## Introduction

Hydrogen peroxide (H2O2) is an important chemical with a wide range of applications in industry, such as paper and textile manufacturing and environmental protection for detoxification and color removal of wastewater1. Currently, H2O2 is produced indirectly via the anthraquinone oxidation process, which is an energy-demanding multi-electron process and requires large plants1. Moreover, transportation of H2O2 to the place of use adds additional challenges due to safety concerns. Broader usage of H2O2 could benefit from the capability of direct on-site production. Electrochemical synthesis of H2O2 provides a straightforward route for on-site production and ideally solves the issues associated with the indirect anthraquinone route2,3,4,5,6,7,8,9. One of the attractive possible routes for electrochemical H2O2 generation is via two-electron oxidation of water (Eq. 1)10,11,12:

$$2{{\rm{H}}_2}{\rm{O}} \to {{\rm{H}}_2}{{\rm{O}}_2} + 2\left( {{{\rm{H}}^ + } + {{{e}}^ - }} \right)\quad E^\circ = 1.76\,{\rm{V}}$$
(1)

This process (Eq. 2) is desirable since it can be coupled with hydrogen evolution reaction (Eq. 2) to simultaneously produce two valuable products: H2O2 and H2 (Eq. 3) in a single electrochemical device using only water as raw material. Such a device can also be coupled with photoabsorbers to utilize sunlight for both reactions:12,13,14

$$2\left( {{{\rm{H}}^ + } + {{{e}}^ - }} \right) \to {{\rm{H}}_2}\quad E^\circ = 0.0\,{\rm{V}}$$
(2)
$$2{{\rm{H}}_2}{\rm{O}} \to {{\rm{H}}_2}{{\rm{O}}_2} + {{\rm{H}}_2}$$
(3)

However, the two-electron water oxidation (Eq. 1) must compete with the four-electron oxidation reaction for O2 generation (Eq. 4) and the one-electron oxidation reaction for producing OH radical (Eq. 5)12.

$$2{{\rm{H}}_2}{\rm{O}} \to {{\rm{O}}_2} + 4\left( {{{\rm{H}}^ + } + {{{e}}^ - }} \right)\quad E^\circ = 1.23\,{\rm{V}}$$
(4)
$${{\rm{H}}_2}{\rm{O}} \to {\rm{O}}{{\rm{H}}^ \bullet }\left( {{\rm{aq}}} \right) + \left( {{{\rm{H}}^ + } + {{{e}}^ - }} \right)\quad E^\circ = 2.38\,{\rm{V}}$$
(5)

The relevant intermediates of the one- (Eq. 5 12), two- (Eq. 1) and four-electron (Eq. 4) water oxidation reactions are OH*, O* and OOH*. Historically, the O2 generation reaction (Eq. 4) has been the main focus of the water oxidation research15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 and less attention has been paid to the selective two-electron oxidation reaction of water to H2O2 (Eq. 1), which is considered as a much more difficult process. A main challenge in realizing such a photoelectrochemical production of H2O2 system is to find a material that can selectively and efficiently produce H2O2 from water. Electrochemical oxidation of water has been reported over various metal oxides, such as MnO x 10, 11, WO3-BiVO4 14, 30, 31 and TiO2 32,33,34,35,36. These pioneering works have not only demonstrated the potential of H2O2 production over metal oxides but also suggested that BiVO4 is the best oxide for H2O2 production14, 31. Nevertheless, little is known about the energy barrier and the limiting potential for H2O2 generation for different metal oxides. Even less is known about how the H2O2 generation efficiency of these metal oxides vary with applied biases both theoretically and experimentally. Such study on the bias-dependent H2O2 production is critical for understanding the competition among one-, two- and four-electron pathways under different bias, a prerequisite for identifying the optical bias range for H2O2 generation.

In the present work, we theoretically investigate the activity trends of four different oxides (i.e., WO3, SnO2, TiO2 and BiVO4) towards water oxidation for H2O2 production with further experimental validation. Both the calculated and measured onset potentials for H2O2 production increase in the sequence of WO3, BiVO4, SnO2 and TiO2. Among all these four oxides, BiVO4 is identified as the best catalyst for the two-electron water oxidation in dark and under illumination, and this result is consistent with previous studies on comparing different metal oxides for H2O2 production14, 31. Importantly, we identify the optimal bias range for BiVO4 to produce H2O2 in dark (~2.9–3.3 V vs RHE) and under illumination (~1.7 V–2.3 V vs RHE). As such, BiVO4 achieves a high faraday efficiency (FE) of 70% in dark and 98% under 1 sun illumination.

## Results

### Theoretical analyses

As discussed above, H2O2 synthesis from water oxidation is a challenging reaction. This is due to the fact that selectivity and activity of the materials are largely limited by several criteria imposed by the thermodynamics of the competing reactions13. The adsorption free energies of relevant intermediates of the one- (Eq. 5), two- (Eq. 1) and four-electron (Eq. 4) water oxidation reactions, i.e., OH*, O* and OOH* can be calculated using density functional theory (DFT). We show here that the free energies of OH* and O* are key parameters determining the selectivity and activity towards different oxidation products, O2 (Eq. 4), OH radical (Eq. 5) or H2O2 (Eq. 1)13. Using DFT, we calculated the free energies of OH*, O* and OOH* on BiVO4 (details of calculations in Supplementary Note 1). We only focus on the (111) surface, which has been shown theoretically and experimentally to be stable and exposed in the BiVO4 crystal structure37. In addition, we have taken the OH*, O* and OOH* free energies for WO3(100), TiO2(110) and SnO2(110) from reported DFT calculations (Supplementary Note 1, Supplementary Fig. 1 and Supplementary Tables 1, 2)13, 38,39,40. We use the computational hydrogen electrode (CHE) model, which exploits that the chemical potential of a proton–electron pair is equal to gas-phase H2 at standard conditions. The electrode potential is taken into account by shifting the electron energy by –eU, where e and U are the elementary charge and the electrode potential, respectively41. The limiting potential for the electrochemical reaction to occur is defined as the lowest potential, at which all the reaction steps are downhill in free energy following the previous report13. Figure 1 shows the activity volcano plots based on the calculated limiting potentials as a function of the calculated free energy of OH* $$\left( {\Delta {G_{{\rm{O}}{{\rm{H}}^{\rm{*}}}}}} \right)$$ for both two-electron (black) and four-electron (blue) oxidation reactions. The corresponding equilibrium potentials for each reaction have been shown in dashed lines.

From the thermodynamic point of view, materials with strong OH adsorption energy (shaded in blue in Fig. 1) will further oxidize OH* to O* and OOH*, following the complete four-electron oxidation reaction (Eq. 4) to evolve oxygen. Therefore, electrocatalysts with weak OH* free energy will have low selectivity towards the four-electron pathway but high preference towards the two-electron route. At the same time, the OH* free energy should be strong enough to dissociate the water molecule and provide a good thermodynamic driving force, for the two-electron pathway towards H2O2. The free energy for H2O2 formation is ~3.5 eV, twice of the equilibrium potential for Eq. 1, so the electrocatalyst should have $$\Delta {G_{{\rm{O*}}}}$$$$3.5\,{\rm{eV}}$$. Given the fact that the *O and *OH energies are generally found to scale ($$\Delta {G_{{\rm{O*}}}} = 2\Delta {G_{{\rm{OH*}}}} + 0.28$$)38, this sets a lower limit for OH* free energy, i.e., $$\Delta {G_{{\rm{OH*}}}}$$$$\frac{{3.5}}{2} - \frac{{0.28}}{2} \sim 1.6{\kern 1pt} \,{\rm{eV}}$$. The upper limit for $$\Delta {G_{{\rm{OH}}}}$$ is set by the free energy of OH radical formation in the solution (Eq. 5), since too weak OH* free energy with ΔG OH* > ~2.4 eV drives the reaction towards OH radical formation (pink shaded area in Fig. 1). Hence, the combined thermodynamic criteria and scaling relation indicates a selective catalyst for H2O2 evolution should have $$\Delta {G_{{\rm{OH*}}}}$$ from ~1.6 to 2.4 eV. This thermodynamic analysis suggests that WO3, SnO2, BiVO4 and TiO2 should be able to generate H2O2 within certain values of the OH* free energy (shaded in green in Fig. 1). To increase the selectivity region for H2O2 evolution, we need to identify catalyst materials that largely deviate from the O* and OH* scaling relation42.

Aside from the high selectivity, the two-electron oxidation reaction (Eq. 1) ideally should also have high activity with low overpotential. The theoretical overpotential is defined as the difference between the limiting potential and equilibrium potential (1.76 V for the two-electron path). The overpotential is governed by the binding of OH* to the catalyst surface, so controlling the overpotential is a matter of tuning the free energy of OH*41. An OH* free energy ($$\Delta {G_{{\rm{OH*}}}}$$) of 1.76 eV, when calculated at zero potential and relative to liquid water, will give zero overpotential. The calculated theoretical limiting potential for BiVO4 is 1.95 V, hence it has a theoretical overpotential of ~0.2 V for the two-electron oxidation reaction. The activity of BiVO4 can be further improved with different doped metals such as Sr and Ru (Supplementary Note 2, Supplementary Fig. 2 and Supplementary Table 3). The calculated limiting potentials for WO3, SnO2 and TiO2 are 1.82, 2.02 and 2.27 V, respectively. In the following, we show that the trend in theoretical limiting potentials for WO3, BiVO4, SnO2 and TiO2 is in very good agreement with experimental measurements.

### Materials fabrication

Experimentally, we evaluate the H2O2 evolution performance of four oxides: WO3, BiVO4, SnO2 and TiO2 by determining their onset potentials, faraday efficiencies and production rates of H2O2 per geometric area of electrodes. All the oxides were synthesized on transparent and conductive fluorine-doped tin oxide (FTO) substrates. The WO3 was synthesized by flame vapor deposition (FVD). BiVO4, SnO2, and TiO2 were synthesized by a sol–gel process (see Methods and Supplementary Note 3). Since the electrochemical performance of each oxide is affected by its loading, each oxide film was individually optimized to yield the highest FE for the dark electrochemical measurement before taken for comparison. For example, Supplementary Fig. 3 shows that the measured FE for H2O2 production varies with the BiVO4 loading, which was controlled by varying the precursor concentration during the spin coating process (Supplementary Fig. 4). The low loading results in low BiVO4 coverage and exposed FTO, leading to a low H2O2 production. On the other hand, the high coverage results in high film resistance that impedes the charge transport process. Hence, for each oxide investigated, its loading on FTO was individually optimized for H2O2 production and the dependence of the FE on sample preparation conditions for each oxide is listed in Supplementary Table 4.

### H2O2 production comparison under dark conditions

Next, we measured the current–voltage (J–V) curves for the four oxides (WO3, BiVO4, SnO2 and TiO2) without illumination (Fig. 2a). The J–V onset, as well as the experimental measured H2O2 evolution onset potentials (defined as the potential at which the H2O2 concentration reaches 1 ppm), are compared with the calculated theoretical potentials in Fig. 2b. It can be seen that both the measured current onset potential (hollow symbols) and the onset potential for H2O2 generation (solid symbols) increase in the order of WO3 < BiVO4 < SnO2 < TiO2, which agrees with the theoretical predication, supporting the validity of using $$\Delta {G_{{\rm{OH*}}}}$$ as a descriptor to analyze the H2O2 evolution onset (Fig. 1). The measured onset potentials are higher than the calculated values, which is likely due to the additional kinetic barriers to be overcome in the actual experiments.

We further quantified the FE and the amount of H2O2 generated from the oxides as functions of the applied biases. As shown in Fig. 3a, all the metal oxides investigated share the similar FE trend with increasing applied bias: the FE first increases to a maximum value and then decreases. Or equivalently, for each metal oxide, there is an optimal potential window for H2O2 production, due to the competition with one-electron and four-electron oxidation reactions as predicted by theory (Fig. 1). Among all the oxides investigated, BiVO4 achieves the highest FE of 70% at 3.1 V vs RHE. In addition, BiVO4 also has the highest H2O2 production rate per geometric area of electrode (Fig. 3b), due to the combined high FE (Fig. 3a) and high current density (Fig. 2a).

### H2O2 production on BiVO4 under different conditions

The above results clearly indicate that BiVO4, among the four oxides investigated, has the best electrochemical properties towards H2O2 production, which is consistent with the previous screening studied of different metal oxides for H2O2 generation31. Next, we further investigated the influence of other conditions on the H2O2 production of using BiVO4, including the electrolyte, light illumination and sample thickness. The two dash lines in Figure 4 are the measured FEs for the thin 1-layer BiVO4 (i.e., spin coating once) under dark using two different electrolytes: 1 M NaHCO3 (pH = 8.3) and 0.5 M Na2SO4 (adjusted to pH = 8.3 with NaOH). Clearly, NaHCO3 is a much better electrolyte than NaOH/Na2SO4 for the H2O2 production from water oxidation. This observation is consistent with recent work by Fuku et al.,14 which reported that HCO3 is beneficial for the H2O2 production. In addition, as shown in Fig. 4, illumination not only shifts the onset potential to lower values but also increases the FEs for H2O2 production from 70% to over 95% for the 1-layer BiVO4 in NaHCO3. The reasons are that illumination introduces additional photogenerated charge carriers for H2O2 production and supplies photovoltage to allow H2O2 generation from water oxidation at a lower external bias43. To further enhance the benefits under illumination, we increase the loading of BiVO4 by spin coating nine times (referred as 9-layer BiVO4) to enhance the light absorption. The increased thickness for BiVO4 further shifts the onset potential for H2O2 to less than 1.1 V vs RHE, which is over 1.1 V lower than that of the dark conditions. This lowered onset potential and increased FEs strongly support that BiVO4 is a promising photoanode material for the H2O2 production in a photoelectrochemical system. The J–V curve and the measured H2O2 generation rate under illumination for this 9-layer BiVO4 are shown in Supplementary Fig. 5. In addition, we have measured the evolved gaseous O2 and H2 and the measured FEs are shows in Supplementary Fig. 6. The figure shows that the sum of the FE (O2) and FE (H2O2) is about 98–103%, confirming the accuracy in our H2O2 concentration measurement. Finally, the photoelectrochemical stability of BiVO4 is known to be an issue when the electrolyte is far from neutral conditions because the V5+ tends to dissolve into solution44, 45. However, we used the bicarbonate electrolyte with a measured pH value of 8.3; hence, BiVO4 is relatively stable in this near neutral region46.

## Discussion

In the present work, we utilized DFT calculations in conjunction with experimental measurements to study the activity of two-electron water oxidation towards H2O2 evolution over four metal oxides, namely WO3, BiVO4, SnO2 and TiO2. Both the calculated and measured onset potentials for H2O2 production increase in the sequence of WO3, BiVO4, SnO2 and TiO2. Among all these four oxides, BiVO4 produces the highest faraday efficiency (~70%) and largest amount for H2O2 under dark. The peak faraday efficiency BiVO4 is further increased to 98% by adding illumination, optimizing electrolyte and optimizing the thickness of BiVO4. Those optimizations also lower the onset potential from 2.2 V to <1.1 V. These results suggest that BiVO4 is an excellent photoanode candidate for electrochemical and photoelectrochemical H2O2 production. The theoretical simulation and experimental demonstration illustrated in this work have furthered the understanding of the activity and selectivity of water oxidation to H2O2 on metal oxide surfaces. Our result has opened an avenue for novel photoelectrochemical device designs with fundamental mechanism study that utilize solar energy and water to produce an oxidative product with higher value beyond O2.

## Methods

### Fabrication of various metal oxides on FTO

The BiVO4 precursor solution was prepared from a mixture of bismuth nitrate hexahydrate (BiN3O9·5H2O, 99.99%; Aldrich) and vanadyl acetylacetonate (C10H14O5V, 98%; Aldrich), which were added to a solution of acetylacetone (C5H8O2; Aldrich) and acetic acid (CH3COOH, 99.70%; Fisher) with a ratio of 1:0.12, followed by sonication for 10 min. After sonication, a dark green solution was obtained and the solution is usually used within a day after the preparation. For the one named 1-layer, the mole concentration of Bi was varied from 0.08 M, and 0.04 M, 0.02 M, to 0.01 M. For a typical spin coating, 100 µl of the BiVO4 precursor solution was dropped on a pre-cleaned FTO glass followed by spin coating (500 r.p.m. for 5 s and 1500 r.p.m. for 30 s). The samples were then annealed at 100 °C for 10 min, and 300, 400, and 500 °C for 5 min at each temperature. Similar step-wise annealing process was commonly used for metal oxide fabrication, and the purpose is to slowly evaporate the solvent to achieve a better film morphology. For spin coating multiple layers, the same process above was repeated for multiple times. Finally, the coated FTO was annealed in a box furnace at 500 °C for 2 h.

SnO2 was fabricated by using a sol–gel process similar with BiVO4. Firstly the precursor solution was made by dissolving 0.1932 g tin chloride in 10 ml 2-methoxyethanol (CH3OCH2CH2OH, 99.8%; Aldrich) and 0.2 ml acetylacetone (CH3COCH2COCH3, ≥99.3%; Aldrich) as the best condition, and sonicated for 30 min. After then the solution was put in a fume hood with aging for one night. The solution was spin coated on top of cleaned FTO with first 5 s, 500 r.p.m. and second 35 s, 2000 r.p.m. steps. Annealing process was carried out by using step by step method (100 °C for 5 min, 300 °C for 5 min and finally 455 °C for 30 min).

TiO2 was fabricated from a paste making and coating process. About 9.5 ml ethanol and 0.5 ml water were mixed and 0.5 g polyethylene glycol (Aldrich) was added and the mixture was sonicated for 30 min. Then 0.25 g TiO2 powder (Aldrich) as the best condition was added and the suspension was sonicated for another 10 min. Then the suspension was put on a hot plate and heated at 120 °C until the total volume reached 5 ml to get the TiO2 paste. The paste was used to spin coat or blade coat on top of FTO glass, followed by the annealing process at 400 °C for 2 h.

WO3 was synthesized by FVD method46, for which a W wire (0.5 mm in diameter; Aldrich) was oxidized by flame as the WOx vapor source. Those WOx vapor further deposited on FTO as W18O49 nanowires. The optimized FVD condition followed the one used in Rao et al.’s work46, with 18.4SLPM:12.5SLPM CH4 to air flow ratio and a substrate temperature 550 °C for 10 min of deposition (Supplementary Table 4). W18O49 nanowires were further converted to WO3 nanowires by annealing at 500 °C in a box furnace for 1 h.

### Characterizations

The H2O2 production from various anodes was detected by using the potentiostat with the three-electrode system, in which the Ag/AgCl electrode was used as a reference electrode and Ti foil as the counter electrode. Silver paste and Teflon tape were used to make metal contact and to define area when necessary. The measurements under illumination were obtained under 1 Sun at AM 1.5 G. The amount of generated H2O2 was detected by using the standard H2O2 strips (Indigo Instruments). In addition, the generated H2O2 concentration was further confirmed with a titration process by using potassium permanganate (KMnO4, ≥99.0%; Aldrich). The permanganate ion has a dark purple color, and the color disappears during titration when the MnO4 is totally consumed based on the following equation:

$$2{\rm{MnO}}_4^ - + 5{{\rm{H}}_2}{{\rm{O}}_2} + 6{{\rm{H}}^ + } \to 2{\rm{M}}{{\rm{n}}^{2 + }} + 5{{\rm{O}}_2} + 8{{\rm{H}}_2}{\rm{O}}$$
(6)

In this work, the sulfuric acid (H2SO4; Acros Organics) was used as the H+ source. We measured five H2O2 solution samples with different degrees of dilution from a same initial concentration 100 ppm, by both the standard strips and the permanganate titration methods. The results are shown in Supplementary Fig. 7, which shows that two methods basically agree with each other, confirming the accuracy of the H2O2 concentration measurement.

To make the result of the onset potential of H2O2 generation value more fair and accurate, in addition to the dark current onset here it was also defined as the potential at which the H2O2 generation starts to be detected (beyond 1 ppm), by measuring a 1 cm2 sample in a 20 ml electrolyte for 10 min. H2 and O2 were detected by the gas chromatography analysis, and the morphology of the samples were obtained using scanning electron microscopy (FEI XL30 Sirion SEM). The FE for H2O2 production (%) is calculated by

$${\rm{FE}} = \frac{{{\rm{Amount}}\,{\rm{of}}\,{\rm{generated}}\,{{\rm{H}}_2}{{\rm{O}}_2}\left( {{\rm{mol}}} \right)}}{{{\rm{theoretical}}\,{\rm{generated}}\,{{\rm{H}}_2}{{\rm{O}}_2}}} \times 100$$
(7)

where the theoretical amount of H2O2 is equal to the total number of electrons divided by two (in mol). The FE of H2O2 is calculated based on the accumulated amount of H2O2 after the 10 min measurement for each condition. The FEs for H2 and O2 are calculated in a similar way, in which the theoretical amount of H2 is also equal to the total amount of electrons divided by two (in mol), while the theoretical amount of O2 is equal to the total amount of electrons divided by four (in mol), respectively.

### Computational details

Density functional theory calculations are done using the projector-augmented wave method and a plane-wave basis set as implemented in the Vienna Ab Initio Simulation Package (VASP). The valence configurations are treated as 6s 26p 3 for Bi, 3d 34s 2 for V, 2s 22p 4 for O and 1s 1 for H. The cutoff energy for plane-wave basis functions is 400 eV. The bulk and surface properties of BiVO4 are optimized within GGA-PBE. For a more accurate description, the calculations are done within GGA-rPBE for the adsorption energies of OH*, O* and OOH* species on the BiVO4(111) surface. The reference energies of the pristine slab, H2, H2O and O2 molecules are also carefully treated within GGA-rPBE. For periodic slab calculations, slabs of six metal-oxygen layers are separated by at least 12 Å of vacuum. The atomic positions within the top two layers of the slabs were allowed to relax with the force convergence of 0.02 eV per Å. Spin polarization is considered in all the calculations.

### Data availability

Data supporting the findings of this study are available within the article and its supplementary information files, and from the corresponding author upon reasonable request.