Reaction mechanism on Ni-C2-NS single-atom catalysis for the efficient CO2 reduction reaction

Abstract Ni-based single-atom catalysis (Ni-SAC) has been experimentally reported with superior performance in reducing CO2 to CO. However, due to the ambiguities in its structures, the active sites of Ni-SAC that are responsible for superior performance have not yet been resolved. This work investigates the CO2 reduction reaction (CO2RR) mechanism on Ni-SAC by carrying out quantum mechanics (QM) simulation to consider both solvation effects. After exploring multiple possible combinations of N, S, and C, we distinguish a Ni-SAC site with two C, one S, and one N, representing the best performance. The predicted formation energy is closely consistent with experimental onset potential. Our prediction also suggests further improvement by finely tuning the electronics state of metal sites by changing the SAC support. Graphical Abstract

answer the questions, such as if the catalytic performance can be improved, what the specific catalytic structure is.

Method
All of the calculations were first performed with the Vienna ab initio simulation package (VASP 5.4.4) [33][34][35], using generalized gradient approximation (GGA-PBE) [36] to describe exchange-correlation energy and the projector augmented wave (PAW) method [37] to account for electron-ion interactions. Meanwhile, van der Waals (vdW) interactions were taken into account using the DFT-D3 method [38][39][40]. The kinetic energy cutoff for plane wave expansions was set to 480 eV, and the gamma-centered k-mesh sampled the reciprocal space with a grid of 3 Â 3 Â 1. And using an implicit solvation model makes the calculated reaction conditions closer to the actual situation of the experiment [41]. The implicit solvation model of VASPsol is employed to describe the effect of electrostatics, cavitation, and dispersion on the interaction between a solute and solvent. The relative permittivity of the solvent is 78.4. The debye screening length is 3.0 Å [42,43]. In structure optimizing, the atoms were relaxed until the maximum residual force and energy went below the threshold value of 0.01 eV Å À1 and 10 À6 eV. The model is based on Ni-C 2 N 2 , in which a sulfur atom is doped to replace any nitrogen atom to form a Ni-C 2 -NS structure. The PBE-optimized lattice parameter 14.816 Å and the vacuum layers of at least 15 Å. the slab sizes are 6 Â 6 or 4 Â 4, depending on the number of atoms in simulation for enough computational efficiency. The optimized structures are shown in Figure S1.
The convergence criteria are 10 À5 eV energy differences for solving for local minima (initial states (IS) and final states (FS)) searching transient state (TS). All IS, TS, and FS geometries (atomics coordinates) are converged to within 0.02 eV Å À1 for the maximal component of forces and the vacuum level at least up to 20 Å net of the water model. The TS search was conducted by using the climbing image nudged elastic band (CI-NEB) method [44] to generate initial guess geometries, followed by the dimer method [45] to converge to the saddle points.
Zero-point energies (ZPE) and enthalpy and entropy contributions to free energies at room temperature (298.15 K) were calculated from vibrational modes of surface species. Due to the explicit water molecules are not properly constrained by the hydrogen bonding network, and low-frequency modes can cause unphysically large entropy contributions. They were reset to a threshold value of 60 cm À1 . The Gibbs free energy of each intermediate in CO 2 R ( Ã COOH, Ã CO) is given by Equation (1): E DFT is the energy of intermediates in each elementary step during CO 2 R, and the adsorption entropy S is obtained through frequency calculation and calculated only for the surface adsorbate. For the catalytic activity, the formation energies of critical elementary steps are calculated by Equation (2), Equation (3) under the CHE model (Computational Hydrogen Electrode), which was proposed by Norskov et al. [46].
G sol means the Gibbs free energy is calculated under implicit solvation correction, Ã means the surface without adsorbate. Equation (2) and equation (3) show the formation energy of the Ã COOH (potential determined step, PDS) and Ã CO. For the stability of the Ni atom in Ni-SAC, we calculated the binding energy for the Ni atom in Equation (4).
In Equation (4), E ðNiÀC 2 ÀNSÞ The total energy for the surface E C 2 ÀNS ð Þ is the surface energy without center Ni atoms. E ðNiÞ is the energy of a single Ni atom.

Advantage of implicit solvation
In the experimental research of Yang et al., they show Ni-atom is the main catalytic atoms and three steps that can take place on Ni-SAC: referred to as the Ã CO formation step; and (3) Ã CO ! Ã þ CO, referred to as the CO desorption step. The first two steps are electrochemical, while the last is a thermal step. However, the formation energy of Ã COOH obtained by their vacuum calculation is very high, indicating that CO 2 R is difficult to occur.
Considering the implicit solvation correction, we repeat the reaction mechanism of CO 2 R on the two structures of Ni-N 4 and Ni-N 3 -S in Yang's work. The optimized geometries of the reactive intermediates are shown Figure 1(a-h), and the free energy profile is in Figure 1(i). According to the DFT results, the implicit solvation correction can better describe the whole reaction process. Firstly, implicit solvation correction significantly reduces the formation energy of the PDS, Ã COOH on both active sites (at least reduce 0.25 eV). Secondly, the result shows the desorption energy of CO on Ni-N 3 -S reduces by 0.168 eV, which indicates that CO is easier to desorb. However, the formation energy of Ã COOH remained high under the solvation model, each of the active sites at least higher than 1. 5 eV. This indicates that reducing carbon dioxide to carbon monoxide is difficult to occur at these two catalytic sites, which is not consistent with the observed phenomenon. Therefore, we believe that Ni-N 3 -S is unlikely to be the active site in sulfur-doped Ni-SAC.

Search for the active site
Therefore, we first searched for possible sites of sulfur-doped Ni-SAC. As shown in Figure S6, the formation energy of Ã COOH is the PDS, which is 0.717 eV on Ni-N 2 -S 2 and 1.257 eV on Ni-N-S3. Instead, the PDS on Ni-C 2 -NS is only 0.461 eV. Thus, one S already reaches the best performance, while adding more S has no further improvements. Meanwhile, more S severely worsen the stability as shown in Table S1. Depending on two references, one is the formation of Ã COOH, which is the PDS of the whole reaction process and refers to the overpotential of the entire reaction process. The other is the desorption energy of CO. Combined with these two points, we screened out the catalytic sites of different combinations of carbon and nitrogen atoms connected to nickel. The calculated Ã COOH formation energy and CO desorption energy is shown in Figure 2(a), and the optimized geometries are shown in Figure 2(b-g). It can be seen from Figure 2(a) that nitrogen and sulfur atoms have a significant influence on the whole catalytic reaction. According to Ni-N 4 and Ni-N 3 -S, the doping of sulfur atoms dramatically reduces the formation energy of Ã COOH. The doping of nitrogen atoms promotes the formation of Ã COOH through the reaction at the two catalytic sites of Ni-C 3 -S and Ni-C 2 -NS, which is also conducive to the desorption of CO. In the whole reaction, the formation energy of PDS in Ni-C 2 -NS is the lowest, which is most conducive to the reaction. Therefore, the DFT calculation indicates that Ni-C 2 -NS is a possible catalytic site.

CO 2 R on Ni-C 2 -NS
The DFT calculation in vacuum indicates that CO 2 is weakly physisorbed, which can not explain the experimentally observed chemisorbed CO 2 . With consideration of applied voltage and solvation, we find the chemisorbed CO 2 on Ni-C 2 -NS from DFT calculations. The free energy profile of CO 2 reduction on Ni-C 2 -NS site is shown in Figure 3(a). The DFT calculation indicates that there exists the Ã COO intermediate in CO 2 R in the Ã COOH formation step, which can divide into two steps: (1) Ã e À þ CO 2 ! Ã COO À , Ã e À is one election on the surface. This step refers to the chemisorbed CO 2 on the one negative charge surface with implicit solvation correction. The optimized geometries are shown in Figure 3(b). CO 2 was from the physical adsorption change to chemical adsorption due to the bond for linear CO 2 was bend and the angle of bonding up to 142.08 . The distance for Ni to CO 2 decreases 1.13 Å from physisorbed CO 2 (3.283 Å) to chemisorbed CO 2 (2.105 Å). The geometries are shown in Figure S2. The barrier for this process only 0.516 eV. (2) Ã COO À þ H þ þ e À ! Ã COOH À , this is the Ã COOH formation step. This process was in acid condition. As shown in Figure S3, four H 2 O atoms and one H 3 O þ were added. The hydrogen which in H 3 O þ transfer to Ã COO to form Ã COOH indirectly. The barrier in this step is 0.376 eV. In the last step, the hydrogen from H 3 O þ direct transfer to COOH to form CO and H 2 O.

Stability of Ni-C 2 -NS active site
In electrochemical reactions, the stability of a single atom catalyst is essential because it can lead to the destruction of the active site after many cycles. In the Ni-C 2 -NS catalyst, Ni is the main active site as indicated from the PDOS shown in Figure 4(a). The binding energy of Ni with the surrounding atoms is À3.54 eV, which is higher than that of Ni in Ni-N 4 (shown in Figure S4). This indicates that Ni atoms are relatively stable in catalysis. In Figure 4(b), Ni in the Ni-C 2 -NS catalyst shows a stronger interaction with the surrounding atoms due to the high peak overlap of Ni bonding atoms compare with Ni-N 3 -S (PDOS in Figure S5), which also proved the stability of the Ni site.

The application of M x -C2-NS catalytic sites
To expand its application, we have calculated the CO 2 R of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ag, Cd, Mo, Pd, Rh, Ru, Au, Ir, Pt, W transition metal atoms at this site. There are two important factors: the Ã COOH formation and the other is the desorption of Ã CO. As shown in Figure 5, Ti and Cd are two better catalysts than Ni. In the figure, we also found that Co, W, Fe, and other catalyzed central metal atoms have better formation  energy of Ã COOH. Still, they have a high CO desorption energy (higher than 1.02 eV). This type of catalyst is likely to get depth products in CO 2 RR, such as HCOOH.

Conclusion
In this work, we studied the catalytic reaction of CO 2 on sulfur-doped SAC using the DFT method. Solvation is fully considered in our calculation. Our calculation method can completely repeat the results of explicit water molecule calculation, verifying the reliability of our theoretical calculation. We scanned for a variety of possible SAC sites. Different from previous studies, we found that Ni-C 2 -NS was the active site. The onset potential predicted by theoretical calculation was 0.67 eV, which was highly consistent with the experimental results. Our work provides a theoretical basis for designing better catalyst structures in the future.