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Development of a Comprehensive Microkinetic Model for Rh(bis(diazaphospholane))-Catalyzed Hydroformylation Anna C. Brezny, and Clark R. Landis ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.9b00173 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 3, 2019
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Development of a Comprehensive Microkinetic Model for Rh(bis(diazaphospholane))-Catalyzed Hydroformylation Anna C. Brezny† and Clark R. Landis* Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States ABSTRACT: Asymmetric hydroformylation (AHF) of alkenes is a prototypical, complicated catalytic transformation with a mechanism that comprises three concurrent, isomeric catalytic cycles. A persistent challenge to understanding such complex systems concerns efficient development of quantitative kinetic models. In this work, we demonstrate development of a comprehensive, empirical microkinetic model of AHF. Central to these studies is exploitation of the information-rich, operando Wisconsin HighPressure NMR Reactor to collect data for a variety of non-catalytic transformations that focus on different regions of the overall catalytic cycle. Kinetic analysis of these transformations leads to kinetic models for segments of the full cycle; we call these “minimodels.” According to a divide-and-conquer strategy, these individual “mini-models” are combined to build up the full microkinetic catalytic model. This comprehensive model fits all non-catalytic and catalytic data simultaneously, and enables detailed examination of the steps controlling reaction rate, regioselectivity, and enantioselectivity. Scaled sensitivity analysis indicates that, even under catalytic conditions with different resting states, just a few steps impart the largest degree of rate control. In comparison with a simple pedagogical model, we quantitatively demonstrate that we cannot assume the catalyst resting state immediately precedes the turnoverlimiting step in mechanisms that include off-cycle catalyst species. These models conclusively demonstrate that even when most of the catalyst lies off-cycle, if the catalyst speciation is at steady-state then the rates of off-cycle steps are irrelevant to rate control. Under steady-state conditions the presence of off-cycle species serves only to lower the catalytic efficiency by lowering the on-cycle catalyst concentrations. hydroformylation, mechanism, operando spectroscopy, kinetics, microkinetic modeling, sensitivity analysis
INTRODUCTION
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Hydroformylation is an iconic organotransition metal catalyzed reaction performed on a large industrial scale. Commodity applications of hydroformylation focus on the production of achiral aldehydes. These products serve as intermediates for the production of solvents, plasticizers, and detergents.1 Enantioselective or asymmetric hydroformylation (AHF) for the synthesis of chiral, branched aldehydes is comparatively underdeveloped, despite the attractiveness of these precursors in fine chemical synthesis and pharamceuticals.2 A major challenge of hydroformylation is achieving high regio- and enantioselectivity at useful rates. The class of bis(diazaphospholane) ligands (BDP) impart excellent selectivity and rates for a variety of diverse substrates (Figure 1).3 The mechanism for hydroformylation as proposed in 1961 by Breslow and Heck outlines the elementary steps of the overall transformation (Scheme 1).4 This proposal does not account for the origins of selectivity, and a long-standing goal in the field has been to understand how both rate and selectivity are controlled in hydroformylation. This work focuses on asymmetric hydroformylation (AHF) catalyzed by state-of-theart rhodium bis(diazaphospholane) (BDP) complexes (Figure 1).
N P N O
P N N O
Figure 1. Bis(diazaphospholane) (BDP) ligand used in this work. Watkins and Landis demonstrated that hydroformylation regio- and enantioselectivity depend on CO pressure (Figure 2).6 They proposed that pressure-dependencies arise from competitive trapping of the branched alkyl intermediate (4si) versus reversion to styrene and metal hydride (2). This hypothesis implies a kinetic preference for forming the branched alkyl (4b), but a competing thermodynamic preference for a linear intermediate (6l or 7l). This kinetic preference agrees with the observation that inductively electron withdrawing substituents tend to produce branched aldehydes.1d Ultra low pressures of gas (90% of all catalyst exists offcycle as 7, the overall rate of aldehyde appearance exceeds the rate of 7→product. Such kinetic behavior enables the discrimination of “direct” and “shunted” pathways to the aldehyde product. Additionally, this previous work highlights the complicated competition between isomerization of the kinetic, branched species to the slower linear pathway that contains the thermodynamic sink (7l). Under common hydroformylation conditions, many processes could exhibit competitive rates: alkene insertion to produce alkyl species (4), interconversion amongst isomers of 4, and trapping of 4 to produce acyls 6, hydrogenolysis of 6, and return of off-cycle species 7 onto the catalytic cycle. Although the previously discussed work qualitatively explains trends in activity and selectivity of AHF, we desire a quantitative understanding the full catalytic cycle. Can all of these data and models be tied together with one quantitative, all-encompassing kinetic model? To address this question we sought to develop a robust, empirical microkinetic model. Microkinetic models comprise the full set elementary steps and accompanying ordinary differential equations of the reaction mechanism. A microkinetic model is complete if the activation parameters for all elementary steps are known. Transition state theory provides a method for calculating rate constants from the activation parameters (eq 1). Numerical integration of the differential equations that constitute the complete microkinetic model enable one to predict rate, selectivity, and catalyst distribution under any conditions. This is beneficial from a practical standpoint, because one can quickly determine the ideal operating conditions to achieve a given reactivity profile, including temperature, pressure, and concentration. From the standpoint of understanding catalytic phenomena, the quantitative microkinetic model encodes all
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information needed to reproduce observable behavior. An accurate microkinetic model enables exploration of fundamental questions about the reversibility of a step under any set of reaction conditions, the transient concentrations of intermediates not observed spectroscopically, and the selectivity changes as a function of reaction conditions.
Microkinetic models commonly are based on ab initio computations and may be analyzed using techniques such as energetic span analysis.11 The fundamental limitation of ab initio approaches concerns the absolute accuracy of the derived rate constants. This is particularly important for multistep catalytic reactions such as hydroformylation because small errors in relative rate constants can lead to large deviations from experiment with respect to computed rates, selectivity, and catalyst speciation. In this paper, we limit ourselves to construction of a microkinetic model using empirical data. A model based on ab initio computations will be the focus of a later manuscript. Microkinetic models have been applied to heterogeneous catalysts more so than homogeneous systems.12 This is surprising given the well-defined nature of the catalysts and intermediates, which, in theory, more readily lends itself to detailed quantitation based on empirical data along with ab initio computations. This paper details the development of a microkinetic model for the catalytic hydroformylation of styrene using Rh(BDP) catalysts that is based on empirical data. A divide-and-conquer approach13 builds up the full microkinetic model from kinetic studies of non-catalytic transformations which we call “mini models”. In developing the first model, we expanded the noncatalytic hydrogenolysis experiments reported previously10 to other temperatures to obtain ∆H‡ and ∆S‡ for these steps (mini
model 1). For the second model, we obtained information about the rate of CO loss from 1 (mini model 2). WiHP-NMRR measurements of the rates of formation of 7 from the hydrido dicarbonyl and styrene gave rise to mini model 3. Previous work10 highlighted the importance of alkyl isomerization during catalysis; therefore, we collected and analyzed data regarding the isomerization of the alkyl species 4 (mini model 4). Finally, under catalytic conditions at warm temperatures, the acyl dicarbonyl species 7 are known to isomerize. We used WiHPNMRR to follow the isomerization of 7si to 7l; analysis of these data provided mini model 5. By combining these five mini models we create a full microkinetic model that can globally fit all of the non-catalytic and catalytic data. Such a model constitutes a comprehensive description of hydroformylation catalysis. The fits and activation parameters presented below are those of the final, combined kinetic model. The resulting microkinetic model is verified by comparison of independently measured catalytic rates, selectivity, and catalyst speciation with those predicted by the microkineic model. Sensitivity analysis of the microkinetic model lends insight into selectivityand rate-control under varied reaction conditions. Such empirical microkinetic modeling requires rich, distinctive, and varied data; operando NMR studies with WiHP-NMRR enable such data-rich information to be collected efficiently.14
RESULTS As described above, our approach is to create a set of ‘mini models’ that can be combined to create the full, microkinetic model of the catalytic reaction (Figure 3). Developing this comprehensive model required combination of experimental data collected at different temperatures. Therefore, we obtained activation parameters, as opposed to rate constants, for every elementary step in the mini models.
Figure 3. Full kinetic model for asymmetric hydroformylation.
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energy surface. With a kinetic model of these experiments in hand, we sought to build the models to account for other data.
Mini Model 1: Hydrogenolysis of Acyl Dicarbonyl Species (7 → product). We previously reported a method for studying the hydrogenolysis steps of AHF under non-catalytic conditions by WiHP-NMRR.10 The acyl dicarbonyl species 7b and 7l were formed in a ~1:1 ratio in the reactor, subjected to a high pressure of H2, and the disappearance of 7 and concomitant appearance of aldehyde products were monitored. In order to obtain activation parameters for the hydrogenolysis steps of AHF (7 to product), single-turnover data were collected from –15 to +17 °C, CO pressures from 18 to 70 psia, and H2 pressures from 20 to >400 psia (Figure 5). The data were modeled as described previously;10 the model assumes a single pseudo-elementary step for the reaction of acyl monocarbonyl 6 with dihydrogen (Figure 4, Figure 5). This step is “pseudo-elementary”15 because it combines dihydrogen binding, oxidative addition, and aldehyde formation into a single kinetic step. Because intermediate 6 is not directly observable spectroscopically, k4 and k5 cannot be determined independently, rather, we obtain their relative rates and the difference between ∆H‡4 and ∆H‡5 as well as the difference between ∆S‡4 and ∆S‡5 (eq 2–3). These results demonstrate that 6 undergoes hydrogenolysis and CO association at similar rates, arising from very small differences in the activation enthalpies, ca. 0.6 kcal/mol, for binding CO vs. hydrogenolysis of 6 to produce aldehyde. These features highlight a critical attribute of rhodium-catalyzed hydroformylation: hydrogenolysis is an extraordinarly fast process that competes with simple CO association. This feature must be reproduced in any ab initio study that purports to represent quantitative aspects of the hydroformylation free
Figure 4. Model used to optimize activation parameters for noncatalytic hydrogenolysis experiments. Species in boxes are observable in the WiHP-NMRR.
Figure 5. Example non-catalytic hydrogenolysis data and modeled fits. (~20 mM Rh(BDP) as ~1:1 mixture of acyls, 18 psia CO, 20 psia H2, and varied temperature: 270 K (left); 280 K (middle); 290 K (right). Experiments chosen to highlight temperature ranges modeled; for all data, see SI. Points indicate the experimental data and solid lines represent the modeled fits.
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Figure 6. Pulse program for saturation transfer 13C(1H) NMR experiment (top) and kinetic model for the exchange of 13CO in this experiment (bottom).
The model includes a species “sat-CO” which refers to free without magnetization (i.e. saturated). Although this species is NMR silent, it is necessary to include for mass balance in the kinetic model describing saturation transfer. The pulse program continuously saturates 1, and therefore, this species is saturated on both sides of the equation (even after it 13CO
∆H ‡ ex c hange = ∆H ‡ 1 = 24.26(1) kcal/mol ∆S‡ ex c hange = ∆S‡ 1 = 16 cal·mol -1 K-1 CO Signal
Mini Model 2: CO Dissociation from the Hydrido Dicarbonyl Species (1 → 2 + CO). Another point at which catalyst can remain productively on-cycle, or bind CO to go off cycle, lies at the hydrido monocarbonyl 2. Therefore, it is pertinent to estimate the rate of CO loss from the hydrido dicarbonyl species (1). We note that van der Veen et al. have used isotopic labels and IR spectroscopy to measure the rate of CO dissociation from Xantphos-ligated hydrido carbonyls. At 40°C they measured dissociation half -lives around 4s.16 We used saturation transfer 13C{1H} NMR experiments to estimate the rate of CO dissociation from RhH(13CO)2(BDP). Using this pulse sequence, 13C-labeled 1 is continuously saturated for a known length of time and then a non-selective detection pulse is applied. The signal for free 13CO decreases over time, due to exchange between the saturated ligands of 1 and free dissolved gas (Figure 6).17 By collecting many of these experiments for varied saturation times (d5) we can obtain a time course for the loss of magnetization of free CO (Figure 7). Due to relatively slow exchange compared with relaxation, the observed changes in signal height are small (corresponding to >k–1, and K1 is not too favorable (scenario 3). The on-cycle intermediate int is the resting state only if the formation of int is thermodynamically favorable, k1+k–1 >> k2, and Koff is unfavorable (Figure 14, scenario 2). Such conditions are relatively uncommon for the
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Figure 14. Simple catalytic reaction, the full steady-state rate law, and four scenarios highlighting the different resting states and rate controlling step combinations and simplified rate laws obtained with different rate constant values.
range of rate constant values examined. The product-forming (k2) step can be rate limiting with catalyst accumulation as cat so long as cat is thermodynamically favored over the other catalyst species. (3) For an on-cycle, but non-product-forming, step to have the largest RKSS requires low concentrations of the subsequent on-cycle intermediates. For scenario 1, cat is the resting state and k2 > 10*k–1. Under these conditions int is trapped by product formation and its concentration remains low. (4) In the steady-state, numeric values of the CSS equal the fractional concentrations of the catalyst-derived species. The fractional concentration is simply the concentration of an on- or off-cycle species divided by the total catalyst concentration. This a consequence of the general principles described above. Because the sensitivity analyses described above were performed under steady-state conditions, the conclusions can also be derived from the steady-state rate law (Figure 14). However, as one moves to more complex mechanisms the application of the SSA leads to increasingly unwieldy rate expressions. Furthermore, analysis of non-steady-steady state conditions may be needed, as for the analysis below. For such cases, numerical analysis of scaled sensitivities is more practical. Such numerical analyses require reliably parametrized kinetic models, such as the model for AHF that is described in the preceding sections. Scaled Sensitivity Analysis for AHF. We have applied degree of rate control analysis to four conditions for which we have experimental catalytic data that include operando measurement of catalyst speciation. Under experimental conditions the concentration of styrene is changing with time and the steady-state is not reached immediately. The sensitivity analyses were performed under conditions matching those shown in Figure 13. The observable catalyst and styrene concentrations were fixed based on the measured values at a time point in which the catalyst speciation is relatively stable: Figure 13A at 500 s, B at 700 s, C at 5,000 s, and D at 10,000 s. Because the three products (re, si, and l) do not necessarily form according to the same rate laws, RKSS and CSS values were determined for each product.
Sensitivity analysis of the four catalytic reactions reveals a single rate controlling step (k5) for each product but large differences in the resting state composition. For all three products and all four scenarios, the product-forming hydrogenolysis step has RKSS values >0.8 (Table 1). Only scenario 1 (PH2 =200 psia and PCO= 20 psia) shows significant rate control for reaction of styrene with the rhodium hydride 2 (RKSS(k2) ≈ 0.10–0.2). The RKSS values for rates of production of re, si, and l products are shown separately; conversion of the RKSS values to the sensitivities of the total rate with respect to a rate constant is achieved by scaling the RKSS values according to the fraction of that product amongst the total product. The concentrations of the various catalyst species are not consistent across the reaction scenarios of Table 1; the catalyst resting state varies from the acyl hydride 1 to the acyl dicarbonyls 7. Because the resting state exclusively comprises off-cycle species, the step that takes them back oncycle never is rate-controlling. The RKSS results of Table 1 corroborate the pedagogical example of Figure 14, with the caveat that steady-state conditions do not apply to the experimental data. Under all the conditions explored, the product-forming step, k5, exerts the greatest degree of rate control, regardless of resting state. Furthermore, the rate is not controlled by the steps that take the catalyst on- or off-cycle (k1/k–1 or k4/k–4) under any conditions. Interestingly, the CSS is greatest for the off-cycle species 7 for all three products under all four scenarios, despite wide variations in the resting state composition over the four scenarios. In part this occurs because the sensitivities are computed for each product, but the more important consideration concerns whether the reaction is in the steady-state. Unlike the pedagogical model, the data shown in Figure 13 and Table 1 do not correspond to steady-state conditions. First, the operando catalytic conditions chosen correspond to just ~5 catalyst turnovers. These conditions were chosen so that catalyst speciation could be quantified during turnover. As shown by the inset of Fig. 13B the catalyst speciation redistributes significantly over the first 15% conversion of
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Table 1. Scaled sensitivity values for selected rate constants on the rate of product formation (si, re, or l) and the corresponding resting state under four reaction conditions displayed in Figure 13. Reaction Conditions
Product Selectivity
Rate controlling step / RKSS value
Scenario
P CO (psia)
P H2 (psia)
% si
% re
%n
Resting state / Fraction of catalyst
si pathway
re pathway
l pathway
1
20
200
83%
10%
6%
1 / ~1
k 5 s i / 0.84
k 5 re / 0.82
k 5 l / 0.79
2
20
20
86%
9%
5%
7si / 0.55 7l / 0.25 1 / 0.20
k 5 s i / 0.98
k 5 re / 0.98
k 5 l / 0.97
3
200
200
89%
8%
3%
1 / ~1
k 5 s i / 0.98
k 5 re / 0.98
k 5 l / 0.97
4
200
20
87%
8%
5%
7si / 0.70 7re / 0.10 1 / 0.20
k 5 s i / >0.99
k 5 re / >0.99
k 5 l / >0.99
styrene. Microkinetic simulations show that the fundamental criterion of steady-state, equal fluxes within the catalytic cycle, is far from satisfied. Thus, the CSS values for the real, nonsteady-state reactions do not reflect the fraction of catalyst in each species, as was seen for the pedagogical model. This analysis highlights the general conclusion that the overall reaction rate is not necessarily equal to the rate at which the resting state transforms into product. Both the pedagogical model and our comprehensive microkinetic model of AHF provide illustrative examples. Comparison with Previous Models. Analysis of the full microkinetic model is consistent with our previous examination of “shunted” vs. “direct” hydroformylation.10 The prior work demonstrated that conversion of the acyl dicarbonyls 7 to product was slower than catalytic turnover, even under conditions where the catalyst pools in the form of 7. Sensitivity analysis using the current, comprehensive kinetic model reveals that the absolute values of the rate constants between mono- and dicarbonyls 6 and 7 (k4/k–4) wield no control over the rate of reaction; their ratio, the equilibrium constant, only is important. While the magnitude of the equilibrium constant affects the concentration of active catalyst, the steps for exiting (k4) and entering (k–4) the cycle are not turnover-limiting. Instead, analysis of this model reveals that reaction of 6 with H2 (k5) predominately controls the overall reaction rate, with minor contributions (up to 20%) on the reaction of styrene with 1 that depend on the temperature and pressure. More simply, this indicates that k5 has the greatest impact on how fast a given catalyst molecule can turnover. Quantitative microkinetic analysis is consistent with the qualitative model put forth by Watkins and Landis.6 Primarily on the basis of CO pressure influence on regio- and enantioselectivity, they proposed that selectivity largely is controlled by competition between reversion (k–2si) of the major, branched alkyl 4si and its trapping by CO (k3si). In contrast, the minor, branched and linear alkyl intermediates (4re and 4l, respectively) were proposed to be formed irreversibly. Corroborating this hypothesis, sensitivity analysis of the kinetic model reveals an equal and opposite dependence on k–2si and k3si at low CO pressures (Figure 13A). At high CO pressure (Figure 13D), the selectivity dependence on k–2si and k3si is negligible because of effectively irreversible trapping by CO. Additionally, under all conditions, there is no dependence on the minor branched or linear species reverting to the hydride
2 and styrene, indicating these steps are effectively irreversible under the conditions explored, consistent with Watkin’s model. The caveat to this analysis of the microkinetic model is that we could not experimentally probe alkyls 4re and 4l. Therefore, the pseudo-elementary step in our model is acyl 6→ hydrido dicarbonyl 2. Thus the kinetic model can obtain information about the reversibility of the acyl monocarbonyls 6, only. It has been reported previously that increasing the pressure of CO decreases the rate of the reaction by pulling the catalyst offcycle, thus lowering the on-cycle catalyst concentrations.6 Should one run AHF at low pressures (
