Supporting Information

Supporting Information Electrocatalytic Activity and Design Principles of Heteroatom-Doped Graphene Catalysts for Oxygen-Reduction Reaction Feng Li, Haibo Shu,,,* Xintong Liu, Zhaoyi Shi, Pei Liang, and Xiaoshuang Chen College of Optical and Electronic Technology, China Jiliang University, 310018 Hangzhou, China, National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, China * Corresponding author. Tel. +86-0571-86875622. shu123hb@gmail.com (Haibo Shu) S-1

S1 Doping configurations and formation energies of heteroatom-doped graphene Heteroatom X-doped graphene (X = N, P, As, Sb, and S) are obtained by substituting edge or central carbon atoms in the graphene matrix, consequently yielding 14 different doping configurations (see Figure S1). The doping configurations have been divided into three types, including of X-doping onto graphene basal plane (G-X), zigzag edge (Z-X), and armchair edge (A-X), respectively. The stability of these doping configurations is evaluated by the comparison of formation energies, as listed in Table S1. The relatively stable doping configurations are indicated in bolded (see Table S1). Figure S1 Potential doping configurations of heteroatom (X)-doped graphene (X = N, P, As, Sb, and S). Here G-X, Z-X, and A-X denote the dopant atom X at the graphene basal plane, zigzag edge, and armchair edge, respectively. Table S1. Total energies and formation energies of various X-doped graphene structures (X= N, P, S, As, and Sb). Z-X, A-X, and G-X denote the doping at the graphene zigzag edge, armchair edge, and basal plane, respectively. The relative stable configurations for each dopant types have been indicated in bold. Here denotes that the doping configuration is unstable during the optimization. Dopant Type Configuration E tot (ev) Formation Energy(eV) Z-N 1-591.655-0.742 Z-N 2-590.546 0.367 Z-X Z-N 3-592.684 4.077 Z-N 4-587.13 0.404 Z-N 5-588.251 5.131 A-N 1-568.441 0.48 N A-N A-X 3-573.810 0.959 A-N 4-568.766 2.624 A-N 5-565.284 0.258 G-N 1-884.248 0.62 G-X G-N 2-858.459 6.996 G-N 3-870.476 3.282 G-N 4-870.194 5.412 Z-P 1-586.052 1.874 P Z-X Z-P 2-586.072 1.854 Z-P 3-589.960 3.814 S-2

S As Sb A-X G-X Z-X A-X G-X Z-X A-X G-X Z-X A-X G-X Z-P 4-583.405 1.142 Z-P 5-587.134 3.261 A-P 1-563.115 2.819 A-P 2-563.836 2.098 A-P 3-569.860 1.922 A-P 4-566.794 1.609 A-P 5-561.273 1.282 G-P 1-879.145 2.701 G-P 2-853.427 6.054 G-P 3-858.919 5.877 G-P 4-868.845 3.774 Z-S 1 Z-S 2-583.163 3.534 Z-S 3 Z-S 4-582.903 0.415 Z-S 5-586.323 2.843 A-S 1 A-S 2-561.538 3.167 A-S 3 A-S 4-566.41 0.764 A-S 5-559.735 1.591 G-S 1-877.031 3.586 G-S 2-849.531 7.492 G-S 3-855.126 5.985 G-S 4-866.397 4.993 Z-As 1 Z-As 2-583.586 3.67 Z-As 3-588.334 3.689 Z-As 4-581.939 1.938 Z-As 5-586.293 3.432 A-As 1 A-As 2-562.078 3.186 A-As 3 A-As 4-565.753 1.98 A-As 5-559.671 2.214 G-As 1-877.209 3.967 G-As 2-850.408 7.732 G-As 3-854.621 8.166 G-As 4-866.286 5.663 Z-Sb 1-581.503 4.672 Z-Sb 2-582.098 4.077 Z-Sb 3-587.315 4.708 Z-Sb 4-580.325 2.471 Z-Sb 5-585.668 2.976 A-Sb 1-561.012 2.949 A-Sb 2-560.582 3.601 A-Sb 3-566.523 3.508 A-Sb 4-564.818 1.834 A-Sb 5-557.947 2.857 G-Sb 1-875.413 4.861 G-Sb 2-847.936 8.042 G-Sb 3-850.695 8.85 G-Sb 4-864.891 5.977 S-3

S2 Calculation details of ORR free-energy diagram The oxygen-reduction reaction (ORR) scheme in both acid and alkaline aqueous conditions follows two possible pathways: four-electron (4e - ) and two-electron (2e - ) reduction pathways. In the acid aqueous environment, the four-electron reduction pathway is that O 2 is reduced directly to H 2 O without the formation of H 2 O 2 intermediate (see eq. 1) and the two-electron reduction pathway is that O 2 is reduced to H 2 O via H 2 O 2 (see eq. 2 and 3). 1 Here we consider the complete four-electron reduction pathway because previous studies have shown that the ORR proceeds on most of graphene doping structures follow the four-electron mechanism. O 2 + 4(H + + e - ) 2H 2 O (1) O 2 + 2(H + + e - ) 2H 2 O 2 (2) H 2 O 2 + 2(H + + e - ) 2H 2 O (3) In the acid aqueous environment, the four-electron reduction pathway has two different reaction mechanisms: (i) associative mechanism that involves a *OOH species and (ii) direct O 2 dissociation mechanism (i.e., O 2 + 2* 2*O). We find that both X-doped (X= N, S, As, and Sb) and dual-doped graphene structures prefer to the associative mechanism, except for P-doped ones. The four-electron reduction pathway with the associative mechanism goes through the following elementary steps: O 2 + * + H + + e - *OOH (4) *OOH + H + + e - *O + H 2 O (5) *O + H + + e - *OH (6) *OH + H + + e - * + H 2 O (7) where * denotes an active site on a graphene surface, *O, *OH, and *OOH are adsorbed ORR intermediates. In the alkaline aqueous environment, the ORR following the associative mechanism can be described by the following elementary steps: O 2 + * + H 2 O + e - *OOH + OH - (8) *OOH + e - *O + OH - (9) *O + H 2 O + e - *OH + OH - (10) *OH + e - * + OH - (11) To insight into the ORR pathway and mechanism, free-energy diagrams of ORR on various graphene doping structures have been calculated using a computational hydrogen electrode (CHE) S-4

model proposed by Nørskov et al. 2 The CHE model defines that the chemical potential of a proton/electron (H + + e - ) in solution is equal to half of the chemical potential of a gaseous H 2. The change of free energies ( G) in each a reaction step is calculated by the following equation, ΔG = ΔE + ΔZPE TΔS + ΔG U + G ph (12) where ΔE is the reaction energy of reactant and product molecules adsorbed on a catalytic surface in each an ORR step, ΔZPE is the change in zero-point energies (ZPE), T is temperature which refers to the room temperature (T = 298.15 K), and ΔS is the change in entropy. The effect of an external bias (ΔG U ) is shifted by eu in each (H + + e - ) transfer step, where e is the number of electrons transferred and U is the applied bias. ΔG ph = k B T ln10 ph where k B is the Boltzmann constant, T is the room temperature (T = 298.15 K), and the ph value is set to 0 for the acidic medium and 14 for the alkaline medium, respectively. Zero-point energies and entropies of ORR intermediates on various doped graphene catalysts are calculated from vibrational frequencies and those of gas phase molecules are obtained from the standard thermodynamic database, 2,3 as listed in Table S2-S4. S-5

Table S2. DFT total energies (E), zero-point energies (ZPE), entropies multiplied by temperature (= 298.15 K) (TS), free energies (G) of gas molecules. Molecule E (ev) ZPE (ev) TS (ev) G (ev) H 2 O -14.209 0.588 0.584-14.205 H 2-6.758 0.276 0.404-6.894 O 2-9.857 0.097 0.634-9.702 H 2 O 2-18.103 0.811 0.725-18.017 Table S3. DFT total energies (E), zero-point energies (ZPE), entropies multiplied by T (T = 298.15 K) (TS), free energies (G) and adsorption free energies ( G ads ) of key ORR intermediates on X-doped graphene structures (X= N, P, S, As, and Sb). Z-X, A-X, and G-X denote the doping at graphene zigzag edge, armchair edge, and basal plane, respectively. Here denotes that the adsorption configuration is unstable during the geometric optimization. Dopant Configuration Intermediate E (ev) ZPE (ev) TS (ev) G (ev) G ads (ev) N P Z-N 1 Z-N 2 A-N 1 A-N 5 G-N 1 Z-P 2 Z-P 4 A-P 4 A-P 5 *OOH -605.659 0.469 0.118-605.308 4.416 *OH -601.479 0.393 0.068-601.154 1.259 *OOH -605.116 0.473 0.117-604.76 3.945 *OH -601.040 0.399 0.066-600.707 0.597 *OOH -583.471 0.468 0.119-583.122 3.388 *OH -579.304 0.394 0.068-578.978 0.221 *OOH -578.626 0.552 0.075-578.149 5.204 *OH -574.468 0.391 0.068-574.145 1.897 *OOH -897.901 0.457 0.123-897.567 4.75 *OH -893.735 0.388 0.07-893.417 1.589 *OOH -601.257 0.445 0.131-600.943 3.198 *OH -597.295 0.359 0.079-597.015-0.185 *OOH -598.791 0.455 0.126-598.462 3.012 *OH -594.805 0.374 0.071-594.502-0.339 *OOH -582.359 0.422 0.146-582.083 2.78 *OH -578.234 0.374 0.071-577.931-0.379 HO*+O* -579.634 0.462 0.116-579.288 0.054 *OH -571.645 0.372 0.072-571.345 0.686 S As G-P 1 Z-S 4 HO*+O* -896.198 0.455 0.120-895.863 1.351 *OH -890.701 0.371 0.073-890.403-0.5 *OOH -596.782 0.476 0.116-596.422 4.55 *OH -592.669 0.301 0.04-592.408 1.253 Z-S 5 *OOH -601.025 0.44 0.133-600.718 3.674 *OH -596.897 0.372 0.072-596.597 0.484 A-S 4 *OOH -574.885 0.44 0.133-574.578 3.226 *OH -570.772 0.397 0.067-570.442 0.051 A-S 5 *OOH -579.961 0.475 0.114-579.6 4.879 *OH -575.8 0.396 0.068-575.472 1.696 G-S 1 *OOH -890.329 0.439 0.135-890.025 5.075 *OH -886.373 0.352 0.081-885.963 1.826 Z-As 4 *OOH -597.171 0.439 0.135-596.867 3.141 *OH -593.105 0.363 0.078-592.82-0.123 Z-As 5 *OOH -601.655 0.439 0.134-601.35 3.012 *OH -597.591 0.362 0.077-597.306-0.255 A-As 4 *OOH -580.907 0.448 0.129-580.588 3.234 *OH -576.824 0.369 0.075-576.53-0.019 A-As 5 *OOH -574.021 0.44 0.133-573.714 4.026 S-6

Sb G-As 1 Z-Sb 4 Z-Sb 5 A-Sb 4 A-Sb 5 G-Sb 1 *OH -569.887 0.364 0.077-569.6 0.829 *OOH -891.187 0.44 0.135-890.882 4.396 *OH -887.194 0.357 0.08-886.917 1.05 *OOH -595.924 0.439 0.145-595.63 2.764 *OH -591.565 0.353 0.081-591.293-0.21 *OOH -601.045 0.434 0.139-600.75 2.987 *OH -597.049 0.351 0.081-596.779-0.353 *OOH -572.885 0.439 0.134-572.58 3.436 *OH -568.834 0.348 0.084-568.57 0.135 *OOH -580.051 0.443 0.133-579.741 3.146 *OH -576.035 0.359 0.079-575.755-0.179 *OOH -889.16 0.433 0.144-888.871 4.611 *OH -884.978 0.329 0.225-884.874 1.297 Table S4. DFT total energies (E), zero-point energies (ZPE), entropies multiplied by T (T = 298.15 K) (TS), free energies (G) and adsorption free energies ( G ads ) of key ORR intermediates on dual-element doped graphene structures. Here denotes that the configuration is unstable with the adsorption of oxygenated species. Complex Configuration Intermediate E (ev) ZPE (ev) TS (ev) G (ev) G ads (ev) B-N B-P B-As Z-B-N A-B-N G-B-N Z-B-P A-B-P G-B-P Z-B-As A-B-As G-B-As Z-B-Sb HOO* -604.368 0.447 0.277-604.198 2.837 HO* -600.198 0.383 0.07-599.885-0.161 HOO* -581.129 0.451 0.127-580.805 3.859 HO* -576.997 0.383 0.071-576.685 0.668 HOO* -896.798 0.450 0.128-896.476 4.241 HO* -892.639 0.375 0.074-892.338 1.068 HO*+O* -603.886 0.459 0.174-603.601-1.253 HO* -595.586 0.369 0.076-595.293-0.256 HOO* -576.718 0.449 0.130-576.399 3.618 HO* -572.828 0.370 0.075-572.533 0.173 HOO* -891.553 0.493 0.108-891.168-1.051 HO* -887.635 0.357 0.08-887.358-0.08 HOO* -593.892 0.429 0.14-593.603 3.385 HO* -589.797 0.355 0.081-589.523 0.154 HOO* -571.269 0.434 0.137-570.972 3.324 HO* -566.816 0.564 0.08-566.332 0.653 HOO* -888.653 0.433 0.141-888.361 4.361 HO* -884.647 0.345 0.086-884.388 1.023 HOO* -595.534 0.435 0.141-595.24 4.134 HO* -591.586 0.350 0.083-591.319 0.744 B-Sb A-B-Sb N-P G-B-Sb Z-N-P A-N-P G-N-P HOO* -887.023 0.433 0.141-886.731 4.076 HO* -882.874 0.348 0.081-882.607 0.889 HO*+O* -604.783 0.466 0.117-604.434-0.181 HO* -596.467 0.374 0.07-596.163 0.779 HO*+O* -581.581 0.467 0.114-581.228 0.261 HO* -574.242 0.376 0.07-573.936 0.242 HO*+O* -897.960 0.455 0.176-897.681-1.031 HO* -889.660 0.363 0.076-889.373-0.034 Z-N-Sb N-Sb A-N-Sb G-N-Sb HOO* -575.822 0.434 0.142-575.53 3.544 HO* -571.751 0.345 0.087-571.493 0.27 HOO* -889.818 0.417 0.151-889.552 3.85 HO* -885.857 0.343 0.085-885.599 0.492 S-7

S3 Activity volcano plot and activity-determining steps To identify the activity-determining step and the relative ORR activity of various graphene doping structures, we calculated the adsorption free energies of *O, *OH, and *OOH. The adsorption energies are calculated as follows, 2,4 E ads(*o) = E (*O) E (*) (E H2O E H2 ) (13) E ads(*oh) = E (*OH) E (*) (E H2O 1/2E H2 ) (14) E ads(*ooh) = E (*OOH) E (*) (2E H2O 3/2E H2 ) (15) where E (*), E (*O), E (*OH), and E (*OOH) are total energies of a catalytic surface and the surface adsorbed with *O, *OH, and *OOH, respectively. E H2O and E H2 are the energies of H 2 O and H 2 molecules in gaseous phase, respectively. Based on the calculated adsorption energies, the adsorption free energies ΔG ads of *O, *OH, and *OOH can be calculated as follows, ΔG ads = ΔE ads + ΔZPE TΔS (16) According to eq. 12 and 16, the free-energy change of four reaction steps (i.e., ΔG 1, ΔG 2, ΔG 3, and ΔG 4 ) can be expressed with the adsorption free energies of ORR intermediates as follows, ΔG 1 = ΔG ads(*ooh) 4.92 + eu k B T ln10 ph (17) ΔG 2 = ΔG ads(*o) ΔG ads(*ooh) + eu k B T ln10 ph (18) ΔG 3 = ΔG ads(*oh) ΔG ads(*o) + eu k B T ln10 ph (19) ΔG 4 = ΔG ads(*oh) + eu k B T ln10 ph (20) The ph value is set to 0 and 14 in acidic and alkaline solutions, respectively. Using calculated adsorption free energies listed in Table S3 and S4, we can estimate the standard limiting potential of each step, U i (i = 1, 2, 3, or 4), under conditions that ΔG i = 0. The potential-determining step of the elementary reactions of ORR is the step with the lowest standard limiting potential. Namely, U ORR = min{u 1, U 2, U 3, U 4 } (21) Overpotential η ORR that is an efficient parameter to measure intrinsic ORR activity of a catalyst is equal to the difference between U ORR and the equilibrium potential (U eq ), namely, η ORR = U ORR U eq (22) The equilibrium potential is 1.23 V in the acid medium and 0.402 in the alkaline medium, respectively. Therefore, calculating the adsorption free energies of key ORR intermediates (i.e., *O, *OH, and *OOH) is key for obtaining the potential-determining step. We plotted ΔG ads(*ooh) and S-8

U ORR (V) ΔG ads(*o) as a function of ΔG ads(*o) on various graphene doping structures (see Figure 2b and Figure S2), respectively. The relationship between ΔG *OOH and ΔG *OH can be described by ΔG *OOH = ΔG *OH + 3.25 (see Figure 2b) and the relationship between ΔG *O and ΔG *OH can be described by ΔG *O = ΔG *OH + 0.92 (see Figure S2). According to the two scaling relationships, U i (i = 1, 2, 3, or 4) can be determined by eq. 17-20. The corresponding results about the standard limiting potentials U i (i = 1, 2, 3, or 4) of four ORR steps as a function of ΔG *OH on various graphene doping structures have been shown in Figure S3. It can be found that the potential-determining step is either the O 2 protonation (U 1 ) or the *OH desorption (U 4 ) in the alkaline condition. Similar results have also been found in the acid condition (see Figure S7). Figure S2 The scaling relation between adsorption free energies of *O (ΔG *O ) and that of *OH (ΔG *OH ) on various graphene doping structures. 2.0 1.5 1.0 0.5 U=0.402 V U 2 U 1 G-X A-X Z-X U 4 0.0 U 3-0.5-1.0-1.5-0.5 0.0 0.5 1.0 1.5 2.0 G *OH (ev) Figure S3 Thermodynamic Volcano plot for the ORR activity as a function of ΔG *OH at the active sites of various single-doped graphene catalysts in the alkaline condition. U i (i= 1-4) represent standard limiting potentials of four elementary ORR steps. Black dash line indicates the level of the equilibrium potential (0.402 V) for the ORR in the alkaline condition. S-9

S4 Spin configuration of pristine and doped zigzag graphene edges To identify the stable spin configuration of pristine and doped zigzag graphene edges, the energies of these edges with the FM coupling and the AFM coupling have been compared, as listed in Table S5. It can be found that the pristine zigzag edge with the AFM coupling is energetically favorable and its magnetic moment is zero, which is in good agreement with previous studies. 5,6 With the introduction of nonmetal dopants X (X= N, S, P, As, and Sb) onto the zigzag edge, P-, As-, and Sb-doped zigzag edges with the AFM coupling are energetically favorable, but N- and S-doped zigzag edges present cannot maintain their AFM orderings. Nevertheless, the energy difference of two spin configurations (< 0.05 ev) is very small for both pristine and doped zigzag graphene edges. Moreover, the energy difference of two spin configurations is also very small for the adsorption of ORR intermediates on these graphene edges. Therefore, the results of adsorption free energies and overpotentials on various Z-X catalysts are not sensitive to the initial setting of spin configurations at the zigzag graphene edges. Table S5. The calculated magnetic moments and total energies of the pristine (Z-G) and the stable doped zigzag graphene edges (Z-X, X = N, S, P, As, Sb) with different initial spin configurations. Structure Initial setting Magnetic moment (μ B ) Total energy (ev) Z-G Z-N 1 Z-S 4 Z-P 4 Z-As 4 Z-Sb 4 FM 1.33-591.837 AFM 0-591.884 FM 0.51-591.655 AFM 0.51-591.655 FM 0.59-582.903 AFM 0.59-582.904 FM 1.29-583.405 AFM 0-583.467 FM 1.28-581.939 AFM 0-581.985 FM 1.20-580.325 AFM 0-580.364 S-10

S5 ORR energetics of nonmetal-doped graphene catalysts using the DFT-D2 method Table S6. The binding energies of *OH on various X-doped graphene structures (X = N, S, P, As, Sb) calculated using DFT-D2 and PBE-GGA methods. Dopant Structure E b (*OH) DFT-D2 PBE-GGA Z-N 1 2.285 2.186 Z-N 2 2.96 2.856 N A-N 1 3.333 3.225 A-N 5 1.645 1.546 G-N 1 2.005 1.849 Z-P 2 3.666 3.585 Z-P 4 3.8 3.762 P A-P 4 3.87 3.802 A-P 5 2.832 2.734 G-P 1 4.016 3.918 Z-S 4 2.218 2.218 Z-S 5 3.032 2.936 S A-S 4 3.523 3.399 A-S 5 1.868 1.752 G-S 1 1.855 1.704 Z-As 4 3.613 3.528 Z-As 5 3.717 3.66 As A-As 4 3.501 3.433 A-As 5 2.686 2.578 G-As 1 2.416 2.346 Z-Sb 4 3.666 3.602 Z-Sb 5 3.79 3.743 Sb A-Sb 4 3.36 3.249 A-Sb 5 3.636 3.579 G-Sb 1 2.013 1.927 S-11

U ORR (V) (a) G *OOH (ev) 5 4 3 G *OOH = G *OH + 3.21 2-1 0 1 2 G *OH (ev) (b) 0.5 0.0-0.5-1.0-1.5 U = 0.402 V A-As 5 A-P G-As 1 5 Z-N Z-N 1 ORR 2 Z-S5 Z-S 4 G-Sb G-N 1 1 A-S A-N A-S 1 4 5 A-Sb A-Sb 4 5 Z-Sb Z-As 4 A-As Z-Sb 5 Z-As 4 G-S 1 5 Z-P 4 A-N 5 Z-P 2 A-P 4 4 G-P 1-0.5 0.0 0.5 1.0 1.5 2.0 G * OH (ev) Figure S4 (a) The scaling relation between adsorption free energies of *OOH (ΔG *OOH ) and *OH (ΔG *OH ) in various graphene doping structures. (b) Volcano plot of U ORR as a function of ΔG *OH on various single-doped graphene catalysts in the alkaline aqueous condition. Red and blue lines correspond to the rate-determining step in the first and fourth proton-electron transfer steps, respectively. These calculated data were obtained by the DFT-D2 method. S6 Optimized atomic structures and adsorption energies of nonmetal-doped graphene Figure S5 Optimized atomic structures and adsorption energies (in ev) of X-doped (X= P, Sb As, N and S) graphene catalysts with the adsorption of O 2 molecule. The negative adsorption energies mean that the adsorption of O 2 is an exothermic process. G-X, Z-X, and A-X denote X-doped graphene basal planes, zigzag edges, and armchair edges, respectively. Here the most stable configuration for each nonmetal-doped graphene is selected as the adsorption surface based on the result of formation energies. S-12

Relative free energy (ev) Relative free energy (ev) S7 Free-energy diagrams for the ORR on P-doped and Sb-doped graphene structures (a) 2 1 0 O 2 *O 2 *OOH M-P 1 AM DM OH -1 *O+*OH -2 2*O *O *OH (b) -3 2 1 O 2 *O 2 Reaction Pathway Z-Sb 4 *O+*OH 2*O AM DM 0 *OOH *O OH -1 *OH Reaction Pathway Figure S6 Free-energy diagram for the ORR on (a) M-P 1 and (b) Z-Sb 4 catalysts with the 4e - reduction pathway in the alkaline aqueous condition. AM and DM represent the associative 4e - reduction mechanism and the direct O 2 dissociation mechanism, respectively. S-13

U ORR (V) S8 Activity volcano plot of heteroatom-doped graphene in the acid condition 1.0 A-As A-P 5 5 Z-N G-As 1 2 0.5 ORR Z-S 5 Z-N Z-S 1 4 G-Sb A-N 1 1 A-Sb G-N 1 0.0 A-S 5 A-Sb 5 A-S 4 A-As 4 Z-As 4 Z-Sb Z-As 4 4 G-S 1 5 Z-P Z-Sb 2 5 Z-P A-N 5-0.5 A-P 4 G-P 4 1-0.5 0.0 0.5 1.0 1.5 2.0 G * OH (ev) Figure S7 Volcano plot of U ORR as a function of ΔG *OH on various single-doped graphene catalysts in the acid condition. The calculated data points are the U ORR on these catalysts and theoretical overpotentials (η ORR ) are the vertical difference between U ORR and the equilibrium potential (U = 1.23 V, labelled by green dash line). Red and blue lines correspond to the potential-determining step in the first and fourth proton-electron transfer steps, respectively. S-14

S9 Normalized kinetic current density In order to provide a comparison between the theoretical prediction and experimental results, we summarized the experimental data of kinetic current density in X-doped graphene catalysts (X= N, P, S, and Sb) in the alkaline medium reported from previous literatures. Experimentally, the kinetic current density of ORR on catalysts is obtained by linear scan voltammogram (LSV) measurements, which represents the ORR activity of catalysts. To reliably make comparison between the data form different source, the kinetic current densities of different samples are normalized by the benchmarked Pt/C electrode current density measured under the same condition (i.e., saturated calomel electrode). Although the ORR activity of catalysts is also affected by other factors, such as surface area, morphology of materials, and dopant content, here we have averaged the data that are carefully selected form the literatures to further minimize the effect of these factors. Table S7. Experimental data of kinetic current densities and normalized kinetic current densities in X-doped graphene catalysts (X= N, P, S and Sb). All these data were extracted from previous literatures. All samples reported in these literatures were measured under the same condition (i.e., saturated calomel electrode) Element N P S Sb Kinetic Samples Current Density (j/ma cm -2 ) N-G(900) -2.9 Loading (µg cm -2 ) Normalized Kinetic Current Density 1.04 Pt/C -2.8 4.85 1 NG600 2.5 0.49 NG800 6.7 1.31 NG900 7.8 7.5 1.53 NG1000 7.2 1.41 Pt/C 5.1 1 N-Graphene -0.44 2.17 7.5 Pt/C -0.2 1 P1-MCNTS -3.2 0.89 P2-MCNTS -4.2 1.17 P3-MCNTS -4.0 1.11 P4-MCNTS -2.4 159 0.67 P5-MCNTS -2.2 0.61 P-M6CNTS -4.6 1.28 Pt/C -3.6 1 P-doped graphite -3.4 0.69 159.1 Pt/C -4.9 1 S-graphene-600 2.4 0.77 S-graphene-900 3.4 1.1 - S-graphene-1050 5.5 1.78 Pt/C 3.1 1 SG500 3.4 0.67 SG700 3.5 0.69 7.5 SG900 5.3 1.04 Pt/C 5.1 1 3D S-GNs -4.1 0.81 200 Pt/C -5 1 SbGnPs -3.2 0.91 - Pt/C -3.5 1 References 7 8 9 10 11 12 8 13 14 S-15

DOS (arb.units) DOS (arb.units) S10 Electronic structures of heteroatom-doped graphene edges (a) Z-N 1 (b) Z-S 4 (c) Z-As 4 (d) Z-Sb 4 (e) Z-P 4-2 -1 0 1 2 Energy (ev) Figure S8 Electronic density of states (DOS) of X-doping (X = N, P, S, As, and Sb) at graphene zigzag edges (Z-X) with the AFM coupling. The DOS for (a) Z-N 1, (b) Z-S 4, (c) Z-As 4, (d) Z-Sb 4, and (e) Z-P 4, respectively. The Fermi level is shifted to zero. The filled DOS denotes occupied electronic states. For each X-doped structure, only the most stable configuration is selected to calculate its DOS. (a) A-S 5 (b) A-N 1 (c) A-As 5 (d) A-Sb 4 (e) A-P 4-2 -1 0 1 2 Energy (ev) Figure S9 Electronic density of states (DOS) of X-doping (X = N, P, S, As, and Sb) at graphene armchair edges (A-X). The Fermi level is shifted to zero. The DOS for (a) A-S 5, (b) A-N 1, (c) A-As 5, (d) A-Sb 4, and (e) A-P 4, respectively. The filled DOS denotes occupied electronic states. For each X-doped structure, only the most stable configuration is selected to calculate its DOS. S-16

S11 Doping configurations and stability of N-P codoped graphene catalysts Figure S10 (a) Doping configurations and (b) formation energies of N-P codoped graphene catalysts as a function of the distance between N and P dopants. S-17

U ORR (V) S12 Structures and activity volcano plot of dual-doped graphene catalysts Figure S11 Optimized atomic structures of dual-doped graphene materials. The red circles denote the catalytic site for the ORR. denotes that the doping configuration is unstable during the optimization. 1.0 0.5 0.0-0.5 U = 1.23 V Z-N-P Z-B-Sb A-B-N A-B-As G-N-Sb A-N-Sb A-N-P A-B-P Z-B-As G-N-P Z-B-N G-B-P Z-B-P G-B-Sb G-B-N G-B-As ORR -0.5 0.0 0.5 1.0 1.5 2.0 G *OH (ev) Figure S12 Volcano plot of ORR limiting potentials (U ORR ) on various dual-doped graphene structures as a function of ΔG *OH in the acid condition. Theoretical overpotential (η ORR ) corresponds to the vertical difference between U ORR and the equilibrium potential (U = 1.23 V, labelled by dash line). Red and blue lines denote the potential determining step of doping structures in the first and fourth reaction steps, respectively. S-18

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