Analysis of Stereochemistry Control in Homogeneous Olefin

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Analysis of Stereochemistry Control in Homogeneous Olefin Polymerization Catalysis Giovanni Talarico† and Peter H. M. Budzelaar*,‡,§ †

Dipartimento di Scienze Chimiche, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada § Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands ‡

S Supporting Information *

ABSTRACT: We propose a new method, using statistical analysis, to quantify factors contributing to stereo- and regiocontrol in olefin polymerization catalysis and competing β-hydrogen transfer to monomer. The method has been applied to three rather different Zr-based catalysts: (1) racMe2Si(3-Me-C5H3)2ZrR+, a representative of “standard” ansa metallocenes; (2) [2,2′-bis(2-indenyl)biphenyl]ZrR+, a sterically congested and rather atypical metallocene; and (3) [1,2(2-O-3-tBu-C6H3CH2NMe)2-C2H4]ZrR+, an example of an octahedral “ONNO”-type catalyst. The analysis produces separate numeric values for repulsive ligand−chain, chain−monomer, and ligand−monomer interactions. For insertion in the Zr−iBu bond of 1 and 3, the ordering is syn (∼2.3 kcal/mol) > ligand−chain (∼1.6) > ligand−monomer (∼1.3), while for more crowded system 2 the three interactions are all around 2.0−2.5 kcal/mol. Despite the non-negligible magnitude of the ligand− chain interaction, the standard Corradini model of stereocontrol was found to apply for all cases. Our results also indicate that the stereocontrol penalties are sensitive to the nature of the chain and the olefin and that extrapolation from H or Me “chains” to more realistic chains is not warranted.

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INTRODUCTION Polyolefins, in particular polythene and polypropylene, are among the most widely used polymeric materials of today.1 Olefin polymerization processes used in industry typically use Ziegler−Natta-type catalysts, usually MgCl2-supported Tibased systems.2 While there is a broad consensus on general aspects of this catalysis, such as the Cossee−Arlman complexation/migratory insertion propagation mechanism,3 detailed knowledge of the actual active sites of ZN catalysts is still lacking. One of the most crucial aspects of this catalysis, namely, stereochemical control in propene polymerization, remains a matter of intense debate and discussion. Metallocenes, the first efficient and well-defined homogeneous olefin polymerization catalysts, are not just of commercial importance4 but have contributed immensely to our understanding of polymerization catalysis.5,6 In contrast to ZN systems, metallocenes lend themselves to standard structural characterization techniques such as X-ray diffraction and NMR;7−9 modeling of metallocenes is also relatively straightforward.10 Thus, these systems have acquired the status of a “standard model” for polymerization catalysts, and any new insights in metallocene chemistry are usually translated immediately to other polymerization catalysis systems. This applies especially to the stereoregulation mechanism. The classical “Corradini mechanism” of stereocontrol, originally based on molecular mechanics calculations for a model of the active site of heterogeneous systems11,12 but later extended to metallocenes13,14 and © XXXX American Chemical Society

supported by more sophisticated quantum-mechanical (DFT) studies,6,10,15 describes stereocontrol in a sequence of distinct “steps”:16 • The metal center has two reactive coordination sites in mutually cis orientation. The growing chain occupies one of these; the other is used to bind an incoming monomer. • At the transition state (TS), the growing chain has one αagostic interaction opposite the monomer position. As a consequence, the chain itself must point either “up” or “down” from the first metal-bound carbon atom.17−19 • Steric hindrance (by the ligand) will favor one of these two chain orientations. • The incoming monomer avoids the growing chain, and hence insertion preferentially happens in an anti fashion. • Insertion errors are caused by (a) chain misorientation (with the monomer still inserting anti) or (b) monomer syn orientation relative to the preferred chain orientation.6 Remarkably, this model does not include any direct ligand− monomer interaction, yet it accounts for most observations of dominant stereocontrol in metallocene polymerization. Because of this success, it has been assumed to be generally valid, not Received: April 7, 2014

A

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just for metallocenes but also for nonmetallocene homogeneous systems20,21 as well as heterogeneous ZN catalysts.22 However, it is not obvious that the neglect of direct ligand− monomer interaction is justified for all these systems or even for the parent metallocene case. The main argument against such direct interactions comes from the observed lack of stereoselectivity, for a few otherwise stereospecific catalysts, of propene insertion in M−H or M−Me bonds. For example, Zambelli, based on the results of the 13C NMR analysis of the end groups of isotactic polypropylene samples prepared with heterogeneous23,24 and metallocene systems,25,26 found that the initiation process is less stereospecific than chain propagation. Similarly, Erker found that the first propene insertion reaction at the rac-[Me2Si(1-indenyl)2]Zr-derived single-component system is not stereoselective.27 Finally, Bercaw found very little stereopreference for the insertion of pentene in the Y−H bond of an ansa-yttrocene.28 As we will see, these results should not be extrapolated to the more general metal−polymeryl case. It should be noted here that there are cases where direct ligand−monomer interactions play an important and generally accepted role, the best documented example being 2,1-insertion at metallocene centers.15,29 The observed stereochemistry is the result of many contributions that are hard to disentangle by experiment. From polymer microstructure analysis, one can obtain the frequency (and distribution) of stereoerrors,30 but separating these even into the two sources mention above (chain and monomer misorientation) is not possible. Nevertheless, we believe that quantitative knowledge of the various contributions to stereocontrol is important, because it can guide the design of new and improved ligands. Therefore, we are developing a method for extracting the magnitudes of various contributions to stereocontrol from calculated transition-state energies. The idea is more general, and we have applied our analysis also to regiocontrol as well as the dominant chain transfer reaction (βhydrogen transfer from the polymer chain to the monomer, BHT). In the present paper we report on the development of this new computational−statistical approach to arrive at separate contributions for the various interactions affecting the selectivity in polymerization promoted by a few homogeneous catalysts. We started with the archetypical metallocene (racMe2Si(3-Me-C5H3)2ZrR+, 1), where the 3,3′ substitution pattern represents the standard approach toward C2-symmetric, isospecific metallocene catalysts.6 The next system is a less typical metallocene ([2,2′-bis(2-indenyl)biphenyl]ZrR+, 2) designed to have chirality enforced by the ligand backbone rather than a particular substitution pattern.31,32 Finally, we included an “ONNO”-type catalyst ([1,2-(2-O-3- t BuC6H3CH2NMe)2-C2H4]ZrR+, 3),21,33 which can be considered typical of octahedral postmetallocene catalysts (Scheme 1). The method works as follows (for catalyst 1). We start with the simple system L1ZriBu+ + propene(1,2). There are four possible insertion transition states (A−D, Figure 1).34 A is the preferred one. B is worse than A because it suffers from an unfavorable syn interaction between chain and monomer. C is also worse than A, this time because of an unfavorable interaction between ligand and chain. Finally, D should be the least favorable possibility because it combines unfavorable chain−monomer and ligand−chain interactions. In the remainder of this paper we will call such interactions or contributions “penalties” because they correspond to the

Scheme 1. Catalysts Studied

Figure 1. Four transition states for propene 1,2-insertion in L1ZriBu+: (A) the Corradini insertion; (B and C) stereoirregular insertions; (D) non-Corradini stereoregular insertion. Ligand−chain and syn interactions are indicated by solid arrows; the dotted arrows represent ligand−monomer interactions. H atoms are omitted for clarity.

energy penalties associated with specific unfavorable interactions. Assuming the chain−monomer and ligand−chain penalties to be additive, we can fit values for them to reproduce calculated transition state energies for each of A−D. Since we also need to fit a “reference energy” (representing, for example, the best or the average case), this is a fit of three parameters to four data points, which is not particularly meaningful. If, however, we also include all possibilities with only a single methyl group at the ligand (in either the 3 or 3′ position), or none at all, the number of relevant TS energies increases to 14, while the number of parameters increases only from 3 to 5;35 this makes for a much more meaningful fit. The availability of a larger set of “data points” also allows testing for additional relevant penalties. For example, a direct ligand−monomer interaction penalty can be included in the model, and the fit results will then indicate whether this is a significant interaction B

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Transition-state free energies for these were fitted to sets of reference energies and linear combinations of penalties. A number of reasonable contributions, illustrated in Figure 2, were included in preliminary fits.

(within the assumed model): irrelevant interactions will show small fitted values and/or high standard deviations. Further data are obtained by also including ethene as a monomer, the propene 2,1-insertions, and to also cover competing the BHT reaction, provided penalties for relevant interactions are included. The energy Gi⧧ of each transition state TSi is written as ⧧ Gi⧧(stat) = Gref +

∑ cjiPj j

G⧧ref

where is the appropriate reference energy for this particular TS,36 the Pj are the various penalties that could in principle apply, and the coefficients cij are usually 1 if penalty j applies to TSi, or 0 if it does not.37 Linear least-squares fitting of G⧧i (stat) to the actual Gi⧧(calc) obtained from DFT calculations produces the “best” values of reference energies G⧧ref and penalties Pj. The advantage of a statistical treatment is that it smoothes out differences caused by specific but small effects. For example, based on Figure 1 one could take as a measure for the syn penalty either the AB or the CD difference. These numbers will not be identical, and it is not obvious which one is “correct”. The proposed statistical treatment automatically produces values that best represent all transition states included in the fit.38 The main assumption underlying our analysis is the additivity of the various interactions that determine the relative energies of the transition states. Once could argue that in the absence of additivity it is no longer even meaningful to talk about “contributions”. The quality of the fit provides a numerical indication of the degree to which additivity applies for the systems studied.

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Figure 2. Schematic representation of penalty contributions. X1 (close to chain) and X2 (close to olefin) represent the two ligand substituent positions. (a) Olefin complex/insertion TS; penalties for (b) chain to X1; (c) 1,2-propene vs ethene; (d) syn 1,2-propene; (e) 1,2-propene to X2; (f) 1,2-propene to X1; (g) 2,1-propene vs ethene; (h) syn 2,1propene; (i) 2,1-propene to X2. (j) BHT TS; penalties for (k) 1,2propene vs ethene; (l) chain/monomer to X1/X2; (m) syn Me groups.

METHODS

All transition-state structures were fully optimized at the b3-lyp39−41/ TZVP42,43 level using Turbomole 44 coupled to an external optimizer.45,46 The nature of each stationary point was checked with an analytical second-derivative calculation (one imaginary frequency, corresponding to olefin insertion or β-H transfer, for each transition state). The vibrational analysis data were also used to calculate thermal corrections (enthalpy and entropy, 273 K, 1 bar) for all species considered. Entropy values were scaled by a factor of 0.67 to account for the loss of entropy in solution.47,48 Analysis of the data in the main text of this paper is based on Gibbs free energy values, but analysis of enthalpy data leads to the same conclusions. Least-squares fits were produced using the statistical package “R”.49 To check for the effect of including dispersion, fits were repeated for (a) energies including a DFT-D3 dispersion correction50 (“Becke−Johnson” damping) to the b3-lyp energies and (b) energies calculated at the final b3-lyp/TZVP geometries with Gaussian 09,51 the M06-2X functional,52 and the def2TZVPP basis set.53 These results are discussed briefly at the end of the next section.

Some penalties were found to apply across all three alkyl chains (2,1 vs 1,2 insertion; BHT syn orientation), while others clearly depended on the type of chain (ligand−chain and chain−monomer interaction). The final set of fitted contributions and their standard deviations are collected in Table 1. We observed that the quality of the fit decreases as more reaction types or more extreme combinations are included in the procedure. Therefore, Table 2 contains fit results for a more limited set of energies only covering ethene and propene insertion (88 transition states); these numbers are believed to be more reliable, although the differences in fitted penalty values are modest. Insertion for Metallocene System 1. Results for olefin insertion in catalyst 1 are summarized in Table 2. The fit of 25 parameters to 88 energy values results in an rms deviation of 0.21 kcal/mol in predicted transition-state energies. Considering that we have a data:parameter ratio of ∼3.5, it appears that this set of penalty values provides a fair description of the various interactions. We checked for nonadditivity by introducing cross-terms (one at a time), but none of these resulted in a substantial further improvement of the fit quality. From this we conclude that additivity is a reasonable assumption for this particular ligand at least. The first thing to note about the penalties is that the “chain orientation” penalty of 1.69 kcal/mol for propene insertion into

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RESULTS AND DISCUSSION Separation of Contributions. A total of 134 transition states were generated and optimized, covering (for variations of L1 with two, one, or no methyl groups) the following: 1. insertion of ethene and propene (1,2 as well as 2,1) in L1ZriBu+, L1ZrnPr+, and L1ZrMe+ 2. insertion of 3-methyl-1-butene (1,2) in L1ZriBu+ to analyze the effect of increased monomer bulk (for increase in stereoregularity on going from propene to 1butene, see, for example, work by Mercandelli54) 3. β-H transfer from L1ZriBu+ and L1ZrnPr+ to ethene and propene (1,2) C

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Table 1. Fitted Penalty Values and Standard Error Margins (kcal/mol) for Olefin Insertion and β-Hydrogen Transfer in LZrR+ (R = iBu, nPr, Me)a

Table 2. Fitted Penalty Values and Standard Error Margins (kcal/mol) for Olefin Insertion in LZrR+ (R = iBu, nPr, Me)a system

system

no. data, params; rmsd: description

1

2

3

134, 37; 0.37

172, 40; 0.59

133, 32; 0.47

value

value

esd

value

esd

5.50

0.36

2.16

0.30

2.08 0.39 2.48 2.13 1.22

0.33 0.33 0.34 0.45 0.45

1.28

0.24

b

b

2.19 1.15 −0.61

0.34 0.40 0.49

7.10 2.05

0.41 0.41

1.74 0.09

0.34 0.43

d

d

1.91

0.28

3.79

0.36

1.64

0.28

1.40 −0.44 3.63 1.23 0.87

0.34 0.30 0.34 0.43 0.45

0.38

0.21

b

b

2.24 0.35 −0.55

0.27 0.35 0.35

8.89 3.38

0.31 0.26

4.46 0.11

0.25 0.28

d

d

1.32

0.19

3.15

0.43

0.40

0.34

0.68 0.03

0.63 0.63

0.67 0.13

0.50 0.50

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

8.28

0.22

5.45

0.17

0.68 4.78 1.87

0.23 0.26 0.24

0.74 1.62 1.90

0.18 0.20 0.27

esd

no. data, params; rmsd: description

2

3

88, 25; 0.21

100, 27; 0.46

97, 25; 0.43

value

esd

value

esd

value

esd

0.14

5.34

0.28

2.04

0.28

0.10

0.27 0.27 0.27 0.36 0.36

1.41

0.23

b

b

0.13 0.18 0.18

2.57 0.86 2.48 2.45 1.54

2.27 1.38 −0.36

0.31 0.38 0.46

0.14

3.72

0.28

1.48

0.26

0.10

0.33 0.29 0.27 0.36 0.36

0.58

0.20

0.13 0.18 0.18

1.73 −0.16 3.63 1.42 0.99

2.24 0.70 −0.25

0.24 0.33 0.33

0.18

3.15

0.35

0.39

0.31

0.24 0.24

0.70 0.05

0.51 0.51

0.68 0.16

0.46 0.46

0.09

8.24

0.18

5.41

0.16

0.09 0.09

0.68 4.93

0.18 0.21

0.74 1.77

0.17 0.19

i

Bu chain, insertion propene (1,2) vs 3.38 ethene R to X1c 1.69 b R to X2c R syn to olefin 2.35 olefin to X2c 1.37 olefin to X1c −0.45 n Pr chain, insertion propene (1,2) vs 1.86 ethene 1.14 R to X1c b R to X2c R syn to olefin 3.47 olefin to X2c 1.03 olefin to X1c −0.12 Me chain, insertion propene (1,2) vs 0.83 ethene olefin to X2c 0.45 olefin to X1c 0.06 Shared for Me, nPr, iBu chains propene (2,1) vs 5.70 ethene R syn to olefin (2,1) 0.71 olefin (2,1) to X2c 2.65

i

Bu chain, insertion propene (1,2) vs 3.47 0.25 ethene e R to X1 1.61 0.18 b b R to X2e R syn to olefin 2.35 0.23 olefin to X2e 1.21 0.29 olefin to X1e −0.58 0.29 i Bu chain, BHT BHT vs insertion 3.91 0.28 propene (1,2) vs 0.92 0.37 ethene 1.58 0.24 Me to X1/X2e n Pr chain, insertion propene (1,2) vs 1.96 0.25 ethene R to X1e 1.03 0.18 b b R to X2e R syn to olefin 3.47 0.23 olefin to X2e 0.83 0.29 Oolefin to X1e −0.29 0.29 n Pr chain, BHT BHT vs insertion 5.73 0.22 propene (1,2) vs 1.14 0.24 ethene Me to X1/X2e 1.22 0.18 Me chain, insertion propene (1,2) vs 0.83 0.31 ethene olefin to X2e 0.43 0.43 olefin to X1e 0.06 0.43 i Bu chain, 3-Me-1-butene insertion Me-butene vs 5.52 0.26 ethene R to X1e 1.18 0.28 R syn to olefin 4.37 0.23 olefin to X2e 4.44 0.29 olefin to X1e −1.33 0.31 Shared for Me, nPr, iBu chains propene (2,1) vs 5.73 0.15 ethene R syn to olefin (2,1) 0.71 0.16 olefin (2,1) to X2e 2.55 0.17 BHT Me groups syn 1.96 0.23

1

b

b

b

b

a Fitted values of reference energies omitted from table. bNot included in final fitted parameter set. cX1 and X2 indicate the “hindering” substituent (Me for 1; Ind for 2; tBu for 3) near the position of the alkyl (X1) or olefin (X2); see also Figure 2.

most likely an indirect effect. In any case, the largest single interaction term is the syn/anti difference of 2.35 kcal/mol. Propene is predicted to insert intrinsically more slowly than ethene, with a difference of 3.38 kcal/mol (but see Method Sensitivity below). The ability of the fitted penalties to reproduce the original TS energies is demonstrated by Table 4, which shows predicted (row “rel”, based on penalties) and original DFT energies for the four structures of Figure 1. The three “non-Corradini” insertion transition states (B−D) all have rather similar energies. The spread in the DFT barriers is a bit smaller than in the penalty-based predictions (0.48 vs 0.66 kcal/mol), indicating that perhaps interactions are not perfectly additive, but the order of the values is the same and the magnitudes of the ΔΔG⧧ values agree well. The most difficult insertion mode (B) has the chain and monomer pointing up, paying the syn and ligand−monomer repulsion penalties; anti insertion with chain misorientation (C) is actually the easiest stereoirregular insertion. Since the presence of direct ligand−monomer interactions has generally been ignored, we checked how well the TS energies could be reproduced without inclusion of such interactions. The fit quality is substantially poorer (rmsd 0.40 kcal/mol, as opposed to 0.21 with inclusion), and estimated standard deviations are substantially higher. More importantly,

a

Fitted values of reference energies omitted from table. bNot included in final fitted parameter set. c3Me-1-butene insertion included only for system 1. dFour separate penalties fitted for nonequivalent Me positions; see SI for details. eX1 and X2 indicate the “hindering” substituent (Me for 1; Ind for 2; tBu for 3) near the position of the alkyl (X1) or olefin (X2); see also Figure 2.

the Zr−iBu bond (Table 2, “R to X1”) is rather modest; the corresponding monomer orientation penalty (“olefin to X2”) is of comparable magnitude (1.37 kcal/mol). The fit actually produces a slightly stabilizing (−0.45 kcal/mol) contribution for the monomer Me pointing toward the Me(X1) group, which is D

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atom and the ligand Cp groups much more closely than the Me group of a 1,2-inserting propene.15,29 In addition to the β-branched iBu chain model, we have also looked at nPr as a model for a linear chain. Obviously stereochemistry is not an issue for ethene homopolymerization, but occasional insertion of an α-olefin comonomer could still have a stereopreference. Comparing the behavior of L1ZrnPr+ with that of L1ZriBu+, we find (see Table 2) that the chain orientation preference is reduced substantially (1.14 kcal/mol for nPr vs 1.69 for iBu), reflecting the smaller size of the alkyl group. Similarly, the magnitude of the ligand−monomer interaction penalty decreases from 1.37 to 1.03 kcal/mol on going from an iBu to an nPr chain. The preference for ethene over propene is decreased from 3.38 to 1.86 kcal/mol, presumably due to the same steric effect. Interestingly, the fitted syn insertion penalty is higher for an nPr than for an iBu chain (3.47 vs 2.35 kcal/mol). We believe this is a somewhat artificial consequence of our penalty scheme. In anti insertion, chain and monomer substituents can avoid each other rather well for nPr, resulting in a low “propene penalty”, whereas for i Bu also the anti insertion suffers from some steric hindrance. The combined penalties for syn propene insertion (vs ethene insertion), however, are nearly the same for nPr (1.86 + 3.47 = 5.33 kcal/mol) and iBu (3.38 + 2.35 = 5.73 kcal/mol). As mentioned in the Introduction, one of the arguments against direct ligand−monomer interaction is the low stereopreference of olefin insertion in a metal−hydride or metal− methyl bond. To investigate this issue further, we also looked at insertion of olefin in L1ZrMe+; the resulting penalty values are included in Table 2. 1,2-Insertion of propene is now only 0.83 kcal/mol more difficult than ethene insertion, as compared to 3.38 kcal/mol for the L1ZriBu+ case. Clearly, even in the most favorable (anti) geometry there is some steric repulsion between the iBu chain and the incoming monomer, while there is much less of that with an Me “chain”. The ligand− monomer penalty is also smaller than in the iBu case and is in fact nearly negligible (0.45 kcal/mol vs 1.03 for nPr and 1.34 for i Bu chains). We attribute this difference to the much larger flexibility of the four-membered ring TS with a Me group than with an iBu group: the iBu group “interlocks” with the 1,2inserting propene monomer, so that monomer and chain cannot as easily avoid steric interactions with ligand substituents. In any case, regardless of the explanation, it is clear that the stereoselectivity of insertion into the Zr−Me bond does not provide a good measure for interactions in systems with larger alkyl chains. In contrast, for 2,1-insertion in the Zr−R bond both the 2,1-propene insertion penalty (5.70 kcal/mol) and the ligand−monomer interaction penalty (2.65 kcal/mol) are equal within error margins for all three chains and were fitted as shared parameters independent of the chain. It seems that these penalties are related to unfavorable steric interactions (of the propene Me group with the metallocene skeleton and with the ligand Me group, respectively) that cannot be relieved by increased TS flexibility. The above results paint an internally consistent picture of ligand−monomer penalties. They appear to be more relevant for larger chains (iBu > nPr >Me), and for iBu/1,2-propene they are smaller than the two “Corradini model” (ligand−chain and chain−monomer) penalties. This latter observation is perhaps not surprising: the chain is closer to the metal and ligand than the substituent at the olefin, so chain steric effects can be expected to dominate. However, if the bulk of the olefin is increased while the chain is kept constant, one could expect

Table 3. Most Important Fitted Penalty Values and Standard Error Margins (kcal/mol) for Olefin Insertion in L1ZriBu+ as a Function of DFT Methoda DFT method

rmsd: description

M06-2X/ TZVPPb

b3-lyp+dftd3b

b3-lyp/TZVP 0.21

0.21

0.23

value

esd

value

esd

value

esd

3.38

0.14

0.55

0.14

0.62

0.16

1.69 2.35 1.37 −0.45

0.10 0.13 0.18 0.18

1.79 2.84 1.32 −0.58

0.10 0.13 0.18 0.18

2.17 3.19 1.49 −0.60

0.11 0.14 0.18 0.18

i

Bu chain, insertion propene (1,2) vs ethene R to X1 R syn to olefin olefin to X2 olefin to X1 a b

Data fitted for all olefin insertion transition states used for Table 2. At b3-lyp/TZVP geometries.

Table 4. Penalty-Based Predictions and DFT Results for the Four Insertion Transition States of L1ZriBu(1,2-propene)+ (kcal/mol)a structure:

A

B

C

D

chain:

up

up

dn

dn

dn

up

monomer: i

Bu to X1 syn monomer to X2 monomer to X1 tot rel DFT rel (no L−mon)b

1.69 2.35 1.37 −0.45

up 1

1 −0.45 (0) (0) (0)

1 1

1

3.72 4.17 4.35 2.35

3.07 3.51 3.87 1.54

dn 1 1 1 3.60 4.04 3.88 3.89

Using penalty values from Table 2. The “propene vs ethene” penalty has been omitted since it applies equally to all four structures. bBased on fit without ligand−monomer interaction penalties.

a

the magnitudes of the chain orientation and syn penalties fitted this way are virtually identical to those fitted with ligand− monomer interactions. This means that the ligand−monomer penalties describe a real effect, orthogonal to ligand−chain and chain−monomer penalties. The poor predictive value of the model lacking ligand−monomer interactions is illustrated by the data in Table 4 (row “rel (no L−mon)”), which shows a much poorer agreement with the direct DFT results than the row “rel” including those interactions. We conclude that within the penalty scheme used heredirect ligand−monomer interactions are real, are non-negligible, and affect the ordering of the nonpreferred transition states B−D to a significant extent. Comparing the above regioregular insertions with the regioirregular ones, the first notable point is that 2,1-insertion is intrinsically 2.32 kcal/mol (5.70−3.38) more difficult than 1,2-insertion. The syn penalty is relatively small (0.71 kcal/mol) and is likely not related to a direct interaction between the chain and the monomer Me group, but rather to better accommodation of the twisted four-center TS in the anti than in the syn arrangement. Finally, the direct ligand−monomer interaction for 2,1-insertion (2.65 kcal/mol) is much larger than for 1,2-insertion. This is hardly surprising, given that the Me group of the 2,1-inserting monomer approaches the metal E

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monomer interactions are larger in 2 (2.57 and 2.45 kcal/mol vs 1.69 and 1.37 kcal/mol in 1) and are very similar in magnitude to the syn penalty (equal within error limits), presumably as a result of steric crowding. On the basis of these higher penalties, one might expect an increased stereoregularity compared to, for example, 1. However, neither direct DFT results nor predictions based on fitted penalties bear out this expectation: the unfavorable interactions of chain and monomer with the “wrong” indenyl group cause stereoregular insertion to also be hindered to a significant amount. The end result is that the four transition states A−D for propene insertion in L2ZriBu+ show a pattern of relative energies (Table 5) very similar to that for L1ZriBu+.

larger ligand−monomer interactions. To verify this, we included 1,2-insertion of 3-methyl-1-butene in L1ZriBu+ in the model (for homopolymerization of 3-methyl-1-butene with metallocene catalysts, see ref 55). The results (included in Table 1) show that now the ligand−monomer penalty of 4.44 kcal/mol dominates over both the syn penalty (4.37 kcal/mol) and the ligand−chain penalty (1.18 kcal/mol). Thus, in principle ligand−monomer interactions can be quite large. However, if the size of the olefin is increased, then at least in homopolymerization the chain would also become more bulky, resulting in a parallel increase of syn and ligand−chain penalties. Thus, having a ligand−chain penalty larger than the ligand− monomer penalty is probably the most common situation. Insertion for Metallocene System 2. This biphenylbridged system is somewhat unusual in the sense that it has a much longer bridge between the two indenyl groups than the more common silyl- and ethylene-bridged ansa-metallocenes, which results in less bending of the metallocene “sandwich” and hence less available space at the mouth of the catalyst. Also, chirality is not caused by asymmetric connection of the indenyl groups (at C1 or C3) to the bridge, but rather by the folding of the biphenylene bridge. As a result, these ligands cannot occur in the meso form when coordinated to a metal center. Ligand synthesis and coordination has been described by the groups of Bosnich31 and Brintzinger,32 and the use of Zr and Hf complexes in olefin polymerization has been patented.56 The Zr complex has been reported56 to produce a propene polymer with 91.6% mmmm at 40 °C, which is comparable to the stereoselectivity obtained with L1ZrR+ (92.5% at 30 °C57). Interestingly, the stereoselectivity of L2ZrR+ appears to be rather sensitive to temperature (only 78.7% at 80 °C), while the corresponding Hf complex is both more stereospecific and less temperature sensitive (95.1% mmmm at 40 °C, 91.5% at 80 °C).56 The chirality of this system is induced by the twisted biphenyl bridge. This makes the benzene rings of both indenyl groups point to the side, producing a C2-symmetric environment around the metal. However, the indenyl groups do not point as much to the side as they do in, for example, Me2Sibridged bis(1-indenyl) systems. On the basis of visual inspection, we suspected that there might be significant ligand−chain interactions even with the “wrong” indenyl group (the left-pointing one in Scheme 1), but fit results indicate that this is not a major effect (0.86 kcal/mol, Table 2). However, both indenyl groups have significant interactions with the monomer, and penalties for both interactions had to be included in the model (fitted values: 2.45 and 1.54 kcal/mol). Final fitted penalty values for catalyst 2 are included in Tables 1 and 2. The first thing to note is that the fit quality is decidedly worse than for system 1. We believe that this is due to the crowded nature of the system, which results in many “special case” situations and reduces the validity of the crucial additivity assumption. Nevertheless, some trends emerge clearly from the numbers in the tables. First, propene has a harder time competing with ethene for insertion in this system compared with 1, as evident from penalty values (“propene (1,2) vs ethene”) of 5.34 vs 3.38 kcal/mol. Interestingly, propene regiopreference is not predicted to be particularly high: 2.90 kcal/mol (8.24−5.34) for 2 vs 2.32 kcal/mol (5.70−3.38) for 1. Experimentally, 2 produces about 3% regiomistakes (2,1- and 1,3-insertions).56 Second, the syn penalty is comparable for 2 and 1 (2.48 vs 2.35 kcal/mol), but both the ligand−chain and the ligand−

Table 5. Penalty-Based Predictions and DFT Results for the Four Insertion Transition States of L2ZriBu(1,2-propene)+ (kcal/mol)a structure:

A

B

C

D

chain:

up

up

dn

dn

dn

up

monomer: i

Bu to X1 i Bu to X2 syn monomer to X2 monomer to X1 tot rel DFT

2.57 0.86 2.48 2.45 1.54

up 1

1

1 2.40 (0) (0)

1 1 1

1

5.79 3.39 3.27

5.01 2.62 3.18

dn 1 1 1 6.58 4.19 4.26

Using penalty values from Table 2. The “propene vs ethene” penalty has been omitted since it applies equally to all four structures.

a

Insertion for ONNO System 3. This system was included as a typical octahedral nonmetallocene system.21,33 Experimentally, this system is stereoselective (but not highly so, 87% mm at 25 °C) in propene polymerization and produces polymers of rather low molecular weight.21 Our analysis in principle follows the same procedure as for catalysts 1 and 2. There is, however, one significant difference. For metallocenes, the strong α-agostic interaction of the chain with the metal center forces a well-defined chain orientation, and hence we can always find distinct transition states for “chain up” and “chain down” insertion. For this nonmetallocene system, however, the α-agostic interaction appears to be much weaker and does not strictly enforce a particular chain orientation.58 As a result, optimized transition states with an unfavorable chain orientation (i.e., chain toward ligand tBu group or syn with propene Me group) show much larger deformations from the ideal α-agostic geometry, and in three of the 136 cases the relevant transition state does not appear to exist at all. These cases were necessarily left out of the fit, which results in fitted penalties (Tables 1 and 2) being somewhat less reliable. However, in most respects the results for 3 are comparable to those for 1 and 2. The penalty for propene insertion (vs ethene) is decidedly smaller for 3 than for 1 (2.04 vs 3.38 kcal/ mol), but the three penalties relevant to stereochemistry (syn, ligand−chain, and ligand−monomer) are virtually the same as for 1 and show the same pattern of syn > ligand−chain > ligand−monomer (2.27, 1.41, and 1.38 kcal/mol, respectively). Again, there is less ligand−chain and ligand−monomer interaction with an nPr chain and virtually no stereocontrol with a methyl “chain”. F

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β-Hydrogen Transfer to Monomer Results. Analyzing the results of the fitted model for the BHT reactions reported in Table 2, we noted that for metallocene 1 the fit results produce an intrinsic preference of 3.91 kcal/mol in favor of insertion. In addition, the iBu chain will always have one Me group pointing toward a ligand Me substituent, costing an additional 1.58 kcal/mol and resulting in a 5.49 kcal/mol preference of an iBu group for insertion over BHT to ethene. Having propene as monomer raises the insertion barrier by 3.47 kcal/mol, as mentioned above. At the same time, the BHT barrier increases by contributions from the ethene → propene replacement (0.92 kcal/mol) and a syn interaction between alkyl and monomer Me groups (1.96 kcal/mol) so that the preference for insertion over BHT actually decreases by 0.59 kcal/mol. The BHT penalty for an nPr chain (5.73 kcal/mol) is larger than for iBu (3.91 kcal/mol), corresponding to a thermodynamically less favorable transfer reaction, whereas the preference for ethene (vs propene) as a transfer target is rather similar for nPr (1.14 kcal/mol) and iBu (0.91 kcal/mol). For metallocene 2, the situation is more complicated. The biphenylene bridge is large, which decreases the amount of space available at the front of the complex. Experimentally, these catalysts produce reasonable molecular weights: for ethene/octene copolymerization, higher than (EBI)ZrR+ under the same (high-temperature, 100−150 °C) conditions.56 In our models, we see a reflection of this in the strong distortion of BHT transition states. While insertion happens more or less at the front of the complex, BHT (which requires more space than insertion) would not “fit” there. Instead, the indenyl groups adapt their twist relative to the phenyl rings they are connected to, increasing the amount of available space either at the “chain” or the “monomer” side of the original wedge opening. Thus, the coordination environment loses all symmetry, and the number of BHT transition states is double that found for catalyst 1. Figure 3 illustrates this behavior for L2ZriBu+ + propene(1,2), showing the preferred insertion transition state as well as the two corresponding asymmetric

BHT transition states. Because of this asymmetry, more parameters (penalties) are needed to properly fit the BHT data. Since these are not central to the present discussion, their selection is described in the SI. The intrinsic BHT penalty emerging from the fit (7.10 kcal/mol for an iBu chain) is so high that it is in any case doubtful whether the dominant chain transfer mechanism is β-hydrogen transfer to monomer. For propene polymerization, in particular, it seems reasonable to expect important contributions from β-hydrogen elimination59 and/or β-methyl elimination.60−62 In contrast, fits for ONNO system 3 produce very low BHT penalties (1.74 for an iBu chain, less than half of the value for 1), in agreement with the observed low molecular weight.21 Method Sensitivity. We briefly investigated the method sensitivity of the values obtained. Many of the “traditional” DFT methods suffer from a relatively poor description of soft interactions (dispersion). Add-on methods63 as well as modified functionals52 have been introduced to address this issue. One problem with these so-called dispersion corrections is that they are typically introduced with a “damping” that turns them off rather abruptly at short distances, which potentially makes their use for transition states (like the ones studied here) problematic. To check on this issue we redid all fitting with b3lyp free energy values corrected using Grimme’s DFTD3 procedure,50 as well as using M06-2X52//def2-TZVPP53 energies at the b3-lyp/TZVP geometries. Results for the most important parameters for catalyst 1 are compared in Table 3; the other two systems show very similar trends. Fit quality is hardly affected. Dispersion corrections actually appear to increase the ligand−chain and syn interaction penalties somewhat but leave the ligand−monomer interaction penalty basically unchanged. The only substantial change is in the ethene → propene replacement penalty, which decreases strongly: for 1, from 3.5 to about 0.5 kcal/mol. It is somewhat curious that dispersion corrections appear to favor transition states where a methyl group is added to the olefin, but not those where a methyl/tert-butyl/arene group is added to the ligand. We tentatively ascribe this to the different distances involved, the propene Me group being closer to the reacting atoms. However, in view of the uncertainties associated with dispersion corrections for transition states we refrain from making a choice here and simply conclude that this specific penalty may have a relatively large uncertainty.

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CONCLUSIONS Statistical analysis, including all mono- and unsubstituted ligand variations and all possible stereochemical arrangements, allows an approximate separation of the various contributions to stereocontrol (as well as regiocontrol and competition with βhydrogen transfer). For the systems studied, it appears that ligand−chain and ligand−monomer contributions are comparable in magnitude, which differs somewhat from the standard Corradini model (although conclusions from that model remain valid). It also emerges that one cannot extrapolate stereochemical penalties from a hydride or methyl “chain” to the more realistic iBu chain; therefore, it is probably not justified to draw conclusions about ligand−monomer interactions based on stereochemistry of insertion in such minimal chains23−26,28 The present statistical approach presupposes additivity of the various penalties and hence is likely to hold only for cases where the individual contributions are modest; for ligands with very bulky substituents a more sophisticated analysis method is

Figure 3. Skeletons (hydrogens omitted) of optimized transition states for L2ZriBu+(propene): (A) insertion, (B, C) β-hydrogen transfer, all drawn with the biphenyl bridge in approximately the same orientation. G

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probably required. The approach is based on DFT calculations and, hence, cannot be more reliable than the underlying DFT method used. Also, the resulting penalty values apply only to the specific catalyst systems studied; other catalysts will have other values for specific penalties, in particular for chain and monomer orientation and for BHT. We do not propose use of our analysis as a general tool for ligand fine-tuning: the amount of work required per system would be unreasonably high. However, when starting on a completely new ligand framework, an analysis like the present one should be helpful in establishing which aspects of ligand structure are the most important contributors toward stereoselectivity. In a more general sense, the trends that emerge from the present study are useful in understanding ligand effects and guiding ligand design: • The syn penalty is expected to be a major component of the stereopreference for common types of catalysts, with probably in most cases ligand−chain interaction coming next. This confirms Corradini’s original idea of the dominant interactions responsible for stereocontrol. The syn penalty, in particular, is not very sensitive to ligand structure. • Direct ligand−monomer interaction is likely to be a nonnegligible but also nondominant factor in determining stereochemistry. • The penalties related to stereocontrol (syn, ligand−chain, and ligand−monomer) are sensitive to the nature of the growing chain and the olefin. • The tendency toward 2,1-insertion and the stereoregulation of this insertion mode are dominated by direct ligand−monomer interactions, with a rather limited contribution of the growing chain. From the specific cases studied here, it appears that overcrowding (as in metallocene 2, relative to 1) does not necessarily improve stereoselectivity: contributions from unwanted interactions may well cancel any gain caused by introducing ligand bulk. Precise placement in space is probably the key to highly stereospecific catalysts. Our results demonstrate that this requires taking ligand−monomer interactions into account.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

Listings of total energies and thermal corrections; matrices indicating which penalties apply to which transition state; the R program used for the fitting; fit results; Cartesian coordinate listings for all species considered. This material is available free of charge via the Internet at http://pubs.acs.org.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from SABIC Netherlands and NSERC is gratefully acknowledged. Monitoring of the transition-state optimizations used in this work was greatly facilitated by software developed in the context of DPI project no. 641. H

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