Unveiling real active site for photocatalytic H2O2 evolution: A combined experimental and DFT-TDDFT study

Photocatalyst with multiple modication sites (MSs) exhibited better performance than single site in photocatalytic H 2 O 2 evolution, while the corresponding reaction mechanism is more complicated. However, neither experiment nor density functional theory (DFT) based on ground state wavefunction cannot precisely conrm the role of each site in photocatalyst with multiple MSs. Here, we propose a universal method that exibly combines experiments, DFT and time-dependent DFT (TDDFT) calculations to reveal the photocatalytic mechanism and active site of nitrogen deciency g-C 3 N 4 (NDCN) containing two MSs (bicoordinated nitrogen vacancy and cyano group). Characterization techniques and control experiments prove that generation of H 2 O 2 on NDCN is a two-step single electron transfer process, and NDCN exhibits enhanced charge separation eciency and higher selectivity for two-electron oxygen reduction. DFT-TDDFT calculations further indicate that nitrogen vacancy is the real catalytic site for activating O 2 , which promotes O 2 adsorption and continuously formation of •O 2− , thus inhibiting electron-hole recombination. Rotating (RDE) measurements. The measurements were performed on a Model workstation using an Ag/AgCl electrode and a Pt wire electrode as the reference and counter electrode, respectively. 48 The linear sweep voltammogram (LSV) were obtained in an O 2 -saturated 0.1 M phosphate buffer solution (pH = 7). The average number of electrons (n) involved in the overall O 2 reduction was determined by the slopes of the Koutecky-Levich plots with the following equation:


Introduction
Hydrogen peroxide (H 2 O 2 ), an liquid resource, is useful for water puri cation, antibacterial, pulp bleaching and fuel cells 1,2 . The most commonly used anthraquinone method for preparing H 2 O 2 has the shortcomings of high cost and emission of toxic by-products 3 . In contrast, photocatalytic technology provides a new opportunity for H 2 O 2 preparation in a low-cost and environmentally friendly way.
Photocatalytic H 2 O 2 production through the O 2 two-electron reduction process (O 2 + 2H + + 2e − → H 2 O 2 ) has attracted wide attention 4,5 . With the continuous efforts of researchers, a large number of photocatalysts for H 2 O 2 evolution have been developed [6][7][8][9][10][11][12][13][14][15][16][17][18] . Among them, photocatalysts with multiple modi cation sites (MSs) exhibited more superior performance as compared to their catalytically inaccessible counterparts of single sites materials [14][15][16][17] . Nevertheless, it is worth noting that the same kind of MS exhibited diametrically opposite effects when the other MSs are different in the same primitive material [15][16][17]19 . For instance, Shiraishi et al. reported that amino group reduced the selectivity of H 2 O 2 in mesoporous graphitic carbon nitride (CN) 19 . But in the CN modulated by carbon vacancies, the amino group was the active site that signi cantly enhanced the H 2 O 2 production 17 . Besides, Zhu et al. reported that the cyano group acted as an electron acceptor to promote the photocatalytic H 2 O 2 evolution under the synergistic effect of nitrogen vacancy 16 . However, Xie et al. proposed that in the defect CN containing three kinds of MSs, the cyano group has no effect on the formation of H 2 O 2 15 . Different preparation methods led to different coordination environments at the same kind of MS. In addition, there are also some differences between analysis methods used in the reports mentioned above, which also be an pivotal reason for the opposite effect of the same MS. Therefore, the research method of investigating the role of MS should be emphasized.
To reveal the true reaction mechanism of photocatalytic H 2 O 2 evolution promoted by photocatalysts with multiple MSs, experimental scholars have made many efforts. In order to determine the role of each site in a material with three MSs (CKCN-0.03), Xie et al. rst prepared a material, CN (V1), containing only two MSs in CKCN-0.03. Then CN(V1 + V2) was prepared by introducing the third MS into CN(V1), which also has three MSs in CKCN-0.03 with the same content. By comparing the properties of CKCN-0.03, CN (V1) and CN(V1 + V2) experimentally, the speci c role of each site was con rmed, respectively 15 . Similarly, Dong and his co-workers also used the controlled variable method to study the role of each MS experimentally 17 . Regrettably, this method has inherent limitations: (1) More materials need to be prepared and characterized to ensure the same MS content in the materials used for comparison, which greatly increases the cost and research time. (2) Compared with the simultaneous introduction of multiple MSs into the material, stepwise modi cation must change original preparation method, which could not guarantee that other important factors affecting the catalytic effect are completely unchanged. lowest unoccupied molecular orbital (LUMO) 22 . However, electronic excitation process is a transition from the ground state to excited state, rather than an occupied orbital to a non-occupied orbital 24,25 . Excited state is formed by linear combinations of different orbital transitions 24 . In order to more accurately explore the complex light reaction process, time-dependent DFT (TDDFT) calculations need to be performed. Unfortunately, only a few reports focusing on experimental research have used TDDFT calculations 5,19,26 . The huge potential of multiple MSs in the photocatalytic H 2 O 2 evolution, as well as the current challenges in revealing the in-depth photocatalytic mechanism, provide us with a strong motivation to explore a universal method to uncover the speci c reaction mechanism, role of each MS, and essential reason for O 2 activation.
In this work, we use the nitrogen de ciency CN (NDCN) containing two MSs as a model photocatalyst, and combine the experimental method with DFT-TDDFT calculation to reveal the mechanism behind the enhanced photocatalytic activity. The structural information of photocatalyst, separation e ciency of light-excited charge, as well as the active specie and reaction pathway are studied in detail experimentally. Based on the characterization results, accurate models are constructed and use for simulation. The DFT-TDDFT calculations verify the real active site and its speci c catalytic role, and reveal the essential reason for the effectively charge separation of and generation of active specie.

Results
Discussion of experimental characterization. NDCN was successfully prepared by adding NaOH to the precursor of CN (see Methods for details).The chemical structure of CN and NDCN were rst characterized by X-ray diffraction (XRD) patterns. The XRD pattern of CN (Fig. 1a, top line) showed two distinct diffraction peaks at 13.0° and 27.4°, which can be assigned to the in-plane packed heptazine units (100) and interfacial stacking (002) of graphitic CN, respectively 27 . It can be observed that the two characteristic peaks of NDCN were weakened and broadened, implying the loss of ordered structures within the framework to some extent. The Fourier transform infrared spectroscopy (FTIR) spectrum for CN ( Fig. 1b) showed that the peak at 810 cm − 1 can be assigned to the out-of-plane bending mode of heptazine rings, and the peaks in the range of 900-1800 cm − 1 refers to N-C = N heterorings in CN framework. Multiple broad peaks located in the region of 3000-3500 cm − 1 can be attributed to N-H stretching vibrations. After adding NaOH, the peak at 2156 cm − 1 typical for the cyano groups (-C ≡ N) was emerged 28 . Meanwhile, the intensity of the N-H stretching peaks was signi cantly reduced. The results indicate that the addition of NaOH leads to the decrease of N-H groups and introduction of cyano groups.
Organic elemental analysis (OEA) was used to con rm the changes in bulk elemental composition of the samples. The N/C atomic ratio of NDCN was slightly reduced in compartion to that of CN ( Supplementary  Fig. 2). Next, the changes of surface element composition were further studied by XPS. Compared with that of bulk, the addition of NaOH made the surface N/C atomic ratio decreased more signi cantly ( Supplementary Fig. 2). It is worth noting that the introduction of cyano groups and reduction of N-H groups does not cause the reduction of N elements. Therefore, this indicates that the treatment of NaOH resulted to the generation of surface N defects. Meanwhile, the O/C atomic ratio in NDCN increased ( Supplementary Fig. 1a), which may be attributed to the increase of oxygen-containing species adsorbed on the surface 29 . On the other hand, valence band (VB) XPS spectra ( Supplementary Fig. 1b) showed that the treatment of NaOH did not affect energy level position of VB. In addition, the morphology of NDCN had not changed signi cantly compared to that of CN ( Supplementary Fig. 3).
Narrow scan C1s and N1s XPS spectra further proved the introductions of cyano group and N defects. For the C1s XPS spectra (Fig. 1c), it contained three peaks of 287.89, 286.23, and 284.5 eV, representing N-C = N, C-NH x (x = 1, 2) and adventitious hydrocarbons, respectively. The corresponding peak of C-NH x of NDCN was higher than that of CN, which proves the generation of C ≡ N, because the cyano group has similar binding energy of C1s 30 . For the N1s XPS spectra (Fig. 1d), the intensity of bicoordinated nitrogen (N 2C ) in NDCN was reduced in comparison to that of CN. Combined with the decrease of N/C in XPS ( Supplementary Fig. 2), it can be inferred that the generation of nitrogen defect was caused by the absence of N atoms in N 2C . The intensity of tricoordinated (N 3C ) increased and the peak shifted to lower binding energy. This can be attributed to the introduction of C ≡ N groups, because their binding energy lies between the binding energy of N 3C and N 2C 30 . Based on the above characterization, we can conclude that after NaOH treatment, N 2C vacancies (NVs) were formed. Meanwhile, with the decrease of N-H groups, cyano groups were generated.
The optical properties of the samples were further characterized by DRS. Compared with CN, the absorption edge of NDCN has a signi cant red shift ( Supplementary Fig. 4a) and the band gap is reduced from 2.64 to 2.04 eV ( Supplementary Fig. 4b).
Combining the above results of the VB XPS, the narrowing of the band gap is due to the decrease of conduction band (CB) position, while the VB position remains unchanged.
Evaluation of photocatalytic performance. The photocatalytic performances of CN and NDCN were evaluated. Under the irradiation of visible light, the 60 min production of H 2 O 2 for NDCN was 476 µM (Supplementary Fig. 5a), which is 9.7 times higher than that of CN (47 µM) and better than many reported yields in recent years (Supplementary Table 1). In addition, after 5 cycle experiments, the photocatalytic performance did not decrease signi cantly ( Supplementary Fig. 6). Comparing the XRD patterns of samples before and after 5 cycles, there was no obvious difference ( Supplementary Fig. 7), indicating that NDCN has excellent stability in the photocatalytic H 2 O 2 production. Therefore, it is meaningful to investigate the reaction mechanism of photocatalytic H 2 O 2 production for NDCN.
The effects of defects on separation e ciency of photoexcited charge carriers were investigated.
Photoluminescence (PL) spectroscopy measurements were performed to examine the charge separation ability 31 of samples. As shown in Supplementary Fig. 5b, a intense PL signal was observed on CN, due to the serious recombinations of carriers. In contrast, the PL intensity of NDCN was weaker, indicating a signally suppressed electron-hole recombination. Supplementary Fig. 5c showed the transient photocurrent response curve of the samples, which is directly related to their charge separation ability.
Compared with CN, NDCN exhibited a larger photocurrent density, indicating that nitrogen defects can greatly accelerate the separation of photoexcited carriers 32 . The electrical conductivity and interfacial charge transfer capability of the samples were evaluated by electrochemical impedance spectroscopy (EIS). As shown in Supplementary Fig. 5d, the EIS slop of NDCN decreased signi cantly in compartion to that of CN, implying that NDCN has better electrical conductivity, which is conducive to effective charge separation and transfer in the photocatalytic process.
Experimental research on reaction mechanism. To understand the reaction mechanism of photocatalytic reaction, a series of control experiments and measurements were conducted. Figure 2a showed  33 . In the dark, the H 2 O 2 production was also 0 (blue curve in Fig. 2b), implying that light irradiation is a necessary condition for the catalytic reaction. In the absence of isopropanol (IPA), the yield of H 2 O 2 was signi cantly reduced (yellow curve in Fig. 2b Con rmation of the optimal model. First, the most stable and reasonable geometry was constructed and veri ed. Eleven possible models (M 1 -M 11 in Supplementary Fig. 9) were considered, and the most stable geometric structure of NDCN was selected by comparing their Gibbs free energy. As shown in Supplementary Fig. 10, model with the lowest Gibbs free energy is M 3 whose cyano group and NV are located at the edge of the two melon frameworks, respectively. The calculated FTIR spectrum for M 3 was similar to the experimentally measured spectrum (Fig. 3a), which again proved the rationality of M 3 .
Meanwhile, the structure of M 3 was also consistent with what Zhang et al. reported 21 . Thus, we will directly label the M 3 as NDCN for discussion below. In order to clearly describe each site of NDCN, the NDCN model was divided into three regions: NV, cyano, and primitive melon. The key atoms were numbered to clearly identify each site (Fig. 3b).
Con rmation of •O 2 − and active site. In order to initially con rm the possible O 2 activation sites, the calculated ultraviolet visible (UV-vis) spectrum and electron-hole distribution of each excited state were analyzed. The oscillator strength (f) in the UV-vis spectrum represents the transition probability of electrons from ground state to each excited state. The f of 0.01 is generally the critical point of transition 24 . Speci cally, if the f is lower than 0.01, the corresponding transition is generally considered to be forbidden, otherwise the transition can occur with a probability determined by f. For NDCN, the f of D 0 →D 1 , D 0 →D 2 , and D 0 →D 4 excitations were all greater than 0.01 (Fig. 4a), indicating that photogenerated e − can indeed be excited to the green regions of Fig. 4c1, 4c2 and 4c4, respectively, that is, these excitations are bright. The f of the D 0 →D 3 excitations was almost zero (Fig. 4a), implying that the excitation is dark. On the basis, the electron-hole distribution of each excited state was visualized. As shown in Fig. 4c, for the D 0 →D 1 , electrons were mainly concentrated at 1,4 site near the NV (NV 1,4 site).
In   Fig. 11b, 11c and Supplementary Table 2), but the corresponding oscillator strengths were too low ( Supplementary   Fig. 12b, 12c and Supplementary  (Fig. 4d). Although the f of D 0 →D 1 excitation was negligible, through the D 0 →D 2 excitation with f of 0.0428 (Fig. 4b) Con rmation of endoperoxide. In electronic excitation, the transition of electrons occurs rst, leading to a change in the electronic structure, which inevitably cause the evolution of geometry. In this section, the kinetic process of reaction system was investigated. Adding excess electrons to the photoreaction system for simulating light conditions is a common method 35,36 . First, two excess electrons were added to the O 2 @NDCN (NV site) and O 2 @NDCN (NV 1,4 site) models, respectively. After the structure was fully relaxed, O 2 in the O 2 @NDCN (NV site) and O 2 @NDCN (NV 1,4 site) models nally both stabilized on the NV site (inset of Fig. 4e and Supplementary Fig. 13a), and the bond length of O-O increased from 1.199 and 1.194 Å to 1.383 and 1.382 Å, respectively. Moreover, the density of states (DOS) of two models were almost the same. Meanwhile, the two β-LUMO orbitals that were originally degenerate in the isolated O 2 ( Supplementary Fig. 13b) were split, one of which became β-HOMO-1 and the other β-LUMO + 1 ( Fig. 4e and Supplementary Fig. 13a Fig. 5b-d). When the excess electrons in the two models increased to 3, the O-O bond length in the O 2 @NDCN (NV site) and O 2 @NDCN (NV 1,4 site) models further increases to 1.600 and 1.591 Å, respectively. Meanwhile, the two β-LUMO orbitals that were originally degenerate in the isolated O 2 all became occupied orbitals ( Supplementary Fig. 14), indicating that O 2 obtained two electrons, which became endoperoxide on the NDCN surface 38,39 .
For CN, the S 0 →S 3 and S 0 →S 4 excitations were con rmed to be bright by f (Supplementary Fig. 16a). The photogenerated electrons were mainly distributed in the 1,4 site of melon ( Supplementary Fig. 15a 3 , a 4 ), indicating that this position may be the O 2 activation site in CN, which is consistent with the previous report 4,19 . However, compared to the 2.08 eV excitation energy of the rst bright state of NDCN (596 nm for D 0 →D 1 in Fig. 4a), that of CN was as high as 3.7 eV (330 nm for S 0 →S 3 in Supplementary Fig. 16a), indicating that nitrogen defects can signi cantly expand the light response range of CN, in agreement with UV-vis DRS experimental results (Supplementary Fig. 4). When O 2 was adsorbed on the 1,4 site of CN, the S 0 →S 1 and S 0 →S 2 excitations (Supplementary Fig. 15b) that might allow O 2 to obtain photogenerated e − were all dark states ( Supplementary Fig. 12d). The photogenerated electrons could only be promoted to the S 0 →S 25 excitation with an energy as high as 3.8 eV (Supplementary Fig. 12d Investigation on the role of NV and cyano. The above discussion proved that after introducing cyano and NV, the NV and NV 1,4 site were both the real active sites for photocatalytic H 2 O 2 production. Although the cyano cannot e ciently activate O 2 , whether the high catalytic activity of NDCN is due to the synergy between cyano group and NV need to be veri ed. For this purpose, we constructed nitrogen de cient CN containing only NV (NDCN-NV) and cyano group (NDCN-cy), respectively. The results indicated that the excited energy in the same excitation (Fig. 4f), UV-vis spectrum (Fig. 4a vs. Supplementary Fig. 16b) and electron-hole distribution (Fig. 4c vs. Supplementary Fig. 17a) of NDCN and NDCN-NV were almost identical, while those of CN and NDCN-cy were very similar (Fig. 4f, Supplementary Fig. 16a vs. Supplementary Fig. 16c, and Supplementary Fig. 15a vs. Supplementary Fig. 18a). Subsequently, based on the electron-hole distribution of bright excited state, O 2 was adsorbed to the corresponding sites of NDCN-NV ( Supplementary Fig. 17b-d) and NDCN-cy ( Supplementary Fig. 18b, c), respectively. By observing the number of transferred electrons and f for each excitation (Supplementary Table 3 Table 4). It can be concluded that the introduction of NV is the only reason to promote high-e ciency production of H 2 O 2 , while cyano group do not make any contribution to this.
The essential reason for O 2 activation. In order to reveal the essential reason for O 2 activation, the electronic structures of each substance before and after adsorption were analyzed. To facilitate discussion of the role of each region and molecular orbitals (MO), NDCN was divided into three regions: cyano modi ed melon (melon-cy), NV modi ed melon (melon-NV) and primitive melon (melon-pri), as shown in Fig. 5. The key molecular orbitals (MO 1 -MO 10 in Fig. 5) were marked in DOS (Fig. 5a-c). It can be seen from Supplementary Table 1 that no matter where O 2 was adsorbed on NDCN, the transition orbital pairs corresponding to the excited state all belonged to β spin. Thus, the focus of analysis was on the β spin orbits. For NDCN, β-HOMO (MO 5 in Fig. 5) was concentrated on melon-NV, while β-LUMO (MO 4 in Fig. 5) was distributed on melon-cy and melon-pri, indicating that NV and cyano have impacts on the original optical response range of CN, which is consistent with previous report 21 . It is worth distinguishing that photogenerated e − could be excited to the cyano 1,4 site of NDCN (Fig. 4a, 4c 2 ), but they could not further effectively activate O 2 due to the negligible f mentioned above.
Before interacting with NDCN, the β-LUMO of O 2 is degenerate (MO 9 and MO 10 in Fig. 5).  (Fig. 5d). Note that MO 8 was an occupied orbital. The contribution of nonoccupied MO 9 and MO 10 to MO 8 indicated that the NV site was chemically adsorbed with O 2 in the ground state, making O 2 obtain a small amount of e − . Moreover, the adsorption energy of O 2 at NV site was − 0.12023 eV, which is the lowest value among the four sites of NDCN ( Supplementary Fig. 19a), indicating that the NV site could effectively adsorb O 2 , and thus is bene cial for subsequent O 2 reduction process. The spin density map ( Supplementary Fig. 19b) showed that there was unpaired β e-on melon-NV, so that the NV site could be acted as an electron donor to effectively adsorb O 2 in the ground state.
On the other hand, the key point of activating O 2 was the electron excitation from MO 8 to MO 7 (see "Hb -> Lb 97.4%" in Supplementary Table 2). The formation of MO 7 was also due to the interaction of MO 5 , MO 9 and MO 10 . The lower energy MO 5 contributed 6.24% to the MO 7 (Fig. 5d), effectively reducing the excitation energy for activating O 2 . O 2 @NDCN (NV 1,4 site) was basically the same as O 2 @NDCN (NV site). Since oxygen was located on the NV 1,4 site instead of the NV site, the corresponding adsorption energy increased slightly, but the value was still negative (Supplementary Fig. 19a). Moreover, the contribution of MO 5 to MO 7 was also slightly reduced (Fig. 5e), leading to a slight increase in the excitation energy of O 2 activation, but the NV 1,4 site could still effectively transfer photogenerated e − to O 2 . Combining the results of the control experiment in air (green curve in Fig. 2b), it can be concluded that when the saturated O 2 environment was replaced with air, the reason why NDCN could still maintain high catalytic activity was the strong adsorption capacity of NV for O 2 . On the other hand, cyano 1,4 and primitive 1,4 sites showed complete inertness for O 2 adsorption due to the positive adsorption energy ( Supplementary Fig. 19a). It is worth mentioning that in the simulation of structural optimization, even if O 2 was placed on top of the cyano group as the initial structure, O 2 eventually stabilized at the cyano 1,4 site, indicating that cyano cannot adsorb O 2 . This was due to its own quite stable C ≡ N. Moreover, since O 2 was not on melon-NV, MO 9 and MO 10 could not interact with MO 5 , but could only interact with higher energy orbitals corresponding to cyano 1,4 ( Supplementary Fig. 20a) or primitive 1,4 site ( Supplementary  Fig. 20b), making the corresponding excitation energy higher.
For materials containing more modi cation sites, there are more possible geometries and O 2 activation sites, resulting in an increase in the workload and complexity of simulation. But it should be emphasized that even so, the amount of work required is still far less than the currently widely used rst-principles molecular dynamics 43 and transition state calculations 44 . The more complex simulations resulting from more MSs can be completed accurately and quickly through high-throughput calculations 45 and machine learning 46 . Therefore, the proposed method is universal and extensible.
We proposed a universal method combining experiments and DFT-TDDFT calculations to investigate the in-depth reaction mechanism of NDCN containing two Data availability. The authors declare that the data supporting the ndings of this study are available within the paper and its supplementary information. Further information is also available from the corresponding authors upon reasonable request.

Declarations
Competing interests: The authors declare no competing interests.  Figure 1 Characterizations of photocatalysts. a XRD patterns and b FTIR spectra of CN and NDCN. c C1s and d N1s XPS spectra of CN and NDCN.

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