■ INTRODUCTION

Oxygen reduction reaction (ORR) is essential to a variety of renewable energy technologies such as fuel cells and metal-air batteries. Platinum is the best-performing catalyst for ORR. However, it suffers from high cost, which impedes its commercial use. [1][2][3][4] To overcome this obstacle, tremendous research efforts have been dedicated to finding cost-effective alternative catalysts to Pt. [5][6][7][8][9][10] One of the most promising candidates is single iron atoms embedded in nitrogen-doped graphene (Fe-N-C), which is often used in acidic conditions. [11][12][13][14][15][16][17][18] Despite extensive studies on this catalyst, it is still unknown what step limits the ORR rate on Fe-N-C. The lack of this critical information significantly limits catalyst development.

A commonly suggested pathway for ORR on Fe-N-C has the following steps (Figure 1a): * + O 2 → *OO, *OO + H + + e -→ *OOH, *OOH + H + + e -→ *O + H 2 O, *O + H + + e - → *OH, *OH + H + + e -→ * + H 2 O. Experimental determination of the rate-limiting step is challenging. On the other hand, density functional theory (DFT) offers a means to calculate the reaction energetics, including activation energies, and thus in principle can answer the question about the rateliming step. However, directly calculating activation energies of heterogeneous electrochemistry is difficult due to the complexity of the system, which requires careful treatments of the effects of solvation and electrode potential. [19][20][21][22][23][24][25][26][27][28][29] Therefore, most computational studies calculate the thermodynamics of each step and use it to infer the kinetics, based on the assumption that the most thermodynamically uphill (or the least downhill) step has the highest activation energy. Those papers typically show that either the *OO + H + + e -→ *OOH or the *OH + H + + e -→ * + H 2 O step is the thermodynamically limiting step. [29][30][31][32][33][34][35][36] Both steps involve hydrogenation of the adsorbate. However, thermodynamics does not necessarily correlate with kinetics. Hence, the information on activation energies is indispensable to identify the rate-limiting step.

To address this critical need, here we calculate the activation energies of ORR steps on Fe-N-C, using a recently developed model: "constant-potential hybrid solvation-dynamic model" (CP-HS-DM). 20 This model enables effective simulation of electrochemical kinetics at the solid-water interface, by directly including the explicit solvation and electrode potential into the model. The results reveal a different reaction mechanism from the commonly believed one: instead of the hydrogenation step, the rate-limiting step is the replacement of the preadsorbed H 2 O molecule by the O 2 molecule on the Fe atom; despite being an apparent "thermal" process, the activation energy of this step decreases with decreasing electrode potential, due to the enhanced Fe-O 2 binding while weakened Fe-OH 2 binding at a lower potential. Our work provides new insights into the ORR and Fe-N-C catalytic mechanisms and highlights the significance of kinetic information that is generally lacking in the current study of heterogeneous electrocatalysis.

■ METHODS

The CP-HS-DM 20 is one realization of the constant-potential ab initio molecular dynamics (cp-AIMD) with explicit water. The supercell contains a thin film of explicit water molecules on top of the catalyst. The remaining space is filled with implicit solution modeled as a continuous dielectric medium with point ionic charges. This implicit solution serves to balance the extra charges in the explicit region and introduces a region with a flat electrostatic potential profile that can be used to extract the relative electrode potential. The structure is evolved using AIMD with an enhanced sampling technique, and the electron number changes under potentiostat.

In this work, we perform CP-HS-DM simulation using Vienna Ab initio Simulation Package (VASP), 37,38 leveraging the VASPsol 39,40 implicit solvation model. We have implemented the cp-AIMD method as a patch to the VASP code (the patch file is available to the readers upon reasonable request). To compute the free energy profile, we employed thermodynamic integration. Specifically, we first run slowgrowth simulation 41 to obtain a preliminary profile and then run blue moon simulation 42,43 to obtain a more accurate one. To model the acidic conditions, we add one H to the explicit water molecules. The details of our calculations can be found in the Supporting Information (SI).

■ RESULTS AND DISCUSSION

Our study first focuses on U = 0.5 V vs SHE because it is within the typical range of working potentials. 12,44,45 Our cp-AIMD simulations show that when Fe-N-C is in contact with water, a H 2 O molecule is adsorbed onto the Fe site. When we intentionally desorb H 2 O via slow growth, another H 2 O molecule will occupy the Fe site (see SI Section 3). This result indicates that before ORR, the Fe site is already occupied by a H 2 O molecule, consistent with a recent paper. 29 Then how does the adsorption of O 2 take place? We find that the adsorption of O 2 occurs concertedly with H 2 O desorption. As shown in Figure 1c H 2 O step as an example. In this step, as the *O-OH bond breaks, the proton attacks the generated OH to form H 2 O.

During this process, the system gradually acquires excessive electron concentrating on the higher O, which attracts the proton closer and facilitates the H 2 O formation. Consequently, the barrier is low, only 0.15 eV. It is worth noting that this change in electron number cannot be observed in the conventional constant-charge simulation, thereby necessitating the use of the constant-potential method as we employed here. Additionally, the Fe-N-C surface exhibits a positive charge under 0.5 V. This is because its potential of zero charge (PZC) is lower than 0.5 V. In other words, at a charge-neutral state,

Journal of the American Chemical Society

the Fermi level of Fe-N-C is higher than that of the electrode. To align the Fermi levels, Fe-N-C has to lose electrons, thereby acquiring a positive charge. Another interesting finding is that at the initial state, the proton is located closer to the higher O than the lower O in the *O-OH on Fe-N-C. This contrasts the Co-N-C catalyst, where the proton prefers the lower O. 20 Therefore, after the proton attacks the closer O, Fe-N-C will generate H 2 O, whereas Co-N-C will produce H 2 O 2 . This explains the difference in ORR selectivity observed for these two catalysts. To check if our conclusion still holds at a lower potential, we also study ORR at U = 0.1 V vs SHE. This potential is chosen because it is not too low to be unrealistic but low enough to show a significant difference. 12,44,45 As shown in Figure 3, we find that all electrochemical steps become barrierless while the *H 2 O + O 2 → *O 2 + H 2 O step still has a barrier of 0.26 eV. Therefore, the rate-limiting step is still

It is interesting to see that the activation energy of *H 2 O + O 2 → *O 2 + H 2 O noticeably decreases when the potential is decreased (Figure 3). This challenges the conventional view that it is a thermal step (as it does not explicitly involve electron(s)) and should be potential-independent. To understand the origin, we calculate the adsorption energies of O 2 and H 2 O on Fe-N-C under different potentials (without solvent molecules for simplicity). As shown in Figure 4a, decreasing the potential enhances the O 2 adsorption while weakening the H 2 O adsorption. Therefore, the lower barrier at the lower potential can be explained by the stronger driving force provided by the enhanced binding with O 2 and the weakened binding with H 2 O.

The potential-induced change in the binding strength can be attributed to different surface charges under different potentials. Our calculations (without solvent for simplicity) show that the bare Fe-N-C acquires ∼1 electron as the potential decreases from 0.5 to 0.1 V. This large change in the surface charge results in a significant change in the electronic state occupation, thereby altering the chemical reactivity of Fe-N-C. 21 But why do O 2 and H 2 O have opposite responses to the surface charge? This can be explained by the opposite directions of charge transfer. We find that upon adsorption, O 2 gains electrons from Fe-N-C while H 2 O donates electrons (see Figure 4b). Increasing the electronic charges on Fe-N-C will enhance the electron transfer to the adsorbate while suppressing the back-transfer. Therefore, reducing the potential strengthens the binding with O 2 while weakening that with H 2 O. This mechanism suggests that to design more active sites for ORR, one may target those that are more negatively charged (under the same electrode potential), because they can have lower activation energies for the rate-

The charge transfer theory also explains the potential dependence of the adsorption energies of other intermediates (*OOH, *O, and *OH). As shown in Figure S9a, the potential decrease enhances their bindings with the catalyst. This can be attributed to the fact that they all gain electrons from the catalyst (Figure S9b).

Although our focus here is on the acidic conditions, as Fe-N-C is mainly used in proton exchange member fuel cells, it is worth considering other pH conditions. For the same RHE potential, the SHE potentials are lower under alkaline conditions than under acid conditions. In other words, the catalyst surface is more negatively charged under alkaline conditions. According to our findings, a more negatively charged site should have a lower barrier for the *H 2 O + O 2 → *O 2 + H 2 O step. On the other hand, the proton source is a water molecule under alkaline conditions and it is more difficult to donate protons than H 3 O + . Therefore, compared with acidic conditions, we anticipate that in alkaline conditions the *H 2 O + O 2 → *O 2 + H 2 O step will become easier, whereas the hydrogenation steps will become more difficult.

■ CONCLUSIONS

In this study, we employed an advanced first-principles model to reveal the rate-limiting step of ORR on Fe-N-C. We discovered a new mechanism that O 2 replaces the preadsorbed H 2 O on Fe through a concerted motion without leaving the Fe site bare. This step was found to have the largest activation energy among the ORR steps. The barrier of this step counterintuitively lowers with decreasing electrode potential, due to the stronger O 2 adsorption and weaker H 2 O adsorption when the surface carries more electronic charges. This can be further explained by the fact that O 2 adsorption gains electrons from the surface while H 2 O donates electrons to the surface. These results suggest that a more negatively charged site would be more active for the ORR. Our work emphasizes the importance of kinetic information in understanding and designing heterogeneous electrocatalysts.

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c09193.

General settings of DFT calculations; details of electronic charge calculation; structure evolution for water adsorption dynamics; details of energy barrier calculations; more reaction kinetics data; and adsorption energies and electronic charge transfer of ORR intermediates (PDF)