DFT Study on the Impact of the Methylaluminoxane Cocatalyst in

A computational study within the framework of density functional theory is presented on the oligomerization of ethylene to yield 1-hexene using ...Mis...
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DFT Study on the Impact of the Methylaluminoxane Cocatalyst in Ethylene Oligomerization Using a Titanium-Based Catalyst Farhan Ahmad Pasha,†,‡ Jean-Marie Basset,‡ Hervé Toulhoat,† and Theodorus de Bruin*,† †

IFP Energies Nouvelles, 1-4 Avenue de Bois Préau, 92852, Rueil-Malmaison, France KAUST Catalysis Research Center, King Abdullah University of Science and Technology, Thuwal 23955-6900 Saudi Arabia

‡

S Supporting Information *

ABSTRACT: A computational study within the framework of density functional theory is presented on the oligomerization of ethylene to yield 1-hexene using [(η5-C5H4CMe2C6H5)]TiCl3/MAO] catalyst. This study explicitly takes into account a methylaluminoxane (MAO) cocatalyst model, where the MAO cluster has become an anionic species after having abstracted one chloride anion, yielding a cationic activated catalyst. Hence, the reaction profile was calculated using the zwitterionic system, and the potential energy surface has been compared to the cationic catalytic system. Modest differences were found between the two free energy profiles. However, we show for the first time that the use of a realistic zwitterionic model is required to obtain a Brønsted−Evans−Polanyi relationship between the energy barriers and reaction energies.

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INTRODUCTION

The increasing demand of higher order linear α-olefins1 stimulates both academia and petrochemical sectors to develop new, more active and more selective catalysts to transform simple alkenes such as ethylene into 1-hexene, 1-octene, etc.2−4 Among the applications of 1-octene we can mention the use as a copolymer in the production of low-density polyethylene or the functionalization of the olefinic bond to a wide variety of organic products, e.g., linear aldehydes.5 Teuben and coworkers published a highly selective catalyst to produce 1hexene using a titanium complex with a hemilabile ancillary ligand (Figure 1a) that is activated with methylaluminoxane (MAO).6,7 They proposed a plausible reaction pathway for the catalytic trimerization of ethylene, involving metallacycle intermediates, that was shortly later validated by density functional theory (DFT).8−10 Subsequent DFT studies were later published to predict the impact of changes on the activity and/or selectivity of the oligomerization reaction by varying the nature of the coordinating ligands or the transition metal.11−13 However, up to now the MAO cocatalyst has not explicitly been taken into account for this particular catalytic system. Since it is assumed that MAO does not play an active role in the catalytic cycle, most theoretical studies did not take MAO explicitly into account, apart from the work of Janse van Rensburg and co-workers on chromium-based catalysts.14 In this paper we compare the profile of the Gibbs potential energy for this zwitterionic chemical system, i.e., the activated cationic Ti catalyst with the [MAO-Cl]− anionic species for the tri/tetra/pentamerization reaction (Scheme 1), and compare the results with those for the system without MAO. © XXXX American Chemical Society

Figure 1. (a) Precatalyst; (b) schematic structure of the studied [MAO-Cl]− anion, where the methyl groups on the aluminum atoms are omitted for clarity; and (c) B3LYP-optimized configuration of the [MAO-Cl]− anion.

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COMPUTATIONAL DETAILS

The mechanistic aspects of the oligomerization for ethylene have been studied using the B3LYP15 functional as implemented in the Gaussian Received: September 10, 2014

A

DOI: 10.1021/om5008874 Organometallics XXXX, XXX, XXX−XXX

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model is present, giving an overall neutral catalytic system. We have used a plausible hexagonal structure of MAO as displayed in Figure 1b. We have examined singlet, triplet, and quintet spin multiplicities for both profiles, and it follows that the singlet state was the most stable spin state for titanium along the whole reaction profile. The transition states were located using the synchronous transit-guided quasi-Newton (QST2) approach. In addition, the intrinsic reaction coordinate (IRC) procedure has been used to extrapolate the two minima connected by each transition state. The character of all stationary points has been checked by analytical frequency calculations. The Gibbs energies were computed at 298.15 K and 1 atm (unless specified otherwise) assuming an ideal gas behavior using unscaled harmonic vibrational frequencies obtained within the rigid rotor approximation. We have verified that the inclusion of solvent effects, here toluene, by applying the PCM model on the gas-phase-optimized geometries, does not change the overall conclusions presented below, as compared to the gas-phase energies.

Scheme 1. Reaction Pathway for the Oligomerization of Ethylenea

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a

RESULTS AND DISCUSSION 1. MAO Model. Despite numerous experimental19,20 and theoretical studies21,22 the structure of MAO remains poorly defined. Structural properties of “pure” MAO were studied using an ab initio approach. Recently, Zakharov et al.23 presented a detailed comparison of cyclic and cage models with Cnh and Cnd symmetries, respectively (where n is half of the total number of aluminum present). The cage structure models were composed of two parallel [Al(Me)O]n rings connected by an n square face composed of Al2O3. These workers found that the cage structure was more stable than the cyclic one. It is now generally agreed that MAO consists of oligomers that have three-dimensional cages in which the aluminum atoms are connected to three oxygen atoms and a methyl group to yield cages where hexagonal and square faces are privileged. Here, we have considered a stable MAO cage built from six aluminum atoms (Figure 1b) that is negatively charged due to coordination of one chloride anion that has been abstracted

For clarity reasons the [(AlOMe)6Cl]− anion has been omitted.

09 package.16 Two different basis sets, BS1 and BS2, have been used. BS1 corresponds to the 6-31G(d,p) basis set for the elements C, H, O, Al, and Cl, while Ti is described by the effective core potential LanL2DZ.17 In the case of BS2 all elements are described by the ccpVTZ basis set.18 Two different reaction profiles have been designed: a cationic profile (CP) where the catalytic system is positively charged and there is no counteranion, as already calculated,8,9 and a zwitterionic profile (ZP) where besides the positively charged catalyst an anionic MAO

Figure 2. Comparative reaction profile over the potential energy surface for a cationic (gray) and zwitterionic (black) catalyst. The solid line indicates the main path, while the dotted line an alternative, but energetically less favorable path. B

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Organometallics from the [(η5-C5H4CMe2C6H5)TiCl3] precursor. We are well aware that this is a relatively small cage with respect to the cages studied in the work of Janse van Rensburg.24 Indeed, Zurek et al.21,22 and Boudene et al.25 have shown that the cage structures with about 12 aluminum atoms are the most stable ones from a thermodynamic viewpoint. However, it can be reasonably assumed that if this negatively charged species with six aluminum atoms is (only) loosely coordinated to the cationic activated titanium species, also the larger cage structures of [MAO-Cl]− are likely to be even more weakly interacting, since the overall net charge is distributed over more atoms. In this mechanistic study two different potential free energy reaction profiles have been modeled (Figure 2): the first takes into account only the cationic catalyst, which we will call a cationic profile, while the second profile describes the energy changes of the catalyst in the presence of a chlorinated MAO model, which was inspired by the work of Zurek and Ziegler, who used a closely related MAO model in the description of the ethylene polymerization of ethylene with [Cp2ZrMe]+,26 thereby having become a zwitterionic system, which we will call a zwitterionic profile. The overall reaction cycle is displayed in Scheme 1. All configurations obtained for the stationary and saddle points are presented in the Supporting Information. Their Gibbs energies relative to M1 in both cases are presented in Figure 2. The reaction starts with the activated catalyst M1, where two ethylene molecules are coordinated to the cationic Ti(II) species. Once the oxidative coupling has taken place (M2), a third ethylene molecule coordinates and inserts to yield a seven-membered metallacycle (M3). This species can undergo a beta hydrogen transfer followed by reductive elimination reaction (M4A), which in turn releases 1-hexene. Alternatively a fourth ethylene may coordinate to M3 and insert to yield a nine-membered metallacycle M4B. This latter species can then undergo a ring-opening reaction to yield 1-octene (M5A), or a fifth ethylene coordination and insertion can take place, etc. The energy profile for the cationic system has previously been reported11−13 by some of us and is included in Figure 2 to allow direct comparison with the profile of the zwitterionic system, which has not been described before. It is seen that the formation of the five-membered metallacycle M2 is an exergonic reaction (−5.5 kcal·mol−1) with an energy barrier of ΔG⧧ = 8.9 kcal·mol−1 to form transition state T1 (along ZP). In principle metallacycle M2 can also undergo ring opening via a reductive β-hydride transfer to form 1-butene. Recently, it has been published8,9,11 that the β-hydrogen transfer to form 1-butene is energetically less favorable than the coordination and insertion of the third ethylene; hence the latter is preferred. Here, we have calculated the β-hydrogen transfer to form 1-butene using the zwitterionic catalytic system (Scheme 1). This is a two-step process: the β-hydrogen is first transferred to the Ti+ center with a barrier M2 → T2A of 17.5 kcal·mol−1, and in a second step the hydride is transferred from the Ti+ center to a carbon and the formation of 1-butene takes place. This second step, M2A → T2B, has a barrier of 26.2 kcal mol−1. This PES diagram (Figure 3) shows that the β-H transfer to form 1-butene has therefore an overall energy barrier of +34.7 kcal mol−1, while the insertion of a third ethylene and metallacycle growth M2 → T2 is energetically favorable (+26.0 kcal mol−1). The calculations thus corroborate the fact that 1butene is not found experimentally at least with this particular Teuben system. It is to be noted that the barrier M2 → T2 of 26.0 kcal·mol−1, corresponding to the coordination and

Figure 3. Gibbs energy profile for the ring opening of the fivemembered ring to generate 1-butene via a two-step mechanism in the presence of the [MAO-Cl]− anion.

insertion of the third ethylene, is the largest barrier along the PZ path and, thus, represents the rate-determining step. Interestingly the introduction of [MAOCl]− in the system increases drastically the energy barrier M2 → T2 as compared to the cationic system without MAO. Since the barrier (ΔG⧧ = 12.8 kcal mol−1) for the ring opening of the seven-membered ring M3 to yield T3A is significantly lower than the energy barrier (ΔG⧧ = 18.6 kcal·mol−1) for the fourth ethylene insertion (T3B), our calculations including the effect of an [MAO-Cl]− anion are consistent with the previous findings along PC27 and provide an explanation for the experimental fact that this catalytic system essentially forms 1-hexene.11−13 2. Impact of MAO. Figure 1c presents the optimized conformation of a model [MAO-Cl]− anion used in this study and is the result of the exergonic reaction (−37.0 kcal·mol−1) between a commonly used model of pure MAO, i.e., with a 1 to 1 ratio of Al:Me and a chloride anion. As a result of this reaction the three-dimensional hexagonal structure of MAO is partly destroyed by breaking two Al−O bonds and forming two equidistant (2.38 Å) Al−Cl bonds and an Al−Cl−Al bond angle of 98.3°. We have calculated the interaction energy between the cationic Ti species and the [MAO-Cl]− anion. The difference in electronic energy between the fully optimized zwitterionic complex and the sum of optimized cationic species and anionic species is −30 kcal·mol−1 for M1 and remained nearly constant (±6 kcal·mol−1) along the reaction coordinate despite the formation of coordinated metallacycles of increasing sizes. This interaction energy is relatively small as compared to separation enthalpies calculated for analogous cationic Ti-based polymerization catalysts and a comparable MAO anion model (∼100 kcal·mol−1).28 Furthermore, the deformation energy of the cationic species in the presence of the anion species is around 1.0 kcal·mol−1 for M1. From these results we conclude that the two ions only weakly interact, and we anticipate that the reaction profile of the zwitterionic system should not deviate too much from the system where only the cation is considered. Indeed, it can be seen from Figure 2 that the black-colored profile (presence of the MAO cage) deviates at only two points from the gray curve (cationic species only) along the path producing 1-hexene. First transition state T2 becomes destabilized in the presence of the [MAO-Cl]− anion. Therefore, the rate-determining step becomes more accentuated and consequently decreases the overall activity of the C

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Å in C-TS4B and Z-TS4B, and the new C−C bond is 2.3 Å in both cases. Note that these bond distance are practically the same in the analogous transition states C-TS3B and Z-TS3B. It is clear from these geometrical observations that in this reaction profile study the counterion has a very little impact. 4. Temperature Effect. The temperature effect on the catalyst’s activity and selectivity in the presence/absence of the [MAO-Cl]− anion was studied at three different temperatures: 0, 25, and 37 °C or respectively 273.15, 298.15, and 310.15 K. The electronic energy was calculated with basis set BS2, while the corrections to the Gibbs energy were obtained from the B3LYP/BS1 level, at which the geometries were optimized. Figure 5a and b display the relative Gibbs free energies (kcal·

catalyst. Second, the energy difference between the two competitive transition states T3A and T3B, leading to 1hexene and the nine-membered metallacycle, respectively, becomes smaller in the presence of the [MAO-Cl]− anion and is essentially the result of a higher stability of T3B. However, in spite of this decrease, the selectivity is still in favor of the hexene-1 production. We were not able to obtain a clear reason why T2 becomes destabilized and T3B stabilized in the presence of the [MAO-Cl]− anion, but it very likely due to slight variations in the interaction energy between the cationic Ti species and the [MAO-Cl]− anion species. Overall it can be concluded that the presence even of this relatively small MAO-cage structure does not impact the selectivity of the reaction product: 1-hexene remains the major product in accordance with the experimental data and thus, a posteriori, justifies the negligence of MAO in the previous study coauthored by some of us.9 3. Geometrical Impacts. The potential energy surface analysis reveals that there is no major effect of a cationic or zwitterionic nature catalyst on the selectivity. We have also explicitly analyzed the geometrical perturbations brought by the presence of a counterion in the system. Figure 1S (in the Supporting Information) presents all transition states involved in the reaction cycle. The C-TSs are the transition states located in cationic form, and Z-TSs are transition states located in the presence of the counterion (MAO). Figure 4 displays the transition states TS1 for the oxidative ethylene coupling to form the five-membered metallacycle in the absence and in the presence of the MAO model.

Figure 4. C-TS1 is the transition state located in the cationic form and Z-TS1 is the transition state located in the presence of the counterion (MAO) for the oxidative coupling of two ethylenes.

Figure 5. Relative Gibbs free energies (kcal·mol−1) of the reaction intermediates at three different temperatures (blue: 273.15 K, red: 298.15 K, and yellow: 310.15 K) for (a) the cationic system and (b) the zwitterionic system.

In these geometries the average C−Ti bond length is 2.1 Å in both (the cationic) C-TS1 and (zwitterionic) Z-TS1. The C−C distance between the new bond is also the same (2.0 Å). In TS2, where the third ethylene is inserting into the Ti−C bond, the cleaving Ti−C bond length equals 2.2 Å in both C-TS2 and Z-TS2, while the incoming ethylene is located at 2.2 Å. Transition state T3A corresponds to the ring opening via β-H transfer assisted by the Ti+ center. In both C-TS3A and ZTS3A the Ti−H distance is 1.7 Å. The bond length for Ti−C is reported as 2.1 Å in both cases. T3B corresponds to the fourth ethylene insertion into the Ti−C bond, which is, from an energy point view, an unfavorable pathway. The to-be-broken Ti−C bond in both C-TS3B and Z-TS3B is 2.0 Å, and the incoming ethylene is located at 2.2 Å. In TS4A, where ring opening via a β-H transfer occurs, the Ti−H distance is 1.7 Å in C-TS4A and Z-TS4A. The Ti−C bond length is also virtually the same (2.2 and 2.1 Å). The transition state T4B corresponds to the fifth ethylene insertion step to form the 11-membered metallacycle. The bond length of the cleaving Ti−C bond is 2.1

mol−1) for the cationic and zwitterionic systems, respectively, with M1 as a reference. It is seen that a temperature increase destabilizes the reaction intermediates and transition states for both systems. This destabilization is more pronounced for those steps that involve ring expansion, i.e., M2 → T2 and M3 → T3B, as seen from Table 2, since the uptake of an ethylene molecule is entropically disfavored. Hence, a temperature increase is favorable for the selectivity, since the δΔG⧧ between M3 → T3A and M3 → T3B increases. Using Eyring’s law (eq 1) absolute reaction rates have been calculated. k=

kBT −ΔG⧧ / RT e h

(1)

where k is the reaction rate, kB is Boltzmann’s constant, and h is Planck’s constant, T is the absolute temperature, R is the gas constant, and ΔG⧧ is the Gibbs activation energy. Table 1 D

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Table 1. Gibbs Energies Barriers (kcal·mol−1) as a Function of Temperature for the Ring Expansion Reactions (M2 → T2 and M3 → T3B) Compared to the Ring-Opening (M3 → T3A) Reaction for the Cationic and Zwitterionic Catalytic System M2 → T2 (expansion C4 → C6)

M3 → T3A (release C6=)

M3 → T3B (expansion C6 → C8)

T (K)

cationic

zwitterionic

cationic

zwitterionic

cationic

zwitterionic

273.15 298.15 310.15

16.6 17.7 18.2

25.2 26.0 26.5

13.8 13.9 13.9

12.6 12.8 12.8

23.5 24.5 25.0

17.7 18.6 18.9

Table 2. Gibbs Energies and k Values for the Ring-Expansion Reactions (M2 → T2 and M3 → T3B) Compared to the Ring-Opening (M3 → T3A) Reaction for the Cationic and Zwitterionic Catalytic System relative overall activity

a general reaction in which a reactant (R) is transformed into a product (P) via a transition state (TS) (see inset in Figure 7),

C6/C8 selectivity (%)

T (K)

cationic

zwitterionic

cationic

zwitterionic

273.15 298.15 310.15

0.07 1.00 2.52

0.13 1.00 2.58

100.00 100.00 100.00

99.99 99.99 99.99

shows how the relative overall rate changes with temperature, taking 298 K as a reference temperature and using the M2 → T2 energy barrier. Both the cationic and zwitterionic systems show the same (expected) tendency: a lower temperature yields lower rates and a higher temperature a higher rate. Furthermore, it is seen that the C6/C8 selectivity, using the rates for M3 → T3A and M3 → T3B, is hardly impacted by the temperature change: the percentage of C8 remains negligible. 5. Brønsted−Evans−Polanyi (BEP) Relationships. In order to prevent computationally intensive transition-state optimizations, we have analyzed if a linear relationship exists that correlates the Gibbs reaction energy (ΔG) with the Gibbs activation energy (ΔG⧧) of the same reaction. This type of relationship is also known as the BEP principle. Figure 6 depicts this correlation for both the cationic and the zwitterionic system. The positive slope for both systems is in agreement with the Hammond postulate that activation energies become larger for more endergonic reactions. A poor correlation is found for the cationic system (R2 = 0.43), in which the outlier T1 has a significant weight. The correlation is significantly better for the zwitterionic system (R2 = 0.81). For

Figure 7. Correlations between the backward and forward Gibbs activation energies for the cationic (blue; R2 = 0.44) and zwitterionic (red; R2 = 0.95) system.

we can write that the sum of the Gibbs reaction energy (ΔGi) ⎯⎯→ and the Gibbs activation energy of the forward reaction (ΔG ⧧i ) equals the Gibbs activation energy of the backward reaction ←⎯⎯ ⧧ (ΔG i ): ⎯⎯→ ⎯⎯→ ‡ ←⎯⎯ ‡ ΔGi + ΔGi = ΔGi

(2)

We observe that ←⎯⎯ ‡ ⎯⎯→ ‡ ΔGi = aΔGi + b

(3)

By substituting eq 3 into eq 2 we obtain ⎯⎯→ ‡ ⎯⎯→ ⎯⎯→ ‡ ΔGi + ΔGi = aΔGi + b

(4)

Rewriting eq 4 we get ⎯⎯→ ‡ ⎯⎯→ ‡ ⎯⎯→ aΔGi − ΔGi = ΔGi − b

(5)

⎯⎯→ ‡ ⎯⎯→ (a − 1)ΔGi = ΔGi − b

(6)

⎯⎯→ ‡ ΔGi =

⎯⎯→ 1 b ΔGi − (a − 1) (a − 1)

⎯⎯→ ‡ ⎯⎯→ ΔGi = aΔGi + β

(7) (8)

with a = 1/(a − 1) and β = b/(a − 1). Equation 8 thus states that the (forward) activation Gibbs energy is linearly proportional to the Gibbs reaction energy, which corresponds to the Brønsted−Evans−Polanyi principle.

Figure 6. Correlations between the forward Gibbs activation energies and Gibbs reaction energies of oligomerization steps with cationic (red) and zwitterionic (blue) systems. E

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←⎯⎯ ⧧ Figure 7 shows these correlations between backward (ΔG i ) ⎯⎯→⧧ and forward (ΔG i ), Gibbs activation energies: the correlation is 2 excellent (R = 0.95) for the zwitterionic system and (remains) poor (R2 = 0.44) for the cationic system. Since the difference between forward and backward barriers is exactly equal to the free energy of reaction ΔG for any reaction along the pathway, a good correlation between forward and backward barriers can only be the consequence of the existence of a Brønsted−Evans−Polanyi relationship in the system. We show here that this relationship is revealed under the condition that the influence of the counteranion is taken into account; that is to say, a more realistic modeling scheme is implemented.

ACKNOWLEDGMENTS The authors acknowledge OCRF King Abdullah University of Science and Technology (KAUST) KSA for Award No. UKC0017.

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CONCLUSIONS In this computational study we have explicitly taken into account the presence of a MAO anion species to study its impact on the reaction profile of ethylene oligomerization using the [(η5-C5H4CMe2C6H5)TiCl3] precatalyst and compared the results with the profile where the activated cation alone is considered. At the B3LYP level in combination with a double-ζ quality basis set, it is found that the role of the [MAO-Cl]− anion, built from a three-dimensional cage structure with six aluminum atoms to which an abstracted (from the precatalyst) chloride is coordinated, is limited. The energy barrier of the rate-determining step becomes slightly higher and the energy difference between the two energy barriers responsible for the catalyst’s selectivity becomes smaller in the presence of the MAO counterion. However, the main product undoubtedly remains 1-hexene, and the rate-determining step is the uptake of the third ethylene molecule. From these results it can be concluded that the presence of an explicit MAO model does not necessarily need to be taken into account and that the cationic system alone is sufficiently representative. A temperature increase from 25 to 37 °C improves the selectivity, since the δΔG⧧ of the two competitive reactions increases from 5.8 to 6.2 kcal·mol−1, however, at the detriment of the activity since the barrier of the rate-determining step slightly increases from 26.0 to 26.5 kcal·mol−1. We have investigated whether a linear Brønsted−Evans−Polanyi relationship appears between computed free energy barriers and free energies of reaction along the oligomerization pathways modeled with a cationic or more realistically a zwitterionic catalytic system. We have given evidence of such a relationship only in the latter case and thereby present an excellent example of BEP relationship for a molecular catalytic system. ASSOCIATED CONTENT

S Supporting Information *

A table containing the Cartesian coordinates of all optimized stationary points is presented. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. F

DOI: 10.1021/om5008874 Organometallics XXXX, XXX, XXX−XXX