Supporting Information: Surface Polarons Reducing Overpotentials in. the Oxygen Evolution Reaction

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1 Supporting Information: Surface Polarons Reducing Overpotentials in the Oxygen Evolution Reaction Patrick Gono Julia Wiktor Francesco Ambrosio and Alfredo Pasquarello Chaire de Simulation à l Echelle Atomique (CSEA) Ecole Polytechnique Fédérale de Lausanne (EPFL) CH-1015 Lausanne Switzerland patrick.gono@epfl.ch Computational details All calculations in this work have been carried out with the cp2k suite of codes. S1 In the geometry optimizations the simulation cells contain 4 2 five layer slabs of the rutile structure in the (110) orientation. The middle layer is kept fixed during relaxation. Periodic images of the slab are separated by at least 20 Å of vacuum in the z direction. The optimal lattice constants are found by optimizing the cell of bulk titanium dioxide. For both the RPBE S2 and the PBE0 S3 calculations we use a plane wave energy cutoff of 700 Ry for the electronic density. Core-valence interactions are described by the norm-conserving Goedecker-Teter- Hutter (GTH) pseudopotentials. S4 The wave functions are expanded in triple-ζ MOLOPT basis sets. S5 We employ the ADMM method S6 with CFIT3 auxiliary basis sets to speed up the hybrid functional calculations. The structures are relaxed until the maximum force drops bellow Hartree/bohr ( ev/å) and the maximum step size is less than bohr ( Å). All simulation cells are neutral and the spin is unrestricted. S-1

2 No higher spin state is enforced. The molecular dynamics (MD) simulations involve the same symmetric slab separated by 80 molecules of water from its periodic images along the z axis. The structure of the water layer is taken from a previous MD run of a clean TiO 2 /water interface performed by Guo et al. S7 A density cutoff of 500 Ry and GTH pseudopotentials are employed. Like in the case of the vacuum calculations a PBE0 hybrid functional with 16% Fock exchange is used. In the MD runs we use double-ζ basis sets to reduce the computational cost of a single MD step. CFIT3 basis sets serve as auxiliary bases for the ADMM method. The van der Waals (vdw) interactions are described through the vdw part of the non-local rvv10 functional. S8 Based on the work of Miceli Ambrosio et al. S9S10 we set the b parameter in the rvv10 functional to 7.7 to ensure good agreement of the properties of liquid water with experiment. This value of b was chosen to account for the specific fraction of Fock exchange used in the PBE0 functional. The time step is set to 0.5 fs. The temperature is set at 350 K to ensure proper liquid-like behavior of water S11 and is controlled by a Nosé-Hoover thermostat. To assess the stability of surface polarons in aqueous environment two MD simulations are carried out. The OH covered surface is modeled by removing hydrogen atoms from water molecules attached to the fivefold coordinated Ti atoms corresponding to a coverage of This configuration serves as the initial state for one of the MD simulations. The second MD simulation is started from an initial structure in which four polarons are manually created on both sides of the slab. Computational hydrogen electrode method The CHE method for the calculation of the Gibbs free energy steps is here briefly outlined. S12 The reaction H + aq + e 1 2 H 2 g (1) S-2

3 is reversible at the potential of the standard hydrogen electrode (SHE) at ph = 0 P = 10 5 Pa and T = 298 K. Thus we write µ H + aq + µ e = 1µ H 2 2 g (2) for the chemical potentials effectively replacing the rather complicated left hand side with the computationally simpler chemical potential of gaseous hydrogen. The Gibbs free energy difference corresponding to a reaction A B + H + aq + e can then be expressed as G AB = µ B A + 1µ H 2 2 g. (3) The chemical potentials of species A and B can in turn be approximated by S13 µ = E DFT + E corr (4) where E corr ZPE T S + U 0 T. (5) E DFT is the total DFT energy of the system and T is the temperature. ZPE is the zero point energy of the adsorbed or free species calculated in the harmonic approximation. For the free species (i.e. not adsorbed on the surface) the entropy S consists of vibrational rotational and translational contributions. The changes in the vibrational spectrum of the slab upon the adsorption of a molecule are neglected. S14 In the case of adsorbed species the entropy S comprises only the vibrational part of the molecule as both its rotational and translational degrees of freedom are suppressed. U 0 T represents the internal energy change between 0 K and the temperature T. S-3

4 The various terms above are calculated as: ZPE = 1 ω (6) 2 ω S vib = R ( ω ( ) ln 1 exp ω ) ω ω k B T (7) k B T exp 1 k B T (2πmkB ) 3/2 S trans T k B T = R ln + 5 R (8) h 2 2 P ( ) 8π 2 k B T I R ln + R for linear molecules h 2 σ S rot = (8π ) 2 3/2 (9) k B T πi1 I 2 I 3 R ln + 32 h 2 σ R for non-linear molecules U 0 T = R ω ω ( ) ω k B exp k B T (10) 1 where ω are the frequencies calculated in the harmonic approximation R is the universal gas constant I i are the moments of inertia and σ is the symmetry number representing the number of equivalent orientations of the molecule. S15 Using Eq. (3) we calculate the free energy differences corresponding to the four steps of the oxygen evolution reaction (OER) Eq. (1) of main paper through: G 1 = µ OH ads * H2 O µ H 2 g G 2 = µ O ads OHads µ H 2 g G 3 = µ OOH ads Oads H2 O µ H 2 g (11) G 4 = µ * + µ O 2 g OOHads µ H 2 g with the chemical potentials µ calculated according to Eq. (4). The zero point energies and thermodynamic corrections of the various species are given in Table S1. The final thermodynamic corrections E corr corresponding to the four reaction steps of the OER are S-4

5 listed in Table S2. As the differences between the final RPBE and PBE0 geometries of the free and adsorbed molecules are small we assume that any effect on the zero point energies or thermodynamic corrections is negligible. Therefore we use the same values for both the RPBE and PBE0 free energy calculations. Table S1: Zero point energies (ZPE) and the corrections due to entropy and internal energy for the various free and adsorbed species. All values are in ev. Species: ZPE T S U 0 T H O H 2 O OH ads O ads OOH ads Table S2: Thermodynamic corrections for the four proton coupled electron transfer steps of Eq. (1) in the main paper. See Eq. (5) for the definition of E corr. i Reaction step Ei corr (ev) 1 * + H 2 O OH ads + H + + e OH ads O ads + H + + e O ads + H 2 O OOH ads + H + + e OOH ads * + O 2 (g) + H + + e We define the following DFT energy differences corresponding to the four steps of the OER: E 1 = E OH ads * H2 O E H 2 E 2 = E O ads * H2 O + E H 2 E 3 = E OOH ads * 2E H2 O E H 2 (12) E 4 = E O 2 2E H2 O + 2E H 2. where E X ads represents the DFT energy of the rutile slab with the species X adsorbed on the fivefold coordinated titanium atom and E * corresponds to the clean TiO 2 surface. E H 2 O E H 2 and E O2 are the DFT energies of an isolated water hydrogen and oxygen molecule respectively. To obtain the binding energy per single adsorbate the DFT energies S-5

6 of the slab calculations are divided by eight to account for the eight adsorbed species. The DFT energies of the free molecules (H 2 H 2 O and O 2 ) are calculated using a single molecule in a cubic cell with a side of 20 Å. In the case of oxygen the triplet state is used as ground state. We calculate the binding energies using both the RPBE and PBE0 functionals with and without polarons (Table S3). Table S3: DFT binding energies (12) for slabs (a) without polarons and (b) with polarons using RPBE and PBE0 functionals. Energies are in ev. RPBE PBE0 E E E E (a) Without polarons RPBE PBE0 E E E E (b) With polarons Finally we use the binding energies in Eq. (12) and the thermodynamic corrections listed in Table S2 to rewrite the free energy steps in Eq. (11) as: G 1 = E 1 + E corr 1 G 2 = E 2 E 1 + E corr 2 G 3 = E 3 E 2 + E corr 3 (13) G 4 = E 4 E 3 + E corr 4. These are the equations used to calculate the free energy steps in Table 1 of the main paper. Hydrated surface with explicit solvent The evolution of the total energies pertaining to the MD simulations of the OH covered surface with and without polarons are shown in Fig. S1. We observe an energy gain per polaron of E pol = 1.03 ± 0.03 ev. The errors are estimated using a blocking analysis. S16 In the constrained MD simulation the force acting on the constrained O-O distance S-6

7 Potential energy (ev) Without polarons With polarons 1.03 ± 0.03 ev Time (ps) Figure S1: Time evolution of the potential energy per polaron for the MD simulations with and without polarons. The energies are referred to the average energy without polarons. oscillates around an equilibrium value after a short period of time and is found to be well converged within a duration of 0.75 ps. This is illustrated in Fig. S2(a) for the case in which the O-O distance is fixed at Å. In this way the average force can be extracted for each considered value of the O-O distance as shown in Fig. S2(b). These forces are integrated to achieve the free energy profile shown in Figure 4 of the main paper Force (Hartree/bohr) Force (Hartree/bohr) Time (ps) (a) O-O distance (Å) (b) Figure S2: (a) Force acting on the constrained O-O distance fixed at Å as a function of simulation time. (b) Average value of the force extracted for each fixed O-O distance. S-7

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