Strain in Silica-Supported Ga(III) Sites: Neither Too Much nor Too Little for Propane Dehydrogenation Catalytic Activity

Well-defined Ga(III) sites on SiO2 are highly active, selective, and stable catalysts in the propane dehydrogenation (PDH) reaction. In this contribution, we evaluate the catalytic activity toward PDH of tricoordinated and tetracoordinated Ga(III) sites on SiO2 by means of first-principles calculations using realistic amorphous periodic SiO2 models. We evaluated the three reaction steps in PDH, namely, the C–H activation of propane to form propyl, the β-hydride (β-H) transfer to form propene and a gallium hydride, and the H–H coupling to release H2, regenerating the initial Ga–O bond and closing the catalytic cycle. Our work shows how Brønsted–Evans–Polanyi relationships are followed to a certain extent for these three reaction steps on Ga(III) sites on SiO2 and highlights the role of the strain of the reactive Ga–O pairs on such sites of realistic amorphous SiO2 models. It also shows how transition-state scaling holds very well for the β-H transfer step. While highly strained sites are very reactive sites for the initial C–H activation, they are more difficult to regenerate. The corresponding less strained sites are not reactive enough, pointing to the need for the right balance in strain to be an effective site for PDH. Overall, our work provides an understanding of the intrinsic activity of acidic Ga single sites toward the PDH reaction and paves the way toward the design and prediction of better single-site catalysts on SiO2 for the PDH reaction.


INTRODUCTION
The high demand of light olefins 1 and the large abundance of shale gas, 2 mostly constituted of light alkanes, have stimulated interest in on-site propane dehydrogenation (PDH). 1,3 PDH involves activation of the C(sp 3 )−H bond of propane as a first step, which is still nowadays a very challenging reaction. 4 Because of the highly endothermic nature of alkane dehydrogenation, this reaction is generally carried out at 550°C to obtain reasonable conversion to the alkene product. The two historical heterogeneous catalysts that are used for this reaction in industry correspond to alumina-supported PtSn nanoparticles and the CrO x /Al 2 O 3 system, also known as the Houdry or Catofin catalysts. 5 Recent research developments have also helped to launch a PtGa-based catalyst. 6 The Crbased catalyst is thought to have Cr(III) active sites dispersed on alumina. Among alternative supported catalysts, Ga-based materials are particularly noteworthy. For instance, Gaexchanged zeolites can convert light alkanes such as propane directly into aromatics and H 2 in a process proposed to involve a tandem dehydrogenation−aromatization process. 7−13 Ga 2 O 3 also promotes PDH reaction, but it suffers from fast deactivation, presumably because of reduction of the catalyst under reaction conditions. 14,15 More recently, silica-supported well-defined Ga(III) single-site catalysts have been developed 16 using a combined approach of surface organometallic chemistry 17−23 and a thermolytic precursor using [Ga(OSi-(OtBu) 3 ) 3 (THF)] as a molecular precursor. 16 This approach generates tetracoordinated Ga sites, [(SiO) 3 Ga(XOSi)] (X = −H or Si), according to IR, X-ray absorption near-edge structure, and extended X-ray absorption fine structure (EXAFS) analyses. This catalyst displays high activity and selectivity towards propene as well as remarkable stability compared to Ga 2 O 3 and other single-site catalysts based on Fe, Co, and Zn. 24 29 Other reaction steps, such as regeneration of the propyl group via σ-bond metathesis of an incoming propane molecule releasing H 2 and Special Issue: Heterogeneous Interfaces through the Lens of Inorganic Chemistry regenerating propyl, are significantly more energy-demanding, as we showed recently for our work on the Cr(III) system. 30 Thus, the latter step was not considered in the present study.
To evaluate the catalytic activity of well-defined silicasupported single-site catalysts by first principles, cluster models have typically been used because of the simplicity of these models and their associated low computational cost, but such models do not account for the expected site heterogeneity on an amorphous support like SiO 2 and cannot be used to model highly strained sites that are generated upon thermal treatment at high temperature. 31 In fact, the high degree of heterogeneity has been evidenced on so-called silica-supported single-site catalysts by luminescence spectroscopy 32 and magnetic properties 33 as well as the polydispersity of polyethylene obtained on the corresponding Cr(III) systems. 30,34,35 We have also recently shown that the use of an amorphous SiO 2 model 36 can account for strain in the Cr(III)/SiO 2 catalyst and allows for an explanation of the reactivity of this catalytic system toward olefin polymerization. 37,38 In our previous study for the Cr(III)/SiO 2 system, we have shown that there is a large variability of the reactivity of the Cr−O pairs, and those that are more strained are significantly more reactive than the ones that are less elongated and therefore less strained and prone to react either by cleaving the C−H bond or by inserting the ethylene into the Cr−O bond, forming an oxachromacycle. 37,38 Here, we evaluate the reactivity of isolated Ga(III) sites with different degrees of strain on amorphous silica toward PDH reaction using first-principles calculations. We show the high variability of the reactivity from site to site and encounter Brønsted−Evans−Polanyi (BEP) relationships for the three main reaction steps in the PDH reactions, serving as a guide for future screening studies. We also propose that the most efficient sites toward the PDH reactions in the Ga(III)/SiO 2 system display the "right" balance of strain, where the sites with intermediate strain and not the most strained ones are the most efficient for PDH because they both can activate the C− H bond of propane effectively and are easier to regenerate than the most strained sites, thus yielding an overall more efficient catalysis.

RESULTS
2.1. Construction of Ga(III) Sites. Ga(III)/SiO 2 models are constructed using a recently developed amorphous silica model, 36 which corresponds to a slab of dimensions 21.4 Å × 21.4 Å × 34.2 Å and contains 372 atoms. The silica model exposes five isolated silanol (SiOH) groups and has a surface SiOH density (1.1 OH nm −2 ) close to the density found for silica partially dehydroxylated under vacuum at 700°C (SiO 2-700 , 0.8 OH nm −2 ), which is used experimentally to prepare well-defined Ga(III) sites and related systems. 16 The amorphous SiO 2 model is obtained from a fully hydroxylated amorphous silica model by direct condensation of adjacent SiOH groups and by surface reconstruction steps involving SiO 2 migrations. The amorphous silica model has a high degree of heterogeneity, as evidenced by the large variability in the energetics associated with the dehydroxylation steps. The average Si−O distances of the siloxane bridges formed upon surface dehydroxylation serve as descriptors of the strain present on the silica surface. 36 The Ga sites are introduced to the silica model by substituting surface "SiOH" groups by Ga 3+ , i.e., turning (SiO) 3 SiOH sites into ( SiO) 3 Ga sites, as previously carried out to build the corresponding Cr(III) sites. 37,38 This model provides five types of Ga(III)/SiO 2 models, models I−V. In contrast to Cr, we also consider the coordination of an additional siloxane group to Ga because EXAFS data pointed to the presence of this additional siloxane bridge. 16   Inorganic Chemistry pubs.acs.org/IC Forum Article stable than the initial site III (which does not contain a siloxane bound to Ga). For the latter two structures, the Ga··· O(Si) bond is rather long, ranging from 2.465 to 2.479 Å, possibly because of the high constraint imposed by siloxane groups near the Ga single site. Therefore, in order to consider a less constrained and shorter Ga···O bond, which might also be present on the real system, we added a siloxane ligand to the Ga−O III-site, modeled by H 3 Si−O−SiH 3 to evaluate the effect on the reactivity on this tetracoordinated Ga site, with a shorter bond between Ga and siloxane. For the latter system, the additional Ga−O bond is 2.036 Å long, and the group has a binding energy to the Ga center equal to −18.4 kcal·mol −1 , with respect to the free ligand in the gas phase. Site III is the most stable one among those that we constructed. The relative stabilities of the initial tricoordinated sites are given in Table S1. However, because of the construction method that we adopted (vide supra) and the fact that there are many different degrees of strain on the Si− OH groups of SiO 2 , in our opinion, this does not rule out the fact that sites "less stable" based on this construction are not formed in the real case. At the end, most Si−OH groups react with molecular Ga and generate Ga single sites after calcination.
We also investigate the reactivity of selected tricoordinated Ga(III) sites toward propane for the II−O3, III−O2, V−O2, and V−O3 Ga−O pairs in view of their higher reactivity as found in our previous study on the related Cr(III) sites. 37 In addition, we also investigate the tetracoordinated Ga(III)−O pairs: I−O3 and III-mod−O2. Figure 1 37,38 In Table 1, we have summarized the energy barrier heights (ΔE ⧧ ) and reaction energies (ΔE) for the C−H activation of propane (in kcal mol −1 ) on the evaluated Ga−O pairs. From   Figure S7. 2.4. β-H Transfer and Propene Decoordination. Following the C−H bond activation step, which yields Ga− alkyl and O−H groups, the next step corresponds to a β-H transfer, which forms Ga−H and a propene coordinated to the Ga center. The relative energy barrier (Table 2) for this step is significantly higher than that for the C−H activation of propane, and this step is highly endoenergetic. In this case, the relative energy barriers take values ranging from 41.7 to 51. It is worth mentioning that this step is exoergic in Gibbs free energy (vide infra).
For this reaction step, however, we found that the TS scaling relationship holds very well (R 2 = 0.997; Figure 2). This relationship relates the energy of a given TS and its product, in which the energies of both structures are referenced with respect to the initial reactant molecule and catalyst, 42,43 in our case propane and the respective initial Ga sites.  In order to obtain the BEP relationship for this reaction step, the opposite reaction to the H−H coupling step, i.e., H 2 cleavage, needs to be evaluated. In this case, the BEP relationship between ΔE ⧧ and ΔE of H 2 cleavage is only followed to a certain extent (R 2 = 0.69). Nevertheless, in this case, there is a very good correlation between ΔE ⧧ and ΔE among for the forward reaction; however, it is difficult to interpret the physical meaning behind this correlation (Table  3).

Overall Catalytic Cycles for PDH on the Selected
Sites. Finally, we can evaluate the overall reactivity in the dehydrogenation of propane for all of the evaluated sites, considering the three reaction steps previously described. The Gibbs energy profiles for all of the Ga−O pairs (I−O3, II−O3, III−O2, V−O2, and V−O3) are shown in Figure 3. The graph shows indeed a significant variability among the five evaluated sites. On the basis of the obtained Gibbs energy profile, we can compare the reactivity between the different sites.
Overall, the calculated reaction free energy is endergonic at 550°C and 1 bar by 7.4 kcal·mol −1 , in good agreement with the thermodynamics limitations of the PDH reaction because at this temperature the equilibrium conversion for propane is still of ca. 30% at 550°C and 1 bar. 44 In order to compare the catalytic activity of the different sites, we have used the energetic span model. 45 In this model, the turnover frequency (TOF) of a catalytic cycle is a function of the energetic span (∂E), which depends on the energy of the TOF-determining transition state (TDTS), which in a simplified view is the TS with the highest energy in the Gibbs energy profile, and the TOF-determining intermediate (TDI), which is generally the most stable intermediate in the energy profile. Whenever the TDTS appears after the TDI, ∂E is the energy difference between these two steps, whereas when it is the reverse, ΔG of the reaction (ΔG r ) is added to this difference, where the energetic span model (∂E) follows the equation On the basis of the energetic span, we can then calculate the TOF of the reaction of interest by using the expression The former equation holds for exergonic reactions, leading in this case to a positive TOF value. Within this model, the TOF is understood as the catalytic flux, in analogy with Ohm's law in electric circuits. 45 A positive TOF is found for exergonic reactions, meaning that the catalytic flux goes forward, whereas for endergonic reactions, the TOF is negative because the catalytic flux goes backward. Nevertheless, experimentally the TOF is defined differently. Because it is based on the conversion to products, it will always be a positive quantity. Indeed, for the Ga(III)/SiO 2 catalyst, the reported initial experimental TOF is equal to 20.4 mol of propene per mole of Ga per hour under a kinetic regime (ca. conversion of 10%), despite the reaction being endergonic experimentally at 550°C and 1 bar. Thus, in order to compare the catalytic activity for the evaluated sites to the experimental data in a semiquantitative way, we will make use the abovementioned equation even though the ΔG r term is positive in our case. For a full discussion of how we apply the TOF model for the current case, we refer the reader to the Supporting Information. We also refer to the work of Shaik and Kozuch, who developed the energetic span model, in which the meaning of the TOF within the model is discussed in depth. 45 In any case, when using the rigorous application of the energetic span model, the trend of the reactivity found between the different sites stays the same as the one described here. For the Ga−O pair II−O3, the highest TS (TDS) in the energy profile corresponds to the β-H transfer step; it is located 79.3 kcal·mol −1 above the initial reactants, which are the most stable species of the catalytic cycle. Thus, in this case, the energetic span is equal to 79.3 kcal·mol −1 and the calculated TOF would be equal to 4.57 × 10 −5 h −1 . Therefore, this Ga−O pair would be inactive. Another Ga−O pair site that is unreactive is the V−O2 Ga−O pair but for a different reason. In this case, the initial C−H activation of propane is the TDTS, being located at 29.6 kcal·mol −1 with respect to the initial reactants, in a significantly exoergic step due to the significant release of strain, with the corresponding product being located at −53.1 kcal·mol −1 with respect to the same reference, with the latter species being the TDI of the catalytic cycle. Overall, considering the energy of the TDTS and TDI and the reaction energy, because in this case the TDI appears after the TDTS, the energetic span is equal to 90.1 kcal·mol −1 for the Ga−O pair V−O2. Thus, this site is also inactive, with a calculated TOF equal to 6.05        16 Despite all of the approximations and considerations made to calculate the energetic span and the resulting TOF, it is fair to conclude that V−O3 is the most active among all of the evaluated sites in PDH. A graphical representation of the Ga site V with the corresponding labeling of the O sites is given in Figure 4a Overall, for the C−H activation of propane, the sites that are more strained and more favorable to be cleaved had low energy barriers and significantly more favored reaction energies, i.e., significantly exothermic. Conversely, for the H−H coupling step, the Ga−O pair is formed again and thus the sites that were more favorable for the C−H activation of propane now become less favorable for this step. In addition, if the initial C− H activation is too exothermic, this leads to very stable intermediates in the Gibbs energy profile, which decreases the overall catalytic activity of that specific Ga−O pair.

CONCLUSIONS
Isolated Ga(III) sites dispersed on silica are rather active and selective catalysts for the PDH reaction. After construction of the Ga(III) sites on SiO 2 amorphous periodic models, we have evaluated the reactivity of a variety of Ga−O pairs with different degrees of strain. For the selected sites, we evaluated three reaction steps, namely, the C−H activation of propane, β-H transfer step, and H−H coupling. We considered tri-and tetracoordinated Ga with one additional siloxane group coordinated to the Ga center because these are the proposed initial catalytic sites in the silica-supported well-defined Ga(III) PDH catalyst. For the tetracoordinated sites, the additional siloxane group coordinated to Ga does not seem to play a key role in the PDH reaction on the evaluated catalytic system. After the C−H activation step of propane, the Ga···O interaction between the Ga center and the O site of the siloxane group is lost, and its effect on the energetics is rather small. For the three evaluated reaction steps, we have found that the BEP relationship holds to certain extent for the C−H and H−H activation steps. In addition, the TS scaling holds very well for the β-H transfer step. This is rather interesting because, if true for other single sites based on elements other than Ga, it would allow screening of the reactivity of the different sites only via evaluation of the thermodynamics of the three proposed reaction steps in the PDH reaction. Thus, our current results can serve as a basis for the future computational screening of PDH silica-supported single-site catalysts, especially for those centers in which the β-H transfer is rather energy-demanding. Concerning the overall catalytic activity of the evaluated sites using the energetic span model, we have found that the strain reduces significantly the C−H activation of propane. Nevertheless, if the strain is too high and the product of the C−H activation of propane is too stable, that compromises the overall catalytic activity in the dehydrogenation of propane because the subsequent β-H transfer and H− H coupling reaction steps, as well as the C−H activation of propane, become significantly more energy-demanding, increasing the energetic span and significantly decreasing the activity of the evaluated Ga−O pair. Thus, a compromise is needed between the strain, meaning an elongated Ga−O pair for the effective cleavage of the C−H bond of propane, but not too much in order to regenerate the reactive site effectively. Among all of the evaluated Ga(III)/SiO 2 sites, the one displaying the highest catalytic activity is Ga−O V−O3, which has a rather elongated Ga−O bond, and it is embedded in a highly asymmetric Ga(III) site close to coplanarity, as

COMPUTATIONAL METHODS
Density functional theory calculations based on the Gaussian and plane-wave (GPW) formalism 46 were carried out using the Quickstep (QS) module 47 of the CP2K program package. 48,49 The functional chosen was Perdew−Burke−Ernzerhof (PBE) 50−52 with short-range Gaussian double-ζ basis sets 53 optimized from molecular calculations. The energy cutoff of the auxiliary plane-wave basis set was set to 500 Ry. The Goedecker−Teter−Hutter pseudopotentials 54−56 were used. The orbital transformation method was applied. 57,58 A tetragonal simulation box of base area 21.4 Å × 21.4 Å and thickness 34.2 Å (ca. 24 Å of which corresponds to a vacuum slab added in order to avoid interactions between images in the z direction) was used. 36 Groundstate structures were obtained by energy minimization with the BFGS algorithm. 59