Topics in Catalysis (2022) 65:242–251 https://doi.org/10.1007/s11244-021-01535-9 ORIGINAL PAPER Activity Trends in the Propane Dehydrogenation Reaction Catalyzed by ­MIII Sites on an Amorphous ­SiO2 Model: A Theoretical Perspective C. S. Praveen1,2 · A. Comas‑Vives3 Accepted: 9 November 2021 / Published online: 30 November 2021 © The Author(s) 2021 Abstract One class of particularly active catalysts for the Propane Dehydrogenation (PDH) reaction are well-defined M(III) sites on amorphous ­SiO2. In the present work, we focus on evaluating the catalytic trends of the PDH for four M(III) single-sites (Cr, Mo, Ga and In) on a realistic amorphous model of ­SiO2 using density functional theory-based calculations and the energetic span model. We considered a catalytic pathway spanned by three reaction steps taking place on selected ­MIII–O pair of the ­SiO2 model: σ-bond metathesis of propane on a M ­ III–O bond to form M-propyl and O–H group, a β-H transfer step forming M–H and propene, and the H–H coupling step producing H ­ 2 and regenerating the initial M–O bond. With the application of the energetic span model, we found that the calculated catalytic activity for Ga and Cr is comparable to the ones reported at the experimental level, enabling us to benchmark the model and the methodology used. Furthermore, results suggest that both In(III) and Mo(III) on S­ iO2 are potential active catalysts for PDH, provided they can be synthesized and are stable under PDH reaction conditions. Keywords MIII sites · Lewis acidic sites · Transition-metals · Silica · Propane dehydrogenation reaction · Amorphous model 1 Introduction a way to produce propene, ethene and butene in a single- step [9]. Industrial processes involving the cleavage of strong C(sp3)–H bonds [1] are among the most challenging ones, (1) being highly energy demanding processes [2–4]. Within alkane dehydrogenation, propane dehydrogenation (PDH) Nevertheless, to overcome the thermodynamic limitations to propylene and hydrogen (Eq. 1) has gained major interest imposed by the highly endothermic PDH reaction (standard in the past years due to the discovery of shale gas [5] mainly enthalpy ∆H°298 =  +124 kJ ­mol−1), high temperatures are in the US [6–8]. Moreover, the PDH reaction in combination required to obtain significant conversions (typically above with metathesis, i. e. propane to olefins (PTO) can provide 550 °C). This leads to deactivation and poisoning of the catalysts via coke formation [10]. In industry, there are two historical heterogeneous catalysts used for the PDH reaction: the alumina-supported PtSn nanoparticles and the C ­ rOx/ * A. Comas‑Vives Al2O3 system, also known as the Houdry or Catofin catalyst Aleix.Comas@uab.cat [11], albeit both systems suffer from deactivation and need 1 International School of Photonics, Cochin University frequent regeneration. Therefore, the synthesis of new cata- of Science and Technology, University Road, South lysts is crucial [12]. Among the first family of catalysts, i.e. Kalamassery, Kalamassery, Ernakulam, Kerala 682022, based on Pt NPs, it was shown that silica-supported PtGa- India based catalysts were highly efficient for the PDH reaction 2 Inter University Centre for Nano Materials and Devices, [13] and their high performance and stability was recently Cochin University of Science and Technology, University Road, South Kalamassery, Kalamassery, Ernakulam, rationalized via first principles calculations in combination Kerala 682022, India with metadynamics [14]. 3 Department of Chemistry, Universitat Autònoma de Metal-based single-site catalysts on ­SiO2 have also been Barcelona, 08193 Cerdanyola del Vallès, Catalonia, Spain found to display high activity towards the PDH reaction 13 Vol:.(1234567890) Topics in Catalysis (2022) 65:242–251 243 [10]. For instance, Cr(III) centres on silica [15], analo- 2 Construction of the M(III) single‑sites gous to the Houdry and Catofin catalysts in alumina, are on ­SiO2 also active catalysts in the reaction. Lewis acidic Ga(III) centres on ­SiO2 also display high activity and remarkable M III (Cr,Mo,Ga,In)/SiO 2 models are constr ucted selectivity and stability [16, 17], ­Ga2O3 is also catalyti- using a previously developed amorphous silica model cally active towards the PDH reaction [2, 18] and recently [24], which corresponds to a slab of dimensions Ga(III) sites have also been proposed as their active reac- 21.4 Å × 21.4 Å × 34.2 Å and contains 372 atoms. The tion centers [19]. silica model exposes five isolated silanol groups (SiOH) Moreover, other single-metal centres on S ­ iO2 based on and has a surface silanol density (1.1 OH ­nm−2) close to Fe(II), Zn(II) and mono- and bimetallic Co(II) centres on the density found for silica partially dehydroxylated under silica are catalytically active in the PDH reaction [20–23]. vacuum at 700 °C ­(SiO2–700, 0.8 OH ­nm−2), which is for In previous studies, we showed how the use of an instance, the one used experimentally to prepare well- amorphous ­SiO 2 model [24] is important to understand defined ­GaIII sites active in the propane dehydrogenation the reactivity of single-sites present on silica, being able reaction and related systems [16]. The M ­ III sites can be to account for strain, an aspect which is not as straightfor- introduced into the silica model by substituting surface ward to capture using cluster models [25]. This was exem- “SiOH” groups by a M ­ 3+ i.e. turning (≡SiO)3SiOH sites plified by the olefin polymerization reaction catalyzed by III into (≡SiO)3M sites as previously carried out to build Cr(III)/SiO2 [26, 27]. More recently, for the PDH reaction, the corresponding C ­ rIII and G ­ aIII sites [26–28]. This model we could also show by evaluating the reactivity of different provided five types of Ga, C ­ rIII/SiO2 models, namely mod- Ga(III) sites that strain is a key parameter controlling the els I–V [26–28]. In our previous work on Ga, we probed activity, showing that an intermediate strain of the reac- the reactivity of all sites towards the propane dehydroge- tive Ga–O pair leads to the highest catalytic activity in the nation reaction [28]. We found that the most active site PDH reaction [28]. corresponds to the V–O3 site, in which V refers to the site The considered propane dehydrogenation pathway has label of the metal, while O3 refers to the specific oxygen the following reaction steps: (1) the C–H bond activation involved in the PDH reaction. Therefore, in the current of propane on the M ­ III site forming a ­MIII-propyl interme- study, we selected V–O3 site to compare the reactivity of diate and an OH group (Step 1), (2) the β-hydride transfer the single-site systems composed of the previously dis- producing a hydride and propene (Step 2), (3) the H–H cussed metals: Cr, Mo, Ga and In, respectively. Figure 1 coupling or reverse σ-bond metathesis of ­H2 (Step 3) fol- shows all the constructed tri-coordinated single-sites on lowing the de-coordination of propene to regenerate the the amorphous ­SiO2 model together with the geometrical initial ­MIII site. This catalytic route was already consid- characteristics of each of the four metal sites (see Fig. 1), ered for Cr [29] and Ga-single sites using cluster [30] and such as M–O distances and O-M–O angles. amorphous periodic models, respectively [28]. Given that Cr and Ga single-sites on S ­ iO2 are known to be active catalysts of the PDH reaction, together with the latter elements, we decided to evaluate two additional rep- 3 Evaluation of the Propane resentative elements laying just below Cr and Ga in their Dehydrogenation on the Selected M(III)/ respective groups of the periodic table, i.e. In and Mo. SiO2 Sites Therefore, in this work, we evaluated the reactivity of four different single metal(III) sites on silica (M = Cr, Mo, Ga We evaluated the propane dehydrogenation reaction cata- and In) using the previously mentioned ­SiO2 amorphous ­ III metals (Cr, Mo, lyzed by four different single-site M model [24]. For the present study, we selected the M–O Ga and In) considering the previously discussed catalytic pair that displayed the highest activity towards the PDH cycle, as shown in Scheme 1. for the Ga(III)/SiO2 system. Here, we extend our work on Ga to three additional metals and compare among them. Our study displays the catalytic differences among the 3.1 Step 1: C–H Bond Activation of Propane evaluated metal sites, highlighting their differences in the key PDH steps, finally proposing which one should display The reactivity of the four M(III)–O(3) site towards the the highest catalytic activity in PDH using the energetic C–H activation of propane was the first reaction step eval- span approach. uated. Table 1 summarizes, both the energy barrier heights 13 244 Topics in Catalysis (2022) 65:242–251 Fig. 1  Single sites on the amor- phous model of ­SiO2 based on a Cr, b Mo, c Ga and d In (∆E‡) and reaction energies (∆E) for the C–H activation metal for this reaction step is Cr with a slightly higher of propane (in kcal ­mol−1) on all the evaluated M–O sites. energy barrier (21.9 kcal ­mol−1) than In and Ga (18.9 and This site has a high degree of strain, and therefore is the 18.5 kcal ­mol−1, respectively). In contrast, Mo presents a most active site among all the previously evaluated sites significantly higher energy barrier than the other metals: for the case of the Ga single-sites on ­SiO2 using the same 27.8 kcal ­mol−1. amorphous model than the one used in the current study Similar to what we found when analyzing the C–H acti- [28]. vation of propane on different Ga sites on silica, there is a The energy barriers follow the trend: Ga < In < Cr ≪ Mo. Brønsted–Evans–Polanyi relationship followed to certain The reaction energy barriers take values within 18.5 and extent ­(R2 = 0.816) between the electronic energy barrier 27.8 kcal ­mol −1, while reaction energies range between and the reaction energy (Figure S1 in electronic energies − 2.0 and − 26.2 kcal ­mol−1. In addition, for most metals, and Figure S2 and ­R2 = 0.763 in Gibbs energies). There the energy barrier for the C–H activation decrease when is actually a good correlation between the energy barrier the reaction energy is more favored. The only exception to and the reaction energies of the reverse step of the C–H this trend is between Ga and In, since the C–H activation activation, as reported in the ESI ­(R2 = 0.956 in electronic energy barrier is slightly lower on Ga than on In (18.5 energies, Figure S3 and ­R2 = 0.899 in Gibbs energies, Fig- vs. 18.9 kcal ­mol−1) whereas the reaction is slightly less ure S4). favored on Ga than on In (− 25.2 vs. − 26.2 kcal ­mol−1). The geometries corresponding to the transition-state In any case, the energies obtained for Ga and In are very structures are shown in Fig. 2 together with their most alike, being the two most active metals for the direct pro- important geometric characteristics. The transition-states pane activation via a σ-bond metathesis; forming a M-pro- are characterized by the elongated C–H bond of the pro- pyl group and a new O–H bond. The next most active pane molecule. The corresponding C–H distances are 13 Topics in Catalysis (2022) 65:242–251 245 Scheme 1  The proposed reaction mechanism for the dehydrogenation of propane on ­MIII/SiO2 sites. For some metals, an additional siloxane group coordinates to the ­MIII centre which is shown in grey. In the present work, we report the reaction mechanism on four M(III) centers (M = Cr, Mo, Ga, and In) Table 1  Energy barrier heights (∆E‡) and reaction energies (∆E) for Moreover, the calculated energy barriers take significantly the C–H activation of propane (in kcal ­mol−1) on the four evaluated higher values than the previously evaluated C–H activation M–O sites (M = Cr, Mo, Ga and In) of propane reported in the former subsection (vide supra). M–O pair ∆E‡ (kcal ­mol−1) ∆E (kcal ­mol−1) The values of the energy barriers for the β-H transfer step follow the trend: Cr < Mo < Ga ≪ In. As expected, Cr and Cr 21.9 − 6.8 Mo, which are transition metals with partially filled d orbit- Mo 27.8 − 2.0 als have lower energy barriers (35.4 and 37.2 kcal ­mol−1, Ga 18.5 − 25.2 respectively) than Ga and In (41.7 and 53.7 kcal ­mol−1, In 18.9 − 26.2 respectively), belonging to the group 13 of the periodic Both quantities are referenced with respect to the minima before the table. transition-state, in which propane interacts with the corresponding The corresponding geometries for all the transition-state M–O site structures are shown in Fig. 3, which depicts their most char- acteristic geometrical features concerning the β-H transfer equal to 1.351, 1.353, 1.423 and 1.407 Å for Ga, In, Cr step. The geometry of the corresponding structure for Mo and Mo, respectively. is different than for the other metals. In this case, the TS corresponds to the change of conformation of H from one 3.2 Step 2: β‑H Transfer and Propene side of the O–M–O plane to the other with propene barely Decoordination interacting with the Mo (see Fig. 3c). In this case, the β-H transfer preceding this TS is slightly lower in energy than The next reaction step considered in the PDH reaction is this H migration. Therefore, we took the latter process as the the β-H transfer, in which one H atom in β-position of the key transition state connecting M-propyl and the M–H + pro- propyl group is transferred to the metal atom forming an pene species. M–H bond, while propene remains coordinated to the M(III) In this case, the relation between ∆E‡ (kcal ­mol−1) and center. Table 2 summarizes the energetics of this reaction ∆E does not follow a linear trend ­(R2 = 0.584, Figure S5). step for all the evaluated metals. This step is endoenergetic On the other hand, in our previous study on five different Ga and has rather high energy barriers for all metal atoms. sites, this step followed a rather well transition-state scaling, 13 246 Topics in Catalysis (2022) 65:242–251 Fig. 2  Transition-states corre- sponding to the C–H activation of propane for the four evalu- ated single-metal (III) sites on ­SiO2: a Cr, b Mo, c Ga and d In Table 2  Energy barrier heights (∆E‡) and reaction energies (∆E) for energy barriers of this reaction step with a high degree of the β-H transfer step (in kcal ­mol−1) on the four evaluated M(III) sites confidence. (M = Cr, Mo, Ga and In) on ­SiO2 The next step we considered in our mechanistic analysis M(III)-site ∆E‡ (kcal ­mol−1) ∆E (kcal ­mol−1) was the decoordination of propene from the metal moiety. In all cases, the decoordination is endoenergetic taking val- Cr 35.4 13.2 ues equal to 20.1, 27.2, 18.0 and 21.3 kcal ­mol−1 for Cr, Mo 37.2 6.7 Mo, Ga and In, respectively. The decoordination is preferred Ga 41.7 13.4 in the order of: Ga > In > Cr ≫ Mo. While Ga, In, and Cr In 53.7 18.1 present rather similar values ranging 18.0–21.3 kcal ­mol−1 Both quantities are referenced with respect the minima before the for the decoordination of propene step, the decoordina- transition-state tion of propene from Mo is much more energy demanding (27.2 kcal ­mol−1) since the bond between the propene and relating the energy of a given TS and its product. Both ener- Mo is significantly stronger than for the rest. In any case, gies are referenced against the energy of the initial reactant at the high temperatures needed for the PDH reaction, the and the catalyst, i. e. propane and the corresponding M(III)- propene decoordination is clearly exergonic (∆G < 0) for all site. The transition-state scaling improves ­(R2 = 0.857 in metals as it is a highly entropically-driven step owing to the electronic energies, Figure S6 and ­R2 = 0.843 in Gibbs ener- release of propene into the gas-phase. gies, Figure S7) with respect to the previously mentioned relation between ∆E‡ and ∆E ­(R2 = 0.57). The scaling trend 3.3 Step 3: H–H Coupling and ­H2 Formation is, however, not as high as the one we reported when com- paring the five different Ga sites ­(R2 = 0.997) [28]. Possibly, Finally, we calculated the last reaction step along the pos- more data and complex functions, such as those provided tulated mechanism for the PDH reaction, which is the cou- by machine learning algorithms, are needed to predict the pling of M–H and O–H groups, i.e. the H–H coupling—or 13 Topics in Catalysis (2022) 65:242–251 247 Fig. 3  Transition-states cor- responding to the initial β-H transfer for the four evaluated single-metal (III) sites on S ­ iO2: a Cr, b Mo, c Ga and d In. For Mo this transition-state structure corresponds to a H migration step instead Table 3  Energy barrier heights (∆E‡) and reaction energies (∆E) for The transition-state structures corresponding to all the H–H coupling step (in kcal ­mol−1) on the four evaluated M(III) H–H coupling steps are shown in Fig. 4, which depicts sites (M = Cr, Mo, Ga and In) on ­SiO2 their most characteristic geometrical features. M(III) site ∆E‡ (kcal ­mol−1) ∆E (kcal ­mol−1) Cr 23.3 13.6 4 Overall Catalytic Cycles for PDH Mo 18.1 8.0 Ga 43.1 33.2 At this point, we can discuss the overall reactivity of the In 36.1 27.4 four evaluated metal sites based on the Gibbs energy pro- Both quantities are referenced with respect the minima before the files at 550 °C and 1 bar, which are shown in Fig. 4. The transition-state energy profile in electronic energies is given in the ESI (Figure S10). Figure 5 provides the information to compare the reactivity among all four evaluated metal sites. As pre- inverse σ-bond metathesis step—forming H ­ 2 and recover- viously reported, the propane dehydrogenation reaction is ing the initial M–O bond cleaved during the initial activa- endergonic by 7.4 kcal ­mol–1, in good agreement with the tion of propane. The energy barriers (∆E ‡) and reaction experiment, since the PDH reaction has ca. 30% equilibrium energies (∆E) for this reaction step for the four evaluated conversion for propane at 550 °C and 1 bar [10]. M(III) sites on S ­ iO2 are summarized in Table 3. The energy Subsequently, we used the energetic span model [31] barriers follow the trend in values as: Mo < Cr ≪ In < Ga. to compare the catalytic activity of the four evaluated sys- The two transition metals, i.e. Mo and Cr, have relatively tems. Within this approach, the turnover frequency (TOF) low energy barriers for this step, taking values equal to of a catalytic cycle is a function of the energetic span (∂E). 18.1 and 23.3 kcal ­mol−1, respectively. Conversely, the This quantity (∂E) depends on the energy of the TOF-deter- energy barrier values for this step for Ga and In are 36.1 mining transition state (TDTS), and the TOF-determining and 43.1 kcal ­mol−1, respectively. In this case, all four intermediate (TDI). Simplifying the approach, the TDTS points followed a very clear linear trend when representing corresponds to the highest energy in the Gibbs energy pro- ∆E‡ vs. ∆E of the H–H coupling step, with an R ­ 2 = 0.998 file, while the TDI is generally the most stable intermediate 2 (Figure S8, and ­R = 0.966 in Gibbs energies, Figure S9). in the energy profile. When the TDTS of a catalytic cycle 13 248 Topics in Catalysis (2022) 65:242–251 Fig. 4  Transition-states cor- responding to the initial H–H coupling steps for the four evaluated single-metal (III) sites on ­SiO2: a Cr, b Mo, c Ga and d In appears after the TDI in the Gibbs energy profile, ∂E is the with the reported positive experimental TOF, we will use the energy difference between these two steps. Conversely, when above-mentioned equation to compare the catalytic activity the TDI appears after the TDTS, the ΔG of the reaction of the four metal sites in a semiquantitative way, although (ΔGr) is added to this difference. Overall, the energetic span the ΔGr term is positive in our case. We refer the reader to model defines ∂E using the following equation. our previous work for further details and discussion about { the specificities and caveats of the application of the span TTDTS − ITDI model to the PDH reaction [28]. 𝜕E = TTDTS − ITDI + ΔGr For the Cr(III)/SiO2 single-site, the TDTS corresponds to the β-H transfer step, being located at + 58.5 kcal ­mol–1 Based on the energetic span 𝜕E , the TOF is calculated with respect to initial reactants. Since all intermediates are at 550 °C for all systems using the expression: less stable than initial reactants, the TDI species within the kB T −𝜕E∕RT energetic span model corresponds to the origin of energies TOF = e of the Gibbs energy profile (catalyst + reactants). Therefore, h the value for the energetic span is equal to + 58.5 kcal ­mol–1, The former equation is in principle valid for exergonic leading to a calculated TOF equal to 18.1 ­h−1. Our calculated reactions, which leads to a positive TOF when calculated. TOF agrees rather well with the initial turnover frequency The TOF is understood as a catalytic flux via the span (TOF) of 10.3 ­h−1 reported experimentally for Cr(III)/SiO2 model, in analogy with Ohm’s law in electric circuits [31]. at 550 °C and 1.5 bar [15]. Thus, within the flux analogy, it is positive and goes for- The TDTS of the Mo(III)/SiO2 single-site is the TS of the ward for exergonic reactions, while it is negative and goes β-H transfer step, which is located at 48.1 kcal ­mol−1 with backwards for endergonic reactions. Nevertheless, the TOF respect to the initial reactants. Similar to Cr, the TDI in this is defined differently at the experimental level and is always case also corresponds to the origin of energies of the Gibbs positive, since it is obtained based on the conversion of energy profile. Therefore, taking the energetic span for Mo the reactants to products. The PDH reaction is endergonic equal to 48.1 kcal ­mol–1, leads to a rather high calculated under our evaluated conditions (the ΔGr term is positive at TOF of 1.05·105 ­h−1. 550 °C), and therefore we would obtain a negative TOF, The TDTS of the catalytic cycle for the evaluated Ga meaning the catalytic flux would go backwards. Thus, in site corresponds to the C–H activation step located at order to compare the catalytic activity of the evaluated sites 31.7 kcal ­mol–1 in the Gibbs energy profile. In this case, 13 Topics in Catalysis (2022) 65:242–251 249 Fig. 5  Gibbs energy profile of Beta-H Transfer the propane dehydrogenation reaction on the Cr, Ga, In and 70 C-H acvaon Mo single-sites on Silica (in kcal ­mol–1). The Gibbs energy Physisorpon of propane 60 H-H Coupling M-propyl intermediate + OH of all the species along the Decoordinaon of propene energy profile are referenced Propene + hydride 50 against the sum of the respec- H2 eliminaon tive energy of the site and the energy of the propane molecule 40 in the gas phase Cr 30 G (kcal·mol-1 ) Mo 20 Ga 10 In 0 -10 -20 -30 the TDI of the catalytic cycle appears after the TDTS. The sites should be synthetized and remain stable under reac- TDI corresponds to the gallium hydride species, with a rela- tions, and (iii) surface heterogeneity was not evaluated in tive energy equal to − 19.8 kcal ­mol–1 with respect to initial depth in the present study since we only evaluated one M–O reactants. Thus, the energetic span after summing up the site on the ­SiO2 amorphous model. ∆Gr term (+ 7.4 kcal ­mol–1) is equal to 58.9 kcal ­mol–1 cor- responding to a TOF of 14.2 ­h−1. This result agrees well with the value reported experimentally for the Ga(III)/SiO2 system, which took a value of 20.4 ­h−1 at 550 °C [32]. 5 Conclusions Finally, for In(III)/SiO2, the TDTS corresponds to the β-H transfer step, which is located at 53.5 kcal ­mol–1 above In the present work, we evaluated at theoretical level the initial reactants. In this case, two species compete as the reactivity of four M(III) sites (Cr, Mo, Ga and In) on an TDI, the In-propyl species formed after the activation of the amorphous model on silica towards the propane dehydroge- C–H bond of propane and the In–H species after propene nation reaction (PDH). We considered three activated steps decoordination. Both species have similar energies, being for the reaction, taking place on a M–O reactive pair: namely equal to − 0.39 and − 1.27 kcal ­mol–1, respectively. After the C–H activation of propane, the β-H transfer step from the the application of the energetic span model [31] the for- M-propyl intermediate generating M–H and propene, and mer species is the TDI, i.e. the In-propyl species, located the H–H coupling step, which forms ­H2 and regenerates the at − 0.39 kcal ­mol–1 in the Gibbs energy profile. Making this initial M–O bond. assumption, the energetic span is equal to 53.9 kcal ­mol–1 A comparison in reactivity among the four evaluated and the calculated TOF takes a value of 3.02 × ­102 ­h−1. metals based on electronic energies shows that the most Comparing the calculated TOF for all four metals on the active centres towards the σ-bond metathesis of propane are evaluated sites, the obtained results suggest that the overall the Lewis acidic Ga(III) and In(III) centres, while the least PDH activity follows the trend Ga ≈ Cr < In ≪ Mo. There- active ones are the Cr(III) and Mo(III) sites. Conversely, for fore, the present study suggests In(III) and Mo(III) single- the β-H transfer step, Cr and Mo have much lower Gibbs sites on ­SiO2 could be potentially active catalysts for the energy barriers than Ga and In centres. The H–H coupling PDH reaction, in particular Mo(III). One has to bear in mind, step, i.e. the inverse of the σ-bond metathesis step has also however, the following considerations: (i) the selectivity of much lower Gibbs energy barrier for Cr and Mo than for the PDH reaction was not evaluated in the present work, but Ga and In. only the activity, (ii) the hypothetical In(III) and Mo(III) 13 250 Topics in Catalysis (2022) 65:242–251 When comparing the overall Gibbs energy profiles within Acknowledgements CSP would like to acknowledge DST-India for an the energetic span model for the four evaluated metals, the INSPIRE Faculty Fellowship with Award IFA-18 PH217 for funding. A.C.-V. acknowledges the Spanish MEC and the European Social Fund TDTS for Cr, Mo, and In is the β-H transfer step, while for (Ramon y Cajal Fellowship: RyC-2016-19930) and the Spanish “Min- Ga, it is the C–H activation step, which is located slightly isterio de Ciencia, Innovación y Universidades” (PGC2018-100818- higher than the β-H transfer in the Gibbs energy profile. A-I00) for financial support. Within the energetic span model, Cr and Ga are predicted to have similar catalytic activity with values in good agreement Funding Open Access Funding provided by Universitat Autònoma de Barcelona. with the experimental results. Based on our results, In and Mo centers should have even higher activity, provided they Declarations are stable under reaction conditions and have high selectivity towards the desired products, i.e. propene and ­H2. Conflict of interest The authors declare no competing financial inter- ests. 5.1 Computational Methods Open Access This article is licensed under a Creative Commons Attri- DFT calculations based on the Gaussian and plane waves bution 4.0 International License, which permits use, sharing, adapta- tion, distribution and reproduction in any medium or format, as long (GPW) formalism [33] were carried out using the Quickstep as you give appropriate credit to the original author(s) and the source, (QS) module [34] of the CP2K program package [35, 36]. provide a link to the Creative Commons licence, and indicate if changes The functional chosen was PBE [37–39] with short range were made. The images or other third party material in this article are Gaussian double-ζ basis sets [40] optimized from molecu- included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in lar calculations. The energy cutoff of the auxiliary plane the article's Creative Commons licence and your intended use is not wave basis set was set to 500 Ry. Goedecker–Teter–Hutter permitted by statutory regulation or exceeds the permitted use, you will pseudopotentials [41–43] were used. For the faster conver- need to obtain permission directly from the copyright holder. To view a gence of the wavefunction, the orbital transformation (OT) copy of this licence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/. method was used [44, 45]. The OT method is based on a minimization of the energy functional using a new set of variables to perform orbital transformations. This method References is demonstrated to be very efficient in comparison to diago- 1. Labinger JA, Bercaw JE (2002) Nature 417:507–514 nalisation/DIIS based methods, especially for large systems 2. Coperet C (2010) Chem Rev 110:656–680 and basis sets. A tetragonal simulation box of base area 3. 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