Synergistic Effect of Neighboring Fe and Cu Cation Sites Boosts Fe n Cu m -BEA Activity for the Continuous Direct Oxidation of Methane to Methanol

: Direct oxidation of methane to methanol (DMTM), constituting a major challenge for C 1 chemistry, has aroused signiﬁcant interest. The present work reports the synergistic effect of neighboring [Fe]–[Cu] cations, which can signiﬁcantly boost the CH 3 OH productivity (100.9 and 41.9 → 259.1 µ mol · g − 1cat · h − 1 ) and selectivity (0.28 and 17.6% → 71.7%) of the best performing Fe 0.6% Cu 0.68% -BEA (relative to monomeric Fe 1.28% - and Cu 1.28% -BEA) during the continuous H 2 O-mediated N 2 O DMTM. The combined experimental (in situ FTIR, D 2 O isotopic tracer technique) and theoretical (DFT, ab initio molecular dynamics (AIMD)) studies reveal deeper mechanistic insights that the synergistic effect of [Fe]–[Cu] can not only signiﬁcantly favor active O production ( ∆ G = 0.18 eV), but also efﬁciently motivate the reaction following a H 2 O proton-transfer route ( ∆ G = 0.07 eV), eventually strikingly promoting CH 3 OH productivity/selectivity. Generally, the proposed strategy by employing the synergistic effect of bimetallic cations to modify DMTM activity would substantially favor other highly efﬁcient catalyst designs.


Introduction
Methane, being a primary component of natural gas, constitutes the main feedstock during methanol production, which traditionally follows the syngas route, needing high temperature and pressure [1]. By contrast, the direct oxidation of methane to methanol (DMTM) operated under mild conditions is greatly appealing for CH 3 OH production; however, this process suffers from low selectivity and productivity, due to the extremely high C-H bond energy (413 kJ·mol −1 ) of CH 4 but relatively low thermostability of CH 3 OH [2][3][4].
Although it is still a major challenge to make breakthroughs for the DMTM, the development of suitable catalysts and reaction systems to promote CH 3 OH selectivity and productivity has never ceased.
Methane monooxygenases (MMOs), as a type of methanotrophic bacteria, can readily transform CH 4 into CH 3 OH at room temperature, the active site of which consists of iron or copper [5]. To mimic its catalytic behavior, the Fe-and Cu-exchanged zeolites have been extensively investigated for the DMTM [6][7][8][9][10][11][12][13][14][15][16], wherein the specific active site motifs significantly affect the DMTM activity. For example, Jeong et al. [7] recently reported a continuous DMTM by passing O 2 over Cu-MOR, finding that the binuclear [Cu-O-Cu] 2+ site possessed much higher activity than that of the mononuclear [Cu] + site. To further Table S1 lists the physiochemical properties of the investigated Fe n Cu m -BEA samples (n and m represent the metal loadings), which were prepared by the tradition ionexchange method. Briefly, the H-BEA (5g) was mixed with certain amounts (see Table S2) of Fe(NO 3 ) 3 ·9H 2 O and Cu(NO 3 ) 2 ·5H 2 O and thereby solved by 200 mL deionized water under stirring for 4 h at 100 • C. After being washed, dried (100 • C, 24 h) and calcined (550 • C, 4 h), the final product can be obtained. As noted, for the purpose of comparison the physiochemical properties of the monomeric Fe 1.28% -and Cu 1.28% -BEA, being prepared by the incipient-wetness impregnation method and with a metal loading amount of 1.28 wt.% (see details in Supplementary Materials), was also listed in Table S1. The small crystallite size (~17-18 mm) associated with a high Brunner−Emmet−Teller (BET) surface area (>500 m 2 ·g −1 ) indicates the nano-zeolite catalysts of the prepared Fe n Cu m -BEA and H-BEA. The related XRD patterns confirm the characteristic BEA crystal structures of the prepared samples, with no CuO x or Fe x O y diffraction patterns being observed (see Figure S2a). However, the coexistence of well-dispersed metal oxides cannot be totally ruled out due to their minor amounts, being below the XRD detection limit.
To further identify the chemical states of the loaded Fe and Cu species over the Fe n Cu m -BEA samples, the H 2 temperature program reduction (H 2 -TPR) was thereby conducted, with the results being profiled in Figure 1a. As can be seen, there are four types of reduction peak in total, as marked by orange, purple, dark green and blue, which can be assigned to be the reduction of CuO, Fe 3+ ion, Cu 2+ ions and Fe x O y , respectively [18,24,30]. The species occupations are further depicted in Figure 1b (see details in Table S3), indicating that the Cu 2+ cations constitute the major species over Fe 0.38% Cu 0.74% , while both the Cu 2+ and Fe 3+ cations can be observed for Fe 0.6% Cu 0.68% -BEA (0.56 and 0.40%) and Fe 1.0% Cu 0.5% -BEA (0.37 and 0.28%), although large amounts of Fe x O y species (0.74%, Figure 1b) can also coexist with metal cations over Fe 1.0% Cu 0.5% -BEA. Noteworthily, the Cu 2+ cations' contents (green columns) were higher than those of the Fe 3+ cations (purple columns), even for the sample of Fe 1.0% Cu 0.5% -BEA (0.37 versus 0.28%, Figure 1b) with much higher Fe loadings than those of Cu. This finding reveals that the Cu 2+ cations prefer to occupy the Brönsted acid ion-exchange site compared to Fe 3+ cations, eventually resulting in Fe x O y as the major Fe species, especially for the sample of Fe 1.0% Cu 0.5% -BEA with the highest Fe loadings. The valance states of the loaded Cu and Fe species of Fe n Cu m -BEA were further characterized by XPS, as shown in Figure 1c,d. The main peak located at 933.5 (Cu 2p 3/2 ), being associated with a shake-up peak at 944.5 eV (Figure 1c), indicates the characteristic Cu 2+ valance state of the surface Cu species [18], while the two main peaks located at 712.3 (Fe 2p 3/2 ) and 725.7 eV (Fe 2p 1/2 ), being associated with the satellite peaks at 718.2 and 732.9 eV (Figure 1d), indicate the 3+ valance state of the surface Fe species [31]. For comparison, H 2 -TPR and XPS were also conducted on the monomeric Fe 1.28% and Cu 1.28% -BEA (see Figure 1a and Figure S3a,b), which indicate that both the CuO (0.52%) and Cu 2+ (0.76%) cations can be formed over Cu 1.28% -BEA. The large reduction domain of Fe 3+ species over Fe-BEA-1.28% (250-600 • C of Figure 1a) can be related to the reduction of Fe 3+ cations or oxo-cations into Fe 2+ , 18 which can be further confirmed by the H 2 consumption quantitation (see Table S3). As noted, in comparison to that of Fe-BEA-1.28%, the Fe 3+ cation reduction peaks became narrower for the scenario of Fe n Cu m -BEA samples, which can be related to the much lower Fe 3+ cation amounts resulting from the much stronger ion-exchange ability of Cu 2+ cations at the Brönsted acid site (as stated above).

Activity Comparison with Monomeric Fe-and Cu-BEA
With a basic understanding of the loaded metallic species, the continuous N2O DMTM activity measurements were further conducted over the FenCum-BEA and Fe1.28%-Cu1.28%-BEA samples, as shown in Figure 2a-d and Figure S4, being associated with the CH4 conversion and product selectivities being listed in Table S4. As can be seen, much higher CH3OH productivities ( Figure 2a) and selectivities (Figure 2b & Table S4) can be observed for the samples of FenCum-BEA relative to those of the monomeric Fe1.28%-and Cu1.28%-BEA. Especially for the best-performed sample of Fe0.6%Cu0.68%-BEA, it displays a boosted CH3OH productivity (259.1 μmol•g −1 cat•h −1 , Figure 2a), being respectively of 2.6 and 6.2 times high than those of Fe1.28%-and Cu1.28%-BEA (100.9 and 41.9 μmol•g −1 cat•h −1 ) with the similar total metal loadings. This finding implies that there probably exists some synergetic effect between the loaded Fe and Cu species, which can efficiently promote the H2O-mediated N2O DMTM activity of Fe0.6%Cu0.68%-BEA. This will be further discussed later based on the combined experimental and theoretical studies. As for the monomeric Fe1.28%-BEA, large amounts of CO2 (selectivity of 97.2%, see Figure 2b) can be formed, being   Figure S4, being associated with the CH 4 conversion and product selectivities being listed in Table S4. As can be seen, much higher  Table S4) can be observed for the samples of Fe n Cu m -BEA relative to those of the monomeric Fe 1.28% -and Cu 1.28% -BEA. Especially for the best-performed sample of Fe 0.6% Cu 0.68% -BEA, it displays a boosted CH 3 OH productivity (259.1 µmol·g −1 cat ·h −1 , Figure 2a), being respectively of 2.6 and 6.2 times high than those of Fe 1.28% -and Cu 1.28% -BEA (100.9 and 41.9 µmol·g −1 cat ·h −1 ) with the similar total metal loadings. This finding implies that there probably exists some synergetic effect between the loaded Fe and Cu species, which can efficiently promote the H 2 O-mediated N 2 O DMTM activity of Fe 0.6% Cu 0.68% -BEA. This will be further discussed later based on the combined experimental and theoretical studies. As for the monomeric Fe 1.28% -BEA, large amounts of CO 2 (selectivity of 97.2%, see Figure 2b) can be formed, being accompanied with the N 2 O conversion of 99.1% and CH 4 conversion of 47.8%, which indicates the overoxidation of CH 4 probably due to the strong oxidation property of the generated αO over the Fe cation site; additionally, the Cu 1.28% -BEA displays the lowest CH 3 OH productivity (41.9 µmol·g −1 cat ·h −1 ), which can be related to the lower reaction efficiency to generate αO of the Cu cations relative to that of Fe as well as the coexistence of large amounts of CuO x species (0.52%, see Table S3) that can readily lead to the overoxidation of CH 3 OH into CO 2 (22.6%, Figure 2b). accompanied with the N2O conversion of 99.1% and CH4 conversion of 47.8%, which indicates the overoxidation of CH4 probably due to the strong oxidation property of the generated αO over the Fe cation site; additionally, the Cu1.28%-BEA displays the lowest CH3OH productivity (41.9 μmol•g −1 cat•h −1 ), which can be related to the lower reaction efficiency to generate αO of the Cu cations relative to that of Fe as well as the coexistence of large amounts of CuOx species (0.52%, see Table S3) that can readily lead to the overoxidation of CH3OH into CO2 (22.6%, Figure 2b). In addition to that, it can be found that the simultaneous introduction of 10 vol% H2O into the reaction system can pronouncedly promote the CH3OH productivity (134.8 Figure 2a) and CH3OH selectivity (14.4 → 71.7%, Figure 2b) as well as the long-term stability (passing through 25 h's test, Figure 2d) of the best-performed Fe0.6%Cu0.68%-BEA. This finding gives us a clue that there probably also exits the proton-transfer reaction over the Fe0.6%Cu0.68%-BEA, wherein the H2O molecule could directly participate in the reaction through a proton-transfer route, as proposed in  In addition to that, it can be found that the simultaneous introduction of 10 vol% H 2 O into the reaction system can pronouncedly promote the CH 3 OH productivity (134.8 µmol·g −1 cat ·h −1 → 259.1 µmol·g −1 cat ·h −1 , Figure 2a) and CH 3 OH selectivity (14.4 → 71.7%, Figure 2b) as well as the long-term stability (passing through 25 h's test, Figure 2d) of the best-performed Fe 0.6% Cu 0.68% -BEA. This finding gives us a clue that there probably also exits the proton-transfer reaction over the Fe 0.6% Cu 0.68% -BEA, wherein the H 2 O molecule could directly participate in the reaction through a proton-transfer route, as proposed in our previous work over the Cu 0.6% -BEA zeolite catalyst [24], eventually  Figure 2b), which can be closely related to the undesired side reaction of the accumulated CH 3 radicals being generated during CH 4 activation over the active site. Meanwhile, it is also worth noting that the Fe 0.6% Cu 0.68% -BEA can achieve higher CH 3 OH productivity under a much lower reaction temperature (259.1 µmol·g −1 cat ·h −1 , T = 270 • C) than that of Cu 0.6% -BEA (242.5 µmol·g −1 cat ·h −1 , T = 320 • C) of our previous report [24], which can well verify the viability of the proposed strategy by modifying active site motifs to improve the N 2 O DMTM activity of Cu-BEA.

Activity Comparison among Fe n Cu m -BEA
The diverse catalytic activities of the Fe n Cu m -BEA samples can be closely correlated with the chemical states as well as the correlated synergetic effect of the loaded Fe and Cu species. As is well known, the metal cations constitute the active sites for N 2 O dissociation [17], which are responsible for the production of αO for the scenario of the present reaction system, while the metal oxides readily lead to the overoxidation of CH 3 OH into CO 2 [24]. In this regard, we can deduce that the highest CH 3 OH productivity of Fe 0.6% Cu 0.68% -BEA can be closely correlated with its higher Fe and Cu metal cation amounts (0.56 and 0.40%, Figure 1b), which greatly favor the active O production as well as the reaction synergies between these bimetal cations. Similar findings can also be derived for the sample of Fe 1.0% Cu 0.5% -BEA; however, the relatively lower metal cation amounts (0.37 and 0.28%, Figure 1b [32]. In light of the above statement, we can deduce that the [Fe-O-Cu] would constitute the major active site during the N 2 O DMTM over Fe 0.6% Cu 0.68% -BEA by displaying much more extensive band intensities at 1873 and 1864 cm −1 than those of 1840, 1818 and 1805 cm −1 after the N 2 O pretreatment (see Figure 3a). To make comparisons, the NO in situ FTIR was also conducted over Fe 0.38% Cu 0.74% -and Fe 1.0% Cu 0.5% -BEA (being after in situ N 2 O pretreatment), as shown in Figure 3b. The characteristic v(NO) bands over the bimetallic [Fe-O-Cu] site (1873 and 1864 cm −1 ) can also be clearly observed for these two samples, the band area of which were however much lower than that of Fe 0.6% Cu 0.68% -BEA, as quantified in Figure 3c. This finding gives us a clue that the much higher N 2 O DMTM activity of Fe 0.6% Cu 0.68% -BEA ( Figure 2a) can be closely correlated with its higher amounts of evolved [Fe-O-Cu] active species in comparison to other two samples.

H 2 -TPR after N 2 O and O 2 Pretreatment
The H 2 -TPR was further conducted over the N 2 O and O 2 (taken as a reference) pretreated Fe 0.6% Cu 0.68% -BEA to confirm the evolved [Fe-O-Cu] site. Similarly, a pretreatment strategy to that of NO in situ FTIR was applied, wherein the sample were initially pretreated by He at T = 500 • C for 1 h before the subsequent N 2 O (30 vol% in He, T = 250 • C for 1 h) and O 2 (15 vol% in He, T = 500 • C for 1 h) pretreatments; and to obtain the better signals, the mass spectrometer (MS) was utilized to monitor the H 2 (m/e = 2) consumptions. As noted, the O 2 pretreatment temperature of 500 • C was chosen according to literature reports [26] that it commonly needs a high temperature (T > 500 • C) to generate active O species during DMTM over the zeolitic catalyst. As shown in Figure 3d, three types of H 2 reduction peaks can be clearly observed, which can be respectively corresponding to the reduction of

Experimental Mechanism Study
Based on the above studies, the active-site motif evolutions have been clarified. In this section, the H2O-mediated N2O DMTM reaction mechanism was further investigated by in situ FTIR and D2O isotopic tracer techniques to explore the reaction synergy of the loaded neighboring Cu and Fe cations over the best-performing Fe0.6%Cu0.64%-BEA.  [27] can be observed, which implies that the H2O-mediated N2O DMTM follows the radical mechanism in which the CH4 is activated into the radical of CH3-and OH-at the evolved active site of [Fe-O-Cu] of Fe0.6%Cu0.64%-BEA. To further verify this assumption, in situ FTIR by introducing the CH4 (2 vol% in He) into the N2O-pretreated Fe0.6%Cu0.64%-BEA was further conducted, wherein the H2O was not fed into the system to avoid its influence on v(OH). As shown in Figure 5c, the band at 3675, being related to the v(OH) at metal  To further verify this assumption, in situ FTIR by introducing the CH 4 (2 vol% in He) into the N 2 Opretreated Fe 0.6% Cu 0.64% -BEA was further conducted, wherein the H 2 O was not fed into the system to avoid its influence on v(OH). As shown in Figure 5c, the band at 3675, being related to the v(OH) at metal cations site (α-site), can be clearly observed, which can solidly verify the deduction that the CH 4 activation would follow the radical mechanism over Fe 0.6% Cu 0.64% -BEA, as illustrated by Equations (1) and (2), wherein the M a and M b in Equation (2) represent the metal cations of Cu or Fe, respectively (the specific states will be determined by the DFT, as will be further discussed later).
Catalysts 2021, 11, x FOR PEER REVIEW 10 of 20 cations site (α-site), can be clearly observed, which can solidly verify the deduction that the CH4 activation would follow the radical mechanism over Fe0.6%Cu0.64%-BEA, as illustrated by Equations (1) and (2), wherein the Ma and Mb in Equation (2) represent the metal cations of Cu or Fe, respectively (the specific states will be determined by the DFT, as will be further discussed later).

(b) D 2 O isotopic tracer experiment
According to our previous study [24], the H 2 O molecules could directly participate in N 2 O DMTM through a proton-transfer route after the activation of CH 4 at the evolved [Cu-O-Cu] site of Cu 0.6% -BEA. In light of that, the temperature-programmed surface reaction (TPSR-) MS-based D 2 O isotopic tracer technique was also employed in the present work to explore whether the proton-transfer reaction of H 2 O also occurs during the H 2 O-mediated N 2 O DMTM over the Fe 0.6% Cu 0.68% -BEA. As shown in Figure 6a, the obviously emerged peaks of CH 3 OD (33) and D 3 (3)).
Catalysts 2021, 11, x FOR PEER REVIEW 11 of 20 Therefore, based on the in situ FTIR, we can deduce that the neighboring [Fe]--[Cu] would initially interact with N2O, generating [Fe-O-Cu] (α-site), which thereby favors CH4 activation following a radical mechanism.
(b) D2O isotopic tracer experiment According to our previous study [24], the H2O molecules could directly participate in N2O DMTM through a proton-transfer route after the activation of CH4 at the evolved [Cu-O-Cu] site of Cu0.6%-BEA. In light of that, the temperature-programmed surface reaction (TPSR-) MS-based D2O isotopic tracer technique was also employed in the present work to explore whether the proton-transfer reaction of H2O also occurs during the H2Omediated N2O DMTM over the Fe0.6%Cu0.68%-BEA. As shown in Figure 6a, the obviously emerged peaks of CH3OD (33) and D3O + (33), accompanied by the simultaneous increase/decline in the signals of HOD (19)/[D2O (20)], respectively, provide us with solid evidence that the D2O can also participate in the N2O DMTM through a proton-transfer route after CH4 activation over the evolved [Fe-O-Cu] site of Fe0.6%Cu0.68%-BEA (see Equation (3)). To make comparisons, the TPSR-MS without D2O addition was also conducted over Fe0.6%Cu0.68%-BEA, as shown in Figure 6b. It is observed that the signals of CH3OD (33), D3O + (22), HOD (19) and D2O (22) can also be detected, especially for D2O (22), emerging as a small peak. In fact, this can be related to the overoxidation of CH4 (99.999%), which contains small isotopic abundance of the atomic D, to produce minor D2O that can further participate in the N2O DMTM reaction following the proton-transfer route, eventually generating the detected signals of CH3OD (33), HOD (19) and D3O + (22) in Figure 6b. To make comparisons, the TPSR-MS without D 2 O addition was also conducted over Fe 0.6% Cu 0.68% -BEA, as shown in Figure 6b. It is observed that the signals of CH 3 OD (33), D 3 O + (22), HOD (19) and D 2 O (22) can also be detected, especially for D 2 O (22), emerging as a small peak. In fact, this can be related to the overoxidation of CH 4 (99.999%), which contains small isotopic abundance of the atomic D, to produce minor D 2 O that can further participate in the N 2 O DMTM reaction following the proton-transfer route, eventually generating the detected signals of CH 3 OD (33), HOD (19) and D 3 O + (22) in Figure 6b. Therefore, this finding can also support the H 2 O proton reaction during N 2 O DMTM over Fe 0.6% Cu 0.68% -BEA. Figure 3c further compares the peak areas of the signals of CH 3 OH (31) and CH 3 OD (33) derived from Figure 3a,b, which demonstrates that the addition of D 2 O would lead to N 2 O DMTM following the proton-transfer route by producing much higher amounts of CH 3 OD (33) relative to that of CH 3 OH (31). Small amounts of CH 3 OH can also be generated during the D 2 O-mediated N 2 O DMTM, which may be related to the N 2 O DMTM over the monomeric cation sites, where no proton-transfer reactions can occur [24]. In addition to that, herein, we suggest that the D 2 O direct-reaction route may also exist during the D 2 (4)). This reaction route will be discussed later based on the DFT and with the results being further compared with that of the H 2 O proton-transfer route.

Theoretical Mechanism Simulations by DFT and AIMD
To shed deeper mechanistic insight into reaction synergy of the neighboring Fe and Cu cations of Fe 0.6% Cu 0.68% -BEA, both the DFT and AIMD were employed in this part to simulate the reaction mechanism based on the constructed FeCu-BEA model with the neighboring [Fe]-[Cu] as the active site (auto-reduced form after He pretreatment, see Figure S7). In total, three types of reaction mechanisms were proposed, including the H 2 O absence mechanism (taken for comparison) and the H 2 O proton-transfer mechanism as well as the H 2 O direct-reaction mechanism, as illustrated in detail in in Scheme 1. The derived reaction energy diagrams are depicted in Figure 7a and Figure S8a,b, as stated in detail below.
Catalysts 2021, 11, x FOR PEER REVIEW 13 of 20 Scheme 1. Schematic diagram of proposed N2O DMTM reaction mechanism over the best-performing sample of Fe0.6%Cu0.68%-BEA in the presence and absence of H2O; specifically, after the initial N2O dissociation and CH4 activation steps (black line), three types of routes were proposed, namely: i) in the absence of H2O (blue line); ii) the H2O proton-transfer route (red line); and iii) the H2O directreaction route. The chemical structure was labeled according to constructed models depicted in the energy diagrams of Figure 7 and Figure S8a,b.
(a) N2O dissociation and CH4 activation steps As shown in Scheme 1, the same reaction routes are followed during the initial N2O dissociation and CH4 activation steps (marked by black arrow) for the three proposed types of mechanisms. Specifically, the N2O molecule readily interacts with the neighboring simulate the reaction mechanism based on the constructed FeCu-BEA model with the neighboring [Fe]--[Cu] as the active site (auto-reduced form after He pretreatment, see Figure S7). In total, three types of reaction mechanisms were proposed, including the H2O absence mechanism (taken for comparison) and the H2O proton-transfer mechanism as well as the H2O direct-reaction mechanism, as illustrated in detail in in Scheme 1. The derived reaction energy diagrams are depicted in Figures 7a and S8a,b, as stated in detail below.   [24]. This finding demonstrates that the synergetic effect of the neighboring [Fe]-[Cu] could significantly promote N 2 O dissociation to generate the active O, which constitutes the major reason leading to the much higher CH 3 OH productivity and lower operation temperature of Fe 0.6% Cu 0.68% -BEA relative to that of Cu 0.6% -BEA of our previous work. After that, the CH 4 can be subsequently activated into CH 3 -and OH-(III→IV, Figure 7a); a similar reaction route of III→TSII has also been reported by the literature [35,36], following a radical mechanism as revealed by the in situ FTIR (Figure 5a-d), the free energy barrier of which is calculated to be 0.92 eV (TS-II of Figure 7a). Noteworthily, according to the DFT calculations ( Figure S9a,b), the CH 4 is both kinetically and thermodynamically much more favorable to be activated into the  Figure S8a, the H 2 O absence route would follow the widely reported rebound mechanism, wherein the radical of CH 3 -could migrate from the [Cu] 2+ site to interact with OH-, producing [Fe(CH 3 OH)] (IV→V) by overcoming a relatively high free energy barrier of 1.21 eV (TS-III). After crossing another energy barrier of 1.12 eV (VI), the CH 3 OH can be eventually desorbed. H 2 O proton-transfer mechanism. Based on the above in situ FTIR (Figure 5a-d) and D 2 O isotopic transfer (Figure 6a,b) studies, the AIMD-based metadynamic simulations were employed to explore the H 2 O proton-transfer mechanism (see Movie S1, T = 270 • C, P = 1 atm). As shown in Figure 7a, two H 2 O molecules can be initially inserted between the generated radicals of [FeOH]-[CuCH 3 ] (model V), which is much more thermodynamically favorable than the scenario of the H 2 O direct-reaction mechanism with one H 2 O molecule being adsorbed on the [Cu] 2+ site (as will be further discussed later   Figure S1a), which clearly displays the reaction energy variations from one energy minimum to another minimum.
H 2 O direct-reaction mechanism. As stated above, the H 2 O direct-reaction route may also occur during the H 2 O-mediated DMTM over Fe 0.6% Cu 0.68% -BEA. In this regard, the H 2 O direct-reaction mechanism was further simulated by DFT. As shown in Figure  S8b,

(c) Reaction mechanism comparisons
In comparison to the H 2 O absence mechanism, the slightly lower barrier of the radical rebound step (1.14 (TSIV, marked blue) versus 1.21 eV (TSIII, marked green) (see inserted energy diagram of Figure 7a) combined with the barrierless desorption of CH 3 OH indicates that H 2 O could also favor CH 3 OH production through the direct-reaction route. However, the H 2 O-mediated N 2 O DMTM would generally follow the H 2 O proton-transfer route due to the extremely low energy barrier of 0.07 eV. To make quantitative comparisons, microkinetic modeling was further conducted for these three types of mechanisms, with the results being profiled in Figure S10a-d. As can be seen ( Figure S10a), the overall reaction rates were predicted to be 3.64 × 10 9 s −1 (H 2 O proton-transfer route), 1 Figure 2a (CH 3 OH productivity). This discrepancy is related to the utilized DFT calculation method during the microkinetic modeling, especially for the pre-exponential factor calculations derived by the frequency calculations. However, it does not affect the parallel comparisons of the DFT-based microkinetic modeling results.

Illustration of the Synergistic Effect of Neighboring Fe and Cu Cations
Based on the above experimental and theoretical mechanism studies, we can obtain a comprehensive understanding of the synergistic effect of the neighboring [ [24]) to 0.18 eV. On the other hand, it can also motivate the reaction following the H 2 O proton-transfer route by crossing an extremely low free energy barrier of 0.07 eV, thereby pronouncedly enhancing CH 3 OH productivity/selectivity, as well as long-term stability (reducing carbon depositions). To provide deeper insights, from the electronic structure point of view, into the synergistic effect of neighboring [Fe]-[Cu] on N 2 O dissociation to generate active O, the theoretical simulations including electronic density difference, the Bader charge analysis and density of state (DOS) were further conducted (see Figure 8a- [24]) to 0.18 eV. On the other hand, it can also motivate the reaction following the H2O proton-transfer route by crossing an extremely low free energy barrier of 0.07 eV, thereby pronouncedly enhancing CH3OH productivity/selectivity, as well as long-term stability (reducing carbon depositions). To provide deeper insights, from the electronic structure point of view, into the synergistic effect of neighboring [Fe]--[Cu] on N2O dissociation to generate active O, the theoretical simulations including electronic density difference, the Bader charge analysis and density of state (DOS) were further conducted (see Figure 8a  As can be seen (Figure 8a,b)  As can be seen (Figure 8a,b) Figure 8c). This finding indicates that the neighboring [Fe]-[Cu] site can exert much a stronger electric field effect on the adsorbed N 2 O, which is greatly favorable for the pre-activation of N 2 O and subsequent O-N 2 bond fracture to produce active O. As observed ( Figure S11a

Catalyst Preparation
The commercial H-BEA with the Si/Al of 12.5 (mole ratio) was purchased from Tianjin Nankai University Catalyst Co., Ltd. of China, based on which a series of Fe n Cu m -BEA zeolites (Table S1) were prepared by means of the traditional wet ion-exchange method. For the purpose of comparison, the monomeric Fe 1.28% -and Cu 1.28% -BEA, with the total metal loading amounts being the same as those of Fe 0.6% Cu 0.68% -BEA (1.28 wt.%), were prepared by means of an incipient-wetness impregnation method. More details regarding the catalytic preparations are stated in the Supplementary Materials.

Catalyst Characterizations
The characterizations of X-ray diffraction (XRD), element content (determined by inductively coupled plasma (ICP), X-ray photoelectron spectroscopy (XPS), N 2 adsorption/desorption, H 2 -temperature programmed reduction (H 2 -TPR), UV-vis diffuse-reflectance, in situ FTIR and D 2 O isotopic tracer were conducted as described in detail in our previous work [24]alternatively, please see details in the Supplementary Materials. To prevent condensation, the gas line from the point of liquid injection to then GC unit was heated (T = 200 • C) by resistive heating tape. More details regarding activity measurement can be found in the Supplementary Materials or our previous work [24].

Constructed Model
The model of Fe n Cu m -BEA with the neighboring [Fe]-[Cu] bimetal active site was constructed based on the BEA structure (a = 12.632, b = 12.632 and c = 9.421 Å) from the database of IZA [37], wherein the framework Al was located at the T2 and T5 site according to our previous work [24], and the Si atoms were set to be fixed during the structure optimization and transition state (TS) calculations to keep the structure of BEA.

Computational Method
The periodic density functional theory (DFT) analysis was performed based on the Vienna ab-initio simulation package (VASP) [38], which was employed in the present work to simulate the N 2 O DMTM mechanism (in the presence and absence of H 2 O) and conduct microkinetic analysis, electronic structure analysis (including electronic density difference, Bader charge and density of state (DOS)) and ab initio thermodynamics analysis (evaluating the thermostabilities of active-site motif and generating radical intermediate).
The ab initio molecular dynamics (AIMD) analysis was conducted based on CP2K code [39] to explore the H 2 O proton-transfer mechanism, wherein the AIMD-based metadynamic simulations were conducted utilizing two types of collective variables, the coordination numbers (CN) of [CN a O-H] and [CN b O-H] (as illustrated in Figure S1a). The detailed method descriptions of DFT and CP2K can be found in the Supplementary Materials or our previous work [24].

Conclusions
The present work systematically investigated the H 2 O-mediated continuous N 2 O DMTM over a series of Fe n Cu m -BEA zeolites based on combined experimental and theoretical approaches. The strikingly promoted CH 3 OH productivity (259.1 µmol·g −1 cat ·h −1 ) and selectivity (71.7%), as well as long-term reaction stability, can be achieved over the best-performed sample of Fe 0.6% Cu 0.68% -BEA, which is closely correlated with the synergistic effect of the loaded neighboring Fe and Cu cations. On the one hand, it is much more favorable for N 2 O dissociation to generate the αO (bridge O of [Fe-O-Cu] 2+ , ∆G = 0.18 eV at T = 270 • C) due to the exerted strong electric field effect. On the other hand, it can motivate the N 2 O DMTM reaction following a H 2 O-mediated proton-transfer route to produce CH 3 OH by crossing a much lower energy barrier (∆G = 0.07 eV), eventually pronouncedly enhancing CH 3 OH production and desorption as well as the catalytic reaction's long-term stability (through efficiently reducing carbon depositions). Generally, the present work reported the synergistic effect of neighboring Fe and Cu cations over the Fe n C m -BEA zeolite, which can efficiently promote its CH 3 OH productivity/selectivity during H 2 O-mediated N 2 O DMTM. Thereby, employing the synergistic effect of bimetallic cations to modify zeolitic activity constitutes a promising strategy for a highly efficient catalyst design for the DMTM.