Theoretical investigation of the paring mechanism of the MTO process in different zeolites

The paring mechanism, which belongs to the aromatic cycle of the methanol-to-olefins process and produces propene, is investigated for H-ZSM-5 (MFI structure), H-SSZ-24 (AFI structure) and H-SAPO-34 (CHA structure) with the heptamethylbenzylium cation as a co-catalyst using DFT and ab initio calculations. We focus on the mechanistic pathway of the paring mechanism that we have proposed recently for H-SSZ-13 [Catal. Sci. Technol. 12 (2022) 3516 – 3523.], in which ring contraction occurs from hexamethylmethylenecyclohexadiene and the resulting five-membered ring keeps an unsaturated methylene group throughout the process, leading to tetra-methylfulvene as the intermediate after propene elimination. The highest free energy barriers (at 400 ◦ C) for this mechanism are found to be 139 kJ/mol, 156 kJ/mol and 167 kJ/mol for H-SAPO-34, H-SSZ-24 and H-ZSM-5, respectively, compared to 127 kJ/mol for H-SSZ-13. All these barriers are low enough to be kinetically relevant and can thus explain the observed formation of propene as one of the main products of the MTO-process in these zeolites. The barriers for polymethylbenzene methylation to recover the active species are higher than the barriers for the paring mechanism in all zeolites (164 kJ/mol, 187 kJ/mol and 189 kJ/mol for H-SAPO-34, H-SSZ-24 and H-ZSM-5, compared to 163 kJ/mol for H-SSZ-13). The lowest barriers are found for H-SAPO-34, which is often the commercial catalyst in methanol-to-propene plants.


Introduction
Zeolite catalysts are vividly debated in the chemical industry as catalysts for sustainable carbon-neutral processes as they can facilitate the methanol-to-olefins (MTO) process, which can use renewably produced methanol (MeOH) to produce hydrocarbon products.[1][2][3][4][5][6] The MTO process comprises a complex reaction network, which has been subject of both experimental [4,[7][8][9][10][11][12][13] and theoretical [4,7,[14][15][16][17][18][19][20][21][22] studies.These studies established the concept of the so-called hydrocarbon pool (HCP) originally developed by Dahl and Kolboe.[23][24][25] It divides the co-catalytic reaction within the zeolite pores into two subcycles: The olefin cycle that produces olefins by repeated methylation and cracking of already produced olefins.The other is the aromatic cycle.Here, olefins are produced either by methylation and elimination of the aromatic side chains (side-chain mechanism) or by ring contraction and expansion, producing a propene side chain which can be eliminated.Until recently, the paring pathway was proposed to proceed via contraction of the heptamethylbenzenium cation (heptaMB + ), eliminating propene from a positively charged propylgroup with an antiaromatic intermediate following suggestions from Sullivan et al. dating back to the 1960s.[26] The reaction barriers of this mechanism have been computed to be 240 kJ/mol or higher in H-ZSM-5 and H-SAPO-34 [14,15], which are the two commercially employed catalysts.[27] These rather high barriers lead Wang et al. to conclude, that the paring mechanism is not a feasible reaction pathway.Another study from Chen et al. for H-ZSM-22, H-BEA, H-ZSM-5 and H-SAPO-34 also found barriers for the paring mechanism, that were 200 kJ/mol or higher for all investigated zeolites.[28] In contrast, an experimental study from Olsbye and co-workers [29], investigating the dealkylation of heptaMB + , showed evidence that the paring, rather than the side chain mechanism, was the dominant reaction pathway in H-SSZ-24 (AFI structure).In this study heptaMB + with 13 C-labelled ring carbons was introduced, leading to one or two ring carbons to be incorporated into the product species.Isotope labelling was also used by Hwang et al., who showed that also in H-SAPO-34, propene is produced from hexamethylbenzene via the paring mechanism.[30] In a recent paper from our group using H-SSZ-13 [31], we proposed an alternative paring mechanism (Fig. 1), which does not include antiaromatic intermediates.In this mechanism, propene is eliminated from a neutral propyl group with the positive charge located in the 5membered ring, so that after elimination tetramethylfulvene remains as a neutral intermediate.For H-SSZ-13 the highest free energy barrier (at 400 • C) to be overcome was 142 kJ/mol, rendering this pathway kinetically relevant.
Herein, we study this new paring mechanism for H-ZSM-5, H-SAPO-34 and H-SSZ-24 using DFT and ab initio calculations, in order to investigate the impact of zeolite topology and acidity on this mechanism for the most relevant zeotypes.H-ZSM-5 with MFI structure and H-SAPO-34 with CHA structure were chosen for their industrial relevance.
[27] H-SSZ-24 (AFI structure) was used as a comparison to the experimental study of Olsbye and co-workers [29] and to investigate the difference of a system with larger, one-dimensional pores to the threedimensional pore network of MFI and the cage structure of CHA.

Computational details
Structure optimizations were performed using periodic DFT with the dispersion-corrected PBE-D3 [32,33] functional, a convergence criterion of 0.001 eV/Å and k-point sampling only at the Γ-point.The Vienna Ab Initio Simulation Package [34] (VASP) version 5.4.1 using the atomic simulation environment [35] (ASE) with the projector-augmented wave method (PAW) and an energy cutoff of 400 eV was used to carry out calculations.
The unit cell of the H-SAPO-34 model contains 36 T-atoms, which are alternating aluminum and phosphor atoms, with one phosphor atom exchanged by a silicon atom.The optimized lattice parameters of the unit cell are a = 13.875, b = 13.875 and c = 15.017Å, as used in previous work.[36] The CHA structure of H-SAPO-34 consists of cavities formed by a double 6-membered ring connected by 8-membered ring windows.The effective diameter of the cavity is 10.8 Å, whereas the diameter of the 6-membered ring is only 6.2 Å. [37] The H-ZSM-5 model has a unit cell of the MFI structure with lattice parameters a = 20.34,b Fig. 1.Mechanistic overview of the paring mechanism investigated in this paper.The outer black pathway shows the detailed paring mechanism as introduced in our previous paper [31], with propene elimination taking place before ring expansion.Shown in green is a variant of the paring mechanism in which the ring is expanded again before propene is eliminated, this was also proposed previously.[31].(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A.E. Enss et al.
= 19.988and c = 13.492Å as optimized in previous work.[36] The T12 site, which is typically used in theoretical studies [38][39][40], was chosen as acid site location.The unit cell therefore has a Si/Al ratio of 95.The MFI structure is formed by two channel systems, a straight and a sinusoidal channel, both formed by 10-membered rings.The pore diameter in H-ZSM-5 is 8.7 Å. [37] For H-SSZ-24, optimized lattice parameters from previous work [37] are a = 13.886,b = 13.886 and c = 8.606 Å.To avoid interactions of close acid sites, a supercell containing two unit cells in the direction of lattice parameter c were used in our calculations, thus creating an AFI cell with a Si/Al ratio of 47. [37] The AFI structure is given by a one-dimensional pore system of 12-membered rings with a pore diameter of 11.3 Å. [37] For vibrational analysis, a partial Hessian was calculated including the substrate atoms and the acid site, consisting of the aluminum atom and all adjacent oxygen and silicon atoms.Gibbs free energies were calculated using the harmonic-oscillator, rigid-rotator and freetranslator approximations.Since low vibrational frequencies lead to large entropic inaccuracies in the harmonic-oscillator approximation [41,42], frequencies with less than 12 cm − 1 were raised to that value.Transition states were generally calculated with automated relaxed potential energy surface scans [43] (ARPESS) and in some cases also with the nudged elastic band [44] (NEB) and the dimer method.[45] To confirm the connectivity of transition states, structures were distorted along the direction of the transition mode and subsequently optimized towards the endpoints.DFT calculations usually underestimate transition state energies, e.g. by up to 50 kJ/mol in the case of PBE-D3.[46,47] We therefore calculated clusters including active site and reactant with higher-level methods similar to approaches developed by Sauer and co-workers.[48][49][50][51] The resulting energy correction is added to the DFT energies: [52].
Here, we use complete basis set (CBS) extrapolated Møller-Plesset second order perturbation theory (MP2) calculations to compute E cluster .[53] This includes Hartree-Fock (HF) and MP2 correlation separately extrapolated with cc-pVDZ, cc-pVTZ and cc-pVQZ basis sets using threepoint exponential fit [54] and cc-pVDZ and cc-pVTZ using the two-point X − 3 fit [55], respectively.For HF, MP2 and CCSD(T) calculations, the ORCA program package (version 4.2.1) was used.[56] The basis sets used were cc-pVDZ and cc-pVXZ [57] with X = D,T for CCSD(T) and MP2, respectively.The difference between CCSD(T) and MP2 was evaluated using DLPNO-CCSD(T) [58][59][60] with the cc-pVDZ basis set, which was proven to be reliable in a previous benchmark study.[46] We evaluated this methodology for the reaction of methanol to propene and water in section S6 in the SI.The DLPNO approximation uses the'-TightPNO' threshold.[60][61][62] HF calculations were performed with basis sets cc-pVXZ with X = D,T,Q and the RIJCOSX approximation [63] with GridX6.VASP version 5.4.1 was used to carry out DFT calculations on cluster models, using the PBE-D3 functional.
Cluster models of H-ZSM-5, H-SAPO-34 and H-SSZ-24 contain 44, 46 and 66 T-sites, respectively.Microkinetic modelling was performed with the surfprobe program of the DETCHEM software package [64] at a reference pressure of 1 bar MeOH.Coverages and fluxes were evaluated after 10 4 s to ensure convergence to steady states.With a surface coverage of 1 mol / cm 2 , turnover frequencies (TOFs) were calculated from the propene surface fluxes.

Results and discussion
The paring mechanism (Fig. 1) is usually discussed using polymethylbenzenes as the aromatic co-catalyst.Since methylation of benzene from either MeOH or dimethyl ether (DME) is thermodynamically favored, poly-methylated benzenes such as hexa-and pentamethylbenzene are commonly discussed as the acting co-catalyst.[65] For simplicity, due to its high symmetry, we only consider hexamethylbenzene (hexaMB, structure 14) in this study.Methylation of hexaMB yields the heptamethylbenzenium cation (heptaMB + , structure 1), which is usually employed as the reference point, as this is typically more stable than the neutral hexaMB, in our case by 15 kJ/mol for H-SSZ-13 [31], 7 kJ/mol for H-ZSM-5 and 40 kJ/mol for H-SSZ-24.However, for H-SAPO-34, hexaMB and heptaMB + are similar in stability at 400 • C, differing by 1 kJ/mol in Gibbs free energy (see Fig. 2

a)).
There are two variants of the revised paring mechanism [31], which are both shown in Fig. 1.Propene elimination can occur from the fivemembered ring (black pathway), followed by ring-expansion to a sixmembered ring.Alternatively, ringexpansion can happen first (green pathway) and propene is eliminated from the six-membered ring.We will first discuss propene elimination from the five-membered ring, where the computed Gibbs free energies are shown in Fig. 2. Starting from structure 1 (heptaMB + ), the methyl group in para-position to the ring carbon substituted by two methyl groups is first deprotonated to form hexamethylmethylenecyclohexadiene (HMMC, structure 2).Ring contraction to a five-membered ring with a fused three-membered ring (structure 3) occurs upon HMMC protonation in the ortho-position relative to the methylene group.This reaction proceeds through the structure labeled 2′, which is simply a protonated six-membered ring.However, for all catalysts except H-ZSM-5, structure 2′ is actually not a minimum and protonation of HMMC (structure 2) leads in these cases directly to structure 3 via TS (2)(3).For H-ZSM-5, we found a transition state (TS(1-2′)) that leads through deprotonation and re-protonation in one step from heptaMB + (structure 1) to structure 2′.Therefore, the values shown in Fig. 2 for TS(1-2) and TS(2-3) for H-SAPO-34 and H-SSZ-24 correspond to TS(1-2′) and TS(2′-3) for H-ZSM-5.
The fused three-membered ring opens to give structure 4, in which a positive charge is located on the isopropyl group.The charge is shifted to the five-membered ring during a hydride transfer from a ring-carbon to the isopropyl group (structure 5).From structure 5, the isopropyl group shifts along the ring, and is subsequently eliminated from structure 6.In the elimination step, the isopropyl cation protonates the active site to give propene and the neutral tetramethylfulvene (structure 7).In this pathway of the paring mechanism (black pathway in Fig. 1), propeneelimination through TS(6-7) is the highest reaction barrier for three of the four investigated zeolites (H-SSZ-13, [31] H-ZSM-5 and H-SAPO-34), with a very similar transition state structure as shown in Fig. 2 b)-e).
After protonation of tetramethylfulvene to structure 8, ring expansion to a six-membered ring takes place.Here, the methyl group at the doubly substituted ring carbon inserts into the C-C bond to the adjacent carbon, concertedly donating one of its hydrogen atoms to the ring, yielding the six-membered ring structure 9.In this pathway (black in Fig. 1), this step is the highest reaction barrier for H-SSZ-24.After several protonation and deprotonation steps, 1,2,3,4-tetramethylbenzene (structure 12) is formed.To close the catalytic cycle, two methylation steps are needed to form hexamethylbenzene, and a third methylation to reach the heptamethylbenzenium cation.These can occur by directly reacting with MeOH or by reacting with a surfacemethoxy-species (SMS).PentaMB can also not only be methylated directly at the ring-carbon without a methylgroup, but in a geminal way, followed by methylshifts and finally deprotonation of hexaMB + .In case of H-SAPO-34, isomerization of 1,2,3,4-tetramethylbenzene to 1,2,4,5tetramethylbenzene (structure 12a) leads to a lower methylation barrier than direct methylation of 12.All these methylation pathways have been considered, and only the respective lowest energy pathway for each methylation is shown.In H-ZSM-5, the investigated T-12 site is located at the intersection between the straight and the sinusoidal channel.In the transition state of propene elimination, the fivemembered ring is oriented in a way that propene leaves the structure along the direction of the straight channel, the barrier for this orientation is found to be 185 kJ/mol.However, we also found another transition state in which the ring is oriented such that propene is eliminated in the direction of the sinusoidal channel.The latter orientation leads to a barrier of only 126 kJ/mol, differing from the first transition state by almost 60 kJ/mol.However, due to the large diameter of heptaMB + , the barriers for rotation of the intermediate in H-ZSM-5 required to connect the most favorable obtained transition states are > 200 kJ/mol.Consequently, we presented in Fig. 1 the most favorable seamlessly connected path.We note that experimental studies in H-ZSM-5 hint towards the fact that not hexaMB, but aromatics with fewer methyl groups are most active in the aromatic cycle.[67][68][69][70][71] However, for simplicity and in order to be able to compare the results of H-ZSM-5 with the other zeotypes we focus on the fully methylated pathway herein.While we restricted our study to hexaMB as the starting point for the comparison of various zeolites, we note that other, less methylated MBs, were shown to have higher reaction barriers by earlier studies.[72] The second-highest barrier for H-ZSM-5 is the deprotonation of heptaMB + with a barrier of 167 kJ/mol.
H-SAPO-34 is an aluminophosphate with the same CHA structure as zeolite H-SSZ-13, which we investigated in our first study on the paring mechanism.[31] Compared to H-SSZ-13, H-SAPO-34 has a lower acidity [73,74], which would generally be expected to lead to higher transition state energies, because these are generally protonated species.[14,75,76] However, for the aromatic cycle, an uncommon situation arises, in which a cation (heptaMB + ) is more stable than the neutral state for most zeolites.Therefore, the lower acidity of H-SAPO-34 mainly results in moving the free energy of hexaMB below that of heptaMB + , thus also changing the most stable reference state, albeit only by 1 kJ/ mol.This applies to every neutral intermediate (hexaMB, 2, 7, 10, 12), which are all lower in free energy for H-SAPO-34 than for H-SSZ-13.Overall, the relevant barriers in the paring mechanism are also lower by 1-20 kJ/mol for H-SAPO-34 compared to H-SSZ-13 (see Fig. 2 a)).In a recent study by Ke et al., the revised paring mechanism was integrated in their microkinetic model.[77] The calculated propene elimination barrier in the paring mechanism from the fully methylated fivemembered ring in H-SAPO-34 is 144 kJ/mol at the BEEF-vdW level of theory at 0 K [77], which is 6 kJ/mol higher than our respective value at 0 K (138 kJ/mol), and is thus in good agreement.
H-SSZ-24 has a one-dimensional channel structure composed of 12membered rings, with more space for the substrates than in H-ZSM-5.As opposed to the CHA structure, which consists of cavities, which the aromatics cannot leave through the small windows, the substrate can here diffuse along the direction of the channel.In general, intermediates and transition states are relatively high in free energy, compared to the other zeolites, especially after propene elimination.The highest free energy barrier identified for this zeolite is the ring expansion (TS 8-9) with 164 kJ/mol.
We will now turn to the outcome of the calculations for the second mechanism, where ring-expansion occurs before propene elimination (green path in Fig. 1) which is shown in Fig. 3a)).Starting from structure 5, the ring can directly expand giving structure 6r.After deprotonation of the six-membered ring and protonation of the methylene-group, several methyl-transfer steps lead to structure 10r, in which the propyland methylgroup are located at the same carbon atom.From here, propene can also be eliminated, giving tetra-methyl benzene.For H-SAPO-34, H-SSZ-24 and H-SSZ-13, the highest barrier in this reaction is the ring expansion from 5 to 6r.In the study by Ke et al., the apparent energy barrier for this step is calculated to be 107 kJ/mol at 0 K [77] at the BEEF-vdW level of density functional theory and is also the ratedetermining step.Their barrier is considerably lower than our barrier at 0 K, which is 135 kJ/mol, which we attribute to the difference in level of electronic structure theory.[47] In H-ZSM-5, deprotonation of heptaMB + has a barrier of 167 kJ/mol, which is higher in free energy than the ring expansion barrier by 30 kJ/mol, hence constituting the relevant kinetic barrier in this mechanism.The highest barriers in both mechanisms shown in Fig. 1 (the black and green lines) and the highest methylation barriers are compared in Table 1, which contains the summary of the highest reaction barriers for both mechanistic pathways in all four zeolites.The lowest overall barriers for the paring mechanism are found for H-SAPO-34 (139 kJ/mol) and H-SSZ-13 (127 kJ/mol), followed by H-SSZ-24 (156 kJ/mol) and H-ZSM-5 (167 kJ/mol).These are all kinetically feasible at typical MTO temperatures and much lower

Table 1
Free energy barriers in kJ/mol, calculated at 400 • C and a reference pressure of 1 bar computed for the two variants of the paring mechanism (propene elimination first and ring expansion first) and for PMB (polymethylbenzene) methylation and TOFs for the complete mechanism, calculated by using microkinetic modelling and the energetic span model.The paring barriers are given relative two the lowest state within the paring cycle (first row) and with respect to the most stable state including PMB methylation (second row).In cases, where no intermediate within the PMB methylation mechanism is lower in free energy, no additional barrier is given.For PMB methylation, the lowest reference state is generally a minimum within the PMB methylation mechanism, making the analysis simpler.Values for H-SSZ-13 taken from previous paper [31].than what has been found using the originally proposed paring mechanism where barriers are always well over 200 kJ/mol.[14,15] The methylation barriers, however, have higher free energy barriers than the respective paring mechanism barriers in all zeolites, such that recovering the active hydrocarbon-pool species can be considered the bottleneck in the paring mechanism.Table 1. also shows the TOFs received with microkinetic modelling and by using the energetic span model.For H-SAPO-34, H-SSZ-24 and H-SSZ-13 they agree very well and the TOFs from microkinetic modelling give slightly lower values than using the energetic span model.For H-ZSM-5, the TOF calculated with the energetic span model is lower than the TOF from microkinetic modelling.This is due to the fact that we use a reference pressure of 1 bar MeOH and no H 2 O, i.e. the conditions at the start of the reaction.This makes the methylation barriers irreversible and leads to a higher TOF.In the SI, we also analyzed the microkinetics with additional H 2 O pressure.
Importantly, we thus find that the overall free energy barriers are all kinetically feasible at 400 • C with 133 kJ/mol for H-SAPO-34, 157 kJ/ mol for H-SSZ-24 and 166 kJ/mol for H-ZSM-5.Interestingly, the barriers found for H-ZSM-5 are quite a bit higher than in H-SAPO-34 (by almost 40 kJ/mol), which we ascribe to the limited mobility of heptaMB + in the pore hindering the adsorbate to rearrange and access more favorable transition state structures.The larger pore size of H-SSZ-24 compared to the other zeolites was shown to lead to lower vdWinteractions [37], which results in the generally higher free energy of adsorbed states and the second-highest overall barrier (156 kJ/mol) within the paring mechanism.The higher barriers of H-SAPO-34 compared to the similar H-SSZ-13 (both CHA structure) are due to the lower acidity of H-SAPO-34 [73,74] as discussed above.
In addition to the paring mechanism, we have computed the methylation barriers to recover hexaMB from the tetraMB formed after propene elimination.The barriers for methylation (164 kJ/mol, 187 kJ/ mol and 189 kJ/mol for H-SAPO-34, H-SSZ-24 and H-ZSM-5, compared to 163 kJ/mol for H-SSZ-13) are in all cases higher than those within the paring mechanism and are thus predicted to be rate-limiting for the catalytic cycle.The Si/Al ratios of the considered zeolites have been chosen to correspond to one isolated Brønsted site per unit cell.In a recent paper from our group, the effect of a proximate second BAS on the paring mechanism was investigated [72].In H-SSZ-13, this second site does not actively participate in the reaction mechanism, but increases the reaction barriers indirectly by < 20 kJ/mol, which is in the range also found earlier.[78] Effects can be larger if the second acid site participates in the reaction [72], but we do not expect this in our case.The effect of an additional acid site in CHA zeolites was also investigated by Nystrom et al., who found that a second site affects the acidity of the Brønsted site by changing the deprotonation energy and NH 3 -binding energy up to 20 kJ/mol depending on the position of the second site.[79] Overall, we conclude that the revised paring mechanism is very favorable for the formation of propene in all investigated zeolites giving confidence that propene is indeed mostly originating from the paring mechanism of the aromatic cycle, with overall free energy barriers being around 130-170 kJ/mol, depending on the employed zeotype.This finding can serve as valuable input for kinetic models of this part of the MTO reaction and will lead to a deeper understanding of how selectivity can be tuned and influenced by the catalyst and reaction conditions.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .
Fig. 2. a) Gibbs free energy diagram of the paring mechanism with propene elimination before ring-expansion (Fig. 1, black cycle) for H-SSZ-13 [31], H-ZSM-5, H-SAPO-34 and H-SSZ-24.Barrier heights are referenced to the lowest preceding intermediate state.This is heptaMB + (structure 1) for the first barriers, and structure 8 for the ring expansion from 8 to 9. b) Summary of the mechanism showing only the highest free energy barrier, referenced to the lowest preceding intermediate according to the energetic span model.[66] c) Example of the propene elimination transition state (taken from the H-SSZ-24 zeolite), the dashed line indicates the broken C-C bond.d), e) and f) show the propene elimination transition state in the environment of H-ZSM-5, H-SAPO-34 and H-SSZ-24, respectively.For H-ZSM-5, the propene leaves in the direction of the straight channel.Reaction temperature is 400 • C, reference pressure is 1 bar.Bond lengths are indicated in pm.Color code: blue: Al, yellow: Si, red: O, brown: C, black: H. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)