Design of frustrated Lewis pair in defective TiO 2 for photocatalytic non-oxidative methane coupling

SUMMARY The efﬁcient C–H polarization is the prerequisite for the low-tem-perature photocatalytic CH 4 conversion, which is restricted by the poor C–H stretching ability of short-distance adjacent lattice atoms. Here, a frustrated Lewis pair (FLP) composed of doped metal in TiO 2 as Lewis acid (LA) and neighboring Ti–OH as Lewis base (LB) with a long distance (0.31–0.37 nm) was designed through DFT calculation and fabricated by hydrogenation treatment of metal-doped TiO 2 –SiO 2 with macroporous-mesoporous structure. Beneﬁtting from the long LA-LB distance and matched acid-base intensity, hydrogenated Ga-doped composite achieves superior C–H stretching with a high photocatalytic CH 4 conversion rate (139 m mol g (cid:1) 1 h (cid:1) 1 ). The photo-irradiation causes electron excitation from Ga to Ti–OH according to the time-dependent DFT calculation and in situ EPR analysis, which promotes the formation and coupling of $ CH 3 . This work provides a key underpinning for regulating the characteristics of FLP for C–H activation and C–C coupling via light irradiation. calculation were combined to demonstrate the contribution of light irradiation to tuning the Lewis acidity and basicity of FLP, and with that, the nature of light-irradiated FLP in promoting CH 4 conversion. the time-dependent DFT method, combining the CAM-B3LYP functional and the same level basis functions to consider the long-range electronic correlation, and output all of the conﬁguration coefﬁcients. The electron-hole pair analysis is imple-mented by the Multiwfn-3.8 program and are drawn using VMD-1.9.3. 51–54 ﬁrst-principles calculations in the frame of DFT with the program 42,55


INTRODUCTION
The increasing abundance of atmospheric methane (CH 4 ) as a major potent greenhouse gas and the large-scale exploitation of shale gas/combustible ice have aroused worldwide research interest for the rational utilization of CH 4 , aiming for cleaner energy development and environmental protection. [1][2][3] However, the conversion of CH 4 into high-value chemicals and transportable fuels is a huge challenge because of the high inertness and low electron affinity energy of the C-H bond. Harsh reaction conditions are inevitably required in conventional thermal catalysis, resulting in great energy consumption and low product selectivity. Alternatively, photocatalysis driven by solar light has proven to be a promising technology for overcoming the high energy barrier of CH 4 conversion. The key is to enhance the polarizability of CH 4 at room temperature and the separation rate of photo-induced charge carriers.
Photocatalytic non-oxidative coupling of CH 4 (NOCM) under mild conditions is one of the effective approaches to selectively produce ethane and hydrogen on TiO 2 , ZnO, or other materials. [4][5][6][7][8][9] Our previous work has verified that a Pt d+ -Pt pair loaded on TiO 2 can promote photocatalytic C-H polarization at room temperature. 5,10 However, C-H stretching still should be fairly restricted by the comparatively fixed and short lattice distance of adjacent positive-negative pairs. A polarized environment with a highly tunable and flexible distance is more desirable. Recently, a solid frustrated Lewis pair (FLP) composed of long-distance Lewis acid (LA) and Lewis base (LB) sites on the solid surface have proven efficient for

The bigger picture
The serious greenhouse effect caused by the massive use of fossil energy is an inevitable environmental problem in today's world. In particular, the greenhouse effect of methane is 25 times that of CO 2 . However, the traditional methane conversion process consumes a great deal of energy. This study emphasizes the efficient conversion of methane driven by green and renewable solar energy under mild conditions. Its fundamental principle is to generate a charge by using light in semiconductors. The efficient conversion of methane is attributed to the unique active sites designed on TiO 2 , such as magnets, which attract C and H, respectively, effectively break the C-H bond, and generate high-value products under the action of a photogenerated charge. This research does not require the high temperature and high pressure of traditional industry and is of great significance to realize energy development and environmental protection that is beneficial to all. H 2 , CO 2 , and CO activation. [11][12][13][14] The existence of steric hindrance between LA and LB leads to the unremitting attraction between Lewis pairs rather than bonding with each other, which has been extensively studied on metal oxides with unsaturated metal centers and metal terminal hydroxyl groups mediated by oxygen vacancies such as defective CeO 2 and In 2 O 3-x (OH) y . [15][16][17][18][19] While the C-H activation of arenes and heteroarenes by FLP has been achieved, the activation of aliphatic Csp 3 -H bonds remains a challenge to be solved. [20][21][22][23] Some theoretic studies have explored the nature of FLP for C-H activation, demonstrating the feasibility of FLP to Csp 3 -H activation, which has not been put into practice. [24][25][26][27][28][29] Recently, photo-irradiation has been used to in situ form heterogeneous FLP or tune the acidity-basicity of FLP sites. For examples, Ghuman and colleagues showed that the Lewis acidity and Lewis basicity were strengthened in the photo-excited state, resulting in a lower activation energy of CO 2 . 19 Wang et al. reported that the photo-induced Lewis acid can be generated by oxidizing light-unstable terminal hydroxyls at Sn sites. 30 It is thus necessary to explore the possibility of tuning the FLP property through photo-irradiation for practical CH 4 conversion, regarding facilitating C-H activation and C-C coupling.
Here, based on DFT calculation, an anatase-TiO 2 -based FLP composed of p-type metal dopants (Ga 3+ , In 3+ , Zn 2+ , Ti 3+ ) as LA and Ti-OH as LB with large spacing were designed, in which oxygen vacancy (V O ) is used as steric hindrance between LA and LB. Accordingly, a combined doping and hydrogenation strategy was adopted to form frustrated metal-V O -Ti-OH Lewis pairs in anatase-TiO 2 . The hydrogenated Ga 3+ -doped TiO 2 presents the most prominent photocatalytic CH 4 conversion activity. Electron paramagnetic resonance (EPR) analysis and time-dependent density functional theory (DFT) calculation were combined to demonstrate the contribution of light irradiation to tuning the Lewis acidity and basicity of FLP, and with that, the nature of light-irradiated FLP in promoting CH 4 conversion.

Theoretical calculation
To guide the design of TiO 2 -based FLP for CH 4 activation, DFT calculations were undertaken to screen out an ideal model through a metal doping strategy. Metal ions (Ms) of Ga 3+ , Zn 2+ , In 3+ , and Ti 3+ as typical p-type dopants which are prone to forming LA were adopted to construct FLP in TiO 2 . [31][32][33][34][35][36] It is found that the M dopant substituted for the six-coordinated Ti site (Ti 6c ), together with Ti-OH in the neighboring Ti 5c site, can form M-V O -Ti-OH with long distances of 0.31-0.39 nm between M and Ti-OH (Figures 1 and S1). Since the proton is used to compensate for the charge difference between the p-type metal dopant and Ti 4+ , the p-type dopant in TiO 2 should be beneficial for the hydrogenation of bridging oxygen according to the calculated formation energy ( Figure S2; Table S1). Zn 2+ with a lower charge (0.41 in Zn-doped TiO 2 ; Figure S3) requires two protons to balance the charge, and thus Zn-V O -Ti is more favorably formed from dehydration as compared with Zn-V O -Ti-OH ( Figure S2). According to the Hirshfeld charge analysis, although the metal substitution decreases the acidity of the original Ti 6c site (0.59) or the basicity of bridging oxygen (À0.32) (e.g., the charges of Ga site and bridging oxygen decrease to 0.51 and À0.19, respectively; Figure S3). Both of them can be efficiently improved by hydrogenation treatment (the charge of the Ga site and Ti-OH are increased to 0.54 and À0.32, respectively) ( Figure 1), accompanied by the increased distance between the M dopant and Ti-OH. The metal dopant in M-V O -Ti-OH is supposed to function as LA, and the Ti-OH plays the role of LB. The electronlocalization degree on metal dopants in M-V O -Ti-OH follows the order of In < Ti < Ga < Zn ( Figures 1A-1D), inversely corresponding to the order of LA acidity. Moreover, it is noted that the In dopant has an even more positive charge than all of the Ti atoms in TiO 2 , suggesting it actually behaves in the manner of an n-type dopant, which should be attributed to the stronger delocalization tendency of its 4d electrons.
The effect of FLP on the C-H activation was further studied through the comparison with the corresponding non-hydrogenated system. Non-modified TiO 2 does not stretch the C-H bond when the CH 4 molecule resides over the Ti 6c site, but the bridging oxygen becomes efficient for hydrogen abstraction from CH 4 when Ti 6c is replaced by the metal dopant as observed from M-O-Ti systems ( Figure S4). Meanwhile, the hydrogenated TiO 2 (H-TS) is also effective for hydrogen abstraction due to the formation of LB Ti-OH (Figure 2), and the energy for CH 4 adsorption is further decreased in the hydrogenated metal-doped system (E-adsorb CH 4 : Ti > Ga > In > Zn; Table S1). Therefore, both the doping and hydrogenation treatment can enhance the hydrogen abstraction ability of the original bridging oxygen. The Ti-OH of Zn-V O -Ti-OH is the most energetically favorable for H abstraction, which should be attributed to the higher charge difference between the metal dopant and Ti 5c . However, Zn-V O -Ti-OH is the most kinetically unfavorable for the C-H stretching, mainly because Zn does not adsorb CH 3 (the largest Zn-C distance). Meanwhile, the theoretical calculation shows that Zn doping is not conducive to the formation of FLP, but to the formation of Zn-V O -Ti, which is supposed to further prevent the Zn-doped system from promoting the practical NOCM reaction. The barrier of the C-H bond activation follows the order of Ga < Ti < In < Zn (Figure S5), where the difference between the final state energy and that in Table S1 is attributed to the inconsistency of the calculation parameters. Based on the above results, the M-V O -Ti-OH with the big charge difference between the metal dopant and Ti 5c favors the hydrogen abstraction, and the strong LA acidity of metal dopant is essential to achieve efficient -CH 3 adsorption.

Structural characterizations of FLP catalysts
To verify the theoretical calculation results, hierarchical macroporous-mesoporous TiO 2 -SiO 2 was adopted as the model to form M-V O -Ti-OH through doping-hydrogenation treatment, which is expected to promote the formation of uniformly dispersed LA-LB pairs benefitting from the highly accessible pore system and high specific surface area (Ga-, Zn-, In-, and Ti-doped samples after hydrogenation are expressed as H-TGS, H-TZS, H-TIS, and H-TS, respectively). X-ray photoelectron spectroscopy (XPS) was used to analyze the surface chemical composition. All of the samples show two obvious peaks at 458.3 and 464.0 eV attributed to the characteristic peaks of Ti 2p ( Figure S6). Three peaks of O 1s located at 529.7, 531.1, and 532.2 eV are assigned to lattice oxygen, oxygen neighboring to oxygen vacancy, and surface -OH, respectively ( Figures S7 and S8). According to the theoretically calculated M-V O -Ti-OH model, the ratio of V O to -OH was used to represent the LA/LB ratio. 24 Through the fine deconvolution of the O 1s XPS spectra ( Figure 3; Table S2), the hydrogenation treatment improves the percentage of surface -OH and V O equally for approximately 6% in H-TGS, exceeding those in the other metal-doped samples. Although the atomic contents of O of different metal-doped systems vary in the range of 57%-67% (Table S2), the variation should be partly caused by the detection error, since the variation tendency seems independent of the valence of doped metal. Here, the variation of the ratio between V O and surface hydroxyl from XPS analysis is used to roughly demonstrate that FLP can be more readily formed from the Ga-doped system according to the comparable increasing tendency of V O and -OH. The optimized hydrogenation temperature for the formation of FLP is 773 K, as the lower (573 K, 673 K) or higher temperature (873 K) fails to equivalently enhance the concentrations of V O and surface -OH ( Figure S9). Specifically, the -OH concentration is more obviously improved at a lower temperature of 673 K, which is in accordance with the DFT calculation that the hydrogenation of bridging oxygen is more favorable compared with the formation of oxygen vacancy. More V O is formed when the hydrogenation temperature increases to 773 K, suggesting the formation of uncoordinated LA and LB. The temperature of 873 K should be over high, which may force neighboring -OH groups to leave as H 2 O or cause the severe distortion of the crystal lattice, resulting in a decreased FLP concentration.
The contribution of the porous structure to the formation of FLP was demonstrated using commercial P25 as the control sample. A tiny amount of Ga (1.5 wt %) was doped in P25, and no diffraction peak of Ga 2 O 3 was observed in the X-ray diffraction (XRD) of H-Ga-P25 ( Figure S10). Therefore, no Ga 2 O 3 nanoparticles or clusters were considered to cover the surface. FLP cannot be efficiently formed in commercial P25 through the same Ga doping and hydrogenation treatment, which verifies that the porous H-TGS with highly accessible TiO 2 crystallite embedded in the framework is essential to forming FLP composed of uncoordinated LA and LB ( Figure 3). The Brunauer-Emmett-Teller (BET)-specific surface areas of all porous composites are above 110 m 2 /g. Using H-TGS for demonstration, it has a hierarchical macroporous-mesoporous structure with an average macroporous diameter of 170 nm and an average mesoporous size of approximately 5 nm, according to the N 2 adsorption-desorption isotherm and high-resolution transmission electron microscopy (HRTEM) analyses (Figures S11 and S12). The lower surface -OH concentration of H-TZS is in accordance with the DFT calculation that the hydrogenation of Zn-doped TiO 2 favors the formation of Zn-V O -Ti through dehydration. Moreover, the lower fitted -OH and V O concentrations of In-doped H-TIS may be attributed to the shorter LA-LB distance according to the DFT calculation, which diminishes the difference between V O and surface -OH, making the analysis based on binding energy less discerning. Based on these results, H-TGS with more FLP is considered to be the most potential catalyst for CH 4 conversion, which is in accordance with the DFT calculation results.
To verify the structure-property relationship, the non-oxidative coupling of CH 4 was carried out over different FLPs (Equation 1). The surface temperature of the catalyst was measured by infrared thermometer under the light intensity of approximately 2,200 mW/cm 2 . The results showed that the surface temperature stayed below 120 C and no product was detected in the dark at 120 C. As shown in Figure 4A, the products mainly contain ethane and hydrogen. Propane can be detected in some samples, and there are no other hydrocarbons in the test. The highest CH 4 conversion rate (139 mmol g À1 h À1 ) was achieved on H-TGS with a selectivity to ethane of over 80%. The alkane/H 2 ratio is nearly equal to 1 (Tables S3 and S4), demonstrating that CH 4 is converted in the NOCM way. Compared with that of H-TS, the activity is doubled through Ga doping, but is not obviously enhanced  (Table S5).
To confirm the cooperation between Lewis pairs for CH 4 conversion, pyridine and pyrrole were used to cover the acidic and basic sites, respectively, of H-TGS. The activities are decreased byapproximately 70% and 80% from the quenching of Lewis acidic and basic sites by pyridine and pyrrole ( Figure 4A). Moreover, H-TGS can preserve sound photocatalytic stability for 6 cycles ( Figure S13B), demonstrating that LA and LB cooperate effectively in C-H cleavage and the subsequent intermediate desorption.
In accordance with the calculation results, the activities of H-TS, H-TZS, and H-TIS were much lower than that of H-TGS, verifying the more efficient C-H polarization by Ga-V O -Ti-OH. 37 The contribution of the band-gap narrowing through doping-hydrogenation treatment is excluded since no obvious difference can be observed from different composites (Figures S13C and S13D).
Determination of the local structure of active FLP sites To verify the real local fine structure of H-TGS, synchrotron radiation-based X-ray absorption fine structure spectroscopy (XAFS) was further used to obtain information regarding the valence states and local structural environment of Ti and Ga sites in active H-TGS. X-ray absorption near-edge structure (XANES) spectra of Ti K-edge ( Figure 5A) reveals visible similarities in structural and electronic properties between all of the samples and that of the TiO 2 reference. The pre-edge peaks are assigned to the electric quadrupole and electric dipole transitions, reflecting the symmetry of hybridized orbitals in Ti 3d . 38,39 The higher intensity of the pre-edge peak at 4,972 eV of H-TGS indicates the most distorted octahedral geometry of the Ti sites. In addition, associated with XPS ( Figure S6), the absorption edge of H-TGS obviously shifts toward lower energy, implying the improved electron density of Ti species from H 2 reduction.
The Ga K-edge XANES spectra of TGS and H-TGS ( Figure 5B) also show the an absorption edge similar to that of the Ga 2 O 3 reference, while the Ga K-edge extended X-ray absorption fine structure (EXAFS) spectra indicate the distinct coordination environments of Ga atoms between Ga-doped samples and Ga 2 O 3 reference ( Figure S14). The k 3 -weighted Fourier-transformed (FT)-EXAFS spectra were used to analyze the differences in local structures. Ti K-edge FT-EXAFS spectra of all samples show two obvious peaks attributed to the Ti-O and Ti-Ti bonds ( Figure 5C). A Ti-Ti interaction peak in the shell of the second-nearest neighbors surrounding the Ti atoms (2-3 Å ) in H-TS, TGS, and H-TGS slightly shifts to longer distances compared to the TiO 2 reference, which is in good agreement with XRD for the expanded lattice ( Figure S15). The Ga K-edge FT-EXAFS spectra show a Ga-Ga interaction peak near 2.9 Å , which represents the shell of the second-nearest neighbors surrounding Ga atoms in the Ga 2 O 3 reference (Figure 5D). In contrast, no Ga-metal peak distinctly appears at 2-3 Å and only the first shell peaks at approximately 1.4 Å assigned to Ga-O peak exist, revealing the isolated state of the Ga atom in TGS and H-TGS, which is in accordance with the DFT calculation. The wavelet transform-EXAFS (WT-EXAFS) spectra of H-TGS and TGS show a distinct signal compared with that of Ga 2 O 3 reference ( Figures 5E and S16), further verifying the atomic dispersion of Ga.
To quantify these differences more accurately in local structure, the spectra were also fitted to extract key structural parameter values (Tables S6 and S7). The curve fit of H-TGS fits the main peak of EXAFS shown in k 3 -weighted k-space and R-space through the first-nearest scattering path attributed to the metal-O structure ( Figures 5F and 5G, other spectra are displayed in Figure S17)  To explicitly explore the contribution of light irradiation to the C-H activation and C-C coupling, time-dependent DFT calculation was carried out over H-TGS and H-TIS. The excited state with stronger oscillator strengths (>0.02) is selected within the range of excitation ( Figure S19). In the excited state of Ga-V O -Ti-OH, electrons originally localized near Ga are transferred to the terminal hydroxyl group (green group). As shown in the electron-hole pair analysis ( Figure 6C), the charges are efficiently separated, simultaneously increasing the intensity of LA and LB, which should favor the oxidation of CH 3 dÀ and the reduction of adsorbed H d+ . While in the ground state of In-V O -Ti-OH, electrons are originally localized on Ti. Upon excitation, no electron transition from Ti 6c to In is observed, suggesting that light irradiation should have no effect on tuning the FLP characteristics. Thus, $CH 3 cannot be efficiently transformed from adsorbed CH 3 dÀ to further undergo C-C coupling, which is in accordance with the inefficiency of H-TIS in promoting the CH 4 conversion ( Figure 6D).
Based on the above analysis, the mechanism of photocatalytic CH 4 conversion on TiO 2 -based FLP can be reasonably explained as follows (Figure 7): TiO 2 -based  3 and $H radicals from separated LA and LB and thus resulting in sustainable production of C 2 H 6 through C-C coupling. In contrast, since In has a more positive charge than the neighboring Ti 5c , no excess electron can be excited from In in the In-V O -Ti-OH. Therefore, it is suggested that even if abundant In-V O -Ti-OH can be fabricated on TiO 2 , the mismatching between C-H activation and light-induced charge transition cannot lead to a sound turnover rate over this type of FLP site.

Conclusions
As guided by the DFT calculation, we designed and prepared solid FLPs based on hierarchical porous TiO 2 -SiO 2 by combining metal doping and hydrogenation strategies for photocatalytic non-oxidative coupling of CH 4 . Benefitting from the appropriate atomic structure of the Ga dopant, a high concentration of FLP was formed from Ga-doped composites, providing Ga-V O -Ti-OH with a long LA-LB distance and strong acid and base intensities for C-H bond stretching. The effect of light irradiation on improving the intensities of LA Ga and LB Ti-OH was confirmed based on the calculated electron transition from LA to LB, which is the key to forming methyl and hydrogen radicals for the further coupling production of C 2 H 6 . This work provides in-depth insight into the key to the design and construction of photocatalytically active FLP for Csp 3 -H polarization. This work is expected to significantly promote the application of the FLP system in mild and selective alkane conversion.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Lingzhi Wang (wlz@ecust.edu.cn).

Materials availability
This study did not generate new materials.

Data and code availability
This study did not generate any datasets.
ll Synthesis of PS Polystyrene (PS) microspheres were synthesized by emulsion polymerization according to the literature. 40 A total of 0.45 g sodium lauryl sulfate (SLS) and 0.6 g potassium persulfate (KPS) were dissolved in 120 mL EtOH and 270 mL H 2 O in a 500-mL 3-neck flask and ultrasonic mixed for 30 min. Then, the solution was deoxygenated and exchanged with N 2 . The flask was heated to 344 K under constant stirring in an oil bath, and 35 mL styrene was injected. The reaction was cooled down to room temperature after 19 h. The PS array was finally obtained by drying the PS emulsion in a 343-K oven for 24 h.

Preparation of Ga-P25
The impregnation method was used to prepare Ga-P25. Theoretically, since all of the Ga sources would be deposited on the surface of P25 in this method, to maintain the consistency of Ga loading, we added gallium nitrate (Ga(NO 3 ) 3 ) according to the actual Ga content in TGS. The actual mass fraction of Ga in TGS was 1.5 wt % measured by inductively coupled plasma (ICP). A total of 0.2 g P25 and 0.011 g Ga(NO 3 ) 3 $xH 2 O with 20 mL H 2 O were mixed together for 1 h under continuous stirring. Then, the mixture was dried slowly in a 343-K electric thermostatic drying oven. After that, the samples were collected and annealed in a muffle furnace at 773 K (2 K/min) for 4 h. Finally, the as-prepared samples were washed with water two times and dried for further use.

Hydrogenation treatment
The as-prepared sample was placed in quartzware and was hydrogenated in a H 2 atmosphere (20 mL

Photocatalytic test
Approximately 2 mg sample is filmed on the glass slide. During photocatalysis, the irradiation spot diameter of Xe light was fixed to keep the light intensity constant; therefore, a larger quantity of photocatalyst means a less efficient interaction between the incident light and stacked solid due to a higher stacking density. As a result, the photocatalytic activity as a function of catalyst weight can be improved by decreasing the quantity of photocatalyst in film form, when expressed in per-catalyst weight within a certain weight range. A higher photocatalyst dosage forms a ll Chem Catalysis 2, 1775-1792, July 21, 2022 1787 Article thicker film with a stronger diffuse reflection, decreasing the interaction chance between the incident light and interior active sites of the film. However, the light transmission becomes predominant when an overly thin film is used. In our work, the film coated with 2 mg of the photocatalyst provided the most enhanced activity.
Approximately 2 mg catalyst was evenly dispersed by 3 mL water and spread on the glass slide to form an ultrathin film. Before the test, the catalyst was pretreated under vacuum for 4 h at 393 K to remove the adsorbed water and other molecules. Then, it was placed at the bottom of a sealed quartz reactor (45 cm 3 ), which was then evacuated for 10 min to remove the air. Afterward, 1 mL pure CH 4 (99.99%) was injected into the reactor and was kept for 1 h to achieve an adsorption-desorption balance. The reactor was irradiated by a 300-W Xe lamp for 4 h at room temperature. The hydrocarbon products were analyzed by gas chromatography (GC; Shimadazu GC-2014) with a flame-ionization detector (FID). The relative deviation of detection was less than 5% for GC.
The quenching experiment of the FLP was carried out with pyrrole and pyridine. The catalyst was placed at the bottom of a sealed quartz reactor and evacuated for 10 min to remove the air. Afterward, 0.5 mL pyrrole (or pyridine) was injected and kept in the dark for 1 h to achieve an adsorption-desorption balance. Then, the reactor was evacuated. The subsequent steps were consistent with the photocatalytic test.
In situ EPR analysis A total of 100 mg sample was placed at the bottom of a vacuum-sealed capillary quartz tube and ambient gas (Ar or CH 4 ) was introduced. The EPR signals were collected in the dark and every 15 min under irradiation.

Computational detail
In this work, calculations for the total energy and geometric optimization were performed using the CASTEP program within the framework of DFT. 41,42 The ultra-soft pseudopotential (USPP) was used for electron-ion interactions, and the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA) was used to describe the exchange-correlation functional. 43 We adopted the evaporation-induced self-assembly method to form microporous TiO 2 -SiO 2 using PS microarray as the hard template, in which SiO 2 is used as the buffer for preventing the porous structure from collapse during high-temperature crystallization of TiO 2 . TiO 2 nanoclusters embedded in the porous framework are supposed to be separated from each other by SiO 2 . The non-doped TiO 2 -SiO 2 has negligible activity in the NOCM reaction, demonstrating that the presence of SiO 2 does not contribute to the C-H activation. Meanwhile, the bottom length of the unit cell of the anatase TiO 2 (101) surface that we used in the DFT calculation is approximately 1 nm, which is smaller than the size of the TiO 2 cluster observed from the HRTEM image, demonstrating that the structure model we constructed for DFT calculation is sufficient to explore the effect of metal doping ( Figure S20). Therefore, the addition of Si in the calculation is not considered. In the optimization process, the bulk atoms are fixed and the surface (subsurface) layers are optimized.
For the time-dependent DFT calculation, H-TGS clusters and H-TIS clusters were extracted from the (101) crystal structure. In the optimization process, the main part is fixed, and the Ga and In parts are optimized. In the whole optimization process, the B3LYP functional and Def2SVP basis sets under the framework of the DFT are combined with the Stuttgart/Dresden (SDD) pseudopotential and DFT-D3 dispersion correction in Gaussian 16 A03. [44][45][46][47][48][49][50] The electronic excitation calculation adopts ll the time-dependent DFT method, combining the CAM-B3LYP functional and the same level basis functions to consider the long-range electronic correlation, and output all of the configuration coefficients. The electron-hole pair analysis is implemented by the Multiwfn-3.8 program and are drawn using VMD-1.9.3. [51][52][53][54] We performed the first-principles calculations in the frame of DFT with the program package CASTEP, 42,55 using the plane-wave (PW)-USPP method and the PBE form of the GGA exchange-correlation energy functional. 56 The structure optimizations of initial CH 4 adsorption on Ga-, In-, and Zn-doped and pure TiO 2 (101) surfaces and corresponding decomposed structures have been carried out by means of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm by fixing the bottom 4 layers and allowing other atomic positions to vary. They stop until the total energies are converged to 10 À5 eV/atom; the forces on each unconstrained atom were smaller than 0.3 eV/Å , the stresses were lower than 0.05 GPa, and the displacements were less than 0.001 Å . The plane-wave cutoff, E cut , was chosen to be 340 eV. The k-point mesh of 2 3 4 3 2 was used for Brillouin zone (BZ) sampling. To obtain the decomposition energy barrier of CH 4 adsorption on Ga-, In-, and Zn-doped and pure TiO 2 (101) surfaces, the transition state (TS) searches were performed by using the complete linear synchronous transit/quadratic synchronous transit (LST/QST) method. 57

Characterization of photocatalysts
The morphology was characterized by TEM (JEM1400). The scanning electron microscopy (SEM) analysis was performed using a TESCAN Nova III scanning electron microscope. The structures of samples were analyzed by HRTEM (JEM-2100). The diffraction peak of samples was characterized by XRD (Rigaku D/MAX 2550, Cu K radiation, l = 1.5406 Å ), whose operation voltage and current was set at 40 kV and 40 mA, respectively. The visible light absorption of the sample was tested by an ultraviolet-visible spectrophotometer (UV-2450, Shimadzu). The sample was a solid powder, and BaSO 4 was used as a reference. The test range was from 200 to 800 nm. The BET surface areas of samples were characterized by ASAP2020 (Micromeritics). The surface chemical states in different samples were characterized by high-resolution XPS (Perkin-Elmer PHI 5000C ESCA system: Al Ka radiation, operated at 250 W), and the shift of the spectra caused by the relative surface charging was calibrated according to the standard binding energy of C (sp2) at 284.6 eV. The actual Ga loading in samples was characterized by ICP-atomic emission spectroscopy (AES) analysis (Agilent 725 ICP-OES). The carrier separation efficiency of samples was measured by photoluminescence spectra (RF-5301PC), and the excitation wavelength was 365 nm. EPR was performed on a JEOL-FA200 instrument (fq100.00 md0.35 3 1 am5.00 3 100 tc0.03, tested at room temperature; g factor is used for comparison due to the weak change of the magnetic field). The data analysis of the XAFS spectra was conducted using the Demeter software package (ATHENA and ARTEMIS). 58 All of the fits were performed in the R space with k-weight of 3. We applied the continuous Cauchy wavelet analysis (CCWT) to the EXAFS spectra, which allows the determination of the identity of the atoms in noisy signals. 59