Limitations of Electrochemical Nitrogen Oxidation toward Nitrate

The electrocatalytic N2 oxidation reaction (NOR) using renewable electricity is a promising alternative to the industrial synthesis of nitrate from NH3 oxidation. However, breaking the triple bond in the nitrogen molecule is one of the most essential challenges in chemistry. In this work, we use density functional theory simulations to investigate the plausible reaction mechanisms of electrocatalytic NOR and its competition with oxygen evolution reaction (OER) at the atomic scale. We focus on the electrochemical conversion of inert N2 to active *NO during NOR. We propose formation of *N2O from *N2 and *O as the rate-determining step (RDS). Following the RDS, a microkinetic model is utilized to study the rate of NOR on metal oxides. Our results demonstrate that a lower activation energy is obtained when a catalyst binds *O weakly. We show that the reaction is extremely challenging but also that design strategies have been suggested to promote electrochemical NOR.

function of (∆E * O -∆E * OH ) and ∆E * N 2 , computed at a temperature of 300K. Fig. S7 shows the calculated activation energy for the reactionN 2 (g) + * O → * N 2 O over a IrSnO 2 surface.
A value of 0.343 eV is found at this level of theory if * N 2 is adsorbed on Ir while * O sits on Sn.

Computational Details
The computational analysis was carried out using the grid-based projector-augmented wave (GPAW) method, a DFT code based on a projected augmented wave (all-electron frozen core approximation) method integrated with the atomic simulation environment (ASE). S1-S3 The revised Perdew-Burke-Ernzerhof (RPBE) functional was used as an exchange-correlation functional. S4 The wavefunctions were represented on a uniform real-spaced grid with 0.18 Å grid-spacing and a vacuum of minimum 7 Å was employed. The unit cell of the rutile (110) metal oxide slabs consisted of four tri-layers, in total 24 metal atoms and 48 oxygen atoms corresponding to a (1 × 3) surface unit cell. A k-point mesh of (3 × 3 × 1) was used to sample the Brillouin zone. Besides the calculation for climbing image nudged elastic band (NEB) was performed with GPAW code. S5 The quasi-Newton minimization scheme was employed for the geometry optimizations, and the systems were relaxed until the forces were less than 0.05 eV/ Å. For MnO 2 , spin polarized calculation has been applied while non-spin polarized calculations are conducted for other catalysts. Structures, total energies, scripts to run calculations, and plotting methods are collected in the KatlaDB database available at this link: https://nano.ku.dk/english/research/theoretical-electrocatalysis/ katladb/.
Here, PBE + U method has been tested on SnO 2 (U = 3.5), PdO 2 (U = 7) and TiO 2 (U = 4.92) related to * N 2 , * O and * OH adsorption. Following the table below, there exists a functional dependency for the intermediates adsorption energies. Especially, for PdO 2 and TiO 2 , an enhancing adsorption of * N 2 and a weakening on energy difference between * O S-2 and * OH are observed. As for the PBE + U method, there is no consistency for which value of U should use. Besides, it has been reported that the thermodynamics and the kinetics (transition state) are no longer synchronous, and the choice of U implies an error in one or the other. S6 For now, U is generally obtained from fitting experimental band gaps.
Additionally, when calculating activation energies, the U depends on where you are in the reaction path. As a result, in principle, you should use a different value of U depending on adsorption state. However, the RPBE functional S4 level of theory has previously predicted trends in formation energy of rutile S7 and perovskiteoxides. S8 We therefore expected that it also correctly captured trends on adsorption energies. RPBE is employed here for all simulations. The adsorbates are treated as free molecules whose ∆G corrections are estimated from the reference molecules (Table S3)   As for the water influence, the continuum solvent model (CSM) has been tested for the adsorbates adsorption energies as shown in Table S4. It has been found that solvation effect S-4 is acceptable, especially for key descriptors: ∆E * N2 and ∆E * O -∆E * OH . In addition, almost no change in the NOR adsorbate binding energy with the inclusion of explicit water molecules is found. S10 A total of 10 electrons are transferred for completely oxidizing one N 2 towards HNO 3 .
For N 2 triple bond activation, three different possibilities are evaluated: I Dissociative path: N 2 (g) + 2 * → 2 * N; II Hydroxy path: III Oxygen path: We locate the reaction barriers for I dissociative path and II hydroxy path on different rutile surfaces using the nudged elastic band (NEB) computations. The same NEB method was used to get the * N 2 O(g) + * O → 2 * NO formation.     Regarding to the weak * O binding oxides, like SnO 2 and PdO 2 , the data is a little bit off the correlation fitting line shown in Fig. S6. For water electrolysis, the energy difference S-8 between * O and * OH adsorption is a good descriptor, while the * O adoption is a better parameter for describing the activation energy for * N 2 O, further for the FE of NOR. As a result in 2-D activity heatmap (Fig. 5 and Fig. S6

Microkinetic model
In this part, a more detailed derivation for the rate of NOR is provided. (1) For each step in quasi-equilibrium we can use the Langmuir isotherm: Using ; and * N 2 O + * O → 2 * NO in quasi-equilibrium, then For the rate-determining step, the rate of NOR (R(NOR)) is calculated in the following: At low temperatures, the surface will be dominated by adsorbed * O, such that * O is the most abundant reaction intermediate, implying that θ * can be written as: providing a more reactive oxygen, such as PdO 2 and SnO 2 , the potential dependent step is the formation of * O or * OH (see Figure 5a).
The effect from the partial pressure of N 2 (P N 2 ) and the content of water on the faradiac efficiency of NOR is investigated. A certain promotion is observed when increasing the pressure of N 2 and/or decreasing the amount of water which both aim for suppressing the OER catalytic activity.  In a three dimension dual-site catalyst, an another three dimension active site can have adsorbed * O right above the adsorbed * N 2 not like the neighbouring adsorption in metal oxides. The another active site serves as an * O shuttle, which does not require the * N 2 tilting or moving as shown in Fig. S8.
Initial state Final state Figure S9: Illustration for N 2 (g) + * O → * N 2 O formation on three dimension dual-site catalyst, here using diporphyrin as an example.
The ideal BEP for * N 2 + * O → * N 2 O is ∆E a N 2 O ≈ ∆E. With the utilization of the ideal BEP for * N 2 O formation, a higher activity for NOR can be achieved as shown in the 2-D activity heatmap (Fig. S10). This suggests that other structures, other than metal oxides, should be investigated for finding the BEP of * N 2 O formation close to the ideal. log 10 (FE%) Figure S10: 2-D activity heatmap describing FE for the nitrogen oxidation as a function of (∆E * O -∆E * OH ) and ∆E * N 2 , computed at a temperature of 300K with P N 2 = 1, P H 2 O = 1; It is important to note that the coverage of * O is kept fixed by applying a potential of (∆E * O -∆E * OH )/e. Here we assume that ∆E a N 2 O in BEP relation for * N 2 + * O → * N 2 O is close to ∆E (∆E a N 2 O = ∆E = ∆E * O + 2.8 eV see Fig. S3).