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In Silico Prediction of Catalytic Oligomerization Degrees Roman Raucoules,†,‡ Theodorus de Bruin,*,† Carlo Adamo,‡ and Pascal Raybaud§ †
IFP Energies Nouvelles, 1-4 Avenue de Bois Preau, 92852 Rueil-Malmaison Cedex, France lectrochimie, Chimie des Interfaces et Modelisation pour l'E nergie, CNRS UMR 7575, E cole Nationale Superieure de Laboratoire d’E Chimie de ParisChimie Paristech, 11 Rue P. et M. Curie, F-75231 Paris Cedex 05, France § changeur de Solaize, BP 3, 69360 Solaize, France IFP Energies Nouvelles, Rond-point de l'E ‡
bS Supporting Information ABSTRACT: We have established a predictive theoretical method for the efficient evaluation of the degree of ethylene oligomerization by iron-based bis(imino)pyridine homogeneous catalysts involving a CosseeArlman mechanism. A relevant chemical descriptor of the chain growth, following a SchulzFlory distribution, is identified as the difference of the Gibbs free activation energy for two competitive steps: the insertion of an ethylene molecule into an ethyl iron intermediate and the competitive termination by β-hydrogen transfer. The method is further extended to oligomerization reactions involving a butene monomer.
D
ue to reduced fossil energy supplies and increasing environmental constraints, it becomes crucial for the chemical community to improve the selectivity of (catalytic) reactions toward products with well-defined properties. In particular, organometallic systems are widely used in the petrochemical industry to catalyze the conversion of simple olefin monomers into oligomers or polymers with a well-defined chain length. Many of these reactions follow the CosseeArlman mechanism,1 which may lead to either oligomers or polymers with a chain length tuned by the nature of the metal center and the stabilizing ligands of the organometallic catalyst (Scheme 1). Due to intricate electronic and steric effects, neither a rational nor a straightforward quantitative approach (beyond chemical intuition) is known to predict the oligomer’s chain length. Nowadays, modern computational chemistry tools account for these electronic and geometric effects, thereby opening new routes toward the in silico design of new catalysts. For the CosseeArlman mechanism, the product distribution is controlled by two competitive rates, i.e., monomer insertion into the growing alkyl chain (vins) and the termination reaction (vterm). Among the termination reaction types, β-hydrogen transfer (BHT) often turns out to be predominant. The final product distribution (Figure S1 in Supporting Information) is characterized by the SchulzFlory coefficient (R): R¼
vins vins + vterm
ð1Þ
In line with Scheme 1, involving the general π-complex C2H4---LM-CnH2n+1, we can express the reaction rate for insertion (x = ins) and termination (x = BHT) as vx ¼ kx ½C2 H4 ---LM-Cn H2n+1
ð2Þ
where kx is, according to the transition-state theory, directly r 2011 American Chemical Society
related to the Gibbs free activation energy, ΔGðT, pÞqx kB T exp kx ¼ kx h RT
! ð3Þ
where kB is the Boltzmann constant, h the Planck constant, R the ideal gas constant, and T the temperature. The transmission coefficient, kx, reflecting possible tunneling and/or isotope effects, often equals 1 for insertion reactions (kins = 1). However, it may become significantly greater than 1 for reactions involving hydrogen atom transfers, e.g., a BHT reaction.2 A working expression for R can now be derived by casting eqs 2 and 3 into eq 1: R kBHT δΔGq ðT, pÞ ð4Þ ¼ ln + ln 1R RT kins with δΔGq ¼ ΔGqBHT ΔGqins
ð5Þ
The term ln[kBHT/kins] in eq 4 represents the relative contribution of quantum effects involved in BHT with respect to insertion and is expected to be greater than 1.3 The progress of computational chemistry has made it possible to identify chemical descriptors relevant to the molecular design of either heterogeneous4 or homogeneous catalysts.5 More particularly, density functional theory (DFT)-based methods are known to provide reliable activation energy values critical for catalytic reactions. However, to the best of our knowledge, this is the first time that a theoretical study aims at establishing a general approach to predict the experimental R value for organometallic catalysts. Received: March 14, 2011 Published: July 01, 2011 3911
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Organometallics
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Scheme 1. CosseeArlman Chain Growth Mechanism with BHT Termination Reactions for Ethylene Polymerizationa
a
L = ligand; M = metal. In blue and red, respectively, the competitive insertion reaction of ethylene into the metalethyl bond and termination reaction via BHT as examined in this study.
Chart 1. Iron-bis(arylimino)pyridine Dichloride Complexes A to G
To this end, we have undertaken a systematic theoretical study of relevant activation energies associated with the polymerization process. We are particularly interested in the iron-bis(arylimino)pyridine catalysts, discovered by the research groups of Brookhart6 and Gibson7 (see Chart 1), for which very high catalytic activities are experimentally observed. Moreover, the oligomerization or polymerization degrees are significantly affected upon varying the substituents on the imino-carbon atoms and aryl cycles.8 The nature of the activated species, obtained after activation with methylaluminoxane, remains a point of debate in the literature. For example, for analogous precatalysts that do not necessarily require an activation step using MAO and where the activated species can be isolated for analysis, Chirik and co-workers yielded polymers comparable to those obtained from its analogous MAO-activated species with a Fe(II) active species.9 The presence of ferrous ions is further supported by spectroscopic measurements as in ESI/MS by Castro et al.10 and in NMR/EPR studies by Talsi and co-workers.11 However, from M€ossbauer and EPR studies it was concluded that the Fe(II) precursor is completely oxidized into Fe(III) after treatment with excess MAO.12 In two hybrid QM/MM studies, where a Fe(II) species is assumed to be active, Ziegler and coworkers calculated low-spin states to be more favorable using the BP86 functional,13 while Morokuma and co-workers found that high-spin states are energetically more stable with B3LYP.14 The low-spin state was furthermore supported by Griffiths et al.,15 who calculated the first ethylene insertion step at the singlet spin state with B3P86. However, from a recent DFT/B3LYP study in
which the reactivity of the activated species that can be formed from catalyst E toward ethylene was compared, we concluded that the most active species corresponds to a monomethylated ferric ion characterized by a quartet electronic spin state.16 These results corroborate with the findings of DFT studies by Toro-Labbe and co-workers, being also in favor of Fe(III) as the most active species.17 Additionally, considering an active Fe(III) species, we could explain the dimerization of butene, yielding principally linear octenes.18 We therefore assume in the present study that the iron is present as a ferric ion and that the CosseeArlman mechanism is operational for the ethylene oligo/polymerization reactions.7,1319 In spite of the straightforward relationship between R and the (calculated) activation energies, as defined in eqs 4 and 5, the prediction power of systematic DFT calculations is limited, since the theoretical simulation of the complete catalytic cycle will rapidly become prohibitive with a growing chain, even with the current computer resources. To establish a more efficient approach for the systematic prediction of R, we focus on the very first steps of the reaction and calculate the ab initio Gibbs free activation energies for insertion of an ethylene molecule into a Feethyl bond (Scheme 1, reaction in blue) and its competitive BHT termination (Scheme 1, reaction in red). This suggestion is based on the chemical intuition that the resulting SchulzFlory distribution is inherited from the local chemical properties of the organometallic center. As previously outlined, the starting configurations of the two competing elementary steps are the same and correspond to the π-adduct complex, where ethylene is coordinated to the Fe-ethyl complex (Scheme 1). The two pathways are expected to be controlled by the relative energy levels of their transition states. The critical question remains to identify if a quantitative correlation exists between R and these energy levels. Table 1 classifies six active bis(arylimino)pyridine complexes (AF) with increasing Rexp values, cf. Chart 1 for the precise nature and position of the substituents on the aryl group.6,7,21 A typical example of the two competitive transition structures is shown in Figure S2. All other relevant structures are reported in the Supporting Information. As inferred from eqs 4 and 5, a linear relationship is obtained, eq 6 with a linear regression coefficient R2 of 0.99, Figure 1a. ! Rexp ln ¼ 0:34δΔGqBHT1-ins1 ðT, pÞ 2:08 ð6Þ 1 Rexp where δΔGqBHT1ins1 refers to the difference in the Gibbs free activation of the first BHT and insertion reactions that could occur, i.e., respectively, the reaction of ethylene and Fe-ethyl (ΔGqBHT(C2fC2)) and the insertion of ethylene in the Feethyl 3912
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Table 1. Calculated Gibbs Free Activation Energies According to eq 6 and rexp of the Investigated Catalysts for Ethylene Oligo/Polymerizationa cat.
T/p
ΔGqBHT
ΔGqins
(C2fC2)
(C2fC4)
δΔGqBHT1ins1 Rcalc
Rexp
A
30/1
19.5
15.8
3.7
0.31 0.29
B
2260/3
21.5
16.8
4.7
0.37 0.39
C
30/1
21.9
15.9
6.0
0.48 0.52
D E
30/1 25/1
23.4 26.4
15.6 15.5
7.8 10.8
0.62 0.61 0.82 0.81
F
25/1
25.0
13.4
11.6
0.85 0.87
G
25/1
30.4
13.8
16.6
19.5b
14.8b
4.7
E(C4)b 30/7c
0.97 polymers 0.37 dimers
a
The activation energies are given in kcal/mol under experimental conditions (temperature, T, in °C and pressure, p, in bar). b Oligomerization reaction with catalyst E and but-1-ene with ΔGqBHT(C4fC4), ΔGqins(C4fC8). c An inert gas head pressure of at least 7 bar was used to drive the butene into the reactor as a liquid and to keep the butene liquefied during reaction heating.
bond (ΔGqins(C2fC4)); see also the left part of Scheme 1: δΔGqBHT1-ins1 ¼ ΔGqBHTðC2 f C2Þ ΔGqinsðC2 f C4Þ
ð7Þ
It is important to underline immediately that the numerical values of the calculated descriptor δΔGqBHT1ins1 are not equal to the numerical values of δΔGq in eqs 4 and 5. The former refers to the difference in Gibbs free activation energy for the first insertion and BHT reactions, while the latter refers to the difference of the “apparent” Gibbs free activation energies for the reactions involving the Cn oligomers (vide infra). We then applied eq 6 to predict the SchulzFlory coefficient for catalyst G, which experimentally is known to produce heavy polymers at room temperature6,7 corresponding to R close to 1. According to eq 6, the predicted value for R is 0.97 (Table 1), which is fully consistent with the experimental data. Furthermore, we have addressed the nature of the reacting olefin. As Small et al. found experimentally,22 using but-1-ene monomer catalyst E mainly produces linear octenes and dodecenes. We recently investigated the detailed CosseeArlman mechanism of this reaction and calculated the relevant Gibbs free activation energies for the insertion and BHT reaction of the reaction C4 f C8.18 According to the CosseeArlman mechanism, the corresponding R for butene oligomerization is expected to be rather small. To determine the corresponding R value, we thus use the most favorable reaction path generating the linear octenes18 and the analogous Gibbs free activation energy difference between the lowest activation barrier for the insertion reaction of but-1-ene into the Febutyl bond and the activation barrier for the competitive termination reaction by BHT (the corresponding values are reported in Table 1). Expectedly, we calculate a hypothetical value of R = 0.37. This value indicates that very few insertion steps take place, with a high selectivity in dimerization and trimerization. This result is thus in perfect harmony with experimental data reporting the production of dimers (80%) and trimers (20%).22 Figure 1a summarizes the general correlation between Rexp and δΔGqBHT1ins1 for the catalysts A to F and Figure 1b the corresponding parity plot between the calculated and experimental SchulzFlory coefficients of all studied catalytic systems. The linear master relationship distinctly shows that δΔGqBHT1ins1 is correlated with ln[R/(1 R)], eq 6. It thus appears that the first insertion step into the metalethyl bond and the first termination step act as
Figure 1. (a) Linear variation of ln[Rexp/(1 Rexp)] as a function of δΔGqBHT1ins1 in kcal/mol at experimental T and p for catalysts A to F, with a linear regression coefficient of 0.99. (b) Parity plot between the experimental and calculated SchulzFlory coefficients for the insertion of ethylene for catalysts A to F (open squares). The solid squares refer to predicted R values, by applying eq 6, for the reaction of ethylene with catalyst G and the reaction of catalyst E with but-1-ene: E(C4).
fingerprints of the observed product selectivity. Furthermore, it can directly be deduced that if one is interested in the synthesis of oligomers with a well-defined chain length (0.5 < R < 0.85), q δΔG BHT1ins1 should take a value between 6 and 11 kcal/mol. In contrast, if one aims at producing polymers, the calculated q δΔG BHT1ins1 descriptor should be greater than 16 kcal/mol. The numerical value of the slope in eq 6 (a = 0.33) is smaller than the slope in eq 4 (a = 1.68) at T = 25 °C.23 It therefore follows that δΔGqBHT1ins1 is larger than δΔGq; hence the calculated descriptors may overestimate the energy barrier of the “apparent” termination reaction or underestimate the barrier for the “apparent” insertion reaction, or a combination of both phenomena. Indeed, in the BHT reaction, we consider a methyl group, instead of a methylene (CH2) implicated in a longer alkyl chains, thereby overestimating this energy barrier. However, this is a near constant value, practically independent of the catalyst, and thus effects principally the y-intercept value and not the slope. Alternatively, we have considered the β-hydrogen elimination (BHE) termination reaction, but this reaction has even higher energy barriers, as compared to BHT, for short (smaller than C8) alkyl chains. We also have investigated how the barrier for ethylene insertion changes upon growth of the produced alkyl chain. We computed variations ranging from 10 to +15% for the insertion of the second ethylene molecule, with respect to the insertion of the first ethylene molecule, to 2 to +6% for the third insertion with respect to the second. However, these variations are related to neither the nature 3913
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Organometallics of the catalysts (e.g., increasing steric effects as in catalysts E, F, and G or electronic effects) nor an increasing value of the experimental SchulzFlory coefficient. Consequently, it appears that the use of the energy barriers of higher order for the insertion, BHT, or BHE steps does not improve and even damages the linear relationship between the calculated δΔGqBHT1ins1 and ln(Rexp/(1 Rexp)). The y-intercept value of 2.08 in eq 6 corresponds to kterm/ kins = 7.97. kins being close to unity, this quotient implies that kBHT is close to 8. According to the literature, this latter value is not incongruous, as transmission coefficients may reach values close to 18 for enzymatic systems at 25 °C.24 The presented theoretical results propose a promising and powerful approach for the in silico design of new homogeneous catalysts that produce well-controlled oligomers. It reveals the potential of the calculated δΔGqBHT1ins1 descriptor to predict the oligo/polymer distribution for iron-based bis(imino)pyridine catalysts, represented by the SchulzFlory coefficient (R). However, we underline that δΔGqBHT1ins1 must never be considered as the “apparent” δΔGq component but as a chemical descriptor at best mimicking how δΔGq varies as a function of the catalyst. We are currently investigating the possible generalization of this model to other homogeneous catalysts that yield oligomers.
’ COMPUTATIONAL DETAILS Geometry optimizations and frequency analyses were performed with the B3LYP functional in its unrestricted formalism, combined with the Los Alamos effective core potential and associated valence basis set (the so called LanL2 basis) for Fe and Br and 6-31G(d,p) for H, C, N, O and F as implemented in Jaguar.20 We had calculated for the activated species of catalyst E (Chart 1) with a Fe(III) oxidation state that the quartet spin state is the most favorable for the insertion reactions, while the doublet spin state has the lowest energy for the BHT reaction.16,18 The same spin state stability order was verified routinely for the other iron-based catalysts reported in Chart 1, remaining a Fe(III) oxidation state. Gibbs free energies have been calculated at experimental reaction conditions. Please refer to the Supporting Information for further details. ’ ASSOCIATED CONTENT
bS
Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: +33 147525438. Fax: +33 147527058.
’ ACKNOWLEDGMENT The authors thank IFP Energies Nouvelles and ANRT (French Agency for the Research and Techniques) for the financial support. We also thank Drs. Helene Olivier-Bourbigou and Herve Toulhoat from IFP for fruitful scientific discussions. ’ REFERENCES (1) (a) Cossee, P. J. Catal. 1964, 3, 80–88. (b) Arlman, E. J.; Cossee, P. J. Catal. 1964, 3, 99–104. (2) Caldin, E. F. Chem. Rev. 1969, 69, 135–156. (3) Fernandez-Ramos, A.; Truhlar, D. G. J. Chem. Phys. 2001, 114, 1491–1496.
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(4) (a) Nørskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H. Nat. Chem. 2009, 1, 37–46. (b) Sautet, P.; Delbecq, F. Chem. Rev. 2010, 110, 1788–1806. (c) Klanner, C.; Farrusseng, D.; Baumes, L.; Lengliz, M.; Mirodatos, C.; Schuth, F. Angew. Chem., Int. Ed. 2004, 43, 5347–5349. (d) Ras, E. J.; Maisuls, S.; Haesakkers, P.; Gruter, G. J.; Rothenberg, G. Adv. Synth. Catal. 2009, 351, 3175–3185. (5) (a) Maldonado, A. G.; Rothenberg, G. Chem. Soc. Rev. 2010, 39, 1891–1902. (b) Maldonado, A. G.; Rothenberg, G. Chem. Eng. Prog. 2009, 105, 26–32. (c) Maldonado, A. G.; Hageman, J. A.; Mastroianni, S.; Rothenberg, G. Adv. Synth. Catal. 2009, 351, 387–396. (d) De Bruin, T.; Raybaud, P.; Toulhoat, H. Organometallics 2008, 27, 4864–4872. (e) Burello, E.; Rothenberg, G. Int. J. Mol. Sci. 2006, 7, 375–404. (f) Burello, E.; Rothenberg, G. Adv. Synth. Catal. 2005, 347, 1969–1977. (g) Burello, E.; Marion, P.; Galland, J. C.; Chamard, A.; Rothenberg, G. Adv. Synth. Catal. 2005, 347, 803–810. (6) (a) Small, B. L.; Brookhart, M.; Bennett, A. M. A. J. Am. Chem. Soc. 1998, 120, 4049–4050. (b) Small, B. L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 7143–7144. (7) (a) Britovsek, G. J. P.; Gibson, V. C.; Kimberley, B. S.; Maddox, P. J.; McTavish, S. J.; Solan, G. A.; White, A. J. P.; Williams, D. J. Chem. Commun. 1998, 849–850. (b) Britovsek, G. J. P.; Bruce, M.; Gibson, V. C.; Kimberley, B. S.; Maddox, P. J.; Mastroianni, S.; McTavish, S. J.; Redshaw, C.; Solan, G. A.; Stromberg, S.; White, A. J. P.; Williams, D. J. J. Am. Chem. Soc. 1999, 121, 8728–8740. (8) (a) Bianchini, C.; Giambastiani, G.; Guerrero Rios, I.; Mantovani, G.; Meli, A.; Segarra, A. M. Coord. Chem. Rev. 2006, 250, 1391–1418. (b) Gibson, V. C.; Redshaw, C.; Solan, G. A. Chem. Rev. 2007, 107, 1745–1776. (9) (a) Tondreau, A. M.; Milsmann, C.; Patrick, A. D.; Hoyt, H. M.; Lobkovsky, E.; Wieghardt, K.; Chirik, P. J. J. Am. Chem. Soc. 2010, 132 (42), 15046–15059. (b) Bouwkamp, M. W.; Lobkovsky, E.; Chirik, P. J. J. Am. Chem. Soc. 2005, 127, 9660–9661. (10) Castro, P. M.; Lahtinen, P.; Axenov, K.; Viidanoja, J.; Kotiaho, T.; Leskelae, M.; Repo, T. Organometallics 2005, 24, 3664–3670. (11) (a) Bryliakov, K. P.; Semikolenova, N. V.; Zudin, V. N.; Zakharov, V. A.; Talsi, E. P. Catal. Commun. 2004, 5, 45–48. (b) Bryliakov, K. P.; Semikolenova, N. V.; Zakharov, V. A.; Talsi, E. P. Organometallics 2004, 23, 5375–5378. (12) Britovsek, G. J. P.; Clentsmith, G. K. B.; Gibson, V. C.; Goodgame, D. M. L.; McTavish, S. J.; Pankhurst, Q. A. Catal. Commun. 2002, 3, 207–211. (13) Deng, L. Q.; Margl, P.; Ziegler, T. J. Am. Chem. Soc. 1999, 121 (27), 6479–6487. (14) Khoroshun, D. V.; Musaev, D. G.; Vreven, T.; Morokuma, K. Organometallics 2001, 20, 2007–2026. (15) Griffiths, E. A. H.; Britovsek, G. J. P.; Gibson, V. C.; Gould, I. R. Chem. Commun. 1999, 1333–1334. (16) Raucoules, R.; de Bruin, T.; Raybaud, P.; Adamo, C. Organometallics 2008, 27, 3368–3377. (17) (a) Martinez, J.; Cruz, V.; Ramos, J.; Gutierrez-Oliva, S.; Martinez-Salazar, J.; Toro-Labbe, A. J. Phys. Chem. C 2008, 112, 5023– 5028. (b) Cruz, V. L.; Ramos, J.; Martinez-Salazar, J.; Gutierrez-Oliva, S.; Toro-Labbe, A. Organometallics 2009, 28 (20), 5889–5895. (18) Raucoules, R.; de Bruin, T.; Raybaud, P.; Adamo, C. Organometallics 2009, 28, 5358–5367. (19) Britovsek, G. J. P.; Mastroianni, S.; Solan, G. A.; Baugh, S. P. D.; Redshaw, C.; Gibson, V. C.; White, A. J. P.; Williams, D. J.; Elsegood, M. R. J. Chem. Eur. J. 2000, 6, 2221–2231. (20) Jaguar, version 7.5; Schr€odinger, LLC: New York, NY, 2008. (21) (a) Zhang, Z.; Chen, S.; Zhang, X.; Li, H.; Ke, Y.; Lu, Y.; Hu, Y. J. Mol. Catal. A: Chem. 2005, 230, 1–8. (b) Bluhm, M. E.; Folli, C.; D€oring, M. J. Mol. Catal. A: Chem. 2004, 212, 13–18. (c) Small, B. L.; Rios, R.; Fernandez, E. R.; Carney, M. J. Organometallics 2007, 26, 1744–1749. (22) (a) Small, B. L.; Marcucci, A. J. Organometallics 2001, 20, 5738–5744. (b) Small, B. L.; Schmidt, R. Chem.—Eur. J. 2004, 10, 1014–1020. (23) A linear relationship can thus be identified that correlated the descriptor δΔGqBHT1ins1 with the “apparent” δΔGq following: δΔGqBHT1ins1 = 1.68/0.34 δΔGq = 5 δΔGq. (24) Pu, J.; Gao, J.; Truhlar, D. G. Chem. Rev. 2006, 106, 3140–3169. 3914
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