## Introduction

Hydrogen peroxide (H2O2) is one of the most important chemicals in industry, used in the production of fine chemicals and medicine, rocket fuels, sterilization, bleaching, and so on1,2. In the conventional process, H2O2 is mainly produced via the anthraquinone method, which consists of hydrogenation and oxidation of anthraquinone successively. The quest for an ecofriendly process for H2O2 synthesis is driven by the current disadvantages including high energy consumption and heavy pollution3,4. Under such circumstances, the direct synthesis of H2O2 from hydrogen (H2) and oxygen (O2) is an efficient and clean strategy to replace the anthraquinone oxidation process5. However, this process is challenging because of many parallel and consecutive reactions, as shown in Fig. 1. Specifically, compared to the synthesis of H2O2, it is thermodynamically more favorable to the production of H2O via breaking O–O bonds, while the generated H2O2 also degrade through further hydrogenation and decomposition6,7.

Palladium (Pd)8,9 is a widely used catalyst in the direct synthesis of H2O2 due to its excellent hydrogenation activity. However, Pd is also active for side reactions and subsequent H2O2 degradation10,11, resulting in an inferior H2O2 selectivity and poor yield. Pd-based nanoalloy catalyst (e.g., Pd-Pt, Pd-Au, Pd-Zn, Pd-Ag, Pd-Te, Pd-Sb, Pd-Sn)5,12,13,14,15,16,17,18,19,20,21,22,23 can effectively modify the electronic structure of Pd, thus inhibiting side reactions and H2O2 degradation. Besides, H2O2 can also be stabilized by adding strong acids or halides to the solvent, while it will cause metal shedding and needs a subsequent purification process to obtain pure H2O224,25. Therefore, the rational design of a catalyst with high activity, high selectivity for oxygen hydrogenation to H2O2 as well as low degradation towards the generated H2O2 remains a formidable challenge.

The selectivity toward H2O2 is mainly determined by the competitive reactions between *OOH formation and O–O bond cleavage on catalysts which highly depend on the O2 adsorption configuration18,26,27,28,29,30,31,32. The Pd nanoparticles involve various adsorption modes such as “side-on”, “end-on” and “bridge”, while the adsorption of O2 on isolated Pd atom is usually the “end-on” type and could therefore reduce the possibility of O–O bond breaking. Thus, it would be encouraging to develop a single Pd atom catalyst to improve selectivity towards H2O2.

In this work, we have prepared a series of catalysts, among which the single Pd atom catalyst displays a remarkable H2O2 yield of 115 mol/gPd/h and a selectivity higher than 99%, surpassing the performance of reported Pd-based catalysts. Besides, H2O2 degradation is also shut down, making it an ideal catalyst. The concentration of H2O2 reaches 1.07 wt.% in a batch. Density functional theory calculations reveal that the high yield and selectivity is believed to have originated from the high energy barrier of both O–O bond dissociation and H2O2 dissociation on the single Pd atom catalyst.

## Results

### Synthesis and characterization of materials

X-ray absorption spectroscopy (XAS) measurements were performed to probe the local environment of Pd atoms in O-Pd/TiO2 and M-Pd/TiO2. The X-ray absorption near edge structure (XANES) region of the XAS spectrum provides information about the oxidation state of Pd. The Pd K-edge absorption edge position for O-Pd/TiO2 were like that of standard PdO sample (Fig. 3a), they were at higher photon energies than Pd metal, indicating that the Pd atoms in O-Pd/TiO2 were in the oxidation state. Fourier transformed R-space curves of the Pd K-edge EXAFS spectra revealed the bonding environment of Pd species in O-Pd/TiO2, an obvious peak at 1.75 Å was observed in the R-space spectrum of samples which was believed to be a Pd-O bond (Fig. 3b). The Pd metal foil and 1% M-Pd/TiO2 showed an intense Pd-Pd feature at around 2.5 Å, which was absent in the O-Pd/TiO2 samples (Fig. 3b), confirming that no Pd-Pd bonds were present in the O-Pd/TiO2. And the fitting results showed the coordination number of Pd-O is 4 for 0.1% O-Pd/TiO2 (Fig. 3c and Supplementary Table 1), representative of the oxidized Pd single atoms on the surface of TiO233,34. These results confirmed that the Pd was atomically dispersed on TiO2, which was consistent with the results of AC-TEM. The Pd K-edge absorption edge position and Fourier transformed R-space curves for M-Pd/TiO2 were like Pd foil, indicating that the metallic Pd states in M-Pd/TiO2 samples (Fig. 3a and Supplementary Fig. 3). X-ray photoelectron spectroscopy (XPS) analyses were presented in Fig. 3d, there is a strong signal of Pd2+ species (336.3 eV) in the spectra of 0.1% and 1% O-Pd/TiO2. For M-Pd/TiO2, we find that there is a strong signal of Pd0 (334.9 eV) (Fig. 3d and Supplementary Fig. 4a). The absence of Cl peaks in the XPS spectra indicates that most of the chloride ions have been removed during the washing process, so the influence of chlorine ions on catalytic performance is excluded. (Supplementary Fig. 4b, c).

#### Catalytic performance

The O2 hydrogenation to H2O2 was performed in a batch reactor with temperature at 2 °C controlled by an ice bath. We show that the catalytic performance of Pd catalysts in oxidation state (O-Pd/TiO2) (including single Pd atom (0.1%), Pd cluster (1%)) are all better than that of metallic Pd catalyst (M-Pd/TiO2). (Table 1, Entry 1–11). Particularly, the single Pd atom catalytic performance was up to 115 mol/kgcat/h, and the selectivity of H2O2 was more than 99% (Table 1, Entry 1–2), which is superior to all other samples as well as the reported state-of-the-art catalysts (Table 1, Entry 1–2, 3–20). The Pd cluster catalyst (1% O-Pd/TiO2) has a H2O2 yield of 79 mol/kgcat/h, while the selectivity is 58% (Table 1, Entry 3–5), and the PdO nanoparticles demonstrate only a 7% selectivity to H2O2. For M-Pd/TiO2, the H2O2 yield are much lower than that of O-Pd/TiO2 (Table 1, Entry 8-11). For example, the H2O2 yield of 3% and 5% M-Pd/TiO2 were 46 and 42 mol/kgcat/h, respectively. Interestingly, the catalytic activity of 0.1%M-Pd/TiO2 is very limited (Table 1, Entry8), as H2O2 yield was not detected. Also, we have synthesized 9% Pd/C catalyst, and the activity and selectivity of Pd/C catalyst was inferior to both O-Pd/TiO2 and M-Pd/TiO2 catalysts. (Table 1, Entry 12).

Although the performance of the O-Pd/TiO2 catalyst is superior to that of the M-Pd/TiO2, whether the oxidized Pd species possessing high activity and selectivity remain controversial. The Burch et al. propose that M-Pd species has a higher activity and selectivity to H2O28. Conversely, the Choudhary and Gaikwad et al. showed that oxidized Pd species exhibit better catalytic activity and selectivity by loading M-Pd and PdO on different oxide supports25,35. H2 is easily activated on Pd0 sites, while O2 tends to be dissociated on successive Pd0 sites; however, O2 is stable on the surface of PdO26. Thus, both Pd0 and Pd2+ species play vital roles in H2O2 synthesis. Recently, the DFT calculation by Wang et al. suggested that PdO (101) can effectively inhibit the dissociation of O–O bonds, leading to better activity and selectivity than Pd (111)27, which is consistent with our experimental results.

The influence of reaction conditions (catalyst feeding and reaction time) on catalytic performance were further studied. For 0.1%O-Pd/TiO2, the amount of H2O2 increases with the increase of catalyst feeding. For example, it can produce 144 μmol of H2O2 in half an hour when 2.5 mg 0.1%O-Pd/TiO2 catalysts are fed, 10 mg can produce 390 μmol of H2O2 (78 mol/kgcat/h), corresponding to 0.15% concentration (Fig. 4a), H2 conversion is 10.43%, which is also comparable to PdSn catalysts (9% of H2 conversion, 61 mol/kgcat/h, 96% of selectivity) (Table 1, Entry 17). It is also noteworthy that the H2O2 selectivity of 0.1%O-Pd/TiO2 is >99% regardless of the quantity of 2.5 mg, 5 mg, or 10 mg (Fig. 4b). On the contrary, for clusters and nanoparticles, the increase in the amount of H2O2 production is not obvious, but their H2O2 selectivity gradually decreases (Fig. 4a, b). Reaction time was extended from half an hour to three hours. We found that when the reaction time reached 2.5 h, the production of H2O2 was up to 1877 μmol (0.75% concentration) for 0.1%O-Pd/TiO2 (Fig. 4c). However, when the reaction time is more than 2.5 h, the concentration of H2O2 remains at 0.75%. The explanation might be that the large gas consumption in the reactor hinder the further generation of H2O2. To verify this point, we renew the gas in the reactor after the reaction of 2.5 h, and proceed with the reaction for the following 2.5 h (note the remaining gas in the reactor was completely discharged to 0 Mpa and then injected with 3.0 Mpa 5%H2/CO2 and 1.2 Mpa 25% O2/CO2). The results show that the concentration of H2O2 rose from 0.75% to 1.07% (2685 μmol). In general, H2O2 selectivity will decrease because of the side reactions and H2O2 degradation in a long-term reaction8,23,24,31,32. Interestingly, we found that the selectivity of 0.1%O-Pd/TiO2 is always >99% no matter the reaction time (Fig. 4d). But for clusters and nanoparticles, the H2O2 selectivity does decline (Fig. 4d). One interpretation of this phenomenon is that as H2 conversion increases, selectivity decreases due to H2O2 degradation. This can be better understood by comparing selectivity as a function of conversion for the different catalysts (Supplementary Fig. 5).

Therefore, we further measured the degradation rate of H2O2 under similar reaction conditions (3.0 Mpa 5%H2/CO2, the initial concentration of H2O2 is 2 wt.%). Firstly, the experiment shows that H2O2 does not degrade on TiO2 support itself at 2 °C (Supplementary Table 2), which is consistent with the results previously reported by Edwards et al.22. Interestingly, the H2O2 degradation rate was not detected on the O-Pd/TiO2 catalysts, but there was a significant H2O2 degradation rate on the M-Pd/TiO2 catalysts; with the increase of metallic Pd loading, the degradation rate of H2O2 becomes higher (Table 1, Supplementary Table 3). For example, the H2O2 degradation rate of 1% and 5%M-Pd/TiO2 were 518 and 867 mol/kgcat/h. To further understand the H2O2 degradation performance of catalysts, we have conducted a series of H2O2 degradation experiments under different conditions of atmosphere (5% H2/CO2 (3.0 MPa), 25% O2/CO2 (3.0 MPa) and pure N2 (3.0 MPa), 5%H2/N2 (3.0 Mpa). (Supplementary Table 4).

Under the 5% H2/CO2 (3.0 MPa), the degradation of H2O2 was not detected on O-Pd/TiO2 (Supplementary Table 4, Entry 1); to eliminate the influence of CO2, we used 5% H2/N2 for the degradation experiment, the degradation rate was still not detected (Supplementary Table 4, Entry 8); however, the amount of H2O2 gradually decreased with time for M-Pd/TiO2 catalyst. (Fig. 4e; Supplementary Table 4, Entry 2–3). On the other hand, we have not detected any degradation for both O-Pd/TiO2 and M-Pd/TiO2 catalyst under 25% O2/CO2 (3.0 MPa) or pure N2 (3 Mpa). (Supplementary Table 4, Entry 4–7), which indicates the slow degradation of H2O2 in the absence of H2. These observations suggested that the degradation rate of H2O2 is extremely low on the O-Pd/TiO2 catalyst even in the presence of H2. The result is meaningful for the degradation of H2O2 can be avoided without adding any inhibitors or pretreatment/post-treatment of catalysts.

Finally, we have investigated the stability of 0.1% O-Pd/TiO2 catalyst (Fig. 4f) by measuring the H2O2 yield in the cycle test. The H2O2 yield decreased from 115 to 74 mol/kgcat/h after reused five times. In the HAADF-STEM image of the used 0.1% O-Pd/TiO2 (Supplementary Fig. 6), we have observed some aggregated Pd species (about 3 nm Pd nanoparticle) on the TiO2 particle by using EDS mapping, however, the homogenous distribution of Pd species in other places suggest that many single Pd atom still existed. The XPS results of the used catalyst reveal the existence of oxidized Pd species other than the metallic Pd species (Supplementary Figs. 7 and 8), which is consistent with the STEM result. Since the metallic Pd species showed very poor H2O2 yield in the experiment (Table 1, Entry 9–11), the observed Pd aggregation might mainly account for the loss of H2O2 yield in the recycle test. The decrease of H2O2 yield in the recycle experiment further indicates that the performance of the catalyst after reaction (co-existence of a single Pd atom and Pd nanoparticles) is not as good as that of the fresh catalyst, highlighting the important role of the initial single Pd (2+) state.

To further confirm this hypothesis, we have heated the used catalyst (after 5 cycles) at 350 °C for 3 h in the air, and the H2O2 yield increase from 74 mol/kgcat/h to 100 mol/kgcat/h, which is close to the fresh catalyst (Fig. 4f, round 6). It was also reported that the anneal treatment in the oxidative atmosphere will re-disperse the noble nanoparticle to a single noble metal atom on the oxide support36,37,38. Thus, it’s reasonable to believe that the recovered H2O2 yield might be caused by the recovery of a single Pd2+ atom through annealing in the air, which also suggests the anneal treatment in the air is an effective method to refresh the used catalyst. The result again confirms that the single Pd2+ atom accounts for the high activity and selectivity towards the direct synthesis of H2O2.

### Density functional theory calculations

As mentioned in the introduction section, the H2O2 selectivity is mainly determined by the competitive reactions between *OOH formation and O–O bond cleavage on catalysts. For these reasons, first-principles calculations are used to investigate the dissociation of O2 and H2O2 over single atom and PdO clusters. Single Pd atom (Pd1/TiO2) and PdO clusters (Pd8O8/TiO2) structure models were optimized on the surface of TiO2 (101) (Supplementary Fig. 9). The Pd1/TiO2 model is based on the palladium-oxygen coordination number fitted by EXAFS, and Pd8O8 is extracted from the bulk phase of PdO, which simulates the coordination information of Pd and O in large nanoparticles. It is shown that O2 is adsorbed by “Pd-O-O” configuration on Pd1/TiO2 and is mainly adsorbed by “Pd-O-O-Pd” configuration on Pd8O8/TiO2 (Supplementary Fig. 10). The oxidation state of Pd single atom estimated by bader charge analysis is (+1.73) between +1 and +2 (Supplementary Fig. 11), which is consistent with the XAS results.

Firstly, we have calculated the dissociation energy barrier of O2 on Pd1/TiO2 and Pd8O8/TiO2, respectively. The dissociation of O2 on Pd1/TiO2 is a high energy process that is endothermic by 1.89 eV (Fig. 5a), while the dissociation energy barrier of O2 on Pd8O8/TiO2 needs only 1.08 eV, indicating that the dissociation of O2 on Pd1/TiO2 is not favorable. And compared with the reported results of related DFT work (Supplementary Table 5), we find that the dissociation energy barrier of O–O bond on Pd1/TiO2 is the highest. This difference in the dissociation barrier can be attributed to structural differences (i.e., the adsorption configuration of oxygen on Pd). Oxygen can only be dissociated by migrating one oxygen atom to the nearby Ti site on Pd1/TiO2, whereas on Pd8O8/TiO2 it can be directly fractured by “Pd-O-O-Pd” (Supplementary Fig. 12). Moreover, we found that H2 is more easily activated on Pd1/TiO2 than Pd8O8/TiO2 (Fig. 5b).

Similarly, the formation of *OOH on Pd1/TiO2 only needs to overcome the energy barrier of 0.81 eV, while Pd8O8/TiO2 needs to overcome 1.25 eV (Fig. 5c). Structurally, the reason is that the adsorbed oxygen can directly capture the adsorbed hydrogen at the single Pd atom site, while clusters need to capture hydrogen from other Pd sites (Supplementary Fig. 13).

In addition, the reaction barriers for the step of OOH* hydrogenation to H2O2 and OOH* dissociation were investigated. On Pd1/TiO2, the formation of H2O2 only needs to cross an energy barrier of 0.16 eV, while OOH* dissociation needs to overcome 0.19 eV of barrier (Fig. 5d). In contrast, the formation of H2O2 needs to overcome 0.27 eV on Pd8O8/TiO2, OOH* dissociation needs to overcome 0.35 eV of barrier (Fig. 5e). The calculated results suggest that Pd1/TiO2 is much more favorable than Pd8O8/TiO2 for H2O2 formation.

The H2O2 degradation involved two steps (H2O2 → 2OH*; OH* + H* → H2O). The calculated energy barrier of H2O2 dissociation into 2OH* on Pd1/TiO2 (0.58 eV) is higher than that of Pd8O8/TiO2 (0.07 eV) (Fig. 5f), suggesting that H2O2 is more difficult to degrade on Pd1/TiO2. Moreover, the energy barrier of the reaction of the OH* with H* on Pd1/TiO2 (0.83 eV) is higher than that on the Pd8O8/TiO2 (0.50 eV) (Fig. 5g). Therefore, after the calculation of these transition states, the entire reaction potential energy landscape can be obtained (Fig. 5h). The results reveal that it is conducive to the generation of H2O2 on Pd1/TiO2 than on Pd8O8/TiO2, which is well consistent with the experimental observations. Therefore, a schematic diagram of H2O2 formation on single Pd atom catalyst is shown in Fig. 5i.

To sum up, the DFT calculation results confirm that single Pd atom catalysts favor the formation of the key intermediate (*OOH) and H2O2, but strongly suppress the cleavage of O − O bond in O2 and OOH and H2O2, leading to a higher activity and selectivity. The calculation results also show that the different performances come from various adsorption configurations of O2 on single atom and clusters at the beginning.

In summary, we have synthesized a series of O-Pd/TiO2 (oxidized) and M-Pd/TiO2 (metallic) catalysts for the oxygen hydrogenation to H2O2, the catalytic performance of O-Pd/TiO2 (including single Pd atom (0.1%), Pd cluster (1%)) are all better than that of M-Pd/TiO2 catalyst. Particularly, the single Pd atom catalyst displays ultrahigh activity (115 mol/gPd/h), which is 14 and 135 times higher than that of clusters and nanoparticles, respectively; and the selectivity to H2O2 is more than 99%. More interesting, H2O2 degradation was also shut down. The concentration of H2O2 reached 1.07 wt.% in a batch. DFT calculations show that the O–O bond breaking is significantly inhibited on the single Pd atom and the O2 is easier to be activated to form *OOH and H2O2; and the energy barrier of H2O2 degradation is also higher. As a result, the high yield and selectivity is obtained on single Pd atom catalyst. The work reports the application of single Pd atom catalysts in the direct synthesis of H2O2. We believe it will yield far-reaching implications for subsequent catalyst design in direct synthesis of H2O2 and corresponding mechanism research in the future.

## Methods

### Materials

Titanium (IV) oxide, Aeroxide P25 (Beijing Balinwei Technology Co., Ltd, product of Japan), Ethylene glycol (A.R. Tianjin Damao Chemical Reagent Factory), Na2PdCl4 (>36.0%, Annege Chemical). Methyl alcohol (G.R. Tianjin Guangfu Science and Technology Development Co., Ltd). Fe (NH4)2·(SO4)2·6H2O (Tianjin Institute of Guangfu Fine Chemicals). Cerium sulfate (macklin reagent). Ultrapure water (18.2 MΩ cm). Stainless steel autoclave (Yanzheng Shanghai Instrument Co., Ltd). 5% H2/CO2, 5% H2/N2, pure N2 and 25% O2/CO2 were purchased from Beijing Millennium Capital Gas Co. Ltd.

### Synthesis of catalysts

Synthesis of O-Pd/TiO2 (oxidized): TiO2 was calcination at 450 °C for 4 h in the air (ramping rate: 5 °C/min) to remove surface water before catalysts preparation. The O-Pd/TiO2 catalyst was prepared using a hydrothermal synthesis method. The corresponding amount of Na2PdCl4 (10 g/L) was added to the TiO2 (1 g) carrier suspension and heated to 80 °C for 3 h under magnetic stirring. Then, the obtained Pd/TiO2 powder was centrifuged and freeze-dried overnight. Subsequently, the obtained catalyst was calcined at 350 °C for 3 h in the air at a heating rate of 5 °C/min. In order to obtain larger size palladium oxide nanoparticles, the samples with 3% palladium loading were heated at 450 °C and 600 °C for 3 h and other conditions remain unchanged. The prepared catalysts were denoted as 0.05%, 0.1%, 0.5%, 1%, 2% O-Pd/TiO2 respectively according to the Pd loading. The catalysts with 3% Pd loading were labeled as 3% O-Pd/TiO2−450 and 3% O-Pd/TiO2−600, respectively, according to the calcination temperature.

Synthesis of M-Pd/TiO2 (metallic): The preparation of M-Pd/TiO2 was like that of O-Pd/TiO2, except that the water was replaced with ethylene glycol and the temperature of TiO2 carrier suspension was 100 °C, under reflux conditions. The catalysts were not calcined with air after centrifugally freeze-dried and used directly. The prepared catalysts were marked as 0.1,1,3, and 5% M-Pd/TiO2 by the loading of palladium.

### Characterization

The Pd loading on the catalysts was analyzed using an IRIS Intrepid ER/S (Thermo Elemental) inductively coupled plasma-atomic emission spectrometer (ICP-AES). Transmission electron microscopy (TEM) images were obtained using a Tecnai F20 microscope in conjunction with powder samples deposited onto a copper micro-grid and coated with carbon, applying an accelerating voltage of 200 kV. Spherical aberration corrected (Cs corrected) high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and energy-dispersive X-ray (EDX) mapping images were obtained with an FEI Titan G2 microscope equipped with a Super-X detector, operating at 300 kV. X-ray diffraction (XRD) patterns of the samples were recorded on a Bruker D8 Advance system with Cu Kα radiation at 40 kV and 40 mA. X-ray photoelectron spectroscopy (XPS) analyses were performed using a Kratos Axis Ultra XPS spectrometer with monochromatized Al-Kα radiation and an energy resolution of 0.48 eV. The X-ray absorption fine structure (XAFS) spectrum data were collected on the BL14W1 beamline radiation equipment of the Shanghai Synchrotron Radiation Facility (SSRF) of the Shanghai Institute of Applied Physics (SINAP). Pd foil, PdO samples were used as references. All target samples and references were measured by fluorescence or transmission mode. Extended X-ray adsorption fine structure (EXAFS) fitting was conducted using the software of Artemis.

### Catalytic experimental measurement

Catalytic experiments were operated using a stainless-steel autoclave with a nominal volume of 50 mL and a maximum working pressure of 14 MPa.

H2O2 synthesis. In the typical experiment of H2O2 synthesis, 2.5 mg catalyst and 8.5 g solvent (5.6 g CH3OH (HPLC grade), 2.9 g H2O) were added into the autoclave. Before 3.0 MPa 5%H2/CO2 was injected at room temperature, the reactor was purged three times with 0.7 MPa (5%H2/CO2), then the temperature was reduced to 2 °C (in an ice bath), the pressure was about 2.3 MPa, at this time, 1.2 MPa 25% O2/CO2 was injected, and the total pressure was 3.5 MPa. Temperature and pressure are respectively detected by thermocouple and pressure sensor. The stirring speed was controlled at 1200 rpm.

The H2O2 yield was detected by acidified Ce (SO4)2 (0.01 M) titration in the presence of two drops of ferroin indicator. The Ce (SO4)2 solutions were standardized against (NH4)2Fe(SO4)2·6H2O using ferroin as an indicator. Catalyst yields are marked as mol H2O2 kgcat−1 h−1 according to the following equation.

$${{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{Yield}}}}}}=({{{{{\rm{moles}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{generated}}}}}})/({{{{{\rm{mass}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{\rm{catalyst}}}}}}\times {{{{{\rm{time}}}}}})$$
(1)

Gas analysis was performed by gas chromatography (GC-2020) equipped with a TDX-01 column connected to a thermal conductivity detector. Conversion of H2 was calculated by gas analysis before and after the reaction. H2O2 selectivity was calculated according to the following equation:

$${{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{Selectivity}}}}}}=({{{{{\rm{moles}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{generated}}}}}})/({{{{{\rm{mass\; of}}}}}}\,{{{{{{\rm{H}}}}}}}_{2}{{{{{\rm{reacted}}}}}})\times 100\%$$
(2)

H2O2 degradation. The experiments were manipulated in a similar way to the H2O2 synthesis, but in the absence of 1.2 MPa 25%O2/CO2. In detail, H2O from the 8.5 g of solvent was replaced by a 30% H2O2 solution to give a reaction solvent containing between 2-8 wt%H2O2. The standard reaction conditions adopted for H2O2 degradation were as follows: 2.5 mg catalyst, 8.5 g solvent (5.6 g CH3OH, 2.34 g H2O, and 0.56 g 30% H2O2, 3.0 MPa 5%H2/CO2, 2 °C, 1200 rpm, 30 min). The H2O2 degradation rate is a combination of H2O2 hydrogenation and decomposition. H2O2 degradation rate was calculated following:

$${{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{degradation\; rate}}}}}}=({{{{{\rm{moles}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{{\rm{H}}}}}}}_{2}{{{{{{\rm{O}}}}}}}_{2}\,{{{{{\rm{reduced}}}}}})/({{{{{\rm{mass}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{\rm{catalyst}}}}}}\times {{{{{\rm{time}}}}}})$$
(3)

To ensure the reliability of the data, all the above experiments have to be tested for nine times, the data presented was the average value, the error of H2O2 yield and selectivity are within 1%, 4% respectively.

### Calculation details

All the spin-polarized density functional (DFT) calculations were carried out with the Vienna Ab initio Simulation Package(VASP)39. The ion-electron interaction was described by the projector augmented wave (PAW) method40. The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) functional was used for the exchange-correlation interactions41. The DFT-D3 method was introduced to describe van der Waals interactions42. The 15 Å vacuum slab in the z direction was applied to avoid interactions with adjacent units. The cut-off energy for plane-wave basis set was 450 eV. The convergence criterion for energy and force were set as 10-5 eV and 0.03 eV/Å during geometry optimization, respectively. The Brillouin zone was sampled with 2 × 2 × 1 k-point grids. Transition states were located with the climbing-image nudged elastic band (CI-NEB) method43, and the threshold value for the forces on each atom was 0.05 eV/Å.