Surface Curvature Effect on Dual-Atom Site Oxygen Electrocatalysis

Improved oxygen electrocatalysis is crucial for the ever-growing energy demand. Metal–nitrogen-carbon (M–N–C) materials are promising candidates for catalysts. Their activity is tunable via varying electronic and geometric properties, such as porosity. Because of the difficulty in modeling porosity, M–N–Cs with variable surface curvature remained largely unexplored. In this work, we developed a realistic in-pore dual-atom site M–N–C model and applied density functional theory to investigate the surface curvature effect on oxygen reduction and evolution reactions. We show that surface curving tailors both scaling relations and energy barriers. Thus, we predict that adjusting the surface curvature can improve the catalytic activity toward mono- and bifunctional oxygen electrocatalysis.

For the oxygen reduction reaction (ORR): and the oxygen evolution reaction (OER) is considered as the reverse reaction.
where * indicates the adsorption site.
The free energy (G) of each intermediate was calculated as: where E is the DFT energy with the D4 correction, ZPE is the zero-point energy, T S is the entropic correction, SC is the solvation correction.

S-2
The adsorption free energies (∆G) of each intermediate were obtained for associative mechanism as: and for the dissociative mechanism as: where the computational hydrogen electrode (CHE) was used to calculate the energy of (H + + e -) at potential U as 1 2 G H 2 − eU with e being the elementary charge.* in energies of adsorbed species are omitted for the sake of brevity.S7 In-pore dual-atom site Model  Since the most crucial model descriptor is the metal atom distance, let us consider the distance between metal centers in the planar configuration as d ∞ and the metal atom distance at pore radius r as d r .d r can be expressed in terms of r and θ to yield while the chord length equals to d ∞ and so expressing it in terms of r and θ yields which can be rearranged to find that r = d ∞ 2θ and so expression for d r becomes S-4 The constraint on the size of the pores (representing physical pores) imposes a condition r > 3 Å.The expression can be simplified further by applying Taylor expansion to give In the region of interest (r > 3 Å), only the first two terms of the expansion are necessary to approximate the function sufficiently.Hence the functional form for distance dependence on curvature can be expressed as The comparison of the analytical solution to the approximate form is shown in Figure S2.

S-7
Bayesian error estimation errors and overpotential volcanoes Relative adsorbate errors in terms of covariance ellipses were obtained with the Bayesian error estimation (BEE) method.S8,S9 The BEE values were calculated for the RPBE functional with a modified GPAW code.In Figure S5, a different tilting direction of the covariance ellipses confirms the different scaling relations for the associative and dissociative mechanisms.

S-8
Results of nudged elastic band calculations Nudged elastic band (NEB) calculations were performed using ASE 3.22.1.S2 The complete NEB results are presented in Figure S6.

Figure S1 :
Figure S1: In-pore dual-atom site M-N-C model with two metals and pore radius (r).

Figure S2 :
Figure S2: A plot of analytical and approximate solutions, with an inset showing the realistic region of interest.

Figure S3 :
Figure S3: Partial density of states (PDoS) for the adsorbing metals in the (a) CoCo and (b) CoNi models.Colored dashed lines indicate d-band center ϵ d .Note the general shift of ϵ d to lower energies as r decreases, resulting in weaker adsorption of oxygenated species.

Figure S4 :
Figure S4: Construction of the magenta line shown in main article using data from reference.S5

Figure S5 :
Figure S5: 3D volcanoes contour map for (a) ORR, (b) OER, and (c) bifunctional overpotentials Bayesian error estimation.The blue ellipsis and red lines show the covariance of error and standard deviation in each energy, respectively.The errors are calculated with respect to the flat surface in the CoCo model.

Figure S6 :
Figure S6: Results of nudged elastic band calculations for oxygen dissociation.