Nonoxidative Coupling of Methane to Produce C2 Hydrocarbons on FLPs of an Albite Surface

The characteristics of active sites on the surface of albite were theoretically analyzed by density functional theory, and the activation of the C-H bond of methane using an albite catalyst and the reaction mechanism of preparing C2 hydrocarbons by nonoxidative coupling were studied. There are two frustrated Lewis pairs (FLPs) on the (001) and (010) surfaces of albite; they can dissociate H2 under mild conditions and show high activity for the activation of methane C-H bonds. CH4 molecules can undergo direct dissociative adsorption on the (010) surface, whereas a 50.07 kJ/mol activation barrier is needed on the (001) surface. The prepared albite catalyst has a double combination function of the (001) and (010) surfaces; these surfaces produce a spillover phenomenon in the process of CH4 activation reactions, where CH3 overflows from the (001) surface with CH3 adsorbed on the (010) surface to achieve nonoxidative high efficiently C-C coupling with an activation energy of 18.51 kJ/mol. At the same time, this spillover phenomenon inhibits deep dehydrogenation, which is conducive to the selectivity of the C2 hydrocarbons. The experimental results confirm that the selectivity of the C2 hydrocarbons is maintained above 99% in the temperature range of 873 K to 1173 K.


Introduction
Direct conversion of methane (DMC) to high value-added chemicals (such as ethylene and other compounds) is an effective way to achieve its efficient utilization, which plays a vital role in the economy and environment. Methane is the most stable small molecule in nature, due to its stable tetrahedral symmetric structure, which causes its efficient activation and direct conversion under mild conditions to be extremely challenging. After decades of continuous efforts, researchers have proposed many ways to produce DMC, among which the development of oxidative coupling, nonoxidative dehydrogenation and selective oxidation methods has greatly promoted research on DMC. In recent years, the high utilization rate and high selectivity of the active species of single-atom catalysts (SACs) have attracted extensive attention from researchers [1][2][3][4]. Because of their unique catalytic performance in DMC reactions, SACs have been used in various reactions, and although they have many advantages, they still face many challenges, due to their high surface energy and instability of single atoms along with limitations of characterization methods for the nanoscale to single-atom scale species, catalyst design and preparation, etc. Therefore, the goal is to find catalysts with high catalytic performance, simple preparation and good stability.
Since 2006, Professor W. Stephan has found that homogeneous frustrated Lewis pair (FLP) catalysts could activate the H 2 molecule [5] under mild conditions, and the activation potential of FLP for small molecules in homogeneous fields has constantly been of great interest to researchers. However, the application of homogeneous FLPs is hindered by defects such as product separation and the recycling of catalysts; some researchers have gradually begun focusing on developing heterogeneous FLP catalysts on a solid surface, aiming to make a breakthrough in DMC. At present, all-solid FLPs constructed from a variety of materials, such as doped graphene [6], B/Al-doped phosphorenes [7], and hydroxylated indium oxide [8], have shown good activity performance for H 2 activation and hydrogenation reactions. Since research in this area has just began, there have been relatively few studies on the nonoxidative activation of CH 4 . Metal oxides such as the FLP of γ-Al 2 O 3 (110) and CeO 2 (110) have a remarkable ability to activate the methane C-H bond [9,10], and nonoxidative C-C coupling can be performed on the surface of CeO 2 . Recently, researchers have extended the concept of FLP to multistage porous Ti-based and zeolite molecular sieve catalytic systems [11,12] and made important progress in the research of photocatalytic nonoxidative coupling of methane and dehydrogenation of hydrocarbons above C 3 . To date, the reference research methods and concepts are very limited. However, solid FLPs show the potential to activate methane in catalytic reactions, which attract further research and exploration to achieve different goals in FLP research.
Albite (Ab) is a type of natural mineral that is abundant, cheap, and easy to obtain. It not only has good thermal stability and chemical stability but also has channel structure characteristics similar to those of zeolites. The difference is that the pore diameter of the channel is below 3 Å and belongs to the ultra-microchannel; due to this difference, researchers have not pursued long-term studies using albite. In an experimental study, we found that albite catalysts have a certain activation effect on methane using nonoxidative conditions, and the C 2 hydrocarbon selectivity is above 99% [13]. Using density functional theory (DFT), it is found that FLPs exist on the surface of albite, and we speculate that they activate methane according to the mechanism of FLPs. Therefore, it is necessary to further study the nature and trends of methane activation using albite catalysts in theory, which is of great significance to expand the application of ultra-microchannel mineral materials.
In this study, initially, the FLP active sites on the (001) and (010) surfaces of albite were theoretically analyzed, and the calculation confirmed that they had the characteristics of FLPs. Then, we studied in detail the activation effects and conversion behaviors of surface FLPs to CH 4 and determined the mechanism showing its high selectivity to C 2 hydrocarbons and its non-easy production in carbon deposits. Finally, the static electric field of FLPs was regulated by doping modification, and the influence on CH 4 conversion was analyzed and discussed to obtain a newfound understanding of the application of albite and provide a novel concept and method for the nonoxidative coupling of methane by solid FLPs.

Theoretical Analysis of FLP Sites on Albite Surfaces
The basic structural units of albite (NaAlSi 3 O 8 ) are [SiO 4 ] and [AlO 4 ] tetrahedrons, and each oxygen atom in the skeleton is shared with two adjacent tetrahedrons. Because of the charge imbalance caused by Al replacing Si, a Na + cation with balanced charge is introduced into the structure and is located in the pores of the tetrahedral skeletal structure. Albite minerals have two common exposed surfaces, (001) and (010), in a natural or grinding external force situation [14,15], and the structures are shown in Figure 1.
Initially, we analyzed the active sites in the two surface structures of albite according to Lewis acid-base theory. The tetrahedral central atoms in albite structures Al and Si have four sp 3 hybrid orbitals, which are bonded to four O atoms on the (001) surface. [AlO 3 ] lacking one oxygen is exposed on the surface layer. Al is in the coordination unsaturated state and has an empty orbital, which can accept electron pairs; Al acts as a Lewis acid (LA). The oxygen atom exposed on the surface has an electron rich attribute and acts as a Lewis base (LB). [SiO 3 ] lacking oxygen is exposed on the (010) surface. Si is in the coordination unsaturated state, its valence orbit can accept electrons, and it acts as a LA; similarly, the oxygen atom exposed to the surface acts as a LB. Both LAs and LBs on the two surfaces are distributed on the skeleton of [AlO 4 ] and [ SiO 4 ]. The formation of solid frustrated Lewis acid-base pairs requires not only independent LAs and LBs but also appropriate sterically encumbered matching pairs. Albite is a mineral with an ultra-microchannel structure, and the pore diameter parallel to the channel is mainly below 0.3 nm [16][17][18]. Due to its undulating and uneven surface, many micropores are formed that are not parallel to the crystal surface; that is, the Lewis acid and base sites distributed on the surface skeleton of albite are not in the same horizontal plane. On the (001) surface, there were two sterically encumbered combinations: one group was located on the channel skeleton, with a distance of 4.21 Å, and the other group was located on the pore skeleton, with a distance of 4.39 Å. On the (010) surface, there were also two combinations: the distance on the channel skeleton was 5.10 Å, and the distance on the pore skeleton was 4.20 Å. Using the viewpoint that a distance between Lewis acid-base sites of approximately 4 Å is appropriate [12,19,20], the Lewis acid-base pairs on the channel skeleton of the (001) face and the pore skeleton of the (010) face are matched; therefore, there are FLPs on both surfaces of albite. Initially, we analyzed the active sites in the two surface structures of albite according to Lewis acid-base theory. The tetrahedral central atoms in albite structures Al and Si have four sp 3 hybrid orbitals, which are bonded to four O atoms on the (001) surface.
[AlO3] lacking one oxygen is exposed on the surface layer. Al is in the coordination unsaturated state and has an empty orbital, which can accept electron pairs; Al acts as a Lewis acid (LA). The oxygen atom exposed on the surface has an electron rich attribute and acts as a Lewis base (LB). [SiO3] lacking oxygen is exposed on the (010) surface. Si is in the coordination unsaturated state, its valence orbit can accept electrons, and it acts as a LA; similarly, the oxygen atom exposed to the surface acts as a LB. Both LAs and LBs on the two surfaces are distributed on the skeleton of [AlO4] and [SiO4]. The formation of solid frustrated Lewis acid-base pairs requires not only independent LAs and LBs but also appropriate sterically encumbered matching pairs. Albite is a mineral with an ultramicrochannel structure, and the pore diameter parallel to the channel is mainly below 0.3 nm [16][17][18]. Due to its undulating and uneven surface, many micropores are formed that are not parallel to the crystal surface; that is, the Lewis acid and base sites distributed on the surface skeleton of albite are not in the same horizontal plane. On the (001) surface, there were two sterically encumbered combinations: one group was located on the channel skeleton, with a distance of 4.21 Å, and the other group was located on the pore skeleton, with a distance of 4.39 Å. On the (010) surface, there were also two combinations: the distance on the channel skeleton was 5.10 Å, and the distance on the pore skeleton was 4.20 Å. Using the viewpoint that a distance between Lewis acid-base sites of approximately 4 Å is appropriate [12,19,20], the Lewis acid-base pairs on the channel skeleton of the (001) face and the pore skeleton of the (010) face are matched; therefore, there are FLPs on both surfaces of albite.
Second, to further verify the characteristics of FLPs on the surface of albite, we calculated the reaction barrier for activating H2 (see Figure 2). The results showed that FLPs on both surfaces could enable H2 heterolysis. The dissociation activation energy of the (001) surface was 36.48 kJ/mol, and that of the (010) surface was 1.01 kJ/mol. Heterolysis frag- Second, to further verify the characteristics of FLPs on the surface of albite, we calculated the reaction barrier for activating H 2 (see Figure 2). The results showed that FLPs on both surfaces could enable H 2 heterolysis. The dissociation activation energy of the (001) surface was 36.48 kJ/mol, and that of the (010) surface was 1.01 kJ/mol. Heterolysis fragments of H − and H + were adsorbed on the LA and LB, respectively. Erker et al. studied the activation mechanism of small molecules H 2 by FLPs and thought that the activation of small molecules by FLPs was based on the polarization of the electrostatic field between the electron receptor and donor acid-base pair [21,22]. Using a Lewis acid-base electrostatic field, an activity region would be formed, and the energy barrier in the reaction process was generated in the preparatory entry stage of small molecules. Once small molecules entered the active region of FLPs, the reaction energy barrier disappeared, and a stable dissociated product was finally formed [23]. We also found in the calculation that when H 2 is at a suitable distance from the Lewis acid-base pair on the two surfaces, direct dissociation adsorption occurs. When H 2 enters the active region formed by LA and LB, it is directly dissociated. The transition-state (TS) structure of H 2 dissociation ( Figure 2) shows that the H 2 molecule has not been dissociated; in fact, the activation energies of 36.48 kJ/mol and 1.01 kJ/mol are required for H 2 to enter the activity region from outside. The FLPs on the two surfaces have a strong activation effect on H 2 , showing evident FLP characteristics. Thus, albite is a natural mineral with an ultra-microchannel structure, and its surface coordination unsaturated Si, Al, and O atoms are distributed on the skeleton formed by [AlO 4 ] and [SiO 4 ], which can form mutually independent LAs and LBs. Its ultra-microchannel structure causes the LAs and LBs to form matching subnanoscale sterically encumbered minerals, thus forming FLPs. characteristics. Thus, albite is a natural mineral with an ultra-microchannel structure, and its surface coordination unsaturated Si, Al, and O atoms are distributed on the skeleton formed by [AlO4] and [SiO4], which can form mutually independent LAs and LBs. Its ultra-microchannel structure causes the LAs and LBs to form matching subnanoscale sterically encumbered minerals, thus forming FLPs.

Effect on C-H Bond Activation of Methane
To deeply understand the adsorption and activation mechanism of CH4 on the FLPs of the albite surface, we initially calculated the adsorption energies of CH4, CH3, H and CH3/H on the two surfaces (see Table 1). Using the table, the most stable CH4 is adsorbed on the LA (Al,Si), and the most stable adsorption of the co-adsorption system of CH4 dissociated species CH3/H is located on the LA (Al,Si)/LB (O). Additionally, the adsorption energies of CH4 and dissociated species CH3, H on the two surfaces follow the trend of CH4 < CH3 < H. The adsorption of CH3 and H on the (010) surface is stronger than that on the (001) surface, and their adsorption energies are 150.09 kJ/mol and 102.4 kJ/mol higher, respectively. The adsorption of CH4 on the two surfaces had a similar phenomenon to that of H2, showing different adsorption between the CH4 and LA (Al,Si) distances and degrees of polarization, as shown in Figure 3. On the (001) surface, when CH4 is far from the LA (Al) site (dC-Al > 3.8 Å), the adsorption energy is positive, indicating instability (see Figure 3a). When CH4 is close to the LA (Al) site (dC-Al < 3.8 Å), CH4 is stably adsorbed at a position of 2.34 Å from C to Al (see Figure 3b). The adsorption energy is −27.86 kJ/mol, generating a dipole moment of 0.13 D, indicating that CH4 has been polarized; the C-H bond is weakened and stretched to 1.11 Å. On the (010) surface when CH4 is far from the LA (Si) site (dC-Si > 3.9 Å), the adsorption of CH4 on the surface is weak (see Figure 3c). When CH4 is close to the LA (Si) site (dC-Si < 3.9 Å), heterolysis occurs directly, CH3 is adsorbed on the LA (Si), and H is adsorbed on the LB (O), as shown in Figure 3d. This is completely consistent with the phenomenon described by Grimme S. et al., in that "once the molecule enters the hole of FLPs, the reaction proceeds without a barrier" [23]; that is, CH4 can undergo direct dissociative adsorption in the active area of the Lewis acid-base pairs on the (010) surface.
To analyze the micro-mechanism of its dissociative adsorption process, we observed the dynamic change in the (010) surface adsorption configuration, as shown in Figure 4 and the corresponding Hirshfeld charge distribution and CH4 dipole moments were calculated (see Table 2). Interestingly, there are three stages in the dissociative adsorption

Effect on C-H Bond Activation of Methane
To deeply understand the adsorption and activation mechanism of CH 4 on the FLPs of the albite surface, we initially calculated the adsorption energies of CH 4 , CH 3 , H and CH 3 /H on the two surfaces (see Table 1). Using the table, the most stable CH 4 is adsorbed on the LA (Al,Si), and the most stable adsorption of the co-adsorption system of CH 4 dissociated species CH 3 /H is located on the LA (Al,Si)/LB (O). Additionally, the adsorption energies of CH 4 and dissociated species CH 3 , H on the two surfaces follow the trend of CH 4 < CH 3 < H. The adsorption of CH 3 and H on the (010) surface is stronger than that on the (001) surface, and their adsorption energies are 150.09 kJ/mol and 102.4 kJ/mol higher, respectively. The adsorption of CH 4 on the two surfaces had a similar phenomenon to that of H 2 , showing different adsorption between the CH 4 and LA (Al,Si) distances and degrees of polarization, as shown in Figure 3. On the (001) surface, when CH 4 is far from the LA (Al) site (d C-Al > 3.8 Å), the adsorption energy is positive, indicating instability (see Figure 3a). When CH 4 is close to the LA (Al) site (d C-Al < 3.8 Å), CH 4 is stably adsorbed at a position of 2.34 Å from C to Al (see Figure 3b). The adsorption energy is −27.86 kJ/mol, generating a dipole moment of 0.13 D, indicating that CH 4 has been polarized; the C-H bond is weakened and stretched to 1.11 Å. On the (010) surface, when CH 4 is far from the LA (Si) site (d C-Si > 3.9 Å), the adsorption of CH 4 on the surface is weak (see Figure 3c). When CH 4 is close to the LA (Si) site (d C-Si < 3.9 Å), heterolysis occurs directly, CH 3 is adsorbed on the LA (Si), and H is adsorbed on the LB (O), as shown in Figure 3d. This is completely consistent with the phenomenon described by Grimme S. et al., in that "once the molecule enters the hole of FLPs, the reaction proceeds without a barrier" [23]; that is, CH 4 can undergo direct dissociative adsorption in the active area of the Lewis acid-base pairs on the (010) surface.     To analyze the micro-mechanism of its dissociative adsorption process, we observed the dynamic change in the (010) surface adsorption configuration, as shown in Figure 4, and the corresponding Hirshfeld charge distribution and CH 4 dipole moments were calculated (see Table 2). Interestingly, there are three stages in the dissociative adsorption process of CH 4 . In the first stage (a-d), as CH 4 gradually approaches the LA (Si), the LA (Si) is in a state of acquiring electrons, CH 4 is in a state of donating electrons, and the LB (O) has no electron transfer; the CH 4 dipole moment gradually increases, and CH 4 is in a state of physical adsorption. In the second stage (e-f), when the distance between C and Si is 2.23 Å, CH 4  In the process of CH 4 activation, the LA, as an electrophilic reagent, plays an important role in the polarization of CH 4 ; a greater degree of polarization of CH 4 correlates to a stronger reaction activity. The LB, as a nucleophilic reagent, can obtain protons, and they synergistically complete the cleavage of CH 4 . Since the electrophilicity of the LA on the (001) surface is weaker than that on the (010) surface, its polarization to CH 4 is relatively weak, and CH 4 cannot be directly cleaved.     Second, the reaction barriers of CH 4 activation by two surface FLPs were calculated (see Figure 5); both surfaces show good activity. The reaction heat of CH 4 dissociation on the (001) surface is −71.72 kJ/mol, and an activation energy of 50.07 kJ/mol needs to be overcome. The reaction heat of CH 4 dissociation on the (010) surface is −292.61 kJ/mol, and the activation energy is 2.63 kJ/mol. From the two surface TS structures, CH 4 on the (001) surface has been dissociated, while CH 4 on the (010) surface has not been dissociated. CH 4 was polarized and contained the activation energy required for methane to enter the activity region from outside. Once CH 4 enters the activity region, heterolysis occurs according to the direct dissociation mechanism.
Molecules 2023, 28 Second, the reaction barriers of CH4 activation by two surface FLPs were calculated (see Figure 5); both surfaces show good activity. The reaction heat of CH4 dissociation on the (001) surface is −71.72 kJ/mol, and an activation energy of 50.07 kJ/mol needs to be overcome. The reaction heat of CH4 dissociation on the (010) surface is −292.61 kJ/mol, and the activation energy is 2.63 kJ/mol. From the two surface TS structures, CH4 on the (001) surface has been dissociated, while CH4 on the (010) surface has not been dissociated. CH4 was polarized and contained the activation energy required for methane to enter the activity region from outside. Once CH4 enters the activity region, heterolysis occurs according to the direct dissociation mechanism.
From a thermodynamic point of view, the dissociation reaction heat of the (010) surface is far greater than that of the (001) surface, indicating that the bonding effect between dissociated fragments CH3 and H with acid-base sites of the (010) surface is stronger than that of the (001) surface. From a kinetic point of view, the activation energy of CH4 on the (010) surface is much lower than that on the (001) surface. Although the dissociation activation energy of CH4 on the (010) surface is the lowest, the strong bonding effect between CH3/H and the surface means that desorption requires a higher desorption energy, which is in accordance with the Brónsted Evans Polanyi rule [24].

Effect on the Methyl C-C Coupling Mode
The albite catalyst is prepared by high-temperature calcination and grinding using From a thermodynamic point of view, the dissociation reaction heat of the (010) surface is far greater than that of the (001) surface, indicating that the bonding effect between dissociated fragments CH 3 and H with acid-base sites of the (010) surface is stronger than that of the (001) surface. From a kinetic point of view, the activation energy of CH 4 on the (010) surface is much lower than that on the (001) surface. Although the dissociation activation energy of CH 4 on the (010) surface is the lowest, the strong bonding effect between CH 3 /H and the surface means that desorption requires a higher desorption energy, which is in accordance with the Brónsted Evans Polanyi rule [24].

Effect on the Methyl C-C Coupling Mode
The albite catalyst is prepared by high-temperature calcination and grinding using an external force to physically mix and fully expose the two common exposed surfaces, (001) and (010). In fact, it is a double combination catalyst with (001) and (010) coexisting, and they participate in the catalytic reaction of methane at the same time. Figure 6 shows the catalytic conversion path of methane on the albite catalyst; when methane enters the catalyst surface from the gas phase, the FLPs on both surfaces cause methane heterolysis according to the same activation mechanism, and the dissociated fragments CH 3 and H are located on LA and LB sites on both surfaces, respectively. Since the bonding effect with CH 3 and H adsorbed on the (001) surface is much weaker than that on the (010) surface, they preferentially desorb during temperature rise desorption, causing a spillover phenomenon; at the same time, because the Lewis acid site Al on the (001) surface has an empty orbital and CH 3 − has a lone electron pair, after the two bond, that is, CH 3 − adsorbed on (001) surface can neither give nor gain electrons, C-C coupling does not occur on (001) surface. Similarly, the spilled H + cannot gain electrons from Lewis acid site Al in (001) surface to form H − . Therefore, the coupling reaction of CH 3 and H overflowers on (001) surface can only occur on (010) surface, that is, CH 3 and H preferentially desorbed become overflowers and diffuse to the (010) surface with an increase in the concentration gradient. In the overflow process, since the bonding effect of CH 3 on the (001) surface is much smaller than that of H, CH 3 desorbs first.
Molecules 2023, 28, 1037 8 of 13 Therefore, the coupling reaction of CH3 and H overflowers on (001) surface can only occur on (010) surface, that is, CH3 and H preferentially desorbed become overflowers and diffuse to the (010) surface with an increase in the concentration gradient.
In the overflow process, since the bonding effect of CH3 on the (001) surface is much smaller than that of H, CH3 desorbs first. Figure 7 shows the desorption energy of CH3 spillover and H spillover on the (001) surface and the reaction energy barrier on the (010) surface. The desorption of CH3 requires an activation energy of 306.37 kJ/mol, and the diffusion to the (010) surface is coupled with the adsorbed methyl group through the E-R mechanism. The formation of C2H6 is an exothermic process and only requires an activation energy of 18.51 kJ/mol, indicating that C-C coupling has a strong bonding effect and shows good activity. CH3 is E-R coupled on the surface, which is advantageous both in thermodynamics and kinetics, and part of the C2H6 generated by coupling continues to dehydrogenate and then generates C2H4. The above results are consistent with the experimental results. At 1073 K, the analysis of the relationship between CH4 conversion, C2 hydrocarbon selectivity and space velocity (GHSV) shows that CH4 conversion decreases with increasing GHSV; CH4 activation is fully achieved on the surface FLPs because a higher GHSV corresponds to a shorter contact time and lower CH4 conversion rate. The phenomenon of increasing C2H6 and decreasing C2H4 with increasing GHSV further confirms that the coupling of CH3 to produce C2H6 occurs on the surface rather than in the gas phase. C2H4 is the product of dehydrogenation of C2H6 in the gas phase [13]. When H overflows and diffuses to the (010) surface, and since the electronegativity of the H atom (2.1) is greater than that of the Si atom (1.8), H spillover can easily acquire unpaired electrons from the LA (Si) to form H − . This reaction process produces a strong exothermic reaction with a reaction heat of −431.12 kJ/mol and an activation energy of 24.69 kJ/mol. After that, H adsorbed on the LA (Si) reacts with proton H adsorbed on the LB (O) to generate H2 through the L-H mechanism; the required activation energy is 306.08 kJ/mol, and the closed cycle of methane conversion is completed. Since the desorption energy required for H spillover on the (001) surface (387.36 kJ/mol) is the highest during the whole reaction process, this is the rate-determining step in the whole cycle process.   Figure 7 shows the desorption energy of CH 3 spillover and H spillover on the (001) surface and the reaction energy barrier on the (010) surface. The desorption of CH 3 requires an activation energy of 306.37 kJ/mol, and the diffusion to the (010) surface is coupled with the adsorbed methyl group through the E-R mechanism. The formation of C 2 H 6 is an exothermic process and only requires an activation energy of 18.51 kJ/mol, indicating that C-C coupling has a strong bonding effect and shows good activity. CH 3 is E-R coupled on the surface, which is advantageous both in thermodynamics and kinetics, and part of the C 2 H 6 generated by coupling continues to dehydrogenate and then generates C 2 H 4 . The above results are consistent with the experimental results. At 1073 K, the analysis of the relationship between CH 4 conversion, C 2 hydrocarbon selectivity and space velocity (GHSV) shows that CH 4 conversion decreases with increasing GHSV; CH 4 activation is fully achieved on the surface FLPs because a higher GHSV corresponds to a shorter contact time and lower CH 4 conversion rate. The phenomenon of increasing C 2 H 6 and decreasing C 2 H 4 with increasing GHSV further confirms that the coupling of CH 3 to produce C 2 H 6 occurs on the surface rather than in the gas phase. C 2 H 4 is the product of dehydrogenation of C 2 H 6 in the gas phase [13]. When H overflows and diffuses to the (010) surface, and since the electronegativity of the H atom (2.1) is greater than that of the Si atom (1.8), H spillover can easily acquire unpaired electrons from the LA (Si) to form H − . This reaction process produces a strong exothermic reaction with a reaction heat of −431.12 kJ/mol and an activation energy of 24.69 kJ/mol. After that, H adsorbed on the LA (Si) reacts with proton H adsorbed on the LB (O) to generate H 2 through the L-H mechanism; the required activation energy is 306.08 kJ/mol, and the closed cycle of methane conversion is completed. Since the desorption energy required for H spillover on the (001) surface (387.36 kJ/mol) is the highest during the whole reaction process, this is the rate-determining step in the whole cycle process. This spillover phenomenon not only enables highly efficient coupling of methyl groups but also plays two important roles: (1) to remove CH3 and H, which are firmly adsorbed on the surface of (010), to regenerate the acid-base sites and (2) to avoid deep dehydrogenation, which is conducive to the selectivity of C2 hydrocarbons. Because the heterolytic activation of CH4 by FLPs on the surface of albite is a synergistic catalytic mechanism, the dehydrogenation activation of methane can only be achieved using the joint action of the LAs and LBs. After the Lewis acid-base sites are regenerated, the methane conversion cycle reaction can continue; the desorption order of the dissociated fragments adsorbed on the Lewis acid-base sites directly affects the reaction direction of conversion. When the LB site preferentially regenerates, the carbon species adsorbed on the LA site undergo dehydrogenation, whereas when the carbon species adsorbed on the LA site preferentially desorb, the occurrence of deep dehydrogenation is avoided. Since the bonding effect between the (001) face of CH3 and the surface is much smaller than that of H, the preferential desorption of CH3 avoids further dehydrogenation. At the same time, CH3 preferentially overflowed is coupled on the (010) surface to form ethane, which also avoids further dehydrogenation of CH3 adsorbed on the (010) surface. This reasonably explains the experimental results that the selectivity of C2 hydrocarbons is maintained across up to 99% and there are zero carbon deposits in the temperature range of 873~1173 K.

Effect of Doping Modification on CH4 Conversion
From the above analysis, the albite catalyst shows good catalytic ability for methane C-H bond activation and methyl C-C coupling, has high selectivity for C2 hydrocarbons and does not easily undergo carbon deposition. However, we also find that the conversion of CH4 is relatively low, and it increases with increasing temperature. This phenomenon shows that the conversion of CH4 is closely related to temperature. Since the FLP catalytic This spillover phenomenon not only enables highly efficient coupling of methyl groups but also plays two important roles: (1) to remove CH 3 and H, which are firmly adsorbed on the surface of (010), to regenerate the acid-base sites and (2) to avoid deep dehydrogenation, which is conducive to the selectivity of C 2 hydrocarbons. Because the heterolytic activation of CH 4 by FLPs on the surface of albite is a synergistic catalytic mechanism, the dehydrogenation activation of methane can only be achieved using the joint action of the LAs and LBs. After the Lewis acid-base sites are regenerated, the methane conversion cycle reaction can continue; the desorption order of the dissociated fragments adsorbed on the Lewis acid-base sites directly affects the reaction direction of conversion. When the LB site preferentially regenerates, the carbon species adsorbed on the LA site undergo dehydrogenation, whereas when the carbon species adsorbed on the LA site preferentially desorb, the occurrence of deep dehydrogenation is avoided. Since the bonding effect between the (001) face of CH 3 and the surface is much smaller than that of H, the preferential desorption of CH 3 avoids further dehydrogenation. At the same time, CH 3 preferentially overflowed is coupled on the (010) surface to form ethane, which also avoids further dehydrogenation of CH 3 adsorbed on the (010) surface. This reasonably explains the experimental results that the selectivity of C 2 hydrocarbons is maintained across up to 99% and there are zero carbon deposits in the temperature range of 873~1173 K.

Effect of Doping Modification on CH 4 Conversion
From the above analysis, the albite catalyst shows good catalytic ability for methane C-H bond activation and methyl C-C coupling, has high selectivity for C 2 hydrocarbons and does not easily undergo carbon deposition. However, we also find that the conversion of CH 4 is relatively low, and it increases with increasing temperature. This phenomenon shows that the conversion of CH 4 is closely related to temperature. Since the FLP catalytic reaction is generally a synergistic mechanism, the regeneration of acid-base sites is crucial to the cyclic reaction. For albite catalysts, the desorption of dissociated fragment H on the (001) surface is the rate-determining step of the cyclic catalytic reaction. Under nonoxygen conditions, temperature is the main factor affecting the desorption of H, and higher desorption energy can lead to lower conversion. Therefore, on the basis of a lower desorption energy of CH 3 than that of H, a reduction in the desorption energy of H helps to improve methane conversion. In the albite structure, the Na + in the pores mainly balances the residual negative charges on the skeleton and affects the electrostatic field formed by the LA and LB. According to the principle of field strength superposition, doping high valence metal ions instead of Na + plays a role in regulating the electrostatic field of FLPs. In this experiment, we mixed the prepared albite catalyst with anhydrous lead chloride in different proportions, calcined it at 773 K, and formed a Pb 2+ -doped Pb/Ab catalyst through ion exchange. To investigate the influence of Pb doping on the CH 4 conversion rate, we calculated the desorption energy of H and CH 3 before and after (001) surface doping, and the calculated results were analyzed and compared with the experimental values of CH 4 conversion and C 2 hydrocarbon selectivity before and after doping at 1073 K (see Figure 8). The desorption energy of CH 3 after doping is still less than that of H, and the activation barrier of CH 4 is slightly increased, increasing from 50.07 kJ/mol to 59.21 kJ/mol; this result means that doping has less effect on the catalytic activity of CH 4 , and the desorption energy of H is reduced from 387.36 kJ/mol to 337.46 kJ/mol, showing a decrease of 49.9 kJ/mol. Corresponding to the experimental results at 1073 K, the conversion of methane after doping was promoted by 2.45 times from 3.32% to 8.12%, and the selectivity remained above 99%. After doping, reducing the bonding effect of the (001) surface H has an evident effect on improving the conversion of CH 4 . Therefore, we believe that a nonreduction (or very low reduction) in the activity and a smaller desorption energy of the CH 3 spillover than that of the H spillover using modification maximumly reduces the bonding effect between H and the surface to greatly improve the conversion rate. The above are our preliminary research results, and the application of albite catalysts requires further in-depth research. conditions, temperature is the main factor affecting the desorption of H, and higher desorption energy can lead to lower conversion. Therefore, on the basis of a lower desorption energy of CH3 than that of H, a reduction in the desorption energy of H helps to improve methane conversion. In the albite structure, the Na + in the pores mainly balances the residual negative charges on the skeleton and affects the electrostatic field formed by the LA and LB. According to the principle of field strength superposition, doping high valence metal ions instead of Na + plays a role in regulating the electrostatic field of FLPs.
In this experiment, we mixed the prepared albite catalyst with anhydrous lead chloride in different proportions, calcined it at 773 K, and formed a Pb 2+ -doped Pb/Ab catalyst through ion exchange. To investigate the influence of Pb doping on the CH4 conversion rate, we calculated the desorption energy of H and CH3 before and after (001) surface doping, and the calculated results were analyzed and compared with the experimental values of CH4 conversion and C2 hydrocarbon selectivity before and after doping at 1073 K (see Figure 8). The desorption energy of CH3 after doping is still less than that of H, and the activation barrier of CH4 is slightly increased, increasing from 50.07 kJ/mol to 59.21 kJ/mol; this result means that doping has less effect on the catalytic activity of CH4, and the desorption energy of H is reduced from 387.36 kJ/mol to 337.46 kJ/mol, showing a decrease of 49.9 kJ/mol. Corresponding to the experimental results at 1073 K, the conversion of methane after doping was promoted by 2.45 times from 3.32% to 8.12%, and the selectivity remained above 99%. After doping, reducing the bonding effect of the (001) surface H has an evident effect on improving the conversion of CH4. Therefore, we believe that a nonreduction (or very low reduction) in the activity and a smaller desorption energy of the CH3 spillover than that of the H spillover using modification maximumly reduces the bonding effect between H and the surface to greatly improve the conversion rate. The above are our preliminary research results, and the application of albite catalysts requires further in-depth research.

Calculation Method
In this paper, the DMol 3 module [25] of MS19.1 software was used for simulation, and DFT was used for calculation. The exchange correlation potential is described by the PBE (Perdew, Burke and Enzerhof) function under the generalized

Calculation Method
In this paper, the DMol 3 module [25] of MS19.1 software was used for simulation, and DFT was used for calculation. The exchange correlation potential is described by the PBE (Perdew, Burke and Enzerhof) function under the generalized gradient approximation GGA [26]. The electron wave function used the dual atomic orbital plus the polarization function DNP [25] as the basis set, and the truncation radius was 5.2 Å. The convergence tolerance of energy, gradient and displacement were 1.0 × 10 −5 Ha, 0.002 Ha/Å and 0.005 Å, respectively. In the self-consistent functional (SCF) calculation, the convergence criterion was 1.0 × 10 −6 Ha, and the smearing value was set to 0.005 Ha. The transition state was determined by the complete LST/QST [27] and nudged elastic band method (NEB) [28]. The atomic charge was calculated by Hirshfeld population analysis.
Albite crystals belong to the triclinic system, space group C 1 , and the lattice constants are a = 0.8137 nm, b = 1.2787 nm, c = 0.7157 nm, α = 94.245 • , β = 116.605 • , and γ = 87.809 • [29]. In this paper, surface models of periodic NaAlSi 3 O 8 (001) and (010) were constructed as research objects. Both the (001) surface and (010) surface supercell models were 2 × 1 × 1; this size ensured that there was no interaction between adsorbed molecules. A vacuum layer of 18 Å ensured that there was no interaction between adjacent albite layers in the z-axis direction. The k point parameters of the (001) surface and (010) surface were 2 × 2 × 1 and 3 × 3 × 2, respectively. The upper part and the adsorbate relaxed, while the remaining atoms were fixed in their original crystal positions. The doping calculation used Pb atoms to replace Na atoms in NaAlSi 3 O 8 pores, and the DFT semicore pseudopotentials (DSPP) core treatment [30] was applied.

Conclusions
The effect of albite catalyst FLPs on the nonoxidative coupling of CH 4 was experimentally studied by DFT. The results show that the LA and LB formed on the (001) and (010) surfaces are sterically encumbered by approximately 4 Å due to albite having a unique ultra-microchannel structure and showing significant FLP characteristics. The activity region formed by the electrostatic field of Lewis acid-base pairs could enable H 2 heterolysis. Additionally, it has remarkable activation ability for methane C-H bonds, causes direct dissociative adsorption of CH 4 molecules in the active region of the (010) surface, and requires only a 50.07 kJ/mol energy barrier for the dissociation on the (001) surface. The albite catalyst prepared by sintering and grinding is a catalyst with coexisting (001) and (010) surfaces. The bonding effect of the dissociated species CH 3 with the two surfaces exhibits quite a larger difference; therefore, a spillover effect is triggered during temperature rise desorption. This spillover effect enables CH 3 to achieve highly efficient C-C coupling under nonoxidative conditions according to the E-R mechanism and can avoid deep dehydrogenation, inhibit carbon deposits, and maintain high selectivity of the C 2 hydrocarbons. The desorption of H spillover on the (001) surface is a key step in the CH 4 conversion cycle reaction, and its high desorption energy is the main reason that affects the conversion rate. By doping high valence metal ions, the nucleophilic and electrophilic properties of FLPs can be adjusted, the desorption energy of H can be reduced, the cycle reaction of methane conversion can be accelerated, and the conversion rate can be effectively doubly promoted. Albite, as a natural mineral with an ultra-microchannel structure, is not only abundant, inexpensive, and easy to obtain but also has good chemical and thermal stability. Moreover, the catalyst is simple to prepare, easy to recover and reuse, showing excellent properties for activation of the C-H bond of methane and C-C coupling, as well as high selectivity for C 2 hydrocarbons. This study not only provides a newfound understanding of mineral materials with ultra-microchannel structures but also provides a novel concept and reference for the further use of ultra-microchannel materials to construct new solid FLP catalysts and for the nonoxidative conversion of methane.