Introduction

Exploiting methane (CH4) as the C1 modules to fabricate high-valued muti-carbon (C2+) products, particularly via the thermodynamically favorable route of oxidative coupling of CH4 with oxygen (OCM), is a promising tactic to alleviate the reliance on crude oil in the energy industry1,2. However, the conventional thermocatalytic process largely demands high temperatures due to the stable C-H bonds of CH4 molecules3,4. Therefore, it is of great necessity to seek other alternative schemes with lower energy and capital consumption.

Photocatalysis is an appealing way to trigger the activation of inert molecules by solar energy5,6, and some research works committed to the photocatalytic OCM reaction have also obtained delightful advances in the design of metal oxide (MO) semiconductors, such as ZnO- or TiO2-based photocatalysts7,8,9,10,11,12. Certainly, high-throughput C-C coupling is the premise to acquire a satisfactory yield of ethane (C2H6), in which noble metals (e.g., Au, Ag, Pd, etc,.) are widely employed as the critical mediums for the homogeneous or heterogeneous dimerization of methyl (CH3) bricks8,11,12,13. Nonetheless, the efficient release or migration of CH3 over MO substrates is usually frustrated by violent adsorption interactions with lattice oxygen (OL) units11,14,15, especially at low temperatures. Several reported works revealed that the methyl adsorption energy of MO performs a positive correlation to the formation preference of oxygen vacancies (Ov)16,17,18,19,20, and thus the passivation of OL sites is imperative to deliver CH3. On the contrary, the removal process of residual hydrogen adsorbates (*H) usually involves the participation of active OL atoms, implying the easy generation of Ov favors the release of by-product water8,11,21. Therefore, reverse manipulations in escape ability are demanded for the corresponding OL sites, particularly with uniform coordinations, which are expected to break their electronic structural symmetry and better cater to the subsequent evolution of *CH3 and *H intermediates.

To realize the above conjecture, element doping may be a feasible strategy. Typically, the regulation of heteroatoms on the host is mainly manifested in two aspects. One is to affect the local bonded atoms through direct spin-orbit interaction22,23, and the other is to intervene in atomic characteristics through the long-range strain field24,25. It is possible to disrupt the linearly regulated relationship towards OL sites due to the above two effects may not be completely interdependent in action orientation. Inspired by this, we selected ZnO as the subjective semiconductor, which displays widely accepted potentiality for the destruction of inert C-H bonds, particularly with Au as the cocatalyst. On this basis, the lanthanide (Ln) metals may be suitable candidates for the dopants. On the one hand, they are gifted with distinctive high-order orbital configurations of 4f and 5d, which can effectively adjust the electronic structural characteristics of the atoms in the vicinity by intensive spin-orbit coupling26,27,28,29. On the other hand, the Ln ions (La-Gd:103.2-93.8 pm) have larger ion radii than Zn2+ (74 pm)30,31, suggesting the possible tensile strain after substitution doping.

In this work, the Ce atoms are confirmed to be the suitable dopant by theoretical screening, which were introduced into ZnO lattices through a facile co-precipitation strategy. The Ce dopants are confirmed to serve as the electron acceptor to facilitate the charge separation, which thus largely propels the formation of reactive oxygen species (O−) derived from photogenerated holes. More importantly, Ce heteroatoms can break the electronic structure symmetry between the bonded and the vicinal OL centers of ZnO relying on manipulating the strength of metal-oxygen (M-O) bonds, which promotes the methyl desorption for C-C coupling and the water release for the elimination of *H intermediates. Benefitting from the above improvements, the methane conversion rate achieves a 5.8-fold increase after Ce doping with catalytic durability of 3 days, which can break through to 34000 μmol g−1 h−1 accompanied by ultra-high turnover frequency (TOF) (>500 h−1) and apparent quantum efficiency (AQE, >30%) under more thermal assistance. This work provides insight into the rational design for efficient OCM photocatalysts.

Results

Theoretical design for OL sites in ZnO

To screen for the suitable doping elements for ZnO, we first investigated the feasibility of Ln to regulate the OL release through theoretical simulation. As illustrated in Fig. 1a, the ordered Zn-O chain structures will occur the breaking in the local structural symmetry when the heteroatoms undergo the lattice substitution with the host Zn atoms. Due to the changes in chemical environments, the adjacent OL atoms will remove the original degeneracy evolving from two equivalent OPZ to the non-equivalent ODM and ODZ. Motivated by this, seven kinds of Ln elements were introduced into ZnO (Ln-ZnO, Ln: La, Ce, Pr, Nd, Sm, Eu, Gd), and all the model structures are thermodynamically stable (Supplementary Fig. 1). The corresponding formation energies of Ov (EOv) were calculated as shown in Supplementary Table 1. On this basis, EOv(Ln-ZnO)-EOv(ZnO) was used to intuitively embody the regulation differences, in which the positive or negative values represent the imposed passivation and activation effects on OL atoms, respectively. As shown in Fig. 1b, all the commonly-used Ln elements except Nd can achieve the reverse manipulations with different levels for the escape of OL atoms, and the Ce dopant exhibits the most dramatical behavior. Considering that the difficulty of forming Ov depends on the binding strength of M-O bonds, we accordingly employed the projected crystal orbital Hamilton population (pCOHP) analysis to acquire the evolution of the involved bonding states under the circumstance of Ce doping. In principle, the bond stability is associated with the electron occupancy of anti-bonding orbitals, and it can also be quantified by integrating the energy window below the Fermi level (Ef), named IpCOHP. The increase or decrease in the absolute value of IpCOHP (|IpCOHP|) means the tightening or loosing chemical bonds. Usually, (101) and (111) planes are the major exposed facets of ZnO and CeO2, respectively, with OL coordinated by three metal centers. For CeO2 (111), the three sets of Ce-O bonds are completely equivalent (Supplementary Fig. 2). However, the Zn sites hold significant spatial location differences and include two top and one bottom positions surrounding the OL sites (Supplementary Fig. 3). Nonetheless, they are basically similar in terms of stabilizing oxygen atoms (Supplementary Fig. 4). After Ce doping, the pCOHP and |IpCOHP| of the six M-O bonds derived from the ODZ and ODC (ODM with Ce as the heteroatom) centers were provided in Supplementary Figs. 5–7. Obviously, the Ce dopant can induce the anti-bonding orbitals below Ef of Zn-O bonds to generally shift downwards accompanied by the decreased |IpCOHP| (Supplementary Figs. 5 and 6, and bond 2–6 in Fig. 1c), which implies the relaxed bond strength and thus applies a positive force for the formation of Ov. Note that, the significantly changed bonding states of ODZ suggest the emergence of the long-range stress field, well corresponding to the structural distortion caused by Ce doping (Supplementary Fig. 8). In addition, the above effects are attenuated when the bond is far enough from the Ce atom, such as the bond 5 and 6 in Fig. 1c. More specifically, Ce tends to intervene in the top Zn-O chain structures, but the influences on the bottom Zn-O bonds are more localized. For the ODC center, it performs to be affected by a more complicated superposition state. Except for the weakened Zn-O bonds, the extra Ce-ODC bond displays large losses in the anti-bonding state with the greatly enhanced |IpCOHP| whether compared with the adjacent Zn-O bonds or the Ce-O bond in CeO2 (Supplementary Fig. 7 and Fig. 1c), implying the violent oxygen affinity of the lattice-confined Ce heteroatoms. As such, the Ce dopant triggered a stronger lock to reverse the strain-derived relax effects, resulting in the protection of the ODC center.

Fig. 1: DFT calculations for screening the suitable doping Ln metal.
figure 1

a The schematic diagram illustrating the effects of heteroatom doping on the chemical environment of localized OL atoms. b Comparisons of EOv(Ln-ZnO)-EOv(ZnO) after Ln doping. c |IpCOHP| of the M-O bonds over ZnO (101), CeO2 (111), and Ce-doped ZnO (Ce-ZnO) (101).

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Synthesis and characterizations for Ce-ZnO

Based on the theoretical prediction, we fabricated the Cex-ZnO (x=Ce:Zn, mol/mol) catalysts relying on a typical co-precipitation strategy combined with a post-annealing treatment (See details in Methods). The actual cerium contents were measured by inductively coupled plasma-optical emission spectroscopy (ICP-OES), as summarized in Supplementary Table 2. X-ray diffraction (XRD) patterns confirm the hexagonal wurtzite ZnO (JCPDS No.36-1451) as the common phase structure for all the as-prepared catalysts (Supplementary Fig. 9), but the characteristic peak of (101) planes exhibits a distinct shift towards the low angles (Fig. 2a), implying the significant lattice expansion of ZnO resulted by Ce doping. However, such a preference is basically terminated after Ce:Zn reaches 0.6%, and a weak peak at 28.6° assigned to CeO2 (111) planes can be carefully identified in Ce3.2%-ZnO (Supplementary Fig. 10), which indicates the finite capacity threshold of Ce dopants in ZnO lattices. Furthermore, the existence forms of Ce modifier at different concentrations were investigated by Raman spectra (Fig. 2b). Due to the gradually saturated substitutions between Ce and Zn atoms, the E2H vibration band of Zn-O at 447 cm−1 shows an evident redshift until the Ce content is up to 0.6%, which represents the disruptive lattice orderliness of ZnO after Ce modifications32,33. As the continuous cerium addition, the vibration band of CeO2 at 468 cm−1 begins to emerge for Ce0.8%-ZnO and increases bearing an observable blueshift, further declaring the exacerbating surface aggregations of the excessive Ce modifier34,35. High-resolution transmission electron microscopy (HRTEM) images also present the structural evolution of Cex-ZnO referred to the widened lattice spacing and the subsequent visible heterogeneous interfaces (Supplementary Fig. 11). For Ce0.6%-ZnO, Ce elements present a uniform distribution (Supplementary Fig. 12), and aberration-corrected high-angle annular dark field scanning transmission electron microscopy (AC-HAADF-STEM) displays that the introduced Ce dopants are isolatedly anchored into the ZnO matrix (Fig. 2c), whereas the hybrid configurations of both CeOx nanoparticles and the monoatomic Ce sites (Ce1) co-exist in Ce3.2%-ZnO (Supplementary Fig. 13). On this basis, the local bonding configurations of Ce0.6%-ZnO were acquired by extended X-ray absorption fine structure (EXAFS) spectroscopy. As revealed in R space for Ce L3-edge, merely the shortened Ce-O scattering path (1.61 Å) can be found in Ce0.6%-ZnO compared with the referential CeO2 (1.86 Å) (Fig. 2d and Supplementary Fig. 14), revealing that the abundant mononuclear Ce atoms are encapsulated in the narrower ZnO lattices. Simultaneously, the tensile Zn-O and Zn-O-Zn configurations can also be observed from the peak movement from 1.52 Å and 2.87 Å to 1.55 Å and 2.90 Å in R space of Zn K-edge (Fig. 2e and Supplementary Fig. 15). As seen in Supplementary Fig. 16 and Table 3, the coordination number (CN) of the Ce-O bond in Ce0.6%-ZnO is 3.9, which is far lower than CeO2 (CN = 7.2) but very close to Zn-O (CN = 3.8). What’s more, the fitted Zn-O or Ce-O bond length is also highly consistent with the computational structure models, further verifying the occurrence of cationic substitutional doping. To investigate the changes in OL properties, the temperature-programmed desorption of O2 (O2-TPD) experiments was further conducted (Fig. 2f). The desorption peaks at ~396 °C and >507 °C are usually assigned to the chemisorbed oxygen species and OL signals36. The early-emerged OL release yet with the decreased area can be identified after Ce doping, verifying the coexistence of the activated and passivated OL atoms. However, there are no obvious differences in surface oxygen species between ZnO and Ce0.6%-ZnO may be due to the counteract of the above reverse effects, which is consistent with the X-ray photoelectron spectroscopy (XPS) results of O 1s (Supplementary Fig. 17). In addition, X-ray absorption near-edge structure (XAENS) spectroscopy of Zn K-edge combined with the XPS results of Zn 2p (Supplementary Fig. 18) validate the charge accumulation for Zn sites arising from the doping-induced charge compensation effects37.

Fig. 2: Structural and electronic characterization of the as-fabricated photocatalysts.
figure 2

a Partially enlarged XRD patterns within the diffraction angle range of 35°–38°. b Raman spectra. c The AC-HAADF-STEM image of Ce0.6%-ZnO. d, e EXAFS spectra of Ce L3-edge (d) and Zn K-edge (e). f O2-TPD of ZnO and Ce0.6%-ZnO.

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Photocatalytic OCM performance

Upon acquiring the specific structural information for the series Cex-ZnO catalysts, we further evaluated the photocatalytic OCM performance using a homemade atmospheric flow reactor (Supplementary Fig. 19). Here, Au was selected as the cocatalyst to deposit over ZnO (AZO), CeO2 (ACO), and Cex-ZnO (Cex-AZO) via liquid-phase reduction. Screening based on the pristine ZnO, Au is confirmed to provide the possibility of C-C coupling, and an appropriate dosage is 0.6 wt% with a C2H6 yield rate of 1323 μmol g−1 h−1 and a selectivity of 95.6% (Supplementary Fig. 20). On this basis, the concerning influences brought by cerium modifications were investigated with the same Au decorations (Supplementary Table 4 and Fig. 21). As displayed in Fig. 3a and Supplementary Table 5, there exists a significant volcanic dependence of the OCM performance on Ce contents, and the optimal hybrid configuration is recognized as Ce0.6%-AZO with the saturated Ce dopants, which achieves a 5.8 or 11.6-fold breakthrough in CH4 conversion rate (>16,000 μmol g−1 h−1) than the individual AZO or ACO, respectively. Note that, no oxygenates can be detected during the tests for the catalysts with or without Ce modification (Supplementary Fig. 22). Differently, accompanied by a massive evolution of C2H6 (>6800 μmol g−1 h−1), propane (C3H8) can be obtained over Ce0.6%-AZO, and the C2+ selectivity (94.9%) has almost no loss compared with that of AZO. However, the appearance and accumulation of CeOx aggregations over the catalysts (Ce:Zn>0.6%) lead to the yield drop of C2H6, indicating the intense sensitivity of OCM performance to the Ce-modified forms. As such, only the doped Ce atoms are responsible for the origin of activity enhancement. Furthermore, the effects of the process conditions were discussed in detail. As revealed in Supplementary Fig. 23, no carbonaceous products can be detected without the intake of CH4, and there is merely a trace amount of C2H6 generated under anaerobic conditions. Therefore, the coupling products are mainly derived from the reaction of CH4 and O2, in which Ar has no reactivity in addition to dilution roles. However, the C2+ release rate gradually slows down with the continuous decline of the alkane-to-oxygen ratio, and the valueless total oxidation course is synchronously exacerbated (Fig. 3b). Particularly, when CH4:O2 decreases to 2.5, the C2+ selectivity of Ce0.6%-AZO undesirably drops below 80%. Consequently, a suitable oxygen concentration (CH4:O2 = 175, here) is of great necessity to guarantee both high reactivity and C2+ selectivity. For the contact time, the optimal flow rate is determined to be 50 mL min−1 (Fig. 3c). An excessively quick or slow gas transmission may lead to an insufficient contact or weakened alternation of the feed gas near the catalyst interfaces, which is not conducive to the turnover of OCM cycles. Based on the above process optimization, a long-term catalytic stability test was also carried out as displayed in Fig. 3d. With the almost constant product distribution, the C2H6 yield rate is well maintained during 72 h, indicating the robust catalytic durability of Ce0.6%-AZO. What’s more, the thermogravimetric (TG) analysis further ruled out the possibility of coke deposition over the used catalysts (Supplementary Fig. 24), and there are also no obvious changes in the chemical valence of Ce before and after tests (Supplementary Fig. 25).

Fig. 3: Photocatalytic OCM performance evaluation in the atmospheric flow reactor.
figure 3

a Performance comparisons of the prepared catalysts. b, c The performance of Ce0.6%-AZO under different ratios of CH4:O2 (b) and different flow rates (c). d Continuous catalytic stability tests over Ce0.6%-AZO. e Performance comparisons based on TOF and AQE between Ce0.6%-AZO and the representative reported photocatalysts (C2 or C2+ selectivity >80%, R169, R270, R371, R48, R547, R672, R714, R873, R912, R1010, R1111, R129, R1374) with noble metal decorations. Reaction conditions in a and d: 5 mg photocatalyst, 350 mW cm−2 for the light intensity, 120 °C for the reaction temperature, 50 mL min−1 of mixed reaction gas containing 35 mL min−1 CH4 gas, 1 mL min−1 20 vol% O2/Ar gas, and 14 mL min−1 Ar gas. For other investigations, the reaction conditions remained unchanged except for the concerned factors. The error bars correspond to the standard deviation of at least three independent measurements, and the center value for the error bars is the average of the three independent measurements.

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To understand the essential reaction driving force, we tentatively separated the individual heating conditions to execute the OCM tests. As shown in Supplementary Fig. 26, there are no products detected at 120 °C without illumination, and only negligible CO2 can be obtained after applying a higher temperature of 210 °C in the dark field. Accordingly, the intrinsic triggering for OCM conversion still follows the basic photocatalytic principles but can be accelerated by additional heating. Given that, the photocatalytic OCM reactivity was further measured under different thermal supplies. According to Supplementary Fig. 27 and Table 6, the CH4 conversion rate of Ce0.6%-AZO resumes to grow up to ca. 34000 μmol g−1 h−1 with the reaction temperature elevated from 120 °C to 210 °C, accompanied by only a drop of ~4% in C2+ selectivity. Considering the excellent OCM activity of Ce0.6%-AZO, we also attempted to make a comparison with those representative photocatalysts. Particularly, the TOF for the C2 product of Ce0.6%-AZO can exceed 500 h−1 (350 mW cm−2, 210 °C) with a high AQE of 33.7% at 350 nm (Supplementary Fig. 28), which is superior to the state-of-the-art reported materials with similar component configurations, to the best of our knowledge (Fig. 3e and Supplementary Table 7).

Insight into photocatalytic OCM mechanism

To decipher the structure-activity relationship associated with Ce doping, the photophysical process was firstly taken into consideration. According to the UV-visible diffuse reflectance spectra (UV-vis DRS) and the derived Tauc plots, the bandgap energies (Eg) of ZnO, Ce0.6%-ZnO, and CeO2 were calculated to be 3.19 eV, 3.16 eV, and 2.91 eV, respectively (Supplementary Fig. 29). Combined with the valance band (VB) positions of 2.80 eV, 2.80 eV, and 2.36 eV (Supplementary Fig. 30), the corresponding energy band structures are described in Supplementary Fig. 31, in which the Ce dopants hold an ability to slightly reduce the Eg of ZnO via downshifting the conduction band (CB). On this basis, a higher transient photocurrent density was observed over Ce0.6%-ZnO under the same applied bias voltage, thus validating the enhancement of the photocarrier separation efficiency brought by the Ce modifier (Supplementary Fig. 32). Further, in situ irradiation XPS confirms the available collection at Ce dopants for the photogenerated electrons due to the negative shift of binding energy for Ce 3d under light irradiation (Fig. 4a and Supplementary Fig. 33). However, when Ce undergoes agglomerations on ZnO caused by excessive modifications, the binding energy offset of Ce 3d is changed toward the high energy side (Supplementary Fig. 34), declaring that CeOx serves as the hole trap. Note that, CeO2 has a lower oxidation ability than ZnO as aforementioned, thereby leading to the weakened methane activation ability. Therefore, the optimal photocatalytic OCM activity occurs when Ce:Zn reaches 0.6%, in which Ce dopants approach saturation without obvious CeOx clusters. To better understand the charge transfer process, femtosecond transient absorption spectroscopy (fs-TAS) was also employed upon a 320 nm pulse pump and a white-light pulse (430-780 nm) probe. As illustrated in Supplementary Figs. 35 and 36, both ZnO and Ce0.6%-ZnO show similar absorption bands decaying after fast light excitation. Furthermore, the signals at 486 nm corresponding to the stimulated emission (SE) of hot electrons were used for the photocarrier kinetic analysis and fitted by bi-exponential functions38. As shown in Fig. 4b, the decay traces contain a fast process (τ1) for the electron transfer from CB to the shallow trapping state and a slow course (τ2) for the subsequent electron-hole recombination process39. Clearly, τ1 performs an evident decrease from 4.53 ps to 3.58 ps accompanied by the prolonged τ2 from 86.25 ps to 114.68 ps, implying the Ce dopants provide more sites for electron grabbing to retard the photocarrier recombination. For the introduced Au cocatalysts, the major light absorption occurs at ca. 545 nm (Supplementary Fig. 37), which is produced by the surface plasmon resonance40. However, such a response is definitely out of the test wavelength range (300–400 nm). Consequently, the photocarriers are completely contributed by the light excitation of the semiconductor substrates. Nevertheless, Au is widely used as the typical electron acceptor driven by Schottky junctions in similar catalyst configurations11,41, which is also confirmed to be beneficial for further charge separation (Supplementary Fig. 38).

Fig. 4: Reaction intermediate tracking and mechanism investigations.
figure 4

a Partially enlarged in situ irradiation XPS of Ce 3d over Ce0.6%-ZnO. b The fitted photocarrier kinetic decay curves at 486 nm obtained from fs-TAS. c Time-resolved in situ mass spectra (MS) over Ce0.6%-AZO under the mixed atmospheres of CH4 and 16O2 or isotopic 18O2 gas. d In situ electron paramagnetic resonance (EPR) spectra of AZO and Ce0.6%-AZO in the dark field with an Ar atmosphere and under light illumination with an Ar or CH4 atmosphere. e, f In situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) of AZO (e) and Ce0.6%-AZO (f).

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On the premise of more effective charge separation induced by Ce dopants, we further investigated the possible effects on the following OCM reaction process. Preliminarily, the oxygen cycle was traced through the time-resolved in situ MS with isotope labeling 18O2 or 16O2 as the reactants, in which H216O, C16O2, C16O18O, H218O, and C18O2 were selected for the indicative fragment ions (CH4 + O2 → C2H6 + CO2 + H2O). As shown in Fig. 4c, when CH4 and 16O2 were pumped into the reactor chamber, only H216O and C16O2 can be detected under light illumination. Differently, after switching 16O2 to 18O2, a series of signals of H218O, C16O18O, and C18O2 begin to emerge upon light-on. More importantly, the relative abundance between 16O- and 18O-containing products performs the reversal as the reaction progresses, accompanied by the gradual disappearance of H216O and C16O2 species. As such, the injected O2 is mediated by OL to participate in the removal of accumulative *H species and the formation of overoxidation products, conforming to the Mars-van Krevelen mechanism.

On this basis, in situ EPR was employed to resolve the methane activation units and the stepwise reaction mechanism. As shown in Fig. 4d, both the studied catalysts carry two minor signals of g = 2.002 and g = 1.958 under the Ar and dark conditions, which are usually assigned to the response of Ov and Zn+ species, respectively8,11. Upon applying light irradiation, the new paramagnetic peaks attributed to O− species appear at g = 2.031, g = 2.023, and the overlapping location with the Ov signal42,43. Meanwhile, the synchronous growth in Zn+ contents was also observed. Thus, it can be inferred that the hot holes and electrons are enriched in the OL and Zn2+ centers, respectively. Note that, Ce0.6%-AZO has more excited species than the pristine AZO, further verifying the promotion of Ce dopants on charge separation. More importantly, after the catalysts are exposed to a CH4 atmosphere, the intensity of O− and Zn+ signals can generate an observable decrease, revealing that the Zn+-O− pairs are responsible for CH4 activation. On this basis, the radical trapping experiments by 5,5-dimethyl-1-pyrroline N-oxide (DMPO) confirm the presence of more •CH3 after Ce doping, which is consistent with its higher O− intensity (Supplementary Fig. 39). Thus, a reasonable CH4 activation pathway can be derived as follows44: Zn+-O− + CH4 → Zn2+-O2− + *CH3 + *H. During the next step, *CH3 needs to undergo a dimerization process to form C2H6, and the associated coupling mechanism was deciphered by removing the close contact between Au and the semiconductor substrate (Supplementary Fig. 40). Under the same external conditions, the individual Ce0.6%-ZnO merely holds a feeble C2H6 yield, whereas no carbonaceous products are formed over Au-Al2O3. However, when Au-Al2O3 and Ce0.6%-ZnO were physically mixed, the OCM performance of Ce0.6%-AZO was basically reproduced with only a slight decline. Accordingly, there is less contribution of interfacial contact between Au and Ce0.6%-ZnO on methyl formation and C-C coupling, and the necessary transport of CH3 to Au mainly relies on the gas-phase migration8. For O2 activation, the signals of •O2−, which are formed via e−+O2 → •O2−, can be detected over both AZO and Ce0.6%-AZO (Supplementary Fig. 41), and the latter exhibits a higher concentration due to a lower recombination consumption of available hot electrons. Note that, the introduced cocatalysts can also serve as the electron acceptors to boost the activation of O2, which is confirmed by the elevated •O2− concentration after Au decorations (Supplementary Fig. 42). To better understand the roles of O2, we also tracked the changes of paramagnetic species on Ce0.6%-AZO during aerobic methane dissociation (Supplementary Fig. 43). In addition to O− signals, some new peaks corresponding to O2− species appear at g = 2.001, g = 2.015, and g = 2.037 under illumination and an O2 atmosphere45. After exposure to CH4, O2− species can be consumed with the ongoing methane activation over Zn+-O+ pairs. Combined with the OL-cyclic characteristic, we reasonably infer that O2 follows a typical activation route of O2 → O2− → O22- → 2O− → 2OL2- to backfill the in situ formed Ov sites during OCM8,46. To extract the complete information on O2−, similar experiments were also tested at room temperature to eliminate the interference of O− signals, and the changing pattern of paramagnetic species was consistent with that at 120 K (Supplementary Figs. 44 and 45). Based on the above results, we summarized the entire reaction cycle, as illustrated in Supplementary Fig. 46.

Under the premise of a clear catalytic course, in situ DRIFTS was used to monitor the detailed evolution of reaction intermediates. In the dark and after the stable adsorption of CH4 and O2, a tiny peak at 1540 cm−1 appears over both the studied catalysts (Supplementary Fig. 47), which is assigned to the C-H symmetric stretching vibration of *CH421,47. Further, the above spectrum was adopted as the baseline to better compare and identify the signal changes, which is marked as 0 min in Fig. 4e, f. Upon light irradiation, the adsorption of CH4 gets greatly enhanced and ultimately reaches the steady-state response after ca. 15 min. Meanwhile, some new bands emerge and immediately grow up at 1438 cm−1, 1454 cm−1, and 1633 cm−1, respectively. The series signals are attributed to the vibrational modes of *CH3 deformation47,48, alkyl deformation in *C2H649,50, and symmetry stretching of O-H bonds in *H2O51,52,53, which are involved in the reaction steps of chemical dissociation of *CH4, surface C-C coupling, and *H consumption. In sharp contrast, Ce0.6%-AZO has a stronger signal intensity after illumination, demonstrating a more effective CH4 activation and CH3 dimerization. In addition, the species responsible for deep oxidation11,53, including *CH2 (1473 cm−1)21,51, formate (1591 cm−1)11,21,54, carboxylate (1576 cm−1)55,56,57, mono- or bi-dentate carbonate (1506 cm−1, 1558 cm−1)52,58, and *CO2 (1667 cm−1)47,59, present similar accumulations before and after Ce doping, which is in good line with the well-inherited high selectivity of C2H6. Interestingly, the photogenerated species perform different depletion behaviors after light-off. Based on a similar release rate of *C2H6, the Ce dopants can greatly accelerate the desorption of *CH3 and *H2O, indicating that Ce0.6%-AZO holds a more efficient methyl supply for the C-C coupling at Au sites and a quicker removal of residual *H. As for the overoxidation route, the almost constant surface abundance declares a pretty obstructed course at the test temperature.

Combined with the experiment results, theoretical calculations were also adopted to provide a better understanding towards the effects of Ce dopants during the OCM reaction. For Ce-ZnO, the methane activation center needs to be investigated due to the presence of different localized chemical environments. As illustrated in Fig. 5a, three kinds of possible units were considered for the dissociation of *CH4, involving the top Ce-ODC, Zn-ODC, and Zn-ODZ pairs with significant changes in bond strength as confirmed above. According to Supplementary Fig. 48, we found that the introduction of Ce atoms is not inclined to directly participate in CH4 activation, due to the high reaction energy (ΔGR) of 1.33 eV for Ce-ODC to break C-H bonds. For Zn-ODC and Zn-ODZ, both of the two units are more active in driving methane dissociation (0.90 eV vs. 0.80 eV), but the latter is easy to release *CH3 from the ODC sites (0.89 eV vs. 0.52 eV), which better caters to the following C-C coupling over Au centers. Accordingly, Zn-ODZ is determined as the optimal center over Ce-ZnO (101) to activate CH4 molecules. For the water formation, it has been verified by the isotope exchange experiments to follow the M-vK mechanism involving the pulling out of OL atoms. We thereby simplified their removal process based on the configurations of two *H adsorbed on the adjacent OL sites. As displayed in Supplementary Fig. 49, using ODZ as the oxygen source for H2O holds the lowest reaction energy whether for the formation or the subsequent desorption steps, suggesting its thermodynamic superiority in all the available sites. On this foundation, the detailed comparisons between ZnO (101) and Ce-ZnO (101) are provided in Fig. 5c, d. After Ce doping, the dissociation of CH4 emerges improvement according to the decrease in ΔGR of 0.34 eV (Fig. 5c). More importantly, the methyl desorption energy was greatly reduced from 1.16 eV to 0.52 eV, and the underlying principles were further revealed by DOS analysis. According to Supplementary Fig. 50, the passivated ODC over Ce-ZnO (101) has a lower p-band than OPZ over ZnO (101) due to the intense hybridization of Ce (4f, 5d)-O 2p, which leads to the weakened adsorption ability60,61,62. During the elimination of *H species (Fig. 5d), only slight differences occur in the generation of *H2O between ZnO and Ce-ZnO, but the ΔGR of water desorption changes from 0.5 eV to be thermodynamically spontaneous. The results are well accorded with the weakened Zn-ODZ bond, due to the formation of *H2O also relying on the interaction of the O-terminal and the Zn sites. To further identify the roles of Au, the C-C coupling process was also investigated via simulated calculations (Supplementary Figs. 51 and 52). Compared with ZnO and Ce-ZnO, the formation of C2H6 mediated by Au is more favorable in kinetics, and there is only a low energy barrier of 0.25 eV for Ce-AZO through the direct combination of *CH3 and •CH3, which is very close with that of AZO (Fig. 5e, Supplementary Figs. 53 and 54). In addition, the electronic structure analysis reveals that Au 5d orbitals can largely strengthen the interactions between methyl groups in the transition state distinguished by a larger |IpCOHP| (Supplementary Fig. 55), which thereby raises the possibility of C-C coupling. Overall, the Ce-caused disproportionation of escape ability for ODC and ODZ induces more favorable desorption behaviors of critical intermediates, including the efficient transport *CH3 to Au sites for C-C coupling and the water release, which is highly consistent with the results of in situ DRIFTS.

Fig. 5: DFT investigations for photocatalytic OCM reaction.
figure 5

a, b The screening process for the reaction sites of methane activation (a) and water formation (b) over Ce-ZnO (101). The blue, red, purple, black, and white balls represent the Zn, O, Ce, C, and H atoms, respectively. c, d Free energy profiles for the formation of •CH3 (c) and H2O (d) over ZnO (101) and Ce-ZnO (101). e Free energy profiles for the formation of C2H6 via the direct combination of *CH3 and •CH3 on different surfaces.

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Discussion

In summary, we reasonably designed and synthesized Ce-doped ZnO with Au decorations as an efficient OCM photocatalyst. Based on the performance test results, the C2H6 yield rate of Ce0.6%-AZO reaches 6829 μmol g−1 h−1 (C2+ selectivity: 94.9%) with excellent durability over 72 h. On the premise of more thermal assistance, the corresponding CH4 conversion rate can further increase to ca. 34,000 μmol g−1 h−1 with TOF and AQE (350 nm) elevated from 249 h−1 and 17.0% to 507 h−1 and 33.7%, and the C2+ selectivity can maintain above 90%. According to systematic in situ characterizations combined with theoretical analysis, the Ce dopants can not only inhibit the photocarrier recombination to generate more O− species for CH4 activation, but also achieve the electronic asymmetry manipulations of the OL sites in Zn-O-Zn-O-Ce configurations via the tune-up for the strength of the involved M-O bonds. Specifically, the strong orbital hybridization of Ce (4f, 5d)-O 2p combined with the doping-induced tensile strain effects holds the ability to passivate the O atom in Ce-O-Zn and activate the O atom in the adjacent Zn-O-Zn configurations. As a consequence, the disproportionated OL units largely favor the release of *CH3 and *H2O, respectively, which strengthens the transport of CH3 bricks to Au sites for C-C coupling and accelerates the removal of *H species over the substrate. This work provides insight into the rational design for other photocatalysts with high OCM performance, from the perspective of manipulating the electronic structural characteristics of OL centers.

Methods

Chemicals and materials

Zinc nitrate hexahydrate (Zn(NO3)2·6H2O, 99%), cerium nitrate hexahydrate (Ce(NO3)3·6H2O, 99%), sodium carbonate (Na2CO3, 99%), sodium hydroxide (NaOH, 97%), potassium borohydride (KBH4, 99%), gold chloride trihydrate (HAuCl4·3H2O, 99.9%), aluminum oxide (Al2O3, 20 nm, 99.99%), ammonium acetate (CH3COONH4, 99%), acetic acid (CH3COOH, 99.8%), acetylacetone (C5H8O2, 99%) were purchased from Aladdin Ltd. (Shanghai, China).

Synthesis of ZnO, Cex-ZnO, and CeO2

The Cex-ZnO nanoparticles were prepared based on a facile co-precipitation method with the subsequent annealing treatment. Here, Ce0.6%-ZnO was taken as a case. In detail, 12 mmol Zn(NO3)2·6H2O and 0.072 mmol Ce(NO3)3·6H2O were completely dissolved in 24 mL deionized water to obtain solution A. 16.8 mmol Na2CO3 was added to 14 mL H2O and subsequently conducted an ultrasonic treatment for 10 min to prepare solution B. Then, solution A was heated in a water bath up to 65 °C under stirring, and solution B, with the assistance of an injection pump, was follow-up dripped into solution A at a speed of 2 mL min−1. Afterward, the suspension was continued to be heated for 1 h and then quickly cooled to room temperature through an ice water bath. The white precipitate was collected by centrifugation and washed with water several times before drying at 80 °C overnight. To obtain the final product, the ground precursor was calcined at 300 °C in an air atmosphere for 4 h. As for the synthesis of ZnO, Ce0.2%-ZnO, Ce0.4%-ZnO, Ce0.8%-ZnO, Ce1.6%-ZnO, and Ce3.2%-ZnO, the corresponding feeding of Ce(NO3)3·6H2O in solution A was changed to 0 mmol, 0.024 mmol, 0.048 mmol, 0.096 mmol, 0.192 mmol, and 0.384 mmol, respectively. For CeO2, only 12 mmol Ce(NO3)3·6H2O was used to form solution A, and the solution B was composed of 50.4 mmol NaOH and 14 mL H2O.

Synthesis of AZO, Cex-AZO, and ACO

The loading of Au was conducted by liquid phase reduction driven by KBH4 at room temperature. Taking the loading of 0.6 wt% Au as a case, 250 mg of ZnO, Cex-ZnO, or CeO2 and 3 mg of HAuCl4·3H2O were dissolved in 25 mL of water and continuously stirred for 1 h. For the Au-loading amounts of 0.1 wt%, 0.3 wt%, and 1.0 wt%, only the dosages of HAuCl4·3H2O were changed to 0.5 mg, 1.5 mg, and 5 mg, respectively. Then, 5 mL of 100 mM KBH4 solution was slowly dripped into the suspension. After continuing stirring for 30 min, the purple products were collected by centrifugation and washed several times with deionized water before drying at 80 °C overnight.

Photocatalytic activity measurements

Photocatalytic OCM reaction was conducted in a homemade stainless steel flow reactor with a top sapphire window at atmospheric pressure. Typically, 5 mg of the catalyst was firstly dispersed in 0.5 mL H2O and then dropwised on a quartz sample holder with a diameter of 10 mm. After drying for 3 h in an oven at 80 °C, the holder was carefully placed in the reaction chamber, which was sealed through metal flanges. Subsequently, the reactant gas of CH4, 20 vol.% O2 in Ar, and Ar (volume ratio=35:1:14) with a total flowing rate of 50 mL min−1 was injected and controlled by mass flow meters. Note that, Ar was used as a diluent gas to finely control O2 concentration and avoid the following detecting overload for CH4. The reaction temperature was set to 120 °C and monitored in real-time through a k-type thermocouple, and the light source (300 < λ < 400 nm, 350 mW cm−2) was provided by a 300 W Xenon lamp (CEL-HXF300-T3, Beijing China Education Au-light Co., Ltd.) with a UV reflection filter. To ensure the steady-state reaction process, the product detections were conducted after a continuous reaction of 1 h. The tail gas passed through a cold water bath (5 °C) to collect possible oxygenates, and the absorption solution was further detected by 1H nuclear magnetic resonance spectroscopy (1HNMR, Avance III, JEOL Ltd) and colorimetric method (UH-5300, Hitachi, Japan). For the chromogenic agent, 100 mL of the solution contains 25 g of CH3COONH4, 3 mL of CH3COOH, and 0.25 mL of C5H8O2. Finally, the washed tail gas was analyzed by a gas chromatograph (GC 2060, Shanghai Ruimin Instrument Co., Ltd) equipped with an HP-PLOT Q column, methanizer furnace, and flame ionization detector.

In this work, only CO2, C2H6, and C3H8 can be detected over the studied catalysts. On this basis, the selectivity (S) was calculated according to Eqs. (1)-(4):

$$S({{\rm{CO}}}_{2})=\frac{n({{\rm{CO}}}_{2})}{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})+n({{\rm{CO}}}_{2})}$$
(1)
$$S({{\rm{C}}}_{2}{{\rm{H}}}_{6})=\frac{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})}{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})+n({{\rm{CO}}}_{2})}$$
(2)
$$S({{\rm{C}}}_{3}{{\rm{H}}}_{8})=\frac{3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})}{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})+n({{\rm{CO}}}_{2})}$$
(3)
$$S({{\rm{C}}}_{2+})=\frac{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})}{2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})+n({{\rm{CO}}}_{2})}$$
(4)

Where n(C2H6), n(C3H8), and n(CO2) are the yields of C2H6, C3H8, and CO2 per unit time, respectively.

The conversion rate of CH4 (r(CH4)) was calculated by Eq. (5):

$$r({{\rm{CH}}}_{4})=r({{\rm{CO}}}_{2})+2\times r({{\rm{C}}}_{2}{{\rm{H}}}_{6})+3\times r({{\rm{C}}}_{3}{{\rm{H}}}_{8})$$
(5)

Where r(C2H6), r(C3H8), and r(CO2) are the yield rates of C2H6, C3H8, and CO2, respectively.

AQE determination

For the measurement of AQE, the light intensity (I) at different wavelengths (λ = 350, 365, 380 nm) was uniformly set to 10 mW cm−2. Other reaction conditions were maintained and consistent with the performance evaluation. In this work, the AQE was calculated by Eqs. (6)-(9):

$${\rm{AQE}}=\frac{{N}_{e}}{{N}_{p}}\times 100\%$$
(6)
$${N}_{e}=(2\times n({{\rm{C}}}_{2}{{\rm{H}}}_{6})+4\times n({{\rm{C}}}_{3}{{\rm{H}}}_{8})+8\times n({{\rm{CO}}}_{2}))\times {N}_{{\rm A}}$$
(7)
$${N}_{{\rm{p}}}=\frac{IAt}{{E}_{\lambda }}$$
(8)
$${E}_{\lambda }=\frac{hc}{\lambda }$$
(9)

Where Ne, Np, and NA represent the number of reacted electrons, the number of incident photons, and Avogadro’s constant, respectively. n(C2H6), n(C3H8), and n(CO2) are the yields of C2H6, C3H8, and CO2, respectively. Eλ is the photon energy, t is the light incident time, h is Planck’s constant, and c is the speed of light.

Characterization

XRD was performed on a Rigaku Smartlab diffraction using a Cu Kα source (λ = 0.154178 nm). ICP-OES was conducted on Agilent 730. Before testing, the samples were completely dissolved in HF acid and proportionally diluted to volume for tests. HRTEM images and energy-dispersive mapping were collected on JEOL JEM-F200. AC-HAADF-STEM images were measured on Thermal Fisher Themis Z operated at 300 kV. Raman spectra were recorded on a LabRAM HR Evolution apparatus, and a 532 nm laser was used for the excitation source. Conventional and VB XPS were all carried out on a PerkinElmer PHI-1600 ESCA spectrometer. The binding energy was calibrated using the C 1s peak (284.60 eV) of the inherent contaminant carbon as the internal standard. TG analysis for the used catalyst was performed under an air atmosphere on NETZSCH STA44F5 through heating from 60 °C to 900 °C at a ramp rate of 10 °C min−1. UV-vis DRS were recorded against the BaSO4 reflectance standard on a Lambda 750 UV-vis spectrometer (PerkinElmer) equipped with an integrating sphere. The experimental absorption coefficients of all the X-ray absorption near edge structure spectra were converted to the normalized intensity according to the standard procedures of background subtraction and normalization (Win-XAS3.1 software).

In situ irradiation XPS

In situ irradiation XPS was also conducted on a PerkinElmer PHI-1600 ESCA spectrometer under dark or light conditions. The light illumination (λ = 300–400 nm) was introduced into the testing chamber via a quartz optical fiber with a 5 mm light spot.

Fs-TAS

The fs-TAS measurements were performed on a HELIOS Fire spectrometer (Ultrafast Systems LLC). For the light sources, a 50% beam splitter was employed to divide the regeneratively amplified laser pulse (generated by Ti: sapphire, coherent, 800 nm, 85 fs, 7 mJ/pulse, 1 kHz for the repetition rate) into two parts, and the pump beam (320 nm) was thus obtained by the transmitted pulse processed by a TOPAS Optical Parametric Amplifier. For the reflected part, it was re-split, further attenuated (neutral density filter, <10%), and then converged by crystal to produce the probe beam (white light continuum, WLC). Before tests, the WLC converged by Al parabolic reflector needed to be further collimated, which was then monitored by a fiber-coupled spectrometer (CMOS sensors, frequency: 1 KHz). To manipulate the pump light intensity, a neutral density filter wheel was used, and the delay between the pump beam and WLC was controlled by a motorized delay stage. During tests, the pump pulses were chopped to 500 Hz, and the absorbance change was acquired from two adjacent probe pulses, which were pump-blocked and pump-unblocked states. The samples were placed in 1 mm airtight cuvettes in an N2-filled glove box and measured under ambient conditions.

The decay kinetics was fitted via the two-order exponential decay Eq. (10):

$$I={I}_{0}+{{\rm A}}_{1}{{\rm{e}}}^{-{\rm{t}}/{\tau }_{1}}+{{\rm A}}_{2}{{\rm{e}}}^{-{\rm{t}}/{\tau }_{2}}$$
(10)

where I is fluorescence intensity, A1, I0, and A2 are constants, t is decay time, and τ1 and τ2 reprensent the lifetime under different fluorescence modes.

Isotope tracing experiments

The 18O2 isotope tracing experiments were conducted using CH4/O2 or CH4/18O2 as the mixed reactant gas in a homemade flow reactor with a top sapphire window, and the products were identified using a time-resolved online MS equipped with a RGA triple quadrupole mass analyzer.

In situ EPR

In situ EPR was obtained on a Bruker A300 spectrometer. For the gas-solid reaction monitor, 20 mg of catalysts were loaded into a quartz tube and evacuated at 150 °C lasting for 3 h. Then, the EPR spectra of each sample were collected at 120 K or 298 K under dark or light with different atmospheres. After the switch of each condition, there was a 10-min test interval applied to ensure a stable light intensity or sufficient gas mixing. For the detection of •CH3 and •O2−, DMPO was used as the trapping agent in a solution system. In brief, the as-prepared catalysts and DMPO were first dispersed in an ice-bath tert-butanol or methanol solution, and CH4 or O2 was subsequently bubbled up to saturation, respectively. Then, the signals were collected after applying light for 5 min. Here, tert-butanol was added to increase the solubility of CH4 and capture •OH radicals to avoid its interference with the methane activation process. Methanol was used as the hole sacrificial agent to improve the signal quality of •O2−.

In situ DRIFTS

In situ DRIFTS were performed on the Bruker Vertex 80 V spectrometer equipped with Harrick diffuse reflectance accessory with ZnSe and quartz window. The parallel tests were performed under different reaction atmospheres with or without light illumination. The spectra were recorded by averaging 128 scans with a resolution of 2 cm−1. Firstly, the desorption treatment in an Ar atmosphere was employed at 200 °C for 2 h after the sample loading. Then, the pre-mixed reactant gas (CH4:(20 vol% O2 in Ar):Ar=35:1:14) was introduced into the sample cell and adsorbed under dark conditions for 30 min to collect the signals. Afterward, the background subtraction was conducted. Then, the light (300–400 nm) was applied through a quartz observation window from an optical fiber (light spot: 5 mm) connected to a 300 W Xe lamp equipped with an ultraviolet reflector, and the spectra were continuously recorded until they reached a steady state. Finally, the light illumination was removed and the signal changes were continuously recorded again for 30 min.

DFT calculations

DFT calculations were conducted based on the Vienna Ab initio Simulation Package (VASP)63. The electronic exchange-correlation interactions were described by the Generalized Gradient Approximation (GGA) following the scheme of the Perdew, Burke, and Ernzerrof (PBE) functional64. The kinetic cut-off energy was set to 400 eV, and the Monkhorst-Pack mesh K-point of 1 × 1 × 1 and 9 × 9 × 1 were used for geometry optimization and DOS calculations. The smearing width was set to 0.05 eV. The maximum force tolerance was delimited as 0.05 eV·Å−1 for the convergence criterion of structure optimization. When the energy difference between the two calculations is less than 1× 10−5 eV for each electronic step iteration in geometric optimization, the calculation is considered to be up to the convergent state. Particularly, for the CeO2 model, a Hubbard U term was added to the PBE functional (DFT + U) employing the rotationally invariant formalism by Dudarev et al.65, in which only the difference (Ueff = U − J) between the Coulomb U and exchange J parameters enters. Here, a value of Ueff = 4.5 eV was used for Ce 4 f. COHP calculations were performed using LOBSTER software66. DOS calculations and free energy correction at 393 K were performed using VASPKIT software67. The transition states were searched using the climbing-image nudged elastic band (CI-NEB)68. The bulk crystal structure of ZnO and CeO2 were modeled adopting a K-point mesh of 6 × 6 × 6. The obtained optimal crystallographic parameters are a = b = 3.251 Å and c = 5.256 Å for ZnO and a = b = c = 5.4073 Å for CeO2. The bare ZnO (101) surface was modeled using a 2×3 unit cell of the 4-layer thickness (Zn: 36 atoms and O: 36 atoms) with the fixed two bottom layers to mimic its bulk positions. Replacing a Zn atom over the ZnO (101) surface with an Ln atom (La, Ce, Pr, Nd, Sm, Eu, Gd) to construct the Ln-ZnO model. For AZO or Ce-AZO, the Au11 cluster was constructed on a 2×6 unit cell of ZnO without or with a Ce dopant. The bare CeO2 (111) surface was modeled using a 2×2 unit cell of 6-layer thickness (Ce: 32 atoms and O: 64 atoms) with the fixed three bottom layers to mimic its bulk positions. A 15 Å vacuum gap was introduced along the c-direction.

The formation energy of Ln-ZnO (Ed) is defined by Eq. (11):

$${E}_{{\rm{d}}}={E}_{\mathrm{Ln}-{\rm{ZnO}}}-{E}_{{\rm{ZnO}}}+{E}_{{\rm{Zn}}}-{E}_{\mathrm{Ln}}$$
(11)

Where ELn-ZnO and EZnO are the total energy of Ln-ZnO and ZnO slabs, and EZn and ELn are chemical potentials of Zn and Ln atoms.

EOv is defined by Eq. (12):

$${E}_{{\rm{Ov}}}={E}_{{\rm{def}}}+\frac{1}{2}E({{\rm{O}}}_{2}){-}{E}_{\mathrm{int}}$$
(12)

Where Edef is the total energy of the slab with an Ov, E(O2) is the energy of an oxygen molecule, and Eint is the energy of the initial slab.

The adsorption energy (Eads) is defined by Eq. (13):

$${E}_{{\rm{ads}}}={E}_{{\rm{s}}+{\rm{g}}}{-}{E}_{{\rm{s}}}{-}{E}_{{\rm{g}}}$$
(13)

Where Es+g is the total energy of the absorbates over the building slab, Es is the energy of the building slab, and Eg is the energy of the adsorbents in the gas phase.