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Microkinetic Model as a Crucial Tool for Understanding Homogeneous Catalysis Raquel J. Rama,*[a] Ainara Nova,*[a, b] and M. Carmen Nicasio*[c] Microkinetic modeling is a computational tool that allows simulating the evolution of the concentration of catalytically relevant species with time, providing a description of the catalytic system closer to the experimental. Microkinetic models have been mainly applied in organometallic catalysis as a means for validating mechanistic proposals by comparing experimental and computed rates and concentrations at a given time. However, this tool becomes very useful when studying complicated reaction mechanisms, aiding in identifying the catalyst resting state, optimizing reaction conditions, or improving the catalyst design. In this Concept, we focus on these applications of microkinetic modeling through the discussion of some selected examples. In addition, we also point out some of the challenges and limitations we may face when building microkinetic models, which may explain why they are still underused. 1. Introduction Organometallic catalysis has become instrumental in modern organic synthesis, providing efficient, selective, and costeffective solutions for building molecular complexity.[1–4] The impressive growth of organometallic catalysis in the last decades has been facilitated by the development of computational catalysis,[5–7] an essential tool for gaining an in-depth understanding of the mechanism of a catalytic reaction.[8–13] The accessibility of accurate computational methods[14,15] and the gradual increase in computing power have boosted the routine application of computational chemistry to support and rationalize mechanistic proposals. This is often done by calculating free energy profiles at standard conditions and applying the energy span model[16] to evaluate the reaction kinetics and thermodynamics. However, for complex reaction mechanisms and reactions highly influenced by concentration, microkinetic models (MKMs), built with the information extracted from energy profiles (Gibbs free energies) and the transition state theory, give a more realistic picture (Figure 1). This computational tool allows simulating the evolution of concentrations of catalytically relevant intermediates with time using low computational cost, providing a direct connection between computed energies and experimental data. Microkinetic modeling has been broadly applied in heterogeneous catalysis to analyze reaction mechanisms, optimize reaction conditions, and improve the catalyst design.[17–21] Conversely, they have only very recently been implemented in homogenous catalysis,[22–24] primarily as a tool to validate computed mechanisms by means of a good fit between the experimentally observed and calculated rates or concentrations over time.[22-33] In early studies, DFT methods were applied to calculate kinetic constants and derived reaction parameters (e.g., reaction rates or lifetimes) for simple reaction mechanisms (e.g., those following first- or second-order kinetics).[34,35] For example, M. W. George et al.[36] analyzed in 2010 the different influencing factors on the alkane activation by two Rh complexes, [CpRh(CO)] and [Cp*Rh(CO)] (Cp=η5-C5H5, Cp*=η5-C5Me5), by comparing experimental and simulated reaction lifetimes. Another example reported by Pérez and Maseras in 2011[37] underlined the major impact of the concentration on the selectivity observed in alkane CH functionalization by diazo compounds catalyzed by silver and copper complexes. The [a] Dr. R. J. Rama, Dr. A. Nova Centre for Materials Science and Nanotechnology University of Oslo N-0315 Oslo (Norway) E-mail: [email protected] [b] Dr. A. Nova Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences University of Oslo N-0315 Oslo (Norway) [c] Prof. M. C. Nicasio Departamento de Química Inorgánica Universidad de Sevilla Calle Profesor García González 1, 41012 Sevilla (Spain) E-mail: [email protected] © 2024 The Authors. ChemCatChem published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is noncommercial and no modifications or adaptations are made. Figure 1. Flowchart for building a microkinetic model. Wiley VCH Donnerstag, 05.09.2024 2417 / 351826 [S. 208/214] 1 ChemCatChem 2024,16, e202400224 (1 of 7) © 2024 The Authors. ChemCatChem published by Wiley-VCH GmbH ChemCatChem www.chemcatchem.org Concept doi.org/10.1002/cctc.202400224
better understanding of reaction mechanisms, together with the increase in their complexity, drove the development of commercial software for solving kinetic equations. Indeed, the first mechanistic study comparing the evolution of experimental concentrations with concentrations derived from DFT-com- puted data was reported in 2014[38] using COPASI.[39] Since then, microkinetic models have been increasingly employed, either by using specialized software packages to solve the corresponding differential equations or by writing a script. Microkinetic modeling becomes particularly useful for studying complex reaction mechanisms with interconnected catalytic cycles, for which product distribution, relevant reaction pathways, and rate-determining reactions cannot be assessed using the traditional free energy profile analysis. The construction[23] and application of microkinetic models to complex homogeneous catalytic reactions have recently been reviewed by other authors.[22,24] Herein, we will discuss the type of information that can be drawn from a MKM once built and verified using experimental data. For this purpose, we have selected a series of contributions from our groups and others in the field of homogeneous catalysis. We also discuss the challenges and limitations of these models, with ideas on how to deal with some of them. 2. Determining the Role of Reaction Intermediates The analysis of the concentration over time of the different species present in the reaction is a valuable feature to identify the catalyst‘s resting state and experimentally observable intermediates or byproducts. Recently, we performed this analysis on the palladium-catalyzed aryl amination reaction.[40] The mechanism of this reaction is well-established and consists of oxidative addition to the LPd(0) active catalyst, ligand exchange (amine coordination/deprotonation), and reductive elimination steps. The use of precatalysts containing the optimal Pd/L (1:1) ratio introduces new species in the reaction, the spectator ligands, released during the precatalyst activation. One of the most widely used precatalysts in this transformation is the family of 2-aminobiphenyl-derived palladacycles bearing bulky phosphines. During the activation, an off-cycle step often ignored in mechanistic studies, NHcarbazole is released as a byproduct in the reaction media (Figure 2a). We studied the role of this byproduct experimentally and computationally, as well as by microkinetic modeling.[40] The MKM showed that the carbazolyl complex 8Cz was the catalyst resting state in the reaction with aromatic amines since its concentration remained constant during the progress of the reaction (Figure 2b). Conversely, with alkylamines (Figure 2c), the amine complex 5 M was formed in the first stage of the reaction when the concentration of amine was very high. When 18% of the amine had reacted, the complex 8Cz was found to be the major Pdcontaining species. In the absence of carbazole, the catalyst resting states were complexes 3(with aromatic amines) and 5 M (with aliphatic amines). These results indicated the reaction with the amine or the base (ligand exchange step) was ratelimiting. From this observation, one might think the presence of NHcarbazole is detrimental to the reaction. However, experimental results using in-cycle intermediates as catalysts (complexes 3and 5 M) showed that the formation of the aryl carbazolyl Pd(II) complex prevented the catalyst decomposition. Raquel J. Rama completed her PhD in Chemistry in 2020 at the Universidad de Sevilla (Spain) under the supervision of Prof. M. Carmen Nicasio. In 2021, she was awarded a MSCA-postdoctoral fellowship with Dr. Ainara Nova and Prof. Unni Olsbye at the Centre for Materials Science and Nanotechnology (University of Oslo). Her research focuses on the development of functionalized metalorganic frameworks for environmental applications. Ainara Nova completed her PhD in Chemistry in 2008 at the Autonomous University of Barcelona (Spain) under the supervision of Profs. Agustí Lledós and Gregori Ujaque. She was a postdoctoral fellow with Profs. Eric Clot and Odile Eisenstein at the University of Montpellier (France), Prof. Feliu Maseras at ICIQ (Spain), and Prof. Mats Tilset at the University of Oslo (Norway). In 2018, she started her group as an independent researcher at the University of Oslo, thanks to an NFR project on CO2utilization. Since then, she has been leading a group in computational catalysis in close collaboration with experimental groups. M. Carmen Nicasio completed her PhD in Chemistry in 1993 at the Universidad de Sevilla (Spain) under the supervision of Prof. E. Carmona. She was a postdoctoral fellow with Prof. R. N. Perutz at the University of York (UK) and with Prof. P. J. Pérez at the Universidad de Huelva (Spain). In 2010, she moved to Universidad de Sevilla where she is currently a Professor of Inorganic Chemistry. Her research interest focuses on the development of latetransition metals catalysts for carboncarbon and carbonheteroatom bond-forming reactions and the study of reaction mechanisms. 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The microkinetic model was also tested to reproduce the selectivity observed in competition experiments between aniline and n-hexylamine. Under the standard conditions, there was a clear preference for the N-arylation of the alkylamine over the aromatic amine. As shown in Scheme 1, the model provided an excellent agreement with experimental results. The analysis of the evolution of reaction intermediates was key to explain this behavior, since the largest ratio of alkylamine obtained was attributed to the fast accumulation of species 5 M at the early stage of the reaction. Microkinetic models have also been helpful in gaining an understanding of the hydrogenation of CO2,[31] esters,[41] ketones,[42] and amides[43–45] catalyzed by bifunctional catalysts. In these reactions, the catalyst participates in several hydrogenation steps (CO2to formic acid, amide to hemiaminal, and formaldehyde to methanol). In addition, the catalyst may be involved in the protolytic cleavage of hemiaminal and can be deactivated by the coordination of some reaction intermediates including reactants and methanol products.[44] A way to analyze how these competitive processes affect the overall reaction is to remove them from the reaction network. As an example, the hydrogenation of formanilide (F) by [(PNP)Fe(CO)H2] complex[43] (Fe-cat in Figure 3) was highly influenced by the formation of an adduct, which functioned as a catalyst resting state (RS), resulting from the protonation of the ligand by formanilide (Figure 3). The detrimental effect of the RS formation for the amide conversion was evaluated by excluding this reaction from the MKM (Table 1). In the presence of the RS the amide conversion was 1.5%, while in its absence the conversion raised to 25.8%. Formanilide not only had a detrimental effect, but also co-catalyzed the protolytic cleavage of the hemiaminal intermediate via TSorg in the absence of catalyst. This reaction increased the amide conversion from 0.2 to 1.5% (Table 1, entries 3 and 1, respectively). The co-catalyst effect of formanilide was even Figure 2. (a) Proposed catalytic cycle for the arylation of methylamine catalyzed by precatalyst P1. Evolution over time (h) of the concentration (mM) of Pd-containing species in the CN coupling of chlorobenzene and (b) aniline or (c) methylamine catalyzed by precatalyst P1 at 80°C as a result of microkinetic simulations. Scheme 1. Modeled and experimental results in amine competition experiments using precatalysts P1. Reaction conditions: 3-chloroanisole (0.5 mmol), N-nucleophile (0.6 mmol), [P1] (0.0025 mmol), NaOtBu (0.6 mmol), THF (1 mL), 19 h. Conversions were determined by GC analysis of the reaction mixture using dodecane as an internal standard. Figure 3. Key transition states and catalyst resting state in the hydrogenation of formanilide (F, R1=Ph, R2=H) and dimethylformamide (DMF, R1=R2=CH3) catalyzed by the PNP Fe complex Fe-cat. Table 1. Simulated amide conversion in the presence and absence of reactions associated with the formation of the adduct (RS) and the hemiaminal photolytic cleavage assisted by the catalyst (TSM) and/or formanilide (TSorg) depicted in Figure 3. Entry Amide RS TSMTSOrg % Conv 1F1.5 2F25.8 3F0.2 4 DMF 11.6 5 DMF 31.3 6 DMF 25.9 Wiley VCH Donnerstag, 05.09.2024 2417 / 351826 [S. 210/214] 1 ChemCatChem 2024,16, e202400224 (3 of 7) © 2024 The Authors. ChemCatChem published by Wiley-VCH GmbH ChemCatChem Concept doi.org/10.1002/cctc.202400224 18673899, 2024, 17, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cctc.202400224 by Readcube (Labtiva Inc.), Wiley Online Library on [18/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
more important in the case of dimethylformamide (DMF), in which TSorg was found to be the only transition state for the hemiaminal protolytic cleavage with a reasonable energy at the reaction conditions. In this case, the adduct formation also had a detrimental effect on the DMF conversion, which increased from 11.6% in the presence of RS to 31.3% in its absence (Table 1, entries 4 and 5, respectively). In this case, the consumption of the formanilide co-catalyst was also evaluated by including a reaction with the energy barrier associated with TSM. This reaction decreased the DMF conversion from 31.3 to 25.9% (Table 1, entry 6), which agreed with the experimental conversion. Based on these results, a follow-up study was performed to design an organic co-catalyst able to catalyze the hemiaminal protolytic cleavage, minimizing its consumption by hydrogenation.[45] 3. Upgrading Reaction Conditions Although rarely used in homogeneous catalysis, another remarkable application of microkinetic modeling is the upgrade of reaction conditions. Once a MKM has been built and the mechanism corroborated by experimental data, it is possible to optimize reactant, catalyst and additive concentrations, the reaction time and the temperature. We are aware of only a few studies that highlight this particular usefulness of MKMs.[33,46,47] Selectivity in cooperative catalysis is a very appealing case study from a kinetic viewpoint. The difference in orders of magnitude of the concentration of reactants and intermediates may cause the faster reaction of an intermediate with a reagent prior to the desired process occurring, leading to the formation of unwanted by-products. In 2017, Kalek and Himo[33] reported a computational and kinetic study of synergistic catalysis using two transition-metal complexes based on vanadium and palladium for the reaction between propargylic alcohols and allylic carbonates (Scheme 2A). The proposed mechanism (Scheme 2B) consists of a first 1,3-transposition of propargylic alcohol (A) catalyzed by the vanadium complex to generate nucleophilic vanadium allenolate I. Simultaneously, the palladium catalyst undergoes oxidative addition of allylic carbonate Bto produce electrophilic π-allylpalladium species II. The reaction between species Iand II generates the desired αallylated α,β-unsaturated ketone product C. However, both the vanadium allenolate Iand the π-allylpalladium species II can react with another molecule of propargylic alcohol A, forming the Meyer-Schuster rearrangement compound Dand Tsuji-Trost O-allylation product E, respectively. Experimentally, it was observed that both the nature of the phosphine ligand and the ratio of the two catalysts dictated the reaction rate and product selectivity. The computational study showed that dinuclear Pd species were strongly preferred compared to mononuclear ones, which accounted for the importance of the ligand. However, the product selectivity could not be explained by the direct comparison of the barriers in the calculated free energy diagrams due to significant differences in concentrations of alcohol Acompared to the palladium and vanadium species. Then, a MKM based on computed energies was built to compare computed and experimental data, the latter obtained from optimization experiments (Table 2). Since the experimental selectivity was, to some extent, reproduced by the MKM, this model was further used to study the effect of the catalysts loading on product selectivity. The analysis was performed by gradually modifying the loading of one of the catalysts (0–5 mol%), maintaining the amount of the other catalyst constant (5 mol%). The most interesting data are plotted in Figure 4. An increase in the palladium loading switched the selectivity between products C1 and D1, while the formation of E1 remained almost constant (Figure 4a). Regarding the vanadium loading, its increase favored the formation of products C1 and D1 while the amount of E1 decreased (Figure 4b). It is important to note that the changes in selectivity while changing vanadium loadings up to ~0.5 mol% were very pronounced. These simulated results offered practical guidance for optimizing the reaction conditions. Scheme 2. Reaction of allylic carbonates with propargylic alcohols catalyzed cooperatively by palladium and vanadium (A) and proposed reaction pathways (B). Table 2. Simulated and experimental selectivity with varying amounts of the catalysts.a Experimental product distribution Simulated product distribution [V]:[Pd] (mol %) C1 (E:Z) D1 E1 C (E:Z) D E 5:5 92 (3:1) 6 2 69 (2.6:1) 27 4 5:1 34 (6:1) 64 2 38 (2.7:1) 61 1 1:5 57 (3:1) 3 40 66 (2.6:1) 25 9 [a] Initial concentrations: [A]0=[B]0=1.0 M; simulations were run to 99% conversion of substrate A; amounts of products are normalized to 100. Wiley VCH Donnerstag, 05.09.2024 2417 / 351826 [S. 211/214] 1 ChemCatChem 2024,16, e202400224 (4 of 7) © 2024 The Authors. ChemCatChem published by Wiley-VCH GmbH ChemCatChem Concept doi.org/10.1002/cctc.202400224 18673899, 2024, 17, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cctc.202400224 by Readcube (Labtiva Inc.), Wiley Online Library on [18/10/2024]. 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4. Sensitivity Analysis Sensitivity analysis in MKMs allows the evaluation of the kinetic parameters (energy barriers or rate constants) that have the highest impact on global kinetics. This analysis introduces small changes in these parameters and evaluates their influence on the reaction outcome, such as selectivity or reaction conversion. Sensitivity analysis has been employed in several studies in the literature for different purposes.[25,29,32,33,41,43,48,49] A sensitivity analysis was performed to evaluate the influence of small changes in the energy associated with TSM and TSorg and the adduct RS (see Figure 3) on the amide conversion in the Fe-catalyzed hydrogenation of formanilide.[43] TSMand TSorg were the highest transition states of the reaction by more than 5 kcal mol1. However, the energy of TSorg was not comparable to the transition states involving the Fecomplex. As shown in Figure 5, lowering the energy barriers of TSMand TSorg by 3 kcalmol1raised the overall conversion in both cases, but TSorg produced the greatest effect with a maximum conversion of 40%. Moreover, the destabilization of RS also led to an increase in the amide conversion. However, the most remarkable effect was observed when combining the destabilization of RS by 2 kcalmol1with a decrease in the energy of TSMin 3 kcalmol1, which boosts the conversion from 1% to the experimental 99%. Considering the accuracy of DFT methods, which may reach 3 kcalmol1, we concluded that TSM could explain the experimental observation. On the other hand, the same energy shifts to TSorg and RS did not reach the experimental 99% conversion, suggesting that an organic mechanism alone could not explain the experimental results. In the cooperative vanadium- and palladium-catalyzed reaction of propargylic alcohols and allylic carbonates,[33] sensitivity analysis was performed to analyze how the barriers for the various individual steps of the mechanism affect the selectivity. Selected transition states were evaluated by increasing or decreasing their energies by 1.52 kcalmol1while keeping all the other species constant (Figure 6). This analysis allowed the authors to identify the critical transition steps controlling the selectivity as those involving common intermediates in both V- and Pd-catalytic cycles. The transition states that have no noticeable impact on the selectivity were also detected, e.g., for the regeneration of the vanadium catalyst. 5. Challenges Building Microkinetic Models Some of the benefits of applying MKMs have been summarized in the previous sections. However, constructing a microkinetic model may not be so trivial. In order to obtain a good fitting Figure 4. Dependence of the selectivity of the simulated reactions in the cooperatively catalyzed reaction of propargylic alcohols and allylic carbonates on the amount of (a) palladium and (b) vanadium catalysts. Initial concentrations are [A]0=[B]0=1 M. Figure 5. Amine conversion (after 4 h) vs ΔΔG (shift applied to the energy of RS) and ΔΔG�(shift applied to the energy of transition states TSMand TSOrg). Reprinted (adapted) with permission from ACS Catal. 2018,8, 8751–8762. Copyright 2018 American Chemical Society. Figure 6. Effect on the product distribution of increasing (a) or decreasing (b) the energy of selected transition states. Wiley VCH Donnerstag, 05.09.2024 2417 / 351826 [S. 212/214] 1 ChemCatChem 2024,16, e202400224 (5 of 7) © 2024 The Authors. ChemCatChem published by Wiley-VCH GmbH ChemCatChem Concept doi.org/10.1002/cctc.202400224 18673899, 2024, 17, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cctc.202400224 by Readcube (Labtiva Inc.), Wiley Online Library on [18/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
with experimental data, all kinetically relevant reactions should be included in the microkinetic model. This may include catalyst deactivation reactions as well as byproduct formation, which may be difficult to identify. The automated exploration of reaction pathways using computational methods is an emerging field that could benefit the consideration of all possible reactions, valuable for MKMs.[13,50–53] In addition, some processes are highly sensitive to the computational method or basis set, such as the catalytic activation of CH bonds.[36] The impact of this error on the MKM outcome is something to consider and evaluate with a sensitivity analysis. Furthermore, some reaction steps are considered barrierless since no saddle points are found when scanning the potential energy surface (e.g., formation of adducts, addition of a ligand to a coordinative unsaturated metal center). In these cases, good results are obtained by assuming that such steps are governed by diffusion. Then, the rate constants can be approximated to kd= 8RT/3η,[54] where ηis the viscosity of the solvent. With typical solvent viscosities at room temperature, this corresponds to a free energy barrier of about 4 kcal mol1in the Eyring-Polanyi equation.[55] Rate constants have an exponential dependence on reaction Gibbs energy barriers in the Eyring-Polanyi equation, which introduces some assumptions and errors. Therefore, a small deviation in the Gibbs energy calculation implies a large error in the computed product concentration.[22,56] An error on rate constants by a factor of 10 at room temperature is equivalent to an error on the activation Gibbs energy by about 1.4 kcalmol1.[55] The stoichiometric study of each step of the catalytic cycle provides extra data to train the microkinetic model and reduce computational errors. In addition, evolved experimental instrumentation and equipment may allow detecting low-concen- tration intermediates and metal-containing species during and/ or after the catalytic reaction facilitating to identify off-cycle routes crucial for understanding the reaction kinetics. Reactions that contain gases as reactants or products or the use of insoluble bases introduce extra difficulties in the system.[49] Solubility of gases data in the solvent employed at the desired temperature and partial pressure for gases are not always available in the literature, and those measurements cannot be performed in all facilities. In these cases, additional equations for the phase transition could be added to the MKM, and their rate constants have to be fitted using experimental data. 6. Summary and Outlook Microkinetic modeling is a very useful technique to study complex reaction mechanisms in homogeneous catalysis. Ideally, these models should be built by combining high-quality computational results with experimental data. Experimental measurements can be directly compared with computed energy barriers, but additionally, the kinetic parameters of processes difficult to model computationally (e.g., precipitation, association-dissociation) can be obtained from experiments and added to the MKM. This combination not only provides a way to validate a reaction mechanism but also could help to understand the role of reaction intermediates, upgrade reaction conditions, and evaluate, through a sensitivity analysis, how kinetic parameters associated with key reaction steps affect the overall conversion and selectivity. We expect this contribution will encourage researchers in the field of organometallic catalysis to use microkinetic modeling as a supporting tool for improving catalyst performance. Acknowledgements We thank financial support from MCIN/AEI/10.13039/ 501100011033 (Grant PID2020-113797RB-C22). R.J.R. acknowledges the Horizon Europe Framework Programme (HORIZON) 2021 under the Marie Skłodowska-Curie grant agreement No. 101061858. A.N. acknowledges financial support from the Research Council of Norway through the Centre of Excellence (no. 262695) and for its FRINATEK program (no. 314321). Conflict of Interests The authors declare no conflict of interest. Keywords: Microkinetic modeling ·DFT calculations ·Reaction mechanism ·Organometallic catalysis ·Concentration evolution [1] J. F. Hartwig, Organotransition Metal Chemistry: From Bonding to Catalysis, University Science Books, Mill Valley, California, 2010. [2] L. S. Hegedus, B. C. G. Söderberg, Transition Metals in the Synthesis of Complex Organic Molecules, University Science Books, Sausalito, California, 2010. [3] H. Yorimitsu, M. Kotora, N. T. Patil, Chem. Rec. 2021,21, 3335–3337. [4] T. Rogge, N. Kaplaneris, N. 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