18][19][20]43 This implies that the overpotentials for NO reduction are at least 0.5 V and, in consequence, *NO hydrogenation might be as endothermic as 0.5 eV or more at the equilibrium potential. In this order of ideas, *NO hydrogenation can be used as a proxy to evaluate the activity of the entire catalytic pathway, and promising active sites can be the subject of further, more comprehensive studies, including kinetic analyses and competing reactions such as hydrogen evolution. 20−22 Based on the potential required for *NO hydrogenation, we provide in Table 3 an activity matrix for NO reduction where U onset is estimated as The matrix helps distinguish between very active (U onset > 0.3 V), active (−0.05 V < U onset < 0.3 V), and inactive sites (U onset < − 0.05 V), see further details in section S3. Interestingly, the rows of Table 3 show that the (100) terraces of most transition metals tend to be active for *NO hydrogenation, and that most facets of group 11 metals are also active, particularly those of Cu, which is known in experiments to be considerably active for NO 3 − reduction to NH 3 /NH 4 + via *NO. 44,45 Besides, the activity seems to rapidly decrease from group 11 to groups 10 and 9 of the periodic table. We note that U onset is a thermodynamic descriptor. When used to make activity predictions, it is assumed that reaction thermodynamics and kinetics are proportional throughout the reaction pathway. In particular, the potential-limiting step (PLS) and the ratedetermining step (RDS) should either coincide or at least be modified by the applied potential in the same way. 46 This and other assumptions and simplifications have recently been analyzed by Razzaq and Exner in the light of the free-energy span model. 47 It is possible to mimic the distinction between active and inactive sites in Table 3 by means of multivariate linear regressions, which are a supervised-type of machine learning approach (see section S10). Initially, we used only three attributes of the active sites as input variables, namely cn and the group number and period of the metal in the periodic table. These three parameters are present in catalytic matrices, as they have coordination numbers in the columns and 4d, 5d, and 6d metals in the rows. For Pt(111), for instance, the values are 9, 10 and 6, respectively. As shown in Table S12, the algorithm predicts a catalytic matrix that distinguishes between active and inactive sites in 74% of the cases. To increase the accuracy of the predictions, we added an additional parameter not directly related to the onset potential, ΔG *NHO − ΔG *NOH , which enables the model to correctly distinguish between active and inactive sites in 87% of the cases, see Table 4. We explain why we chose this energetic parameter, why it improves the predicted matrix and compare to other parameters in section S10. To further increase the activity and be able to distinguish between active and very active sites, it is probably necessary to add more parameters to the model and/or use advanced algorithms. However, these results are encouraging, as the main distinction between active and inactive sites can be replicated to a great extent by multivariate regressions using three basic and readily available attributes of active sites and an optional energetic parameter.  The percentages indicate the fraction of sites that prefer a given intermediate (*NOH, *NHO or both) in Table 1 with respect to the total number of sites. Light blue/red indicates that both adsorbates might be formed but lean toward *NOH/*NHO, such that abs(ΔG NHO − ΔG NOH ) < 0.1 eV). The overall percentage for *NHO is generally higher, given that elements in groups 9 and 11 favor its formation, while elements in group 10 favor *NOH.
Finally, it is possible to combine the selectivity and activity matrices (Tables 1 and 3) to simultaneously observe the trends in activity and selectivity of *NO hydrogenation, as shown in Table 5. The activity-selectivity matrix tells whether or not The matrix classifies the sites as very active (U onset > 0.3 V, yellow), active (−0.05 V < U onset < 0.3 V, orange) and inactive (U onset < −0.05 V, red). cn: coordination number of the active sites. Table 4. Predicted Activity Matrix for *NO Hydrogenation Using As Independent Variables cn, the Group and Period in the Periodic Table of   specific metals and facets are active for *NO hydrogenation and via which intermediate. This is important to know in electrocatalysis, as usually a given adsorbate is held responsible for the poor catalytic performance for a given reaction: that is the case of *CHO for CO 2 reduction to CH 4 , 48 and the case of *OOH for oxygen reduction and evolution. 49,50 We observe in Table 5 that group 11 metals are active for *NO hydrogenation via *NHO, and Cu(111) terraces are not active for *NO reduction at moderate overpotentials. Instead, most of the activity of Cu electrodes should come from undercoordinated sites. It is possible to make an overall assessment of transition metal electrodes for *NO hydrogenation. According to Table  5, among all the examined sites on transition metals, 52% are inactive as they need overpotentials larger than ∼0.90 V (i.e., U onset < −0.05 V) for *NO hydrogenation to become exergonic. Sites classified as very active are 11% of the total and all of them are inclined toward *NHO. Active sites inclined to *NHO correspond to 31% of the cases, 2% of the active sites lean toward *NOH, and 4% may concurrently produce *NOH and *NHO. Interestingly, for sites classified as active or very active, the selectivity is clearly inclined toward *NHO (96%) compared to *NOH (4%). Before closing the discussion, we note that Cu−Ni alloys have been shown in experiments to be highly active for nitrate reduction via *NO reduction, but the structural sensitivity of the active sites was not inspected. 45 Judging by the results in Table 5, we propose that the active Cu−Ni sites should have square symmetry and reduce *NO to *NHO.

CONCLUSIONS
Extracting general features of active and selective electrodes is a major challenge in electrocatalysis, where the interplay of pH, applied potential and structural sensitivity influences the intrinsic catalytic activity and selectivity of electrode materials. This is particularly true for reactions with numerous electron transfers and several products, as is the case of NO x reduction. Here we showed that the structural sensitivity of *NO hydrogenation on multifaceted transition metal electrodes can be described by means of catalytic matrices, which provide insightful qualitative and quantitative information in a swift way. Numerous surfaces are inclined to produce *NHO, and the selectivity is divided into three groups: *NHO predominates on Cu, Ag, and Au (group 11); *NOH or both are formed on Ni, Pd and Pt (group 10); and on Co, Rh, and Ir (group 9) *NHO is mostly produced, especially when the adsorption sites are undercoordinated and/or have square symmetry. Furthermore, group 11 elements (especially Cu) The matrix classifies the sites as very active (U onset > 0.3 V), active (−0.05 V ≤ U onset ≤ 0.3 V), and inactive (U onset < −0.05 V) and indicates in each case the most stable product of *NO hydrogenation. cn: coordination number of the surface atoms. tend to be active for *NO hydrogenation and likely for NO reduction to NH 4 + /NH 3 , while the (100) terraces of various transition metals should also be active. Multivariate regressions show that the features extracted from catalytic matrices can be machine-learned using basic features of the active sites, which opens the door for future studies.
Finally, activity-selectivity matrices indicate that active materials for NO reduction should usually contain undercoordinated Cu sites and be mediated by *NHO. This piece of information and others extracted from the catalytic matrices can be used to outline active sites that enhance materials for NO x electroreduction. ■ ASSOCIATED CONTENT