Supporting Information

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1 Supporting Information Indirect Four-Electron Oxygen Reduction Reaction on Carbon Materials Catalysts in Acidic Solutions Guo-Liang Chai* 1, Mauro Boero 2, Zhufeng Hou 3, Kiyoyuki Terakura 3,4 and Wendan Cheng 1 1 State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, People s Republic of China. 2 University of Strasbourg, Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS UMR 7504, 23 rue du Loess F Strasbourg, France. 3 National Institute for Materials Science (NIMS), Sengen, Tsukuba, Ibaraki , Japan. 4 Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa , Japan * g.chai@fjirsm.ac.cn 1. Limiting potential calculations The limiting potential U L for an oxygen reduction reaction (ORR) is the potential (per electron) realized at the elementary step along a given pathway when the free energy difference G i is at its minimum value and the system is in thermodynamic equilibrium: U L = Min[- G i ]/ne (S1) where n is the number of electrons transferred at each electrochemical step and e is the electronic charge. For each elementary step corresponding to a single electron transfer n=1. The acronym Min in the equation above means the selection of the smallest value of - G i. Such a G i is the free energy variation between each 1

2 elementary step along the reaction pathway. This quantity can be directly evaluated in terms of total energy differences in a density functional theory (DFT) framework upon addition of the related corrections for zero point energy, entropy and solvation energy. The correct expression then reads: G = E Total + E ZEP T S + G s (S2) where E Total is the DFT total energy, E ZPE is the zero point energy, S is the entropy contribution, and G s is the solvation energy. The zero point energy and entropy correction used here are identical to the ones formerly used 1. Solvent effects were accounted for implicitly. 2 Calculated solvation energies for *H and *OH intermediates of SWN1 structure are ev and ev, respectively, and these are the values used in the present manuscript. The adsorption energies of ORR intermediates at zero temperature are calculated by using H 2 O (l) and H 2(g) as references. 1,3 2. Mechanisms for H 2 O 2 formation and reduction The formation of H 2 O 2 proceeds mainly along two mechanisms: (i) O 2 adsorption and (ii) H abstraction. Which mechanism dominates in the actual formation of H 2 O 2 depends on the O 2 activation barrier. Here, we focus on the H abstraction mechanism as discussed in the main text. Three elementary steps are realized for the H abstraction and they can be summarized as: * + (H + e ) *H (S3) + ( aq) *H+ e + O * + OOH ( S4) 2( g ) ( aq) * + OOH + H * + H O ( S5) + ( aq) ( aq) 2 2( aq) Where the * indicates a possible active site on the CMCs surface. The reaction free energy for the overall H 2 O 2 formation reaction is ev. The reaction free energy of the first step is the calculated hydrogenation energy G *H. The reaction energy of the third step is constant and has an experimental value of ev under standard conditions. The reaction free energy of the second step can be obtained by subtracting the free energy variations of the other two steps from the total reaction energy, specifically, G *H. 2

3 As discussed in the main text, the H 2 O 2 reduction can occur along three different reaction mechanisms. The first one, termed OH - ion mechanism hereafter, is composed of the following elementary steps: * + H O + 2(H + e ) *OH+ OH + 2H + e ( S6) ( aq) ( aq) ( aq) ( aq) *OH+ OH + 2H + e *OH+ H O + H + e ( S7) + + ( aq) ( aq) 2 ( aq) ( aq) *OH+ H O + H + e * + 2H O ( S8) + 2 ( aq) ( aq) 2 ( aq) According to this mechanism, the H 2 O 2 molecule is dissociated into an *OH intermediate anchored to the CMC surface, and an OH - hydroxyl anion in the first elementary step. In the second step, the OH - anion reacts with a proton H + in solution and the related energy difference is ev under standard conditions. The final step is the removal of the *OH intermediate via an electron transfer process and this is associated to a free energy variation of - G *OH as discussed in main text. The reaction free energy of the overall H 2 O 2 conversion to 2H 2 O is ev. Thus, the free energy variation of the first step can be computed as a direct sum of the three contribution, namely G *OH. As the limiting potential is determined by the elementary step with the minimum free energy decrease, the maximum limiting potential obtained for this mechanism is 1.36 V with a corresponding G *OH =1.36 ev. The second pathway, termed OH radical mechanism hereafter, consists in a reaction summarized by the following four elementary processes: * + H O + 2(H + e ) *OH+ OH + 2(H + e ) ( S9) ( aq) ( aq) ( aq) ( aq) *OH+ OH + 2(H + e ) * + OH+ H O + H + e ( S10) + + ( aq) ( aq) 2 ( aq) ( aq) * + OH+ H O + H + e *OH+ H O + H + e ( S11) ( aq) ( aq) 2 ( aq) ( aq) *OH+ H O + H + e * + 2H O ( S12) + 2 ( aq) ( aq) 2 ( aq) The first step generates an *OH on the catalytic surface of the CMC and an OH radical dispersed in solution. The second step is the removal of the *OH intermediate, occurring with a free energy variation of - G *OH. In the third step, the OH radical binds to the same catalytic site to form another *OH adduct. The fourth step is again a removal of the newly formed *OH intermediate. The free energy variations for the second and fourth steps are - G *OH. The experimental reaction free energy for the 3

4 following reaction is ev: 4 + OH+ H + e H O ( S13) 2 ( aq) Hence, the reaction free energy of the third step is G *OH. As the overall reaction free energy is 3.54 ev, that of the fourth step can be computed as G *OH. The maximum limiting potential that can be obtained for this mechanism is then 0.82 V with a corresponding G *OH =0.82 ev. The third route, termed H 2 O mechanism, consists of three elementary steps: * + H O + 2(H + e ) *O+ H O + 2(H + e ) ( S14) ( aq) ( aq) 2 ( aq) ( aq) *O+ H O + 2(H + e ) *OH+ H O + H + e ( S15) ( aq) ( aq) 2 ( aq) ( aq) *OH+ H O + H + e * + 2H O ( S16) + 2 ( aq) ( aq) 2 ( aq) In this mechanism, the H 2 O 2 molecule is dissociated into an *O intermediate bound to the surface of the catalyst and an H 2 O molecule during the first elementary step. The second step is represented by the hydrogenation of *O, whereas the third step is the removal of the *OH adduct produced by the two former steps. The free energy variation of the second and third step can be calculated as G *OH - G *O and - G *OH as detailed in a former publication. 1 The free energy variation of the first step is then G *O. The linear relationship for *O and *OH is G *O =2 G *OH +0.3 as extensively discussed in our former publication. 1 The maximum limiting potential for this mechanism turns out to be 1.62 V with a corresponding G *OH =1.62 ev. 3. Proton transfer barrier for SW-N3 structure and collective variables variation for SW-N3N3 structure The formation of hydrogen peroxide H 2 O 2 at the cathode is a three phases reaction, in which O 2 activation by H abstraction or O 2 adsorption was thought to be a kinetically rate determining process. As a complement to our investigation, reported in the main text, we checked also the proton transfer barrier on the SW-N3 structure. The results of this analysis are shown in Figure S1. Namely, the proton transfer barrier is about 6 kcal/mol, at least upon a classical treatment of the proton. We do not rule out lower 4

5 values that can possibly exist upon tunnelling processes in a full quantum mechanical treatment of the proton. Anyhow, even limiting the analysis to a classical H +, the barrier found (which is more realistically an upper bound) is much lower than the H abstraction barrier (about 0.52 ev) for this same SW-N3 structure. The H 2 O 2 reduction barrier in the case of the SW-N3N3 system was also computed via metadynamics simulations. The collective variables variation for the coordination number and the distance are show in Figure S3. 4. H 2 O 2 reduction on FePCl center Generally speaking, the ORR performance of Fe containing CMCs is better than that of metal free CMCs in acidic solution. But the durability of Fe containing CMCs is seriously compromised. This might be rationalized in terms of the production of radicals responsible for a destabilization the catalytic system. The H 2 O 2 reduction on a FePCl center was also simulated by metadynamics approaches; these results are shown in Figure S4. The spin state multiplicity was set to a doublet, i.e. 2s+1=2. The calculated barrier is rather modest, namely 0.31 ev, which indicates that the H 2 O 2 should be easily reduced on the FePCl center. The initial and final configurations are reported in Figure S5. The H 2 O 2 is dissociated into a radical *OH and an OH group. As discussed in the main text, the OH group can also be a radical below a half-wave potential of 0.82 V, although this leads to a destabilization and then a degradation of the electrode catalysts which would be irreversibly damaged. 5. H 2 O 2 dissociation in vacuum and pure water As a complementary check, we inspected the H 2 O 2 dissociation barrier in gas phase and in aqueous solution for comparison with the catalytic dissociation on CMCs. The H 2 O 2 dissociation free energy barrier in aqueous solution amounts to 1.89eV. This value is in fairly good agreement with the one reported in a previous paper (1.89 ev). 5 The calculated free energy barrier in gas phase is 2.19 ev. Not surprisingly, these values are much higher than the ones found for CMCs, confirming the active catalytic 5

6 role played by CMCs in the H 2 O 2 dissociation processes. References (1) Chai, G. L.; Hou, Z. F.; Shu, D. J.; Ikeda T.; Terakura, K. J. Am. Chem. Soc. 2014, 136, (2) Andreussi, O.; Dabo, I.; Marzari, N. J. Chem. Phys. 2012, 136, (3) Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jónsson, H. J. Phys. Chem. B 2004, 108, (4) Anderson, A. B. Phys. Chem. Chem. Phys. 2012, 14, (5) Bach, R. D.; Ayala, P. Y.; Schlegel, H. B. J. Am. Chem. Soc. 1996, 118, Table S1. Lattice parameters (in unit of Å) of the simulation cells used in the present study for all the structures considered. All cells are orthorhombic withα=β=γ=90. a b c G-N G-NN AB SW-N SW-N SW-N SW-N3N FePCl

7 Figure S1. The initial and final structures for the H 2 O 2 dissociation on the G-N, SW-N3N3 and FePCl systems. Water molecules representing the solvent are not shown for clarity. (a), (c) and (e) correspond to the initial structures, while (b), (d) and (f) the final products. Grey, blue, red, white, green and brown balls denote carbon, nitrogen, oxygen, hydrogen, chlorine and iron atoms, respectively. 7

8 Figure S2. Proton transfer free energy profile and related barrier to a C c site on the SW-N3 system. The colour code for carbon, nitrogen, oxygen, hydrogen and chlorine atoms is grey, blue, red, white and green, respectively. 8

9 Figure S3. Evolution of the selected collective variables during the metadynamics as a function of the simulation (meta)step for (a) the coordination number and (b) the distance in the case of the SW-N3N3 structure. 9

10 Figure S4. Free energy landscape as obtained by metadynamics simulations for the H 2 O 2 dissociation on a FePCl system. In our selection of collective variables, CV1 is the coordination number between the two O atoms in the H 2 O 2 hydrogen peroxide and CV2 the distance between one O atom in H 2 O 2 and the Fe site on the structure. 10

11 Figure S5. Free energy profiles for the decomposition of one hydrogen peroxide H 2 O 2 molecule into two OH groups in gas phase and in aqueous solution. 11