Yuan Fang

Song-Yuan Ding

Meng Zhang

Stephan N Steinmann

Ren Hu

Bing-Wei Mao

Juan M Feliu

Zhong-Qun Tian

Meng Zhang'

Revisiting the atomistic structures at the interface of Au(111) electrode-sulfuric acid solution

Knowledge of atomistic structures at solid/liquid interfaces is essential to elucidate interfacial processes in chemistry, physics, and materials sciences. The (Ö3´Ö7) structure associated with a pair of sharp reversible current spikes in the cyclic voltammogram on a Au(111) electrode in sulfuric acid solution, represents one of the most classical structures at electrode/electrolyte interfaces. Although more than ten adsorption configurations have been proposed by more than ten groups in the past four decades, the atomistic structure remains ambiguous and is consequently an open problem in electrochemistry and surface science. Herein, by combining high-resolution electrochemical scanning tuning microscopy, electrochemical infrared and Raman spectroscopies, and in particular, the newly developed quantitative computational method for electrochemical infrared and Raman spectra, we unambiguously reveal that the adstructure is Au(111)(Ö3´Ö7)-(SO4•••w2) with a sulfate anion (SO4*) and two structured-water molecules (w2*) in a unit cell, and the crisscrossed [w

n hydrogen-bonding network comprises the symmetric adstructure. We further elucidate that the electrostatic potential energy dictates the proton affinity of sulfate anions, leading to the potential-tuned structural transformations. Our work enlightens the structural details of the inner Helmholtz plane and thus advances our fundamental understanding of the processes at electrochemical interfaces.

INTRODUCTION

Solid/liquid interfacial structures play crucial roles in determining chemical processes, such as electrochemistry, catalysis, corrosion, composite formation, wear and wetting. [START_REF] Zaera | Probing liquid/solid interfaces at the molecular level[END_REF][START_REF] Schmickler | Interfacial Electrochemistry[END_REF][START_REF] Wieckowski | Interfacial Electrochemistry. Theory, Experiment, and Application[END_REF] At electrode/electrolyte solution interfaces, specifically adsorbed anions e.g., sulfate, superoxide, and halide anions and water solvent molecules can reconstruct the interfacial structures, and thus affect the thermodynamics and kinetics of electrode processes. [START_REF] White | Electrosorption of iodide on platinum(111) studied in situ by X-ray absorption spectroscopy[END_REF][START_REF] Braunschweig | Real-time investigations of Pt(111) surface transformations in sulfuric acid solutions[END_REF][START_REF] Bodappa | Early Stages of Electrochemical Oxidation of Cu(111) and Polycrystalline Cu Surfaces Revealed by in Situ Raman Spectroscopy[END_REF] It is of fundamental importance to probe the atomistic details of the electrochemical (EC) interfaces.

Sulfate or bisulfate anions adsorbed on the surface of an atomically flat Au(111) electrode in sulfuric acid is one of the most classical adsorption systems in the long history of interfacial electrochemistry and surface science. [START_REF] Kolb | Electrochemical surface science[END_REF][START_REF] Magnussen | Ordered Anion Adlayers on Metal Electrode Surfaces[END_REF] In 1984, Scherson et al. first observed a pair of sharp reversible current spikes at ~1.06 V vs. SHE below the oxygen evolution potential in the cyclic voltammogram (CV) of Au(111) singlecrystal electrodes in H2SO4 aqueous solutions, and attributed the spikes to a phase transition of the anion adlayer. [START_REF] Scherson | Voltammetric curves for Au(111) in acid media: A comparison with Pt(111) surfaces[END_REF] Since then a series of in-situ electrochemical scanning tunneling microscopy (EC-STM) and electrochemical infrared (EC-IR) spectroscopy have been employed by more than ten distinguished groups in the field of interfacial electrochemistry and surface science to elucidate the detailed structure and process associated with the current spikes. In 1992, Magnussen et al. employed EC-STM to firstly observe a (Ö3´Ö7) patterned adstructure near the sharp current spikes and proposed it to be composed of adsorbed bisulfate anions (HSO4*, the charge of the electro-adsorbed species is usually fractional and depends on the applied potential; * denotes the adsorbed species). [START_REF] Magnussen | In situ scanning tunnelling microscopy observations of a disorder-order phase transition in hydrogensulfate adlayers on Au(111)[END_REF] In 1994, the Weaver group assigned the possible adstructure as the sulfate anion co-adsorbed with a hydronium cation SO4•••H3O* by performing the combined EC-STM and EC-IR method. [START_REF] Edens | The adsorption of sulfate on gold(111) in acidic aqueous media: adlayer structural inferences from infrared spectroscopy and scanning tunneling microscope[END_REF] The Osawa group interpreted the measured synchronous 2D EC-IR spectra on the ultra-flat Au film electrode as a sulfate anion co-adsorbed with one water molecule (w) as SO4•••w* with two possible hydrogenbonding configurations. [START_REF] Ataka | In Situ Infrared Study of Water-Sulfate Coadsorption on Gold(111) in Sulfuric Acid[END_REF] Several possible configurations have been proposed according to the empirical assignments of the bands observed in the EC-IR spectra and/or qualitative assignments of the fuzzy features in the EC-STM images. [START_REF] Shingaya | Comparison of a bisulfate anion adsorbed on M(111) (M=Pt, Rh, Au, Ag and Cu)[END_REF][START_REF] Nakamura | Hydration processes on metal surfaces studied by IR and STM: a model for the potential drop across the electric double layers[END_REF][START_REF] Cuesta | The adsorption of sulfate and phosphate on Au(111) and Au(100) electrodes: an in situ STM study[END_REF] In addition, the Lipkowski and Wieckowski groups deduced SO4* instead of HSO4* by chronocoulometry and radiochemistry. [START_REF] Shi | Investigations of SO42-adsorption at the Au(111) electrode by chronocoulometry and radiochemistry[END_REF] Theoretically, the Jacob group concluded that the configuration with SO4•••H3O* is the most stable configurations by density functional theory (DFT) based binding energies of eight possible configurations. [START_REF] Venkatachalam | DFT Studies on the Nature of Coadsorbates on SO42-/Au(111)[END_REF] However, they did not consider the applied potential and neglected solvation effects. In short, most groups supported that the main adsorbates are sulfate anions.

Although more than ten adsorption configurations for the Au(111)/H2SO4 system have been proposed in the past four decades, the atomistic structure of the Au(111)(Ö3´Ö7)adsorbate associated with the current spikes at approximately 1.06 V remains ambiguous. Consequently, it is one of the open problems in electrochemistry and surface science with several unsolved issues: (1) Are are water or hydronium molecules coadsorbed with each sulfate or bisulfate? And if so, how many? (2) What are the detailed hydrogen-bonding networks that comprise the two-dimensional crystalline adstructure? Importantly, such observations and open questions also exist for other M(111)/H2SO4 solution interfaces (M = Pt, Rh, Cu, Ir, and Pd), [START_REF] Funtikov | Anion adsorption from sulfuric acid solutions on Pt(111) single crystal electrodes[END_REF][START_REF] Wan | Atomic Structure of Adsorbed Sulfate on Rh(111) in Sulfuric Acid Solution[END_REF][START_REF] Li | An in situ STM study of sulphate adsorption on copper(111) in acidic aqueous electrolytes[END_REF][START_REF] Wan | In Situ Scanning Tunneling Microscopy of Well-Defined Ir(111) Surface: High-Resolution Imaging of Adsorbed Sulfate[END_REF][START_REF] Wan | In situ scanning tunneling microscopy of adsorbed sulfate on well-defined Pd(111) in sulfuric acid solution[END_REF] where the (Ö3´Ö7) adstructures prevail as revealed by EC-STM, but the atomistic structures of these interfaces are also ambiguous. [START_REF] Shingaya | Comparison of a bisulfate anion adsorbed on M(111) (M=Pt, Rh, Au, Ag and Cu)[END_REF][START_REF] Shingaya | Model double layer structures on M(111) (M=Pt, Rh, Au, Cu and Ag) in a sulfuric acid solution[END_REF][START_REF] Kolics | Adsorption of Bisulfate and Sulfate Anions on a Pt(111)[END_REF][START_REF] Jinnouchi | First principles study of sulfuric acid anion adsorption on a Pt (111) electrode[END_REF] The difficulties in unambiguously determining the adstructure of the Au(111)(Ö3´Ö7)-adsorbate in previous studies are threefold: (1) The spatial resolution of the EC-STM twenty years ago is not sufficiently high to resolve the atomistic details of adsorbates as sulfate or bisulfate anions, water molecule or hydronium cation; (2) The vibrational frequencies of the EC-IR spectra reported in the literature are higher than 900 cm -1 feature only one or two vibrational modes associated with the sulfate or bisulfate species, while vibrational modes with frequencies below 500 cm -1 , associated with the adsorbate-surface interactions, are missing;

(3) There are no quantitative theoretical methods to calculate the EC-IR and EC-Raman spectra from single crystal electrode/electrolyte interfaces, which play essential roles in precisely interpreting the measured spectra. Therefore, we herein combine the latest experimental and corresponding computational methods to unambiguously reveal the atomistic arrangements of adsorbed anions in association with coadsorbed species, and to comprehensively understand the interactions in the inner Helmholtz plane, which is the heart of the electric double layer at the interface. [START_REF] Zaera | Probing liquid/solid interfaces at the molecular level[END_REF][START_REF] Tian | Surface-Enhanced Raman Scattering: From Noble to Transition Metals and from Rough Surfaces to Ordered Nanostructures[END_REF][START_REF] Liu | Progress of electrode/electrolyte interfacial investigation of Li-ion batteries via in situ scanning probe microscopy[END_REF][START_REF] Wang | Recent applications of in situ ATR-IR spectroscopy in interfacial electrochemistry[END_REF][START_REF] Koper | Fuel Cell Catalysis: A Surface Science Approach[END_REF] In this study, we employed high-resolution EC-STM combined with DFT calculation to quantitatively assign the atomistic arrangement of the adstructure. The EC-IR spectral data in the literature, combined with our in-situ electrochemical shell-isolated nanoparticle-enhanced Raman spectroscopy (EC-SHINERS) with 4-6 orders of magnitude enhancement in Raman signals of adsorbates on metallic (e.g., Au, Cu, Pt, Rh) single-crystal electrodes, [START_REF] Li | Shell-isolated nanoparticle-enhanced Raman spectroscopy[END_REF][START_REF] Li | Extraordinary enhancement of Raman scattering from pyridine on single crystal Au and Pt electrodes by shell-isolated Au nanoparticles[END_REF][START_REF] Honesty | Shell-isolated nanoparticle enhanced Raman spectroscopy (SHINERS) investigation of benzotriazole film formation on Cu(100), Cu(111), and Cu(poly)[END_REF][START_REF] Li | In situ probing electrified interfacial water structures at atomically flat surfaces[END_REF] were employed to unveil the chemical bonding of both sulfate anions and water molecules in the (Ö3´Ö7) adstructure. To accurately interpret the features of the experimental spectra, we employed our newly developed computational method to calculate the EC-IR and EC-Raman spectra of nine possible configurations of Au(111)(Ö3´Ö7)-X (X denotes the speculated adsorbates). [START_REF] Fang | Toward a quantitative theoretical method for infrared and Raman spectroscopic studies on single-crystal electrode/liquid interfaces[END_REF] This computational method quantitatively calculates the vibrational frequencies and, importantly, the spectral intensities of adstructures at the single-crystal electrodes/liquid interfaces by simultaneously considering the surface charge and solvation effect. We found that the calculated EC-STM image, EC-IR and EC-Raman spectra of the Au(111)(Ö3´Ö7)-(SO4•••w2) configuration perfectly match the respective experimental observations. Finally, we sketched a reaction free energy (ΔGre) diagram [START_REF] Jinnouchi | First principles study of sulfuric acid anion adsorption on a Pt (111) electrode[END_REF] by calculating the potential-dependent Gibbs free energies Gads(V) of all configurations to further confirm the energetic preference for the adstructure, Au(111

)(Ö3´Ö7)-(SO4•••w2).
The diagram also reveals that the potential-dependent interplay between the proton affinity of sulfate anions and the electrostatic potential energy determines the structural transformation at the EC interfaces. Our work not only elucidates the detailed adsorption configuration at the Au(111)/H2SO4 solution interface, but also provides a paradigm for the combined theory/experimental tool kit to unveil the atomistic structures at electrodes/electrolyte interfaces.

EXPERIMENTAL SECTION

Chemicals. Sulfuric acid (96%) was purchased from Merck. Deionized Milli-Q water (resistivity of 18.2 MW cm) was used for all aqueous solutions.

Preparation of the Au(111) single crystal electrodes.

The Au(111) half-bead single crystal electrodes were prepared following Clavilier's method [START_REF] Clavilier | Preparation of monocrystalline Pt microelectrodes and electrochemical study of the plane surfaces cut in the direction of the {111} and {110} planes[END_REF] and used as the working electrodes. The surface area of the Au(111) electrode is 3.733 mm 2 .

Electrochemical measurements. Cyclic voltammetry

(CV) experiments were performed on a CHI electrochemical workstation (CHI 660D, CH Instrument). A Pt wire was used as the counter electrode and a reversible hydrogen electrode (RHE) connected to the cell via a Luggin capillary was used as the reference electrode.

STM measurements.

In-situ STM measurements were performed on a Nanoscope V STM instrument (Veeco, Santa Barbara, CA). Mechanically cut Pt/Ir tips were used, which were insulated by apiezon wax or thermosetting glue to reduce the electrochemical current. The STM works in the constant current mode, and the scanning range is 4 nm × 4 nm.

Raman spectroscopic measurements. Pinhole-free

Au@SiO2 nanoparticles with a Au core diameter of ~55 nm and a SiO2 shell thickness of ~3 nm were synthesized according to Li's methods. [START_REF] Li | Shell-isolated nanoparticle-enhanced Raman spectroscopy[END_REF] Au@SiO2 NPs were introduced onto the Au(111) single crystal electrodes by dropping a dilute Au@SiO2 sol solution, followed by the evaporation of the Density functional theory calculations. The metal surfaces were modeled as a symmetric Au(111)(Ö3´Ö7) slab with a lattice constant of 4.21 Å and a thickness of 7 layers in a periodic box of 78.03 Å (the middle three layers were frozen in the bulk position). The first-principles computations were performed using the Vienna ab initio simulation package (VASP) with projector augmented wave (PAW) pseudopotentials. [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] The alternative revision of the Perdew-Burke-Ernzerhof functional, RPBE, was employed to calculate the chemisorption energies of the adsorbates on the Au(111) surface. [START_REF] Hammer | Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals[END_REF] We considered a 550 eV plane-wave energy cut-off and integrated the Brillouin zone with a 5´5´1 G-centered Kpoint mesh for a (Ö3´Ö7) unit cell. The self-consistent field procedure was repeated until a precision of 1´10 -9 eV in the total energy. All geometries were optimized to reach residual forces on all atoms lower than 0.01 eV/Å. The simulated STM images are constructed on the basis of Tersoff-Hamann theory with a bias voltage of + 0.85 V and were visualized using the p4vasp program. [START_REF] Tersoff | Theory of the scanning tunneling microscope[END_REF] To calculate the EC-IR and -Raman spectra, VASPsol implementation was employed to mimic surface solvation effect. [START_REF] Mathew | Implicit self-consistent electrolyte model in plane-wave density-functional theory[END_REF] The relative permittivity er and ionic strength I were set to 78 and 0.3 M (corresponding to Debye screening length l, 5.5 Å), respectively. The surface tension was set to zero (no cavitation energy). Finite difference method was employed to calculate the IR and Raman spectra. The differential step size of Cartesian coordinates Dx and electrostatic field strengths along the z axis DGz were set to 0.01 Å and 0.1 V/Å, respectively. The detailed computational methods of EC-IR and -Raman spectra were listed in ref. 34. Other computational details are provided in the SI.

RESULTS AND DISCUSSION

A typical CV of the Au(111) electrode in 0.1 M H2SO4 was recorded from 0.05 to 1.2 V vs. SHE away from the characteristic voltages regarding hydrogen or oxygen evolution processes (Figure 1A). The CV shows a pair of sharp spikes at approximately 1.06 V (red lines), which is consistent with the results from the literature, [START_REF] Cuesta | The adsorption of sulfate and phosphate on Au(111) and Au(100) electrodes: an in situ STM study[END_REF][START_REF] Sato | Effect of sulfuric acid concentration on the structure of sulfate adlayer on Au(111) electrode[END_REF][START_REF] Suto | In situ Video-STM studies of sulfate dynamics on Au(111)[END_REF] and indicates the high quality of the Au(111) single-crystal electrode in this work.

Determining the adstructure from nine possible configurations at high potentials. In Figure 1B, the measured EC-STM image at potentials of 1.06 V and above (1.06-1.20 V, high potentials) exhibits the well-known (Ö3´Ö7) adstructure rotated by 19.1° from the [1 1 ( 0] direction of the Au(111) surface, with the bright spots at the corners of the yellow (Ö3´Ö7) frame. The STM image shows many detailed features that were not resolved before. [START_REF] Magnussen | In situ scanning tunnelling microscopy observations of a disorder-order phase transition in hydrogensulfate adlayers on Au(111)[END_REF][START_REF] Edens | The adsorption of sulfate on gold(111) in acidic aqueous media: adlayer structural inferences from infrared spectroscopy and scanning tunneling microscope[END_REF][START_REF] Cuesta | The adsorption of sulfate and phosphate on Au(111) and Au(100) electrodes: an in situ STM study[END_REF][START_REF] Suto | In situ Video-STM studies of sulfate dynamics on Au(111)[END_REF] In particular, we observed zig-zag chains (dashed yellow line segments along the Ö3 direction) and two lobes (dashed red lines along the direction of a) going through and inside the yellow frame, respectively.

To unveil the observed ultrafine features in the measured STM image, we first constructed thirteen possible Au(111)(Ö3´Ö7)-X configurations, which yielded nine unique structures after geometry optimization (Figure 2). They span suggested configurations from the literature [START_REF] Magnussen | In situ scanning tunnelling microscopy observations of a disorder-order phase transition in hydrogensulfate adlayers on Au(111)[END_REF][START_REF] Edens | The adsorption of sulfate on gold(111) in acidic aqueous media: adlayer structural inferences from infrared spectroscopy and scanning tunneling microscope[END_REF][START_REF] Ataka | In Situ Infrared Study of Water-Sulfate Coadsorption on Gold(111) in Sulfuric Acid[END_REF][START_REF] Shingaya | Comparison of a bisulfate anion adsorbed on M(111) (M=Pt, Rh, Au, Ag and Cu)[END_REF][START_REF] Cuesta | The adsorption of sulfate and phosphate on Au(111) and Au(100) electrodes: an in situ STM study[END_REF][START_REF] Venkatachalam | DFT Studies on the Nature of Coadsorbates on SO42-/Au(111)[END_REF][START_REF] Shingaya | Model double layer structures on M(111) (M=Pt, Rh, Au, Cu and Ag) in a sulfuric acid solution[END_REF][START_REF] Garcia-Araez | Structural Effects on Water Adsorption on Gold Electrodes[END_REF][START_REF] Simeone | The Au(111)/electrolyte interface: a tunnel-spectroscopic and DFT investigation[END_REF] and our initial guesses. We then compared the various simulated EC-STM images with the measured one. See detailed atomistic labels in Figure 2A and the caption of Figure 2. More convincingly than the calculated STM patterns of other configurations (Figure S1), the calculated STM pattern (Figure 1C) of Au(111)(Ö3´Ö7)-(SO4•••w2) perfectly matches the measured one at high potentials (Figure 1B). The bright and isolated spots are assigned to the upmost oxygen atoms (denoted as O4 in Figures 2A and2F) of SO4*; the zig-zag chains are assigned to hydrogen-bonded dual-water molecules. The two lobes are assigned to the side oxygen atoms (denote as O2 atoms in Figure 2A and2F) of two adjacent SO4* molecules (along the Ö7 direction) which are hydrogenbonded with the two water molecules. As we know, the spot brightness depends on the STM cross-section of the oxygen charge density near the Fermi level EF in Au(111)(Ö3´Ö7)-X. In Figure 1C, the main maxima spots (marked with two red open squares, aligned along the zig-zag chains), secondary maxima spots (marked with two red open circles, aligned along the Ö3 direction), and minima spots (marked with two red open triangles, intertwined with the main maxima spots) in the (Ö3´Ö7) unit cell, are associated with the charge densities of O atoms from the dual-water molecules hydrogen-bonded with each other, O2 and O4 atoms of the SO4*, and O1 and O3 atoms of the SO4*, respectively, since their cross-sections decrease in turn (Figure 1D). The simulated STM images of other configurations failed to reproduce either the zig-zag feature or the two-lope feature. Our finding identifies the experimentally observed structure as highly symmetric crisscrossed

[w•••SO4•••w] and [w•••w•••]n hydrogen-bonding network of the adstructure Au(111)(Ö3´Ö7)-(SO4•••w2).
EC-IR spectroscopy can provide information on the sulfate anions, and particularly reveals rich vibrational information concerning the co-adsorbed water molecule or hydronium cation and in the adstructure of Au(111)(Ö3´Ö7)-X at the high potentials. The EC-IR spectrum (the dark red curve in Figure 3A) at 1.06 V measured by Ataka et al., [START_REF] Ataka | In Situ Infrared Study of Water-Sulfate Coadsorption on Gold(111) in Sulfuric Acid[END_REF] [START_REF] Venkatachalam | DFT Studies on the Nature of Coadsorbates on SO42-/Au(111)[END_REF][START_REF] Simeone | The Au(111)/electrolyte interface: a tunnel-spectroscopic and DFT investigation[END_REF] can be excluded for two reasons: (i) The characteristic hydronium band at around 1700 cm -1 cannot be observed in the EC-IR spectra at high potentials; [START_REF] Ataka | Potential-Dependent Reorientation of Water Molecules at an Electrode/Electrolyte Interface Studied by Surface-Enhanced Infrared Absorption Spectroscopy[END_REF] (ii) Computationally, configurations with a co-adsorbed hydronium cannot be optimized at high potentials, but converge to HSO4•••w* configurations. In summary, only the calculated EC-IR The EC-Raman spectroscopy has the advantage over the EC-IR counterpart to provide much richer vibrational fingerprint information on the sulfate or bisulfate anions with vibrational frequencies of 100-1300 cm -1 . However, it is difficult to obtain high signal-to-noise EC-SHINERS spectra in this study due to the weak Raman activity of the interfacial species in this system. The primarily measured potentialdependent Raman spectra are shown in Figure S2. For comparison with the measured EC-Raman spectra, the Raman spectrum from the bulk solution was taken first (the blue curve in Figure 3C). Three main bands centered at 473, 980, and 1051 cm -1 are shown and assigned to the combinational SO2 wagging and rocking modes ρw+r(SO2), symmetric SO4 stretching mode νs(SO4), and symmetric SO3 stretching mode νs(SO3), respectively (See the detailed analyses in SI 5 and modes in Figures S3-S5). The EC-SHINER spectrum at 1.06 V (dark red curve in Figure 3C) and above shows four bands at 243, 614, 956, and 1185 cm -1 . The considerable difference between the EC-SHINER spectrum and the bulk Raman spectrum indicates that the four bands arise from vibrational modes of the interfacial species instead of bulk species.

The calculated EC-Raman spectra for the configurations that containing adsorbed sulfate anions (SO4•••w2*, SO4•••w* (w12), and SO4* (Figure 3C)) show four bands at 217-231, 633-649, 944-959 and 1188-1196 cm -1 , which in some extent agree with the measured spectrum counterparts at 1.06 V. The SO4•••w* (w13) configuration can, however, be excluded, as the pair of splitting bands at 955 cm -1 cannot be observed in the measured one. Moreover, the Stark tuning slopes (STS, defined as the slope of the vibrational frequency as a function of the applied potential) of the four bands in the measured Raman spectra also in some extent agree with the calculated Raman spectra of the three configurations counterparts, as shown in Table 1. Particularly, the 956 and 1185 cm -1 frequencies of the measured EC-Raman bands at 1.06 V perfectly match the frequencies 955 and 1183 cm -1 of the measured EC-IR spectrum at 1.06 V (Figure 3A and 3C, dark red curves). Furthermore, the STS of the 1185 cm -1 band (59 cm -1 V -1 ) in the measured EC-Raman spectra perfectly matches those of the measured EC-IR band at 1189 cm -1 (45 cm -1 V -1 ) by Edens et al. [START_REF] Edens | The adsorption of sulfate on gold(111) in acidic aqueous media: adlayer structural inferences from infrared spectroscopy and scanning tunneling microscope[END_REF] and the IR band at 1183 cm -1 (60 cm -1 V -1 ) by Ataka et al. [START_REF] Ataka | In Situ Infrared Study of Water-Sulfate Coadsorption on Gold(111) in Sulfuric Acid[END_REF] Therefore, the observed bands at 243, 614, 956, and 1185 cm -1 of the Raman spectrum at 1.06 V, are assigned to the out-of-surface translational-like mode of SO4* T(Au-SO4), symmetric SO3 bending mode ds(SO3), νs(SO4) mode, and ν(SO) mode (Figure S6-S9), respectively. Table 1. STSs (cm -1 V -1 ) of the vibrational frequencies for the adsorbed sulfate configurations at the high potentials. The configurations containing HSO4* at the high potentials can be excluded, since their bands at 300-400 and 800-900 cm -1 (Figure 3D) cannot match any of those in the measured EC-Raman spectrum. The vibrational modes of the configurations containing HSO4* have been visualized and listed in Figures S10-S14. Briefly, the EC-Raman spectra reveal that the adstructure must contain the sulfate anions instead of bisulfate anions, but cannot provide strong evidence to determine the number and atomistic arrangements of coadsorbed water molecules, which might due to the ultraweak cross section of water molecules. Nevertheless, according to joint evidence from the calculated and measured EC-Raman and EC-IR spectra, the Au(111)(Ö3´Ö7)-(SO4•••w2) configuration is the most plausible adstructure at high potentials.

Adstructure of the Au(111)/H2SO4 solution interface at the low potentials. The EC-Raman spectra also show that the band at approximately 300 cm -1 gradually appears, and the 614 and 1185 cm -1 bands diminish when the potential is negatively shifed to the range of 0.66-0.86 V (low potentials). In addition, the STSs at 243, 956, and 1185 cm -1 at high potentials (34, -33, and 59 cm -1 V -1 , respectively) are apparently different from the respective STSs of 24, -25, and 90 cm -1 V -1 below 0.86 V. The discrepancies of the spectral features at high and low potentials indicate that the interface undergoes a potential-determined structural transformation in the potential range of 0.86-1.06 V.

Although the measured STM image in Figure S15 shows that the interfacial structures at the low potentials may be disordered in the acquisition time domain, the theoretical study based on the Au(111)(Ö3´Ö7)-X configurations at low potentials is still relevant to determine approximate adstructures containing sulfate or bisulfate by comparing the calculated EC-Raman spectra with the measured one, as shown in Figure S16 and Table S2-S4. The four configurations containing SO4* can be excluded at the low potentials, because none of their EC-Raman spectra can interpret the appearance of new band at 300 cm -1 and the disappearance of the 1185 cm -1 band of the measured EC-Raman spectrum (dark red curves of Figure S16). In contrast, the calculated EC-Raman spectra of HsSO4•••w* (w13) and HtSO4•••w*(w13) to some extend match the measured one. The new Raman band at 300 cm -1 is assigned to the H2O•••HSO4 stretching mode ν(HB) (see the modes in Figure S10 andS11). By further comparing the calculated and measured STSs of the three bands in 231-233, 294-301, 966-988 cm -1 , as shown in Table S4, we deduce that the adstructure is more likely HsSO4•••w* (w13) than HtSO4•••w* (w13) at low potentials. Reaction free energy diagram and adstructural stability of Au(111)(Ö3´Ö7)-X. The potential-dependent reaction free energies ΔGre was calculated to further determine the adstructures at high potentials and the potential-dependent structural transformation. Figure 4 shows that the Au(111)(Ö3´Ö7)-(SO4•••w2) (solid red line) is the most stable configuration at high potentials. It also shows that HtSO4•••w* (w13) (solid dark blue line) is the most stable structure at low potentials. However, the HsSO4•••w* (w13) (dashed dark blue line) is only slightly less stable than HtSO4•••w* (w13). The ΔGre parabolas of both stable adstructures intersect at 1.12 V vs. SHE, which indicates that a deprotonation reaction (Equation 1) occurs when the potential is positively tuned to approximately 1.12 V. In addition, the potential of the deprotonation reaction can slightly depend on the ionic strength I (see Figure S17).

HSO -••• w * + H 2 O(aq) -𝑒 9 → SO -••• w 2 * + H ; (aq) (1)
To understand the mechanism of the deprotonation reaction, we made a detailed analysis on ΔGre. Figure S18A shows that the adsorbed bisulfate configurations are more stable than the adsorbed sulfate configurations at low potentials, due to the proton affinity of the adsorbed sulfate anion. When the potential is positively shifted, the electrostatic potential energies of the adsorbed sulfate configurations gradually surpass the sum of the proton affinity and the electrostatic potential energies of the adsorbed bisulfate configurations, which stabilizes the sulfate anion adsorption. Moreover, the co-adsorbed water molecules can hydrogen-bond to the O atoms from the adjacent water molecule and O atoms from sulfate anions to effectively stabilize the adstructures, especially at high potentials (Figure S18B).

A limitation of this deprotonation mechanism is that it is obtained on the basis of the ordered Au(111)(Ö3´Ö7)-X configurations, a small unit cells compared to the EC-STM images at low potentials (see Fig. S15) that suggest disordered unit cells. Configurations with much larger unit cells such as Au(111)(2Ö3´5) or (2Ö3´6) unit cells would be helpful for studying more configurations with lower coverages at low potentials, and obtaining a more complete deportation mechanism of the HSO4* species.

CONCLUSION

By combining experimental and computational EC-STM, EC-IR, and EC-Raman spectroscopy, we conclude that the adstructure is Au(111)(Ö3´Ö7)-(SO4•••w2) at high potentials (>1.06 V vs SHE); the electro-adsorbed species SO4•••w2* evolves to HtSO4•••w* when the potential is negatively tuned. The coadsorbed water molecules play an important role in the structural transformation, which can be further supported by the ΔGre diagram of Au(111)(Ö3´Ö7)-X configurations. We found that the potential-dependent interplay between the proton affinity of sulfate anions and the electrostatic potential energy determine the potential-tuned structural transformation on the electrode surface.

This work offers a definite answer that clarifies the 40-year ambiguity in the atomistic adstructure at the Au(111)/H2SO4 solution interface at high potentials. The determined adstructure Au(111)(Ö3´Ö7)-(SO4•••w2) straightforwardly enlightens the studies of similar systems, i.e., other M(111)/H2SO4 solution interfaces (M = Pt, Rh, Cu, Ir, and Pd). The experimental and computational EC-STM, EC-IR and EC-Raman spectroscopies, and the computational diagram of the reaction free energy may provide a standard workflow to obtain multi-perspective evidence for atomistic structures of the inner Helmholtz plane. The methods thus pave the way to explore the reaction mechanisms of electrocatalytic or photoelectrocatalytic reactions, electro-corrosion and electrodeposition reactions at atomistic levels, and guide the rational design of novel interfacial materials with improved functions and performances.

Figure 1 .

 1 Figure 1. Probing atomistic structures in the Au(111)/H2SO4 solution interface. (A) Cyclic voltammetry curve of Au(111) in 0.1 M H2SO4 aqueous solution, scan rate: 20 mV/s. (B) High resolution STM image at 1.06 V vs. SHE. (C) Distribution of charge density of the SO4•••w2* configuration near the Fermi level EF. The unit vectors a, b are the basic vectors of the Au(111)(1´1) along with the [𝟏 𝟎 𝟏 % ] and [𝟎 𝟏 𝟏 % ] directions, respectively. (D) Calculated STM image of the Au(111)(Ö3´Ö7)-(SO4•••w2) configuration. The basic vectors of Au(111)(Ö3´Ö7) are defined as 2b -a (Ö3 direction) and 2a + b (Ö7 direction), respectively. The main maxima, secondary maxima and minima spots correspond to red panes, circle and triangle frames, respectively. solvent water in the sol. Raman spectra were acquired with a Renishaw InVia Qontor confocal Raman instrument. The excitation line was 632.8 nm from He-Ne laser. Electrochemical control was maintained using the CHI electrochemical workstation. A homemade spectroelectrochemical cell with a Pt wire counter electrode and RHE reference electrode was used for the EC-SHINERS experiments.

Figure 2 .

 2 Figure 2. Nine proposed and optimized Au(111)(Ö3´Ö7)-X configurations. (A) SO4*; (B) and (C) HsSO4* and HtSO4* with H bonding with O2 and O4, respectively; (D) and (E) SO4•••w* (w12) and SO4•••w* (w13) consist of a sulfate anion and a coadsorbed water molecule with SO4•••w* hydrogen-bonds through O1 and O2 or O1 and O3, respectively; (F) SO4•••w2* consists of a sulfate anion and a co-adsorbed dual-water (w2) molecules; (G) and (H) HsSO4•••w* (w11) and HsSO4•••w* (w13) consist of a bisulfate anion with H bonding with O2 and a co-adsorbed water molecule with HsSO4•••w* hydrogen-bonds through O1 and O1 or O1 and O3 from different HsSO4* molecules; (I) HtSO4•••w*(w13) consists of a bisulfate anion with H bonding with O4 and a co-adsorbed water molecule with HtSO4•••w* hydrogen-bonds through O1 and O3 from different HtSO4* molecules. The golden, yellow, red, and cyan balls denote Au, S, O, and H atoms, respectively.

  features three main bands at 955, 1183, and 1650 cm -1 , which have been assigned to the symmetric SO4 stretching mode ns(SO4), S-O bond stretching mode n(SO) of SO4*, and bending mode of w*, d(H2O) by the authors. The experimental assignment alone can only provide an ambiguous determination of adstructures. However, the simulated EC-IR spectra of all possible configurations, accompanied with the measured EC-IR spectra evidentially help us to exclude most of the candidate configurations. Figures 3A and 3B show that the possible configurations with HtSO4•••w* (w13), HsSO4•••w* (w13), or HsSO4•••w* (w11) can be excluded since the calculated bands at 1226 or 1243 cm -1 assigned to the n(SO) mode of HSO4*, cannot be observed in the measured EC-IR spectrum. The possible configurations with SO4•••w* (w12), SO4*, or HsSO4*, HtSO4* can also be excluded due to the absence of the d(H2O) bands at around 1650 cm -1 . Additionally, the SO4•••w* (w13) configuration can be excluded because a pair of splitting bands at 944 and 974 cm -1 due to the decrease of the sulfate anion symmetry, poorly match the single band at 956 cm -1 in the measured EC-IR spectrum. The previously suggested well-known Au(111)(Ö3´Ö7)-(SO4•••H3O) configuration

Figure 3 .

 3 Figure 3. Calculated EC-IR and -Raman spectra of the Au(111)(Ö3´Ö7)-X configurations at 1.06 V vs. SHE. EC-IR spectra of the configurations containing sulfate anions in (A) or bisulfate anions in (B). EC-Raman spectra of the configurations containing sulfate anions in (C) or bisulfate anions in (D). The blue curves in panel A and C, respectively, denote the measured IR and Raman spectrum of bulk solution. The dark red curves in panel A and C, respectively, denote the measured EC-IR and -Raman spectrum at 1.06 V. The measured IR spectra were adapted from ref. 12 with permission, copyright (1998) American Chemical Society. spectrum of Au(111)(Ö3´Ö7)-(SO4•••w2) matches well the measured one. To understand the IR activity of the d(H2O) bands of the possible configurations, we analyzed the orientation of the dipole of w*, qw, defined as the included angle between the dipole moment of w* and the surface normal of Au(111). The qw angels in SO4•••w* (w12) and HsSO4•••w* (w13) are 79° and 98°, respectively. As a result, the d(H2O) bands of the two possible configurations are almost IR-inactive according to the surface selection rule of surface IR spectroscopy on metal surfaces. 26 In SO4•••w2*, the qw angles of both water molecules are almost identical (67°). The band centered at 1669 cm -1 of SO4•••w2* is assigned to the symmetric bending mode ds(H2O) of dual hydrogen-bonded water molecules, and is IR-active; the anti-symmetric bending mode danti(H2O)centered at 1685 cm -1 is, however, IR-inactive.The EC-Raman spectroscopy has the advantage over the EC-IR counterpart to provide much richer vibrational fingerprint information on the sulfate or bisulfate anions with vibrational frequencies of 100-1300 cm -1 . However, it is difficult to obtain high signal-to-noise EC-SHINERS spectra in this study due to the weak Raman activity of the interfacial species in this system. The primarily measured potentialdependent Raman spectra are shown in FigureS2. For comparison with the measured EC-Raman spectra, the Raman spectrum from the bulk solution was taken first (the blue curve in Figure3C). Three main bands centered at 473, 980, and

  ModesT(Au-SO4) ds(SO3) νs(SO4) ν(SO)

Figure 4 .

 4 Figure 4. Potential-dependent reaction free energy diagram from 1.00 V to 1.24 V vs. SHE. The black line denotes the reference state (HSO4 -(aq) + 2H2O (aq) + *). The solid and dashed parabolas denote X = HtSO4* and HsSO4* in blue, SO4•••w* (w13) and (w12) in pink, HtSO4•••w* (w13) and HsSO4•••w* (w13) in dark blue.

ACKNOWLEDGMENTS

The authors acknowledge funding supported by the National Natural Science Foundation of China (91950121, 21727807, 21403179, 21872115, and 21533006). The firstprinciples calculations in this work were performed on the supercomputing system in the big data system and computing platform of the State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University. Y.F. and S.Y.D. sincerely thank Dr. Ryosuke Jinnouchi for discussion on the calculation of reaction free energy of Au(111)(Ö3´Ö7)-X configurations.

ASSOCIATED CONTENT

Supporting Information. Computational details, the calculation of reaction free energy, Figure S1-S19, and Table S1-S4 The Supporting Information is available free of charge on the ACS Publications website.

AUTHOR INFORMATION

Corresponding Author syding@xmu.edu.cn bwmao@xmu.edu.cn juan.feliu@ua.es Notes The authors declare no competing financial interest.

For Table of Contents Only

The adstructure with the (Ö3´Ö7) symmetry at the interface of Au(111) electrode-sulfuric acid solution was revealed by combining high-resolution electrochemical scanning tuning microscopy, electrochemical Raman spectroscopy, and especially, the newly-developed computational method on electrochemical infrared and Raman spectroscopies.


Christopher Panaritis

Carine Michel

Martin Couillard

Elena A Baranova

Stephan N Steinmann

Elucidating the role of electrochemical polarization on the selectivity of the CO2 hydrogenation reaction over Ru

Keywords: Electrochemical promotion of catalysis, methanation, reverse water gas shift, density functional theory

Introduction

Due to the importance of carbon dioxide (CO2) in the greenhouse gas effect, the heterogeneous catalytic reduction of CO2 with hydrogen (H2) to base chemicals has been extensively studied [START_REF] Porosoff | Catalytic reduction of CO2 by H2 for synthesis of CO, methanol and hydrocarbons: challenges and opportunities[END_REF][START_REF] Saeidi | Mechanisms and kinetics of CO 2 hydrogenation to value-added products: A detailed review on current status and future trends[END_REF]. Depending on the catalyst and relative partial pressures, the Reverse Water Gas Shift (RWGS) or the methanation reaction is dominant, yielding carbon monoxide (CO) and methane (CH4), respectively [START_REF] Saeidi | Mechanisms and kinetics of CO 2 hydrogenation to value-added products: A detailed review on current status and future trends[END_REF]. Ruthenium (Ru) has been used extensively due to its dual ability of activating CO2 and H2, and it is the most economical noble metal [START_REF] Avanesian | Mechanism of CO2 reduction by H2 on Ru(0 0 0 1) and general selectivity descriptors for late-transition metal catalysts[END_REF]. Based on experimental Fourier transform infrared (FTIR) spectroscopy and Density Functional Theory (DFT) studies, the main reaction pathways of CO2 reduction over Ru catalysts is summarized in Scheme 1 [START_REF] Avanesian | Mechanism of CO2 reduction by H2 on Ru(0 0 0 1) and general selectivity descriptors for late-transition metal catalysts[END_REF][START_REF] Zhang | Hydrogenation mechanism of carbon dioxide and carbon monoxide on Ru(0001) surface: a density functional theory study[END_REF][START_REF] Wang | Controlling selectivities in CO2 reduction through mechanistic understanding[END_REF][START_REF] Yaccato | Competitive CO and CO2 methanation over supported noble metal catalysts in high throughput scanning mass spectrometer[END_REF]. The first step consists of adsorbing CO2 and dissociating it into chemisorbed CO and O. The next step is crucial for the selectivity: either CO desorbs or it hydrogenates further to CHO and ultimately to CH4. This competition depends on the morphology and the presence of promoters as well as on the reaction conditions (temperature and H2/CO2 pressure ratio). Typically, CH4 selectivity is favoured by temperatures of 200-300 °C. Above 250 °C the temperature is high enough to enable the endothermic formation of CO on Ru nanoparticles, although only at about 500 °C a high selectivity was reached in earlier reports [START_REF] Panaritis | Insight towards the role of ceria-based supports for reverse water gas shift reaction over RuFe nanoparticles[END_REF]. Scheme 1. Schematic mechanism of the CO2 hydrogenation pathway under standard conditions on the Ru(0001) surface.

The activity and selectivity of metal supported catalysts can be tuned by metal-support interactions (MSI) [START_REF] Panaritis | Insight towards the role of ceria-based supports for reverse water gas shift reaction over RuFe nanoparticles[END_REF][START_REF] Dole | Quantifying metal support interaction in ceria-supported Pt, PtSn and Ru nanoparticles using electrochemical technique[END_REF], metal alloying [START_REF] Baranova | Infrared spectroscopy on sizecontrolled synthesized Pt-based nano-catalysts[END_REF][START_REF] Daza | CO2 conversion by reverse water gas shift catalysis: Comparison of catalysts and mechanisms and their consequences for CO2 conversion to liquid fuels[END_REF], addition of alkali promoters [START_REF] Yaccato | Competitive CO and CO2 methanation over supported noble metal catalysts in high throughput scanning mass spectrometer[END_REF][START_REF] Su | Catalytic carbon dioxide hydrogenation to methane: A review of recent studies[END_REF] etc. Another strategy is to apply external electrochemical stimuli and exploit the Non-Faradaic Electrochemical Modification of Catalytic Activity (NEMCA), also named Electrochemical Promotion of Catalysis (EPOC) phenomenon. The setup is schematically represented in Scheme 2.

Scheme 2. Schematic representation of the EPOC phenomenon.

In EPOC, the catalyst is deposited on a solid electrolyte and submitted to a small current or potential. Applying an electrochemical potential to the catalyst surface results in an alteration of catalytic activity and in some cases reaction selectivity. EPOC refers to the change in reaction rate that is not affiliated to an electrochemical reaction. Hence, it does not abide by Faraday's Law [START_REF] Vayenas | Electrochemical Activation of Catalysis[END_REF]. EPOC has been observed for over 100 reactions and catalytic systems [START_REF] Vayenas | Electrochemical promotion in catalysis: non-faradaic electrochemical modification of catalytic activity[END_REF][START_REF] Vayenas | Dependence of catalytic rates on catalyst work function[END_REF][START_REF] Wagner | Adsorbed Atomic Species as Intermediates in Heterogeneous Catalysis[END_REF]. When the applied potential is switched off, the modification decays and the system typically returns to its original catalytic activity, i.e., EPOC allows to reversibly tune the activity and selectivity. Many studies were dedicated to rationalize EPOC, leading to general empirical rules [START_REF] Katsaounis | Recent developments and trends in the electrochemical promotion of catalysis (EPOC)[END_REF][START_REF] Vayenas | Bridging electrochemistry and heterogeneous catalysis[END_REF][START_REF] Vernoux | Ionically conducting ceramics as active catalyst supports[END_REF]. According to these studies, EPOC allows for the in-situ control of the spillover/backspillover of promotional species from a solid electrolyte support towards and away from the metal catalyst through the application of a potential difference between the inert counter electrode and the working-catalyst electrode [START_REF] Vayenas | Electrochemical promotion in catalysis: non-faradaic electrochemical modification of catalytic activity[END_REF][START_REF] Brosda | Rules of chemical promotion[END_REF]. The (back-)spillover effect results in the modification of catalyst work function and was evaluated using several surface-sensitive techniques and catalytic reactions [START_REF] Tsampas | Investigation of the Electrochemical Promotion of Catalysis origins on electrochemical catalysts with oxygen ion conductive supports: Isotopic labeling mechanistic studies[END_REF][START_REF] Makri | Atomic resolution STM imaging of electrochemically controlled reversible promoter dosing of catalysts[END_REF]. Nevertheless, a precise atomistic understanding of the origin of the promotional activity is lacking. Comprehending the atomistic origin of this process clarifies the role of promotional species, i.e., if they act as spectator species or directly participate in the bond formation/scission processes. This detailed insight will also improve our understanding of metal-support interactions and chemical promotion effects since these phenomena are functionally equivalent [START_REF] Vernoux | Ionically conducting ceramics as active catalyst supports[END_REF].

Previous EPOC studies of CO2 hydrogenation over Ru films of 2 µm thickness, have demonstrated that the electrochemical polarization alters the CO to CH4 ratio [START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF][START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF], independently from the promoting species used, such as O 2-, Na + , K + and H + , associated with yttriastabilized zirconia (YSZ), Na-β"-Al2O3, K-β"-Al2O3, and BaZrO0.85Y0.15O3-α (BZY) solid electrolytes, respectively [START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF][START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF]. This suggests a universal promoting mechanism, which is not primarily related to surface coverages of active species such as H and O but rather due to the polarization of the electrode and work function modification.

To elucidate the origin of the contrasting impact of the electrochemical potential of the catalyst surface on CH4 and CO production rates, we investigate the competition between CO and CH4 production over Ru catalysts at moderate temperatures of 250 °C, where EPOC allows to tune the competition between the two pathways. We aim at providing qualitative but robust understanding of the EPOC effect. Our model of EPOC that includes the polarization at the interface without specifying the promoting species predicts trends in the competition that are in line with the experimental observations regarding the selectivity of the CO2 reduction. It confirms that when using Ru-based catalysts, the selectivity of the reaction is not driven by the nature of the migrating species but by the induced polarization. The combination of periodic DFT and experiments shows that the relative adsorption energy of CO and CHO as a function of the electrochemical potential at the catalyst surface is key for determining the selectivity between CO and CH4 production.

Experimental

Catalyst preparation

The ruthenium (Ru) nanoparticles were synthesized using the polyol synthesis method [START_REF] Baranova | Infrared spectroscopy on sizecontrolled synthesized Pt-based nano-catalysts[END_REF]. The method incorporates metal precursors, ethylene glycol (EG) and tetramethylammonium hydroxide (TMAOH). The addition of TMAOH serves to stabilize and increase the pH to govern the size of the nanoparticles. The Ru colloid was prepared using 0.105 g of ruthenium chloride (RuCl3) (anhydrous, Sigma Aldrich) mixed in 15 mL ethylene glycol (Fischer-Scientific certified grade) containing 0.15 M TMAOH (Sigma Aldrich, pentahydrate). The solution was then heated up until it reached 160 °C and immediately turned off and cooled to room temperature. Initial pH of the solution was 12 and dropped to 7 after reflux. The final colloidal solution was black in color and stored at room temperature.

Physicochemical characterization

The size of the free-standing Ru nanoparticles was evaluated using scanning transmission electron microscopy (STEM) performed on a FEI Titan 3 80-300 TEM operated at 300 keV, equipped with a CEOS aberration corrector for the probe-forming lens. Annular Dark Field (ADF) images were taken using a Fishione detector to provide a contrast between the nanoparticles and support at convergence and collection angles of 17 and 60 mrad, respectively. The Ru colloidal sample was sonicated in ethanol and then one-drop was deposited onto a 200 mesh TEM copper grid coated with a lacey carbon support film (Ted Pella). The Image J software was used to measure the average size of the nanoparticles. X-Ray Diffraction (XRD) patterns did not show peaks for the free-standing Ru nanoparticles because they were amorphous.

Electrochemical cell and reactor setup

The electrochemical cell consisted of the ionically conductive support 8 mol% Y2O3stabilized ZrO2 (YSZ) (Tosoh) as the solid electrolyte in the form of a disc (diameter = 19 mm and thickness = 1 mm) prepared as described elsewhere [START_REF] Gibson | Sinterability of commercial 8 mol% yttriastabilized zirconia powders and the effect of sintered density on the ionic conductivity[END_REF]. Gold (Au) counter and reference electrodes were painted using Au paste (C2090428D4, Gwent Group, CAS: 98-55-5) next to each other with a surface area of 1 cm 2 and 0.2 cm 2 , respectively. The Au counter and reference electrodes were annealed in air at 500 °C for 1 h. Directly opposing the counter electrode, the working catalyst-electrode was deposited in a surface area of 1 cm 2 . The Ru catalyst was deposited as a colloid solution enclosed in a tape mask mold. It was deposited 10 µL at a time with subsequent heating at 130 °C for 10 min in between deposits to dry the solution until the desired catalyst loading (0.2 mg of Ru free-standing nanoparticles) was achieved. A gold mesh was mechanically pressed on the catalyst-working electrode to act as a current collector, as previously shown [START_REF] Dole | Quantifying metal support interaction in ceria-supported Pt, PtSn and Ru nanoparticles using electrochemical technique[END_REF].

The total flow rate of 100 mL.min -1 consisted of CO2 (Linde, 99.999%), H2 (Linde, 100%) and He (Linde, 100%) balance at 1.5 kPa, 9 kPa and 89.5 kPa, respectively. These were fed to the reactor through three independent mass flow controllers (MFC, MKS Instruments). The catalyst was pre-treated in 20 kPa of O2 for 2 h at 200 °C to remove any residue ethylene glycol and TMAOH from the surface. The pre-treatment was then followed by He purging for 15 min and then H2 (30% in He) for 3 h at 200 °C to reduce the RuO2 surface to Ru. The CO2:H2 ratio of 1:7 was used since it was observed in all previous EPOC reactions that the this ratio displayed the highest selectivity to CH4 with Ru films and additionally allows for CO and CH4 end-products to be produced [START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF]. The high concentration of H2 during reaction conditions ensures a complete reduction at 200 °C. These conditions are chosen in order to conveniently determine the influence of the electrochemical potential at the catalyst surface on product selectivity. The product gases were analyzed using a quadrupole mass spectrometer (QMS, Ametek Proline DM 100), with values for CO2, CO, H2O, CH4, He and H2 corresponding to the m/z (mass-to-charge) ratios 44, 28, 18, 15, 4 and 2, respectively. The electrochemical cell is a modified version of the reactor described in Ref. [START_REF] Hajar | Investigation of heterogeneous catalysts by electrochemical method: Ceria and titania supported iridium for ethylene oxidation[END_REF]. Three gold wires were used to connect the working, counter and reference electrodes to the potentiostat-galvanostat (Arbin Instruments, MSTAT) that supplied the application of potential and constant current to the electrochemical cell.

The EPOC effect was evaluated through the enhancement ratio (ρ) (eq. 1) and apparent Faradaic efficiency (Λ) (eq. 2) defined through the following equations.

𝜌 = 𝑟 𝑟 $ (1) |𝛬| = 𝛥𝑟 𝐼/𝑧𝐹 (2)
Where ro represents the open circuit catalytic rate (i.e. no polarization) and r represents the catalytic rate when potential is applied. The numerator (Dr) in eq. 2, is the difference between r and ro. The denominator represents the rate at which the migration species O δ-travels through the triple-phase boundary to the Ru gas exposed surface, where z is the number of electrons transferred (2e -for CO and 8e -for CH4), F is Faraday's constant and I is the applied current.

Computational details

The VASP code (Vienna Ab-initio Simulation Package) was used to perform all DFT computations [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF]. The dispersion corrected density functional approximation PBE-dDsC was applied. This method has been shown to reproduce experimental adsorption energies [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular dynamcis for liquid metals[END_REF]. In the absence of experimental insight on the most representative surface sites, the most stable Ru(0001) surface was chosen [START_REF] Avanesian | Mechanism of CO2 reduction by H2 on Ru(0 0 0 1) and general selectivity descriptors for late-transition metal catalysts[END_REF][START_REF] Zhang | Hydrogenation mechanism of carbon dioxide and carbon monoxide on Ru(0001) surface: a density functional theory study[END_REF]. A symmetric p(3x3) unit cell with of 5 metallic layers was used. A large (45.2 Å) vacuum layer separates the two surfaces to prevent interactions and provides the necessary space of the description of the double layer. [START_REF] Steinmann | Assessing a First-Principles Model of an Electrochemical Interface by Comparison with Experiment[END_REF] The Brillouin zone was integrated with a Monkhorst-pack k-point of 5x5x1. The basis-set cutoff was set to 400 eV. All geometries have been optimized to forces below 0.02 eV/Å with wave functions converged to 10 -6 eV. Frequencies were computed with the harmonic approximation to determine the vibrational contribution to the enthalpy and entropy. The translational and rotational contributions for the gas molecules were computed within the ideal gas approximation and the rigid rotator approximation. The linearized Poisson-Boltzmann equation with default parameters as implemented in VASPsol module [29] has been used to model the influence of the electrochemical potential at the catalyst surface [START_REF] Steinmann | Assessing a First-Principles Model of an Electrochemical Interface by Comparison with Experiment[END_REF][START_REF] Mathew | Implicit selfconsistent electrolyte model in plane-wave density-functional theory[END_REF]. For detailed explanations on the computational model, we refer the reader to ref [START_REF] Hajar | Theoretical insight into the origin of the electrochemical promotion of ethylene oxidation on ruthenium oxide[END_REF], where we have also demonstrated that the precise technical parameters do not considerably influence the EPOC results. The investigated reaction pathway follows the proposal by Avanesian et al. [START_REF] Avanesian | Mechanism of CO2 reduction by H2 on Ru(0 0 0 1) and general selectivity descriptors for late-transition metal catalysts[END_REF].

The Gibbs Free Energy (Gads) values for each reactant, intermediate and product adsorbed on Ru(0001) were calculated using equation 3. where Gsurface+molecule is the Gibbs Free Energy of the optimized configuration of the species on the surface, Gsurface is the Gibbs Free Energy of the optimized Ru(0001) surface and Gmolecule is the Gibbs Free energy of the molecule optimized in the gas phase. The factor ½ accounts for the use of a symmetric slab, which is also the reason for the use of two gas-phase molecules in the reference.

Results & Discussion

Characterization of Ru Nanoparticles

The STEM image displayed in Fig. 1 confirms that the Ru nanoparticles were between 0.5-1 nm in diameter, in accordance with the modified polyol method. Additionally, the free-standing (i.e. unsupported) nanoparticles were well dispersed and did not display significant agglomeration prior to reaction. Supported STEM images were not possible due to the presence of the solid electrolyte, which blocks the transmission and SEM does not provide enough resolutions to view the nanoparticles. The contrast provided by the ADF image represents the nanoparticles as bright spots on the darker background. Here, RuOx (x ≤ 2) are displayed since they are exposed to air; however, they were reduced back to metallic Ru during the hydrogenation pre-treatment step.

Fig. 1. STEM image of free-standing Ru nanoparticles and corresponding particle size distribution histogram.

EPOC performance for Ru nanoparticles

To evaluate the EPOC phenomenon for the methanation and RWGS reaction on Ru nanoparticles deposited on YSZ, 250 °C was chosen as reaction temperature, since simultaneous production of CO and CH4 is observed at this temperature. We show in Fig. 2a a At open-circuit conditions, the production rate for CO is greater than for CH4. When a positive current of 50 µA is applied, the methanation reaction is promoted, with ρ > 1 and Λ = 34 (Fig. 2a). Conversely, the RWGS reaction is impeded, with ρ < 1 and a low Faradic efficiency (Λ = 15). When the system is switched back to O.C. conditions, it requires over 2 h to return, in line with the slow increase in rate upon positive application. During positive polarization there is a continuous supply of oxygen ionic species to the gas-exposed catalyst surface that act as promoters for CH4 and inhibitors for CO production. The slow return of CO production rate to O.C. upon current interruption indicates that supplied oxygen ions remain on the surface of the catalyst and continue acting as inhibitors for CO formation for over 2 h. A Λ>1 signifies non-Faradaic behavior, which improves as the Λ value increases [START_REF] Vayenas | Electrochemical Activation of Catalysis[END_REF]. However, for hydrogenation reactions with O 2-solid electrolyte as active support, since O 2-is not a reactant, the process is non-Faradaic when ρ ≠ 1. The kinetic study performed by Theleritis et al. [START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF], and Kalaitzidou et al. [START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF], have shown that the selectivity to CH4 can be influenced by three factors: H2 partial pressure (7:1 H2:CO2) in the feed, reaction temperature (< 300 °C) and catalyst loading (>2 mg) under opencircuit conditions. Since the methanation reaction is positive order in the electron donor (i.e. H2) and the application of polarization is equivalent to increasing the partial pressure of H2 in the reaction, the CH4 rate is favored. The underlying hypothesis is that the positive surface charge, increases the coverage of H and thus the hydrogenation to CH4. Therefore, positive potentials induce reducing conditions (i.e. high hydrogen coverage) without having to increase the amount of H2. Fig. 2b summarizes the EPOC response when varying the current from 50 to 150 µA and the corresponding enhancement ratio (ρ). As the current is increased, the CH4 rate increases and the CO rate decreases. It is a rather robust behavior since it was also observed on much thicker Ru films also deposited on YSZ and on other solid electrolytes (i.e. K-β"-Al2O3, Na-β"-Al2O3, and BZY), which generate other promoting ions (K + , Na + , H + ) [START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF][START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF]. The effect of negative polarization was investigated with application of a constant current of -25 µA (UWR = ~-1 V) for 3 h, displayed in Fig. S1a andb (Electronic Supplementary Information) for CH4 and CO rate, respectively. The production rate of CO is barely affected (ρ ~1) while the one of methane is reduced (ρ = 0.46). Upon current interruption, the open-circuit CH4 production rate did not return to its initial values, suggesting that the induced modification (reduction) of the surface state under a negative current and a negative potential difference is irreversible being maintained when the catalyst is left under open-circuit conditions. This is in line with the work by Theleritis et al., [START_REF] Theleritis | Hydrogenation of CO2 over Ru electropromoted catalysts[END_REF], where Ru was in a reduced state inhibiting the formation of CH4 which is favored by the oxidation state. Additionally, once the CH4 rate reached a new steady-state (not shown), negative potential was applied again, which resulted in further decrease in CH4 production and minimally affected CO. This provides a way to permanently suppress unwanted CH4 production and produce only CO at a temperature as low as 250°C. Producing CO clean from CH4 is important when aiming at the production of longer hydrocarbon chains in a downstream Fisher-Tropsch process [START_REF] Daza | CO2 conversion by reverse water gas shift catalysis: Comparison of catalysts and mechanisms and their consequences for CO2 conversion to liquid fuels[END_REF].

Computational Analysis

Given the above reported EPOC effect on the methanation reaction, which is also in line with previous experiments, [START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF][START_REF] Theleritis | Hydrogenation of CO2 over Ru electropromoted catalysts[END_REF] let us now turn to the atomistic modeling. Computational studies to rationalize the EPOC effect are not very numerous and can be divided into two categories: (i) adsorbates are included explicitly [START_REF] Pacchioni | Quantum-chemical study of electrochemical promotion in catalysis[END_REF][START_REF] Leiva | Computer simulation of the effective double layer occurring on a catalyst surface under electro-chemical promotion conditions[END_REF] which results in a significant computational complexity, especially when investigating an entire reaction pathway (ii) the EPOC phenomenon is modelled by including a uniform electric field [START_REF] Pacchioni | Electric field effects in heterogeneous catalysis[END_REF]. Herein, we rely on our recently proposed a third approach, which is to directly model the electrochemical potential at the catalyst surface instead of an electric field [START_REF] Hajar | Theoretical insight into the origin of the electrochemical promotion of ethylene oxidation on ruthenium oxide[END_REF]. This method was successfully employed to highlight the influence of the electrode polarisation on chemical steps involved in electrochemical processes, such as the rotation of adsorbed formate in the electro-oxidation of formic acid to CO2 [START_REF] Steinmann | Modeling the HCOOH/CO2 Electrocatalytic Reaction: When Details Are Key[END_REF]. In short, the potential dependence is determined treating the electrons in a grand-canonical ensemble. Grand-canonical DFT allows to keep the potential constant from one elementary step to the next by varying the number of electrons [START_REF] Hörmann | Grand canonical simulations of electrochemical interfaces in implicit solvation models[END_REF][START_REF] Melander | Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials[END_REF][START_REF] Sundararaman | Grand canonical electronic densityfunctional theory: Algorithms and applications to electrochemistry[END_REF]. The linearized Poisson-Boltzmann equation is used to model a thermodynamic average for the effective double layer, necessary to neutralize the surface charge. The resulting surface polarization is associated with a varying number of electrons as a function of the reaction coordinate in order to keep the potential constant and in agreement with the experimental setup [START_REF] Hajar | Theoretical insight into the origin of the electrochemical promotion of ethylene oxidation on ruthenium oxide[END_REF][START_REF] Hörmann | Grand canonical simulations of electrochemical interfaces in implicit solvation models[END_REF][START_REF] Melander | Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials[END_REF][START_REF] Steinmann | Solvation free energies for periodic surfaces: comparison of implicit and explicit solvation models[END_REF][START_REF] Zhang | The importance of grand-canonical quantum mechanical methods to describe the effect of electrode potential on the stability of intermediates involved in both electrochemical CO2 reduction and hydrogen evolution †[END_REF]. This approach does not require specifying the chemical nature of the promotional species. Note, however, that we have chosen a model Ru(0001) surface at a intermediate coverage and in the absence of co-adsorption to qualitatively understand the EPOC effect. This approximation prohibits quantitative comparisons to experiments, especially ones that assess the influence of the nanoparticle size or differences in promoting species. Furthermore, in contrast to simulations with an explicit electrostatic field, the potential dependent simulations facilitate the comparison with experiment where the potential is the measurable quantity. All computational details follow closely the one of ref [START_REF] Hajar | Theoretical insight into the origin of the electrochemical promotion of ethylene oxidation on ruthenium oxide[END_REF], where interested readers can find details on the approach.. CO* is a critical intermediate for the overall selectivity of the hydrogenation of CO2. It can either desorb or be further reduced into CHO* and then to CH4 through the sequence shown in Fig. 3. With a slightly smaller desorption energy of CO (∆Gdes= 1.10 eV), desorption of CO is more likely than its hydrogenation into CHO* (∆G= 1.15 eV). This is in line with our experimental results in open circuit (O.C.) conditions, displaying a higher selectivity in CO over CH4 (shown in the first hour in Fig. 2a).

Let us now turn to the influence of an applied electrochemical potential at the catalyst surface on the selectivity. The reduction of CO into the CHO* was identified to be the selectivity determining step. We selected a maximum range of ±1 V since it is the typical experimental range evaluated in EPOC reactions [START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF][START_REF] Kalaitzidou | Comparative study of the electrochemical promotion of CO2 hydrogenation on Ru using Na+, K+, H+ and O2-conducting solid electrolytes[END_REF]. The Gibbs free energy values at 250°C are summarized in Table S1 for open-circuit and ±1 V and the full profiles are shown in Fig. S3. Additionally, geometries are provided in the VASP format.

The CO2 chemisorption is improved by the application of a negative potential (from ∆Gads= 0.63 eV in O.C. conditions to 0.21 eV at -1V). In agreement with previous studies, the CO chemisorption is not very much affected at constant potential [START_REF] Mamatkulov | An ab initio study of electrochemical vs. electromechanical properties: The case of CO adsorbed on a Pt(111) surface[END_REF] or constant fields [START_REF] González | Electric field effects in the chemisorption of CO on bimetallic RhCu surface models[END_REF], but it is still stronger under a negative polarization that favors stronger back-bonding (from ∆Gdes= 1.10 eV in O.C. conditions to 1.18 eV at -1V). This is in agreement with EPOC rules [START_REF] Brosda | Rules of chemical promotion[END_REF], where CO is an electron acceptor and its chemisorption increases upon negative polarization (decrease of work function). Because this effect is less pronounced in the present case, where CO is a reaction intermediate or product, it may indicate that the effect of polarization on CO adsorption depends on the presence of other adsorbed species (electron donor or acceptor) on the Ru surface during the RWGS reaction. However, our DFT calculations do not explicitly include co-adsorption; therefore, this requires further investigation. H2O is the most impacted, with an opposite behavior: the chemisorption is strengthened by a positive polarization, switching from exergonic desorption under a negative polarization (∆Gdes= -0.25 eV at -1V) to endergonic desorption (∆Gdes= +0.61 eV) under a positive polarization while it was athermic under O.C. conditions (∆Gdes= -0.08 eV). These general trends are in agreement with empirically established rules of electrochemical promotion where the chemisorption of electron acceptor (i.e. CO2) is favored by a negative polarization and electron donor (i.e. H2O) by positive polarization [START_REF] Brosda | Rules of chemical promotion[END_REF][START_REF] Theleritis | Comparative study of the electrochemical promotion of CO2 hydrogenation over Rusupported catalysts using electronegative and electropositive promoters[END_REF]. The resulting overall profiles (shown in Fig. S3 a andb) are hence modulated by the polarization.

The influence of polarization on the CO/CH4 selectivity is illustrated in Fig. 4 focusing on the branching from CO* to CO and CHO*. As already mentioned, the influence on CO chemisorption is rather weak (less than 0.1 eV). The CO*+H* à CHO* is more sensitive with variations up to 0.23 eV in the reaction Gibbs energy. As previously seen, under O.C. the difference is small between these two competing reactions (0.05 eV), in favor of CO desorption. This difference in favor of CO desorption increases under negative polarization (0.15 eV), due to a destabilization of the CHO intermediate. This is in line with the decrease in CH4 production under a negative polarization which was observed experimentally. Under a positive polarization, this branching turns slightly, by 0.03 eV, in favor of the hydrogenation of CO* into CHO*. In addition, the steps that follow are less endothermic, overall facilitating CH4 production as seen in our experiments (see Fig. 2). However, inferring a quantitative picture on the overall production rates of CO and CH4 would require more advanced modeling, including transition states but also likely an improved description of the active sites of the Ru nanoparticles and perhaps even the effect of co-adsorbed species.

Conclusion

Our computational model of EPOC that includes the polarization at the interface without specifying the promoting species predicts selectivity trends that are qualitatively in line with the experimental observations. It confirms that the selectivity of this reaction is not sensitive to the type of migrating species but to the change of surface electrochemical potential and the associated surface polarization. Hence, we can safely assume that the main EPOC effect stems from the electric field in the effective double layer and the varying number of electrons during the reaction which keep the potential constant as a function of the reaction coordinate. The combination of periodic DFT and experiments shows that the relative energy of CHO as a function of the electrochemical potential of the catalyst surface is key for determining the selectivity between CO and CH4 production. The computational simplicity of our model allows it to be used in future studies to depict the polarization effect for various reactions and catalysts, as well as MSI and other promotional phenomena in catalysis.

  :;<$=:96=: -?𝐺 467829: + 2 𝐺 <$=:96=: A] (3)

  representative transient rate response for application of a positive current of 50 µA at 250 °C, which corresponds to a potential difference between the catalyst-working and reference electrode (UWR) of about 1 V. The open-circuit (O.C.) conditions were maintained for 1 h after reaching a steady-state, followed by 3 h polarization and return to open-circuit for 3 h. The duration of each time window was chosen to let the system reach a steady-state.

Fig. 2 .

 2 Fig. 2. (a) Transient effect for application of 50 µA, and (b) Summary of ρ values under various currents at 250 °C for the production of CO and CH4. 0.2 mg catalyst, H2:CO2 7:1 and total flow rate 100 mL min -1 .

Fig. 3 .

 3 Fig. 3. Computed Gibbs Free Energy profile at 250 °C and atmospheric pressure of the CO2 hydrogenation into CO and CH4 on Ru(0001) in open-circuit conditions. To begin with, we considered the hydrogenation pathway in open-circuit conditions over Ru(0001), theoretically modeled by steady-state, equilibrium thermodynamics. The formation of methane is the thermodynamic product (computed ΔG250°C = -0.74 eV) while CO is the kinetic product (computed ΔG250°C = 0.2 eV). A catalytic cycle beginning with the adsorption of CO2 and 4 H2 was calculated to allow for the formation of CH4. Avanesian et al. proposed that the formation of CO and CH4 over Ru(0001) begins with the direct dissociation of H2 into H*, followed by the adsorption of CO2 and its dissociation into CO* and O* [3,4]. Then, to yield CH4, CO* is hydrogenated either to CHO* or to COH*. The CHO* pathway was selected since transition states conducted by Avanesian et al., show that CHO* is more favorable, even though COH* is thermodynamically more stable [3]. The C-O bond can break in the CHO* intermediate, yielding CH* that undergoes successive hydrogenations to reach CH4. In parallel, O* is hydrogenated to OH* and then H2O. Following this pathway, the open-circuit Gibbs Free energy profile was evaluated at 250°C and at standard pressure conditions and displayed in Fig. 3. Desorption of close-shell molecules was systematically included when feasible (typically, desorption of water as soon as generated along the path). Competitive pathways were also considered, as shown in Figure S2. For instance, the hydrogenation of CO2, yielding COOH*, results in an intermediate that is less stable than the CO*+O* by at least 1 eV. The dissociation of CO* into C*+O* has been shown by Zhang et al., to require a high energy transition state (2.63 eV) when compared to its desorption or its hydrogenation into CHO* or COH* and thus was not included in this study [4].

Fig. 4 .

 4 Fig. 4. Branching from the CO*+H* intermediate to CO and to CHO* in function of the polarization. Energies are provided in eV.

Acknowledgements

The authors thank University of Ottawa, CNRS, and ENS Lyon for support of research conducted within the context of the International Associated Laboratory 'Fundamental catalysis for green chemistry: From well defined active sites to mechanistic explorations -FUNCAT.' and Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. The authors thank the SYSPROD project and AXELERA Pôle de Compétitivité for financial support (PSMN Data Center).

Conflicts of interest

There are no conflicts to declare.