Introduction

Over the past century, nitrogen fertilizer has fed approximately 27% of the world’s population by nourishing crops1,2. Urea is the most common nitrogen fertilizer and its nitrogen content is as high as ~46%, which plays a pivotal role in the agricultural field and population growth3. In addition, urea is widely used in the preparation of dyes, resins and pharmaceutical products4. The traditional industrial synthesis of urea (Bosch–Meiser process) requires high energy consumption arising from high temperature (~200 °C), high pressure (~210 bar) and a complex synthesis process involving artificial nitrogen fixation to form NH35,6. It is worth noting that the synthetic ammonia industry consuming more than 2% of global energy and more than 50% of synthesized NH3 is used for urea synthesis in 2020 alone7. Therefore, it is imperative to explore sustainable and economical routes for urea synthesis.

In recent decades, electrochemical synthesis of urea has drawn increasing attention since the utilization of clean renewable energy and environmental concern8. Various nitrogen sources (e.g., N2, NO3 and NO2) can be coupled with the electrochemical reduction of greenhouse gas CO2 to produce urea9,10,11. Among them, nitrate has a relatively low N=O dissociation energy (204 kJ mol–1)12, making it more suitable as an N source for urea electrosynthesis. Moreover, nitrate can be obtained from N2/air using a non-thermal plasma process13. The total energy consumption of direct electrosynthesis of urea via N2-NO3-urea process can be comparable or even less than the traditional process (Supplementary Note 1), while the CO2 emissions involved in urea electrosynthesis may be reduced by more than 50% compared with the traditional urea synthesis method7, indicating that the electrochemical co-reduction of NO3 and CO2 for urea synthesis with renewable energy holds potential as a new alternative pathway. Recently, some metal oxides/hydroxides catalysts (In(OH)33, Vo-CeO211, CuSiOX14, TiO2/C15, SrCo0.39Ru0.61O3-δ16, CuWO417, etc.) and metal catalysts (Zn/Cu8, Pd4Cu1-FeNi(OH)218, etc.) have been investigated for the electroreduction of CO2 and NO3 to produce urea. Despite these achievements, there are still several challenges that need to be addressed due to the complex 16 electron transfer (CO2 + 2NO3− + 18H+ + 16e → NH2CONH2 + 7H2O) with multi intermediates involved in this process: (1) The overpotential of urea electrosynthesis is relatively high. Although the thermodynamic potential for the conversion of urea from CO2 and NO3 is 0.811 V versus standard hydrogen electrode (0.41 V vs. RHE at pH~6.8)19, the applied potentials in most reported works are generally more negative than −0.3 V vs. RHE2,10. (2) The catalysts usually suffer from unsatisfactory yield rate (mostly <60 mmol gcat.–1 h–1) and poor stability (typically between 10 h and 100 h). (3) The high competitiveness of side reactions such as the generation of CO/NH3 and hydrogen evolution reaction (HER) leads to a low urea selectivity. Therefore, the development of efficient and selective electrocatalysts to generate urea from NO3 and CO2 at low overpotentials is crucial. Some previous works suggest that the rate determining step in urea electrosynthesis is the initial C-N coupling11,14, and promoting the coupling of primary intermediates such as *CO, *NO2 during CO2 and NO3 co-reduction may effectively reduce the overpotential and inhibit the side reactions. Thus constructing heterogeneous catalysts with well-designed tandem active sites that simultaneously facilitates the adsorption and coupling of *CO and *NO2 would be an efficient approach to achieve the selective production of urea. Among the metal catalysts, Ag-based materials exhibit quite high electrocatalytic activity for the conversion of NO320 in addition to CO2 reduction response. While Cd-based nanomaterials can also catalyze the reduction of CO2 to produce C-containing adsorption intermediates and generate CO21,22, which may be beneficial for the C-N coupling in urea electrosynthesis. However, the tandem electrocatalysis of Ag-Cd heterostructured materials for urea synthesis from CO2 and NO3 is rarely been explored.

In this study, we achieved efficient and selective urea electrosynthesis through early *CO and *NO2 coupling at low overpotentials on Ag/CdO heterostructured catalyst. Operando X-ray absorption spectroscopy (XAS), Raman spectroscopy and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) prove that the Ag component in the synthesized Ag/CdO catalyst not only promotes the reconstruction of CdO into CdCO3 with oxygen vacancies, which can efficiently adsorb and activate CO2, but also facilitates the adsorption of electrophilic intermediate *NO2 during the reduction process. Density functional theory (DFT) calculations indicate that the in situ reconstructed Ag/CdCO3 catalyst benefits the adsorption and conversion of N-containing and C-containing intermediates with low free energy differences. The C-N coupling on the reconstructed Ag/CdCO3 sites is possibly spontaneous to form the key intermediate *CONO2 (−0.89 eV), thus would inhibit the generation of by-products such as NH3 and CO compared with the step of *NO2 hydrogenation to *HNO2 (−0.54 eV) and *CO desorption to CO (0.49 eV). Therefore, the optimized Ag0.07/CdO catalyst demonstrates a high urea Faradaic efficiency (FEurea) of 51.2 ± 3.0% even at −0.1 V vs. RHE in an H-cell and a high urea yield rate of 111.6 ± 3.1 mmol gcat.–1 h–1 with a partial current density ~7.2 mA cm–2 at a positive potential of −0.15 V vs. RHE in a flow cell. Moreover, it can achieve a urea yield rate of 427.0 ± 30.2 mmol gcat.–1 h–1 at a current density of ~60 mA cm–2 in an optimized two-electrode cell with stable response for 1000 h, which is quite competitive for the reported urea electrosynthesis system3,8,9,23,24,25,26.

Results

Synthesis and structural characterization of electrocatalysts

The Ag/CdO heterostructured catalysts were prepared via a high-temperature calcination (550 °C, 2 h) after chemical precipitation of Ag and Cd salts. According to the Ag content tested by X-ray fluorescence (XRF) in Supplementary Table S1, the prepared sample is defined as Agx/CdO (Ag0.03/CdO, Ag0.07/CdO and Ag0.16/CdO, x represents the atomic ratio of Ag in metal elements). Pure Ag and CdO are also prepared for comparison (Supplementary Figs. S1 and S2). The X-ray diffraction (XRD) patterns of the synthesized Agx/CdO samples could be assigned to the heterostructure of metallic Ag (cubic phase) and CdO (cubic phase) (Supplementary Fig. S3). The morphology of the synthesized samples manifests as nanoparticles with a size of ~100 nm with clear lattice spacing belonging to Ag and CdO heterostructures according to scanning electron microscopy (SEM, Supplementary Fig. S4) and high-resolution transmission electron microscopy (HR-TEM, Supplementary Fig. S5) test. However, particles tend to agglomerate as the Ag content increases to 14.1 atom%. Additionally, Cd, Ag and O are homogeneously dispersed throughout the nanoparticles in energy dispersive X-ray spectroscopy (EDX) image (Fig. 1a). Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (AC-HAADF-STEM) is conducted to further identify the heterostructures in Ag0.07/CdO catalyst (Fig. 1b–d). The array spacings are 0.270 and 0.145 nm, corresponding to the interplanar spacing of CdO (111) and Ag (220) facets, respectively. Furthermore, Ag, Cd, and O are indicated in the survey spectrum of X-ray photoelectron spectroscopy (XPS) for Ag0.07/CdO (Supplementary Fig. S6a). The peaks located at 404.5 (Cd2+ 3d5/2) and 411.3 eV (Cd2+ 3d3/2) belonging to Cd 3d (Supplementary Fig. S6b) are negative shift compared to pure CdO (405.0 and 411.8 eV), while the spectrum of Ag 3d (Supplementary Fig. S6c) shows two peaks at 367.7 (Ag 3d5/2) and 373.7 eV (Ag 3d3/2) that are lower than metallic Ag (368.0 and 374.0 eV), indicating electron transfer from Ag to Cd27,28. The coordination environment of the metal sites in Ag0.07/CdO electrocatalyst is further validated by XAS. Due to the high proportion of CdO in Ag0.07/CdO, the valence and Cd-Cd/Cd-O bond configuration of Cd in bulk Ag0.07/CdO are similar to CdO29,30, which are illustrated by the X-ray absorption near edge structure (XANES, Fig. 1e) data at the Cd K-edge and the Fourier transform extended X-ray absorption fine structure (FT-EXAFS, Fig. 1f). Meanwhile, wavelet transform (WT) contour plots of Ag0.07/CdO show peaks corresponding to Cd-O and Cd-Cd coordination, which is highly consistent with CdO (Fig. 1g and Supplementary Fig. S7). However, although WT of Ag K-edge coordination environment is metallic Ag with a separate Ag-Ag coordination (Supplementary Fig. S8 and Fig. 1j), XANES and FT-EXAFS (Fig. 1h, i) indicate that the average valence state of Ag in Ag0.07/CdO is slightly higher than metallic Ag, which is consistent with XPS results. The above multiple results indicate that the synthesized Ag0.07/CdO catalyst exhibits a heterostructure of Ag and CdO, with electronic interactions between the two components, which could potentially contribute to the electrocatalytic performance of the catalyst31.

Fig. 1: Structural and compositional characterization.
Fig. 1: Structural and compositional characterization.The alternative text for this image may have been generated using AI.
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a HR-TEM image of Ag0.07/CdO catalyst and the corresponding elemental mappings of Cd, Ag and O. b AC-HAADF-STEM image of Ag0.07/CdO catalyst. c The enlarged view and lattice spacing within the blue box in (b). d The enlarged view and lattice spacing within the red box in (b). e Cd K-edge and h Ag K-edge XANES spectra of Ag0.07/CdO catalyst (The inset shows an enlarged view of the shaded region). Fourier transform of k3-weighted f Cd K-edge and i Ag K-edge EXAFS spectra for the r space. Wavelet transform of the k3-weighted EXAFS data of g Cd K-edge and j Ag K-edge for Ag0.07/CdO catalyst.

Electrochemical urea synthesis

Urea electrosynthesis test is firstly carried out on an H-type cell with a typical three-electrode configuration under ambient conditions (Supplementary Figs. S9S28). The linear sweep voltammetry (LSV) tests were performed to evaluate the current response of the prepared electrocatalysts towards CO2 and NO3 co-reduction in CO2 saturated 0.1 M KHCO3 and 0.05 M KNO3. As shown in Supplementary Fig. S9, Agx/CdO heterostructured catalysts demonstrate higher current densities compared to pure Ag and CdO, indicating a positive response in co-electrolysis of CO2 and NO3 toward C-N coupling, especially for Ag0.07/CdO. In addition, a competitive FEurea of 51.2 ± 3.0% is observed on Ag0.07/CdO catalyst at just −0.1 V vs. RHE (Supplementary Figs. S14 and S2527)3,9,32,33,34,35,36, and the main by-products include H2 (FE = 11.8 ± 3.5%), NO2 (FE = 12.2 ± 1.0%), and NH3 (FE = 13.6 ± 4.3%). The FEurea is also evaluated by ion chromatography (IC) after urea decomposition via urease method, which is not significantly different from the results of UV-vis and HPLC-MS (Supplementary Fig. S27). Moreover, it is observed that the FENO2− on Ag0.07/CdO is lower than that on Ag0.03/CdO and Ag0.16/CdO, which may be due to its efficient utilization of NO2 as an N-containing intermediate for urea synthesis. Additionally, IC is used to verify FENO2− and FENH4+ for different catalysts. Similar trends are observed for these sample (Supplementary Fig. S28). Compared to Ag0.07/CdO, pure Ag and CdO catalysts exhibit poor performance towards urea formation. Specially, pure Ag exhibits almost the highest FEs of NH3 (31.0%) and NO2 (49.4%) compared to other catalysts, which means that Ag may tend to activate NO3 in the co-reduction process of CO2 and NO3. To verify the origin of N element, the 0.05 M isotope 15N-labeled potassium nitrate (K15NO3) added 0.1 M KHCO3 is used as the electrolyte for chronoamperometry measurements (Fig. 2a and Supplementary Figs. S2931) and the results explicitly confirm that the N source in urea comes from NO3. The electrochemical surface area (ECSA) of the prepared catalyst is evaluated and as shown in Supplementary Figs. S32 and 33, the ECSA values of the catalyst are very close, which indicates that it is the inherent activity of the catalytic site rather than simple ECSA contributes to C-N coupling. The durability of Ag0.07/CdO catalyst toward urea electrosynthesis are also examined. As exhibited in Supplementary Fig. S34a, the Ag0.07/CdO catalyst maintains a relatively stable current density of approximately 1.0 mA cm−2 for 24 h at −0.1 V vs. RHE in H-cell, indicating good stability. Further, the stability and reproducibility of urea generation is validated in repeated testing. The final FEurea remains above 50% after 10 h long-term successive runs, demonstrating good reproducibility (Supplementary Figs. S34b and S35). To further understand the structure-performance relationship of Ag0.07/CdO catalyst in urea electrosynthesis, the same proportion of Ag and CdO are physically mixed and the electrochemical performance is tested in Supplementary Fig. S36a, b. The results show that FEurea and partial current density (Jurea) are 34.7% and 0.24 mA cm–2 at −0.1 V vs. RHE, respectively, which are lower than those of Ag0.07/CdO but significantly higher than that of pure Ag (6.5% ± 1.5%) and CdO (11.6% ± 5.0%), indicating the crucial role of the bifunctional Ag/CdO structure in the electrochemical synthesis of urea. Furthermore, XPS (Supplementary Fig. S36c, d) proves that the physical mixture of Ag and CdO do not undergo significant electron transfer, indicating that the electronic interaction between the two components on Ag0.07/CdO catalyst may further promote the generation of urea. In addition, control tests including an experiment on replacing CO2 with argon and an experiment where CO2 and nitrate are left in the cell without applying the electrochemical process are added and the results show that no urea is produced (Supplementary Figs. S3739). A flow cell with three electrode system is further applied to the urea electrosynthesis from CO2 and NO3 (Fig. 2b and Supplementary Figs. S4042). In Fig. 2b, the results show that the FEurea is about 50% and a high urea yield rate is 111.6 ± 3.1 mmol gcat.–1 h–1 at −0.15 V vs. RHE, indicating the efficient electrochemical C-N coupling at a low overpotential in a flow cell. Furthermore, the Ag0.07/CdO catalyst maintains long stability for 1000 h at a current density of ~10 mA cm–2 during urea electrosynthesis (Supplementary Fig. S41) and exhibits the lowest overpotential with a high urea yield rate3,9,12,14,15,16,17,18,32,36,37,38,39,40,41.

Fig. 2: Electrosynthesis of urea.
Fig. 2: Electrosynthesis of urea.The alternative text for this image may have been generated using AI.
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a MS spectra for K14NO3 and K15NO3 with CO2 co-reduction, respectively. b FEurea and urea yield rate at different potentials in a flow cell. c LSV at 10 mV s–1 scan rate for Ag0.07/CdO catalyst in a two-electrode cell, d Faradaic efficiency of each product and e Stability test of urea synthesis during 1000 h of electrolysis at −1.6 V in a two-electrode cell. Electrochemical measurements were performed without iR compensation in a flow cell (R = 6.0 ± 0.2 Ω) and a two-electrode cell (R = 0.5 ± 0.1 Ω) at 25 °C. The electrolyte is 1.0 M KOH and 0.05 M KNO3 (pH = 14.0 ± 0.1) and the flow rate of CO2 during test was maintained at 20 mL min–1 by a gas flow meter.

Furthermore, the performance of Ag0.07/CdO catalyst is significantly improved by optimizing the process conditions (e.g. ionomer, membrane and flow field configurations) in a two-electrode cell (Specific details in “Methods”). As shown in Fig. 2c, d and Supplementary Figs. S43 and 44, Ag0.07/CdO catalyst can achieve a urea yield rate of 427.0 ± 30.2 mmol gcat.–1 h–1 with a FEurea of 59.1 ± 6.6% at a current density ~60 mA cm–2 (−1.6 V). Figure 2e displays that the urea yield rate can maintain around 75% of the initial value and FEurea is over 50% after 1000 h stability test, which is competitive for the electrosynthesis of urea from CO2 and NO3 (Supplementary Table S2).

Mechanism study

To get insights into the high C-N coupling activity of Ag0.07/CdO, structural characterizations are employed in the catalysts after CO2 and NO3 co-reduction. The XRD patterns reveal that Ag maintains the cubic phase, while CdO evolves into CdCO3 during the reduction process (Supplementary Figs. S4547). Furthermore, HR-TEM displays the clear lattice spacing belonging to heterostructured Ag and CdCO3 with the array spacings of 0.272 and 0.236 nm, corresponding to the interplanar spacing of CdCO3 (006) and Ag (111) facets after 10 h and ~100 h of reduction, respectively (Supplementary Fig. S48), indicating the good stability of the reconstructed heterostructure. XPS results show that the binding energy of Cd for Ag0.07/CdO is similar to CdCO3 after reaction (Supplementary Fig. S49a), while the binding energy of Ag in Ag 3d spectrum is transferred to higher energy after co-reduction (Supplementary Fig. S49b), indicating that the Ag component acquires electrons during the reduction process. In order to investigate the effect of in situ reconstructed Ag0.07/CdCO3 on C-N coupling, physical mixed Ag0.07/CdCO3, named as Ag0.07/CdCO3-PM, is prepared, in which CdCO3 is obtained by precipitation method (Supplementary Figs. S50 and 51). Its FEurea and Jurea are measured to be 33.5% and 0.33 mA cm–2 at the optimal applied potential (−0.1 V vs. RHE), which are lower than those of Ag0.07/CdCO3 reconstructed from the Ag0.07/CdO catalyst (Supplementary Fig. S50b, c). However, its FEurea can still reach over 30%, proving that CdCO3 is the main catalytic component derived from CdO. XPS results (Supplementary Fig. S50d–f) show that only lattice oxygen (531.2 eV) is observed in Ag0.07/CdCO3-PM, while in situ reconstructed Ag0.07/CdCO3 exhibits dissociated molecular oxygen adsorbed on oxygen vacancies (534.3 eV)42. Therefore, it can be inferred that in situ reconstructed Ag0.07/CdCO3 with vacancies would promote C-N coupling.

To further understand the structural evolution mechanism of Ag0.07/CdO catalyst during co-reduction, operando XAS spectroscopy are performed. As shown in Fig. 3a, the relative absorption edge positions in the Cd K-edge XANES shows a positive shift as the applied potential decreases, suggesting the gradual structural evolution of CdO towards CdCO343. Additionally, although the k3-weighted Fourier transform of Cd K-edge EXAFS analysis shows the Cd-Cd and Cd-O bonds always exist during reaction (Fig. 3b), the average Cd-Cd and Cd-O coordination numbers show a decrease in the coordination number of the Cd-O bond from 6 to 5.6, while the coordination number of the Cd-Cd bond decreased from 12 to 6.1 (Supplementary Figs. S5255 and Supplementary Table S3), further proving that CdO gradually evolved into CdCO3 during the reduction process. Moreover, the coordination number (5.6) of the Cd-O bond for the reconstructed Ag0.07/CdCO3 catalyst is lower than the theoretical coordination number of CdCO3 (6.0), indicating the possible presence of oxygen vacancies in the in situ reconstructed CdCO3, which is consistent with XPS. These defects may promote CO2 adsorption and activation on Cd sites11. In addition, the relative absorption edge positions in the Ag K-edge XANES for Ag0.07/CdO after reaction shifts slightly negatively towards the position of the Ag foil, indicating that the Ag component acquires electrons during the reduction process, which is consistent with the XPS results (Supplementary Fig. S56). While FT-EXAFS of Ag0.07/CdO after reaction exhibits a separate Ag-Ag bond and with no significant change in coordination number before and after co-reduction (Supplementary Figs. S5759 and Supplementary Table S4). The above characterization results indicate that Ag0.07/CdO reconstructs into Ag0.07/CdCO3 with oxygen vacancies during the CO2 and NO3 co-reduction. The CdCO3 with oxygen vacancies would provide a suitable chemical environment for strong binding with CO2 molecules through the combined action of Cd, C, and O atoms and further generate *CO intermediates44. In addition, the Ag component that accumulates electrons during reduction may form local electron-rich regions that attract the adsorption of electrophilic intermediates such as *NO220. Therefore, in situ reconstructed Ag0.07/CdCO3 with oxygen vacancies would provide tandem dual sites for the adsorption of C-containing and N-containing intermediates and further facilitates C-N coupling to form urea.

Fig. 3: Mechanism study.
Fig. 3: Mechanism study.The alternative text for this image may have been generated using AI.
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a Operando Cd K-edge XANES spectra (The inset shows an enlarged view of the shaded region) and b Fourier transform of k3-weighted Cd K-edge EXAFS spectra for the r space at various potentials (The shaded region highlights the evolving trends in Cd-Cd bonding and coordination-environment). c In situ Raman spectroscopy for Ag0.07/CdO. Operando DRIFTS for d Ag0.07/CdO, e CdO and f Ag. g Three-dimensional operando DRIFTS for Ag0.07/CdO.

To verify the above assumptions, in situ Raman spectroscopy is used to monitor the reaction intermediates on Ag0.07/CdO, Ag and CdO during reduction (Fig. 3c and Supplementary Fig. S60a, b). Characteristic Raman peaks of major species NO3 (1048 cm–1) and carbon paper (1380 and 1600 cm−1) could be observed at open circuit potential (OCP)14,45. For Ag0.07/CdO catalyst, new peaks appear at 1189, 1250, 1550 and 2055 cm–1 due to chelating nitrito (NO2), nitroxyl (ν (N=O)) and *CO vibration as the applied potential decreases46,47, indicating that the catalyst effectively activates NO3 and CO2. It is worth noting that Raman characteristic peak at 1016 cm–1 is the symmetrical stretching vibration of the C-N group (νs (C-N))37,46, confirming the coupling of C-N. Compared to Ag0.07/CdO, pure Ag shows stronger characteristic peaks belonging to chelating nitrito and nitroxyl, while there is no obvious *CO vibration peak, indicating that Ag only facilitates the activation of NO3 to N-containing intermediates under these potentials. On the contrary, the weak vibrational peak of *CO is exhibited on CdO when it transforms into CdCO3 at −0.1 V vs. RHE (Supplementary Fig. S60b), while Raman peaks belonging to transition state N-containing species are almost undetectable. The above comparison results indicate that when Ag0.07/CdO catalyst is applied for co-electrolysis of CO2 and NO3, the Ag component tends to adsorb NO3 and activate it to transition state N-containing intermediates such as *NO2, *NO, etc., while CdCO3 species with oxygen vacancies reconstructed from CdO adsorbs CO2 to produce *CO intermediates. Conveniently, N-containing intermediates are further coupled with adsorbed *CO to efficiently produce urea. In situ Raman spectroscopy further shows the dynamic evolution of catalyst structure. In Supplementary Fig. S60c, d, Raman peaks of CdO (960 cm–1) could be observed at OCP for CdO and Ag0.07/CdO catalysts. As the applied potential shifts negatively, the Ag0.07/CdO catalyst exhibits a significant CdCO3 (1086 cm–1)48,49,50 vibration peak at more positive potential (from −0.05 V vs. RHE) compared with CdO catalyst (−0.1 V vs. RHE), indicating that the presence of Ag may promote the formation of CdCO3. The possible reason for the facilitated non-faradic reconstruction of CdO with the presence of Ag is the enrichment of local CO32– during the reduction process (Supplementary Fig. S61). Since Ag/CdO demonstrates more obvious current for the reduction of NO3 and CO2 compared with CdO, more local protons would be consumed during the reaction, resulting in the quick enrichment of surface CO32– and the promoted formation of CdCO3 at higher potential.

In order to further reveal the urea formation mechanism on Ag0.07/CdO, operando diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) is conducted during urea synthesis. The infrared signals of Ag0.07/CdO, Ag and CdO catalysts are collected from 1000 to 2200 cm–1 from −0.05 to −0.25 V vs. RHE (Fig. 3d–g). For Ag0.07/CdO, a vibrational peak located at ~1210 to 1250 and 1516 cm–1 are assigned to *NO2 and *NH, respectively, and the two bands at around 1150 and 1623 cm−1 could be assigned to the wagging and bending modes of –NH2, suggesting that NO3 is efficiently activated23,51. Additionally, the vibrational peaks located at 1317 and 1395 cm–1 correspond to *CO and νs (OCO). Specially, the band at around 1476 cm–1 is ascribed to the νs (C-N) and the stretching mode of C=O is also observed at ~1680 cm−1, validating the formation of urea14. However, the peak of N-containing intermediates on CdO is quite weak. While pure Ag mainly exhibits stronger vibrational peaks belonging to N-containing intermediates (*NO2, *NH, *NH2, *NH3) and the peak intensity of C-containing intermediates is weaker compared to Ag0.07/CdO. This is consistent with the experimental results of high FENO2− and FENH3 on the Ag catalyst. Therefore, it can be fully assumed that Ag0.07/CdO catalyst exhibits good urea synthesis performance due to the abundant N-containing and C-containing intermediates provided by the Ag and in situ reconstructed CdCO3, creating sufficient collision opportunities for C-N coupling at a low overpotential.

Since the N-containing intermediates are quite complex, different N sources are added to the electrolyte for electrolysis to better identify the specific pathway of C-N coupling during urea synthesis. Supplementary Fig. S62 shows that FEurea is 28.7% at −0.1 V vs. RHE when the N source is NO2, while FEurea decreases to 5.4% when replacing with NH2OH, and almost no urea generation is found in the addition of N2H4·H2O. This alteration elucidates that *NO2 may serve as the key N-containing intermediate for C-N coupling with *CO and subsequently generate urea. However, although NO2 as an N source may provide some *NO2 for C-N coupling, the enhanced generation of NH3 reduces its selectivity of urea (Supplementary Figs. S63 and 64). In addition, CO is also used to replace CO2 for urea electrosynthesis in the presence of NO3. As shown in Supplementary Fig. S65, when the C source is replaced with CO, the FEurea reaches 55.6% and the partial current density of urea increases to 1.33 mA cm–2 (CO2 as C source: 0.59 mA cm–2) at −0.1 V in H-cell, indicating that that *CO is the key intermediate for C-N coupling. Therefore, we further conclude that the electrosynthesis of urea from NO3 and CO2 may require the construction of binary active sites that can effectively activate NO3 and CO2 simultaneously to provide sufficient *NO2 and *CO intermediates.

Although the difficulty of simulating precise materials under catalytic conditions, DFT calculations are carried out on Ag (111), CdCO3 (006), Ag (111)/CdCO3 (006) and Ag (111)/CdCO3 (006) with oxygen vacancies (Ag/CdCO3-Ov) surfaces to further reveal the detailed reaction pathways in urea electrosynthesis (Supplementary Data 1 and Supplementary Figs. S6673). As shown in Supplementary Figs. S66 and 67, the adsorption energies of NO3 are calculated on Ag, CdCO3, Ag/CdCO3-Ov-Ag site and Ag/CdCO3-Ov-Cd site, respectively. Ag and Ag/CdCO3-Ov-Ag site exhibit lower adsorption free energy (−1.02 eV and −1.08 eV, respectively) compared to CdCO3 and Ag/CdCO3-Ov-Cd site (−0.86 eV and −0.89 eV, respectively), implying that NO3 adsorbs more easily on Ag sites. In Fig. 4a, Ag exhibits lower free energy difference (−2.07 eV) compared to CdCO3 (−1.18 eV) for the conversion of NO3 to *NO2, indicating that the *NO2 intermediate is more easily generated at the Ag site compared to CdCO3 during the reduction of NO3 to *NO2. This is also consistent with the experimental results of Ag catalyst to produce NO2, and confirms the results of Raman and DRIFTS. Ag/CdCO3-Ov and Ag/CdCO3 exhibits favorable free energy differences (−1.92 and −1.85 eV, respectively) for the formation of *NO2 intermediates due to the presence of Ag, which would provide abundant N-containing intermediates for subsequent C-N coupling. In addition, the generation of *CO2 on CdCO3 seems to be spontaneous compared to Ag according to the calculated free energy difference, which means that CO2 is preferentially adsorbed on CdCO3. Specifically, it is worth emphasizing that the hydrogenation of *CO2 is the potential determining step and Ag/CdCO3-Ov (0.39 eV) reveals the lowest free energy difference compared to Ag/CdCO3 (0.49 eV), CdCO3 (1.19 eV) and Ag (1.35 eV), indicating that Ag0.07/CdCO3 with oxygen vacancies would promote the activation of CO2 and further facilitate the C-N coupling. Therefore, a lower overpotential is observed on Ag/CdCO3 in urea electrosynthesis. Subsequently, the *COOH is spontaneously reduced to *CO and C-N coupling occurs with the bonding of *NO2 and *CO intermediates. Additionally, the free energy difference of forming *CONO2 (−0.89 eV) on Ag/CdCO3 surface is beneficial for early C-N coupling compared with the free energy difference of *NO2 hydrogenation to *HNO2 (−0.54 eV) and *CO desorption to CO (0.49 eV) in Fig. 4b, which may explain the high selectivity of urea production. As shown in Fig. 4c, the occurrence of the first C-N coupling has an activation energy barrier on Ag/CdCO3 and Ag/CdCO3-Ov. However, Ag/CdCO3-Ov (0.561 eV) displays a lower activation energy barrier than Ag/CdCO3, which may accelerate the reaction. In addition, the activation energy barrier of C-N coupling is found to be further decreased (0.442 eV) under a higher *CO coverage (Supplementary Figs. S74 and 75), indicating that the reaction rate of C-N coupling is facilitated, which is consistent with the experimental results (Supplementary Fig. S65). These results theoretically demonstrate that the in situ reconstructed Ag/CdCO3 catalyst benefits the adsorption and coupling of N-containing and C-containing intermediates at low overpotentials and suppress the generation of by-products such as CO, NO2, etc.

Fig. 4: DFT calculations.
Fig. 4: DFT calculations.The alternative text for this image may have been generated using AI.
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a Free-energy diagram for urea production on Ag (111), CdCO3 (006), Ag (111)/CdCO3 (006) and Ag (111)/CdCO3 (006)-Ov. b Free-energy for *NO2 and *CO reaction paths. c The initial, transition, and final states during the *CONO2 formation of Ag/CdCO3 and Ag/CdCO3-Ov are presented.

Discussion

In summary, we synthesized an Ag/CdO heterostructured catalyst to promote the co-activation of CO2 and NO3 and achieved efficient and selective urea electrosynthesis at low overpotentials. The optimized Ag0.07/CdO catalyst displays a high urea yield rate of 111.6 ± 3.1 mmol gcat.–1 h–1 with a Faradaic efficiency of 50.0 ± 2.7% at a positive potential of −0.15 V vs. RHE in a flow cell, and can further achieve stable response (1000 h) with a competitive urea yield rate of 427.0 ± 30.2 mmol gcat.–1 h–1 at a current density of ~60 mA cm–2 in a two-electrode cell with optimized membrane and flow field architecture. Operando XAS, Raman and DRIFTS prove that the Ag component in the synthesized Ag/CdO catalyst not only promotes the reconstruction of CdO component into CdCO3 with oxygen vacancies, which can efficiently adsorb and activate CO2, but also attracts the electrophilic intermediate *NO2 during the reduction process. DFT calculations indicate that the in situ reconstructed Ag/CdCO3 catalyst benefits the adsorption and coupling of N-containing and C-containing intermediates at low overpotential and suppresses the generation of by-products such as CO and NO2. We believe this work can provide guidance for the design of efficient urea electrosynthesis catalysts via CO2 and inorganic nitrogen sources co-reduction and help enclose the cycle of carbon and nitrogen economy.

Methods

Materials

Cadmium acetate (Cd(CH3COO)2·2H2O, Innochem, 99.9%), Silver nitrate (AgNO3, Chengdu Kelong Co. Ltd., ≥99.8%), Potassium nitrate (KNO3, Aladdin, 99.0%), Potassium nitrite (KNO2, Innochem, 97%), Sodium nitrofenicyanide dihydrate (C5H4FeN6Na2O3, Macklin, 99.0%), Sulfanilic acid (C6H7NO3S, Innochem, 99%), N-(1-naphthyl) ethylenediamine dihydrochloride (C12H14N2·2HCl, Macklin, 98%), Iron chloride anhydrous (FeCl3, Sinopharm chemical reagent Co. Ltd., ≥97.0%), Sodium citrate (C6H5Na3O7, Sinopharm chemical reagent Co. Ltd., 98%), Thiosemicarbazide (CH5N3S, Macklin, 98.5%), Diacetylmonoxime (C4H7NO2, Macklin, 99%), Salicylic acid (C7H6O3, Tianjin Dengfeng Chemical Reagent Co. Ltd., 99.5%), Phosphoric acid (H3PO4, Sinopharm chemical reagent Co. Ltd., AR), Sodium hypochlorite (NaClO, Macklin, active chlorine ≥30%), 15N-Potassium nitrate (K15NO3, Yuanye, abundance 99atom%), Hydroxylamine (NH2OH, Shanghai Titan Scientific Co. Ltd., 50 wt.% in water), Sodium hydroxide (NaOH, Innochem, 99%), Urease (Yuanye, 1.1U/mg), potassium bicarbonate (KHCO3, Aladdin, 99.5%), hydrazine hydrate (N2H4·H2O, Sinopharm Group, 85%). Ethanol (AR) is used without any further purification and the Ultra-pure water (18.25 MΩ cm−1) used in all experiments was prepared by ultra-pure purification system (Ulupure).

Synthesis of Agx/CdO, Ag and CdO

For Agx/CdO, 80 mg Cd(CH3COO)2·2H2O and different quantities of AgNO3 were added to 25 mL of water in a glass beaker and the solution is continuously stirred. When the solution became clear, 0.1 M NaOH (10 mL) was added to the solution. After stirring for 10 min, the solution was allowed to stand for 12 h. Then it was washed with alcohol and water and centrifuged. The obtained product was dried in a vacuum oven at 100 °C. Finally, high-temperature calcination (550 °C, 2 h) is carried out. And during the synthesis process of pure Ag and CdO, Cd(CH3COO)2·2H2O and AgNO3 are not added, respectively, and other conditions are the same as Agx/CdO.

Preparation of working electrodes

The as-prepared catalysts were deposited on the carbon black support for the co-reduction of CO2 and NO3. The electrocatalysts (1 mg) and Vulcan XC-72 carbon powder (4 mg) were dispersed in a mixture of 500 μL isopropyl alcohol and 20 μL of 5% Nafion solution. Ultrasonic treatment of the above mixture for 60 min to obtain a uniform suspended ink. The ink was evenly dripped on both sides of carbon paper (about 1.0 cm × 1.0 cm), and vacuum dried at 60 °C for 1 h to obtain a working electrode. The effective catalyst loading is approximately 0.1 mg.

Characterizations

The morphologies and compositional elements were confirmed by a Field emission scanning electron microscope (FSEM) using the model Sirion 200. Transmission electron microscopy (TEM) was carried out on a Tecnai G2 transmission electron microscope (FEI, USA). High-resolution transmission electron microscope (HR-TEM) characterizations were obtained via a Talos F200X transmission electron microscope (FEI, Netherlands). X-ray diffraction (XRD) patterns were obtained via a DMAX-2400X-ray diffractometer (Rigaku, Japan). Raman measurements were performed using a LabRAM HR Evolution (Horiba Jobin Yvon, France) with 532 nm excitation wavelength. X-ray photoelectron spectroscopy (XPS) was carried out with an Axis-Ultra DLD-600W X-ray photoelectron spectrometer (Shimazu, Japan). The 1H NMR is performed on a Bruker AscendTM 600 MHz. Operando diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) was performed using a Nicolet iS50R spectrometer (Thermo Scientific, USA). X-ray absorption spectroscopy (XAS) was determined by the Shanghai Synchrotron Radiation Facility (SSRF) at the beamline BL11B1. X-ray fluorescence (XRF) patterns were obtained from EAGLE III operated at 40 kV. A UV spectrophotometer with the model TU-1810 was used to obtain absorbance.

Urea electrosynthesis testing in an H-type cell

Urea electrosynthesis tests were performed in a three-electrode two-compartment H-cell (The single-chamber volume is 50 mL) controlled by an electrochemical workstation (CHI660e, Chenhua). Two chambers were separated by a proton exchange membrane (Nafion®212, Dupont, 50.8 μm). The Nafion®212 membrane was first immersed in deionized water (18.25 MΩ cm–1) at 60 ~ 80 °C for 30 min, then transferred to a 3–5 wt.% H2SO₄ solution and soaked at 70 ~ 80 °C for an additional 30 min. Subsequently, the membrane was boiled in deionized water at 80 °C for 30 min, and finally stored under refrigeration at 4 ~ 8 °C. The working electrode (WE) was a catalyst-loaded carbon paper. An Ag/AgCl electrode (saturated KCl solution) and a graphite rod were used as the reference (RE) and counter electrodes (CE). The CO2-saturated 0.1 M KHCO3 + 0.05 M KNO3 solution (40 mL, pH = 6.9 ± 0.1) was applied as the electrolyte and the flow rate of CO2 during test was maintained at 20 mL/min by a gas flow meter (AST10-DBC, Asert Instruments (Beijing) Co. Ltd). The electrolyte was prepared by dissolving 10.01 g of KHCO3 and 5.05 g of KNO3 together, followed by dilution to 1000 mL in a volumetric flask and subsequent storage. Before the test, CO2 gas was pumped into the cathode chamber electrolyte for 30 min, discharging the soluble oxygen in the solution and obtaining the CO2-saturated solution. During the test, the cathode chamber electrolyte was stirred at 600 rpm. All the electrode potentials were measured against Ag/AgCl electrode and converted to the reversible hydrogen electrode (RHE) by ERHE = EAg/AgCl + 0.197 + 0.059 × pH, where pH is the average pH value of electrolyte. All electrochemical measurements in H-cell did not have any iR compensation. And ECSA is estimated via ECSA = Cdl/Cs, Where the double-layer capacitance (Cdl) of the catalysts was estimated by measuring the capacitive current density associated with different scan rates via CV curves in a non-faradaic region in CO2-saturated 0.1 M KHCO3 + 0.05 M KNO3 solution and the value was determined to be half that of the linear fitting slope, and Cs is the specific capacitance of a flat surface with 1 cm2 of real surface area.

Urea electrosynthesis testing in a gas diffusion flow cell

Three electrode system: Urea electrosynthesis tests were performed in a gas diffusion flow cell consisting of a gas-diffusion layer (TGP-H-060, 20% PTFE, TORAY) deposited with Ag0.07/CdO (1.0 cm × 1.0 cm) as the working electrode, nickel foam (1 mm, 1.0 cm × 1.0 cm) as the counter electrode, and Ag/AgCl (saturated KCl solution) as the reference electrode. 1.0 M KOH + 0.05 M KNO3 solution (200 mL, pH = 14.0 ± 0.1) was used as the electrolyte. The electrolyte was prepared by dissolving 56.1 g of KOH and 5.05 g of KNO3 together, followed by dilution to 1000 mL in a volumetric flask and subsequent storage. The electrolyte was maintained at 64 mL/min during electrolysis. Preparation of gas diffusion electrode: The electrocatalysts (1 mg) and Vulcan XC-72 carbon powder (4 mg) were dispersed in a mixture of 500 μL isopropyl alcohol and 20 μL of 5 wt% Nafion solution. Ultrasonic treatment of the above mixture for 60 min to obtain a uniform suspended ink. The ink was evenly dripped on one side of the gas-diffusion layer (1.0 cm × 1.0 cm) to obtain a gas-diffusion electrode. The effective catalyst loading is approximately 0.1 mg. Cathode and anode channels were separated by proton exchange membrane (Nafion®212, Dupont, 50.8 μm). In the gas channel, the flow rate of CO2 during the test was maintained at 20 mL/min. The anodic process is typically the electrochemical oxidation of water to form oxygen in alkaline (i.e., the electrochemical oxygen evolution reaction, OER, 4OH → O2 + 2H2O + 4e) and the potential of the nickel foam counter electrode is about 1.65 V vs. RHE during operation. All electrochemical measurements in the flow cell did not have any iR compensation.

Two-electrode cell (serpentine flow field with thin electrolyte layer of 1 ~ 2 mm): a gas-diffusion layer (TGP-H-060, 20% PTFE, TORAY) deposited with Ag0.07/CdO (1.0 cm × 2.0 cm) was as the working electrode, NiFe-layered double hydroxide catalyst (1.0 cm × 2.0 cm) was as the counter electrode, 1.0 M KOH + 0.05 M KNO3 solution (250 mL) was used as the electrolyte and the effective catalyst loading is approximately 0.2 mg cm–2. Cathode and anode channels were separated by anion-exchange membrane (Sustainion grade RT, 50 μm) and the Nafion binder was replaced with PiperION. The Sustainion grade RT membrane was immersed in a 1 M KOH aqueous solution at 20 ~ 30 °C for at least 24 h, thoroughly rinsed with deionized water, and subsequently prepared for use.

Operando characterizations

Operando Raman spectroscopy was performed on a Renishaw inVia Raman microscope system with in situ Raman gas diffusion H-type electrolytic cell (Gaossunoin, China). The wavelength of the excitation source of the laser is 532 nm (50%). A 50 × long focal length distance objective (Leica) was used for focus. The graphite rod and Ag/AgCl electrode (saturated KCl solution) as the counter and reference electrodes, respectively. The spectrum was collected after 10 min of stable operation for each potential.

Operando diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS): during the testing process, an Ag/AgCl electrode and a carbon rod were used as the reference electrode and the counter electrode, respectively. A CO2-saturated electrolyte containing 0.1 M KHCO3 and 0.05 M KNO3 was used for co-electrolysis of CO2 and NO3. The background spectrum was obtained at the open circuit potential before each measurement. Then, absorption spectra at different potentials with a spectral resolution of 4 cm–1 were collected. In the spectrum, a negative peak indicates the production or increase of a substance or functional group.

Operando X-ray absorption structure (XAS) spectroscopy: the operando Cd K-edge and Ag K-edge XAS spectroscopy were collected on the beamline BL11B1 of the Shanghai Synchrotron Radiation Facility (SSRF). The Ag foil is used to calibrate the energy. During the operando XAS measurements, the method of constant potential is applied. Operando XAS spectroscopy signals were collected in fluorescence mode using an in situ electrochemical cell with polyimide film windows (XAFS-2, Gaossunoin, China). The data reductions of the experimental spectra to normalized XANES and Fourier-transformed radial distribution functions (RDFs) were performed through the standard XAS procedure.

Product analysis

Gaseous products analysis: a gas chromatograph (GC, Shimadzu GC-2014) was applied to quantitative analysis of gaseous products.

The Faraday efficiency of the product is calculated based on the gas chromatographic peak area, and the formula is as follows:

$${{FE}}_{{gas}}=\frac{{{{C}}}_{{product}}\times {{V}}\times 2{{F}}{\rho }_{0}/{{RT}}}{{i}_{{total}}}\times 100\%$$
(1)

where itotal is the current density obtained by direct measurement at this potential, Cproduct stands for the volume density of gas products based on GC calibration, V is the flow rate of CO2, F is the Faraday constant (96,485 C/mol), ρo is the atmospheric pressure (1.013 bar), and T is the test temperature (298 K), R is the ideal gas constant (8.314 J mol/K).

Urea product analysis: (1) Diacetylmonoxime-thiosemicarbazide (DAMO-TSC) method52. For H-cell, 1 mL electrolyte was added into 2 mL acid-ferric solution (10 mL phosphoric acid, 30 mL sulfuric acid, 60 mL deionized water and 10 mg ferric chloride). And then 1 mL DAMO-TSC solution (0.5 g DAMO and 10 mg TSC were dissolved in 100 mL deionized water) was added into the mixture. After that, the solution was heated to 100 °C and maintained for 20 min. UV-Vis absorption spectrum was performed after it was cooled to room temperature, and the absorbance at 525 nm was acquired. A series of standard urea solutions was used to obtain working curves for urea determination. (2) Urease decomposition method11. 0.01 g EDTA-2Na and 0.049 g K2HPO4 were dissolved in urease solution (10 mL, 5 mg mL–1). Then, 2.0 mL electrolyte was added into the above solution (0.2 mL). The final solution was left to stand for 40 min at 37 °C. The produced NH3 was quantified with the indophenol blue method. For the above two methods of flow cell, neutralize the pH of 1 mL of electrolyte with 1 mL of 0.5 M H2SO4, and then take 1 mL of the above solution from this mixed solution and perform the same operation as H-cell. It is worth noting that this is equivalent to diluting the solution twice, so the actual concentration of urea in the electrolyte is twice that obtained from the spectrum.

NH3 product analysis: Indophenol blue method53,54. Typically, 2 mL of the electrolyte after electrolysis was mixed with 2 mL of a 1 M NaOH solution containing 5 wt% salicylic acid and 5 wt% sodium citrate. Subsequently, 1 mL of 0.05 M NaClO and 0.2 mL of 1 wt% sodium nitroferrocyanide solution were added. The mixture was then left to stand at room temperature for 2 h. Afterward, the absorbance at 655 nm was measured using UV spectrophotometry. Standard curves of concentration versus absorbance were prepared using ammonium chloride solutions of varying concentrations, with each solution containing the same electrolyte concentration as that used in the test samples.

NO2 product analysis6,14: a total of 0.5 g of sulfonic acid was dissolved in a mixture of 90 mL of deionized water and 5 mL of acetic acid, followed by the addition of 5 mg of naphthalene ethylenediamine hydrochloride. The final volume was adjusted to 100 mL. This solution was used as the colorimetric reagent. Subsequently, 1 mL of the electrolyte after electrolysis was mixed with 4 mL of the colorimetric reagent and kept in a dark environment for 15 min. The absorbance at 540 nm was then measured using a UV spectrophotometer.

The FEs for urea, NH3, and NO2 were calculated according to formulas:

$${{FE}}_{{urea}}=\frac{16\times {{F}}\times {{C}}\times {{V}}}{60.06\times {{Q}}}\times 100\%$$
(2)
$${{FE}}_{{NH}3}=\frac{8\times {{F}}\times {{C}}\times {{V}}}{17\times {{Q}}}\times 100\%$$
(3)
$${{FE}}_{{NO}2^{-}}=\frac{2\times {{F}}\times {{C}}\times {{V}}}{46\times {{Q}}}\times 100\%$$
(4)

where C is the concentration of generated urea (µg/mL), V is the volume of electrolyte and Q is the total charge passed through the working electrode.

1H NMR, HPLC-MS and IC characterizations

1H NMR:

DMSO-d6 as deuterium reagent: the 1H NMR sample was prepared by mixing 500 μL of post-reaction solution with 200 μL DMSO-d6 and 50 μL of maleic acid solution (200 ppm) (1024 scans).

D2O as deuterium reagent: 500 μL electrolyte mixed with 100 μL DMSO (0.05 μL/mL) and then dissolved in 150 μL D2O solution, and DMSO was used as the internal standard solution.

HPLC-MS: HPLC-MS (Thermo Scientific Q Exactive) spectroscopy achieves the quantification of urea. A 5 μm ZORBAX SB-AQ column (150 × 4.6 mm, Agilent) suitable for increasing the retention value of polar compounds is performed. The corresponding mobile phase, flow rate, detected wavelength and ion source are acetonitrile-0.1% formic acid aqueous solution (1:99), 0.300 mL min−1, 250 nm, and ESI + MS, respectively.

IC: IC data for ammonia, nitrate, and nitrite are obtained on an ion chromatograph model 881 Compact IC pro. In IC of anion test, the column type and eluent composition are prepared using Metrosep A Supp 5-250/4.0 and 3.2 mM Na2CO3/1.0 mM NaHCO3, respectively, and the corresponding flow rate is 0.700 mL min−1. In IC of cation test, the eluent composition and flow rate are 2.0 mM HNO3 and 0.900 mL min−1, respectively.

Computational details

DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP)55,56. Exchange-correlation effects were treated within the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional57,58. Core-valence interactions were described with the projector augmented-wave (PAW) method59. A plane-wave energy cutoff of 480 eV was used, and Brillouin-zone integration employed a 3 × 3 × 1 Monkhorst-Pack k-point mesh60. A vacuum space of 15 Å was introduced normal to the surface to eliminate periodic interactions. Structures were relaxed to 1.0 × 10–4 eV in energy and 0.02 eV Å–1 in forces. When optimizing charged models like NO3 using VASP, we set the model with a negative charge based on the total number of atoms and the corresponding number of valence electrons. The computational hydrogen electrode (CHE) model was used to calculate the Gibbs free energy change (ΔG) of reaction step:

$$\Delta G=\Delta E+\Delta {\mathrm{ZPE}}-T\Delta S$$
(5)

where ΔE is the electronic energy difference directly obtained from DFT calculations, ΔZPE is the zero-point energy difference, T is the room temperature (298.15 K) and ΔS is the entropy change. ZPE could be obtained after frequency calculation by ref. 61:

$${{\rm{ZPE}}}=\frac{1}{2}\,\sum {hv}$$
(6)

And the TS values of adsorbed species are calculated according to the vibrational frequencies62:

$${{\rm{TS}}}={k}_{B}T\left[{\sum }_{k}{{\rm{ln}}}\left(\frac{1}{1-{e}^{-{hv}/{k}_{B}T}}\right)+{\sum }_{k}\frac{{hv}}{{k}_{B}T}\frac{1}{({e}^{{hv}/{k}_{B}T}-1)}+1\,\right]$$
(7)

where kB is the Boltzmann constant, h is the Planck constant and v stands for vibrational frequencies.