1. Theoretical studies on polymerization and co-polymerization processes catalyzed by late transition metal complexes
Artur Michalak and Tom Ziegler
University of Calgary; Calgary, Alberta, Canada

2. Computational details
Introduction
In the olefin polymerization catalyzed by homogeneous single-site catalysts, by modification of the ligands one can potentially control the structure and properties of a resulting polymer. Therefore, it is important to understand the reletionship between the catalyst structure and polymer properties. We present the results of computational studies on the substituent effect on the factors controlling the polymer branching in the olefin polymerization catalyzed by Pd-based diimine catalysts introduced by Brookhart et al. (JACS 1995, 117,6414; 1996,118,11664; 1996,118,267,1998, 120, 888). We studied the effect of ligand modification on the relative stabilities of isomeric alkyl and olefin complexes, as well as the regioselectivity of olefin insertion. Further, based on the results of DFT calculations, the growth and isomerization of a polymer chain have been modeled by a stochastic approach.
The olefin polymerization catalysts based on late transition metals are not only able to polymerize and co-polymerize a-olefins, but also, due to their less oxophilic character, exhibit tolerance towards compounds containing polar functional groups. The Brookhart Pd-based catalysts are able to co-polymerize ethylene and a-olefins with methyl acrylate. The neutral Ni-based catalysts proposed by Grubbs et al. (Organometallics 1998, 17,3149) tolerate presence of functional monomers, and has been shown to co-polymerize ethylene with a-w-functional olefins (Science,2000,287, 460).
In the present studies we investigated the polar monomer binding modes in the complexes involving Ni- and Pd-based catalysts with Brookhart and Grubbs ligands. The result show that while in the case of Ni-based diimine catalyst (inactive in co-polymerization) complexes with polar molecule bound by oxygen atom are preferred, for Pd-based Brookhart system, as well as Grubbs catalysts based on both, Ni and Pd, the C=C bound p-complexes are energetically favoured. The difference between the former and the latter cases comes from the difference in the electrostatic contribution to the energy of the interaction between polar monomer and the catalysts.
Further, we present the results of computational studies on co-polymerization of ethylene and methyl acrylate catalyzed by Brookhart Pd- and Grubbs Ni-based systems. We studied the insertion of acrylate, stability of insertion product, including chelate structures, and the chelate opening by ethylene.
Computational details
DFT calculations (ADF program) with Becke-Perdew XC functional; triple-zeta STO basis set for Pd, double-zeta with polarization function for C,N,H,O; frozen core: 1s for C,N,O, 1s-3d for Pd; first-order scalar relativistic correction. 2

3. I. Substituent effects in olefin polymerization catalyzed by Brookhart Pd-catalyst
The summary of the calculations is presented in Scheme 2. For the generic catalyst model (a) the complete analysis of the reaction mechanism has been performed (Michalak; Ziegler Organometallics, 1999, 18, 3998). For the large models (b-i) the system studied are: (i) the isomeric alkyl complexes involving n- and iso-propyl groups; (ii) the ethylene and propylene p-complexes with n- and iso-Pr; (iii) ethylene and propylene (2,1- and 1,2-) insertion TS with n-propyl.
An analysis of the relative stability of isomeric alkyl complexes is qualitatively presented in Fig. 1. There are two factors important here: the relative stability of alkyl radicals, and the Pd-alkyl bonding energy; they change in the opposite directions: the branched radical is more stable, but it is more weakly bound. As a result of decreasing bonding energy, the preference of the branched isomer observed in a generic system is slightly enhanced for the real catalysts.
For the olefin p-complexes, the preference of the isomer with branched alkyl observed in a generic system, has been reversed for the real catalysts as a result of steric repulsion (Fig. 3a). The p-complex stabilization energies are decreased in a ‘real’ systems, as a result of decreased stability of isomer with branched alkyl and increased stability of reference alkyl complex (Fig. 2). Also, in the ‘real’ systems, ethene p-complexes are stabilized more strongly, than those of propene (Fig. 3b) - the opposite effect has been observed for the generic catalyst model.
The steric repulsion in ‘real’ systems also affects the regioselectivity of propene insertion (Fig. 3c): for a generic system the 2,1-insertion is strongly preferred, while for the catalysts with the largest substituents this is again reversed: the 1,2-insertion TS become lower in energy.
The complete results are presented in the recent article (Michalak, Ziegler Organometallics, 2000, 19, 1850). 3

4. Propene polymerization:
Scheme 1.
two possible insertion paths (1) and (2); each introduces a methyl branch;
chain staightening isomerization reaction (4) removes a branch;
there are alkyl complexes and olefin -complexes with primary, secondary,
and tertiary carbon atom attached to the metal, present in the catalytic cycle. 4

5. - summary of calculations
Substituent effects in olefin polymerization catalyzed by Brookhart Pd-catalyst
- summary of calculations
Scheme 2.
alkyl complexes
(n-, iso-Pr)
ethene, propene
complexes (n-, iso-Pr)
ethene, propene (2,1- and 1,2-)
insertion TS (n-Pr) 5

6. Substituent effects in olefin polymerization catalyzed by Brookhart Pd-catalyst
Fig. 1
Fig. 2
Fig. 3 6

7. II. Simulations of polymer growth and isomerization
The results of our studies on the ethylene and propylene polymerization catalyzed by Brookhart complexes are used as input data for stochastic simulations of polymer growth and isomerization. Based on the assumption that relative probabilities of the events possible in the catalytic cycle are equal to the relative rates of the elementary reactions, these simulations allow one to investigate an effect of the temperature and the olefin pressure on the polymer structure. It is known from experimental studies (Guan Z; et al. Science 1999, 283,2059) that in the case of Brookhart catalyst the change in the olefin pressure does not affect the total number of branches, but strongly influence the microstructure of resulting polymer: from mostly linear polymers obtained for high pressure to hyper-branched structures for low pressure values.
In our simulations we build one polymer chain at a time, starting from a olefin insertion into the Pd-methyl group. The structure of the polymer is remembered, and at every step the stochastic choice of the next event is made, on the basis of relative probabilities, calculated from the energetics of elementary reactions. For example, if the primary carbon (a) [Fig4.] is attached to the metal, then the olefin uptake followed by insertion, as well as one isomerization reaction (leading to a secondary carbon being linked to Pd) are possible; if the primary atom (b) is attached to the metal, a choice is made between olefin capture/insertion and an isomerization leading to a secondary carbon; if the secondary carbon (c) is attached to the metal, then a capture/insertion event is possible, or two equivalent isomerization events; from carbon (d), besides a capture/isomerization, two inequivalent isomerisation reaaction are taken into account; etc. In the propylene case, the two insertion paths (1,2- and 2,1-) are considered.
Energetics of elementary reactions
Relative probabilities of the
elementary reactions
Choice of a path
relative probabilities = relative rates:
e.g. isomerization vs. isomerization:
isomerization vs. insertion:
etc.
Fig.4. 7

8. Simulations of polymer growth and isomerization
As a result of a set of simulations, the polymer structures are obtained, the average number of branches is calculated, and analysis of the branches is performed: number and length of primary branches, secondary ones, etc. (Fig. 5). If the termination reactions were taken into account, the molecular weights could be also obtained. Here, however, since we focused on the polymer structure, we assumed no termination, and each simulation was performed until the chain reached a length of 1000 carbon atoms.
In Figure 6 we show the examples of polymer structures obtained from propene polymerization under different monomer pressure, for the catalyst with unsubstituted phenyl rings. For high pressure (panel a), the structure of the polymer is mostly linear, with relatively long primary branches, and with small number of the higher-order branches. With decrease in the pressure (panels b and c), the number of atoms in the main chain decreases, while the number of the higher order-branches increases, leading to a hyper-branched polymer structure.
In Table 1, we listed some data obtained for propylene polymerization with ‘real’ Brookhart catalyst. Here we can observe a similar effect of the change in the olefin pressure: while the total number of branches remains constant, the structure of the polymer is strongly affected. Again, with decrease in the pressure, the number and length od higher-order branches increases.
Fig.5.
Results:
- Polymer chain;
- Total No. of branches;
- Classification of branches:
no. of branches of a given type,
and their length;
- Molecular weight; 8

9. Simulations of polymer growth and isomerization - results
Table 1: Effect of olefin pressure change -
Brookhart system: R=Me; Ar= Ph(i-Pr)2
p=1 p=0.1 p=0.01
Av. Total No. of Branches
1o branches -av. Length
longest
2o branches -av. Length
longest
3o branches -av. Length
longest
4o branches -av. Length
longest
5o branches -av. Length
longest b) c)
Figure 6: Effect of olefin pressure on polymer structure;
a) p=1, b) p=0.1; c) p=0.01. 9

10. III. Binding mode of polar monomers
The first step in polymerization processes involves a formation of the catalyst-monomer complex; in a-olefins polymerization the monomer is bound by the double C=C bond. In order to incorporate polar monomers into polymer chain in random co-polymerization process, it is required that its insertion follows the same reaction mechanism, i.e. it involves formation of the corresponding p-complex. Therefore, it seem s to be important, that the stabilization energy of the p-complex is larger than that of complexes in which the monomer is bound by polar group.
In this studies we compare the binding modes of methyl acrylate and vinyl acetate for Ni- and Pd-based catalysts with Brookhart and Grubbs ligands. The cationic Brookhart Pd-based systems have been show to co-polymerize olefins with methyl acrylate, while the Ni-based complexes are inactive in co-polymerization process. The neutral Grubbs catalysts tolerate the presence of polar molecules in the polymerization of ethylene and are able to co-polymerize olefins with w-functionalized compounds.
The stabilization energies of the polar monomer complexes are listed in Table 2; the systems with polar molecule bound by C=C bond or by O atom were considered. The results for methyl acrylate and vinyl acetate are qualitatively similar. Namely, in all the systems but Ni-based Brookhart catalysts, the p-complexes are more stable than corresponding O-bound ones. In Table 3, the contributions to the bonding energy are listed for methyl acrylate complexes with generic catalyst models. It can be observed that the main difference between the Ni-Brookhart catalyst and all the remaining systems is an increased electrostatic contribution in O-bound complex in comparison to the p complex case. Thus, it can be concluded that the use of neutral catalyst seems to be promising for co-polymerization purposes. In the case of Gruubs ligands, the preference of the p complexes is enhanced for both, Ni- and Pd-based systems.
A comparison of Brookhart Ni- and Pd-based catalysts also suggests that in a search for random co-polymerization catalyst the systems in which the O-bound complexes are preferred can be excluded. Here, the use of computational studies can be very helpful. 10

11. Binding mode of polar monomers
Table 2.
Catalyst Monomer2 C=C O - E(C=C) -E (O)
Ligand1-Metal complex complex
A) generic catalyst
Brookhart - Ni MA
Brookhart - Ni VA
Brookhart - Pd MA
Brookhart - Pd VA
Grubbs - Ni MA
Grubbs - Ni VA ,
Grubbs - Pd MA
Grubbs - Pd VA
B) ‘Real’ Catalyst
Brookhart - Ni MA
Brookhart - Pd MA
Grubbs - Ni MA
1Brookhart: -N(Ar)-C(R)-C(R)-N(Ar)-; generic: Ar=H, R=H; real: Ar=Ph(i-Pr)2, R=Met
Grubbs: generic: R1=R2=X=H; real R1= Ph(i-Pr)2; R2=X=H
2 MA=methyl acrylate; VA=vinyl acetate
C=C complex
O- complex 11

12. Binding mode of methyl acrylate - contributions to the bonding energy
Eb = Eb,dist. + Eg = [Esteric + Eorb] + Eg = [ (Eel + EPauli ) + Eorb] + Eg ;
Eb,dist. - interaction energy of distorted reactants;
Eg geometry distortion term;
Esteric - total steric interaction;
Eorb - orbital interaction;
Eel - electrostatic interaction;
Epauli - Pauli repulsion.
Table 3.
Catalyst/binding mode Eel Epauli Esteric Eorb Eb,dist
Generic catalyst
Brookhart - Ni / C=C
Brookhart - Ni / O
Brookhart - Pd /C=C
Brookhart - Pd /O
Grubbs - Ni /C=C
Grubbs - Ni /O
Grubbs - Pd /C=C
Grubbs - Pd /O 12

13. Binding mode of polar monomers - ‘real’ systems
Brookhart, Ni - O-complex
Brookhart, Pd - p-complex
Grubbs, Ni - p-complex 13

14. IV. Co-polymerization of ethylene and methyl acrylate
The elementary reactions in olefin-acrylate co-polymerization occurring after insertion of acrylate are shown in Scheme 3. In the present studies we investigated the 1,2- and 2,1-insertion of acrylate, stability of the insertion products: g-and b-agostic complexes, 4-, 5-, and 6-member chelates, as well as chelete opening by the ethylene and acrylate molecules. Since the 1,2-insertion bariier is higher by 4.5 kcal/mol for Brookhart catalyst, we present here only the reaction paths following the 2,1-insertion.
The energetics of the elementary reactions for Brookhart catalyst is shown in Figure 7. The acrylate p-complex stabilization energy lies between the numbers for ethylene and propylene, obtained from the same generic model for the catalyst. One can expect, however, that for the real catalysts with a bulky substituents this trend will be reversed, as for ethylene and propylene (see Fig.3). In agreement with experimental results, the chelates are more stable the the agostic insertion products. The stability of the chelates increases from 4- to 6-member ring. The latter has been found experimentally to be a resting state in the process. In the ethylene p-complexes (Fig. 8) the chelating bond is still present; the Pd-O bond is broken in the TS geometries. The ethylene insertion is easiest in the case of 4-member chelate; the insertion barriers increase for 5- and 6-member structures.
In Figures 9 and 10 we present the corresponding results for the Grubbs Ni-based catalyst. Here, the process is more complicated, due to the asymmetry of the catalyst. There exist two paths starting from two isomeric alkyl complexes, denoted as C or T (corresponding to the Pd-C bond being in cis- or trans- position with respect to nitrogen atom). As in the case of ethylene (Chan, M; Ziegler, T., in press), the path starting from the more stable alkyl complex (C) leads to the less stable acrylate complex, leading to the higher insertion barrier. In comparison to the Brookhart catalyst, the energetic hierarchy of the chelates is different. Here, the 4-member ring is the most stable. This comes mainly from the size of the metal: the Ni orbitals are more ‘compact’. Due to less oxophilic character of the catalyst, the chelate structures are higher in energy with respect to the agostic products than in the Brookhart catalyst case, and the ethylene p-complexes are stabilized more strongly. Therefore, it seems that in the case of Grubbs catalyst the co-polymerization should be easier, leading to larger incorporation of the polar monomer and the polymers characterized by larger molecular weights. However, we have not obtained the ethylene insertion barriers yet; neither we studied the termination reactions. 14

15. Co-polymerization of ethylene and methyl acrylate
acrylate or olefin -complexes can be formed from alkyl species;
after olefin insertion the process proceeds as in the olefin polymerization case;
after acrylate insertion various chelate structures can be formed;
chelates can be opened by either olefin or acrylate molecule;
Scheme 3. 15

16. Acrylate 2,1-insertion path - Brookhart, Pd-based catalyst
kcal/mol
Fig. 7. 16

17. Chelate opening - Brookhart, Pd-based catalyst
kcal/mol
Fig. 8. 17

18. Acrylate 2,1-insertion paths - Grubbs Ni-based catalyst
kcal/mol T C C
+20.5 T -5
-16.0
-18.7
-22.0
-10
+15.7 T C
-15
-22.2
-9.3
-20 T T T
-25 C
-5.1
-8.8 T
+2.4 T
+4.7
-30 C
-4.2
+1.9 C
+0.2 C
-35 C
alkyl agostic
insertion TS
b-agostic
+acrylate
5-memb.
acrylate
chelate
g-agostic
4-memb.
6-memb. chelate
p complex
chelate
Fig. 9. 18

19. 10 5 -5 -10 Chelate opening - Grubbs Ni-based catalyst Fig. 10. 19
6-memb.,cis
6-memb.,trans
5-memb.,cis
5-memb.,trans
kcal/mol 10
-9.9; 6-memb. trans 5
-8.4; 5-memb. trans
-3.4; 5-memb.trans -5
-5.6; 6-memb. cis
-7.7; 4-memb. trans
-10
-12.0; 4-memb. cis
4-memb.,cis
4-memb.,trans
chelates
ethene p
complexes
+ ethene
Fig. 10. 19

20. Conclusions
A increase in the substituents size in Brookhart diimine catalyst strongly affects the factors controlling branching of the polymers: the preference of the branched alkyl complexes is enhanced, the olefin complexes with linear alkyl become more stable, and the regioselectivity of insertion is reversed, leading to the preference of the 1,2-insertion path for larger catalysts.
Stochastic modeling of the polymer growth and isomerization based on the energetics of the elementary reactions from DFT calculations allows one to qualitatively investigate the effect of the temperature and the olefin pressure on the structures of resulting polymers; the general trends obtained from a simplified model are in agreement with experimental observations.
A comparison of the binding mode of polar monomers for the Ni- and Pd-based complexes (inactive and active co-polymerization catalysts) with diimine ligands reveals that the preference of the O-bound complex in Ni case is reversed in Pd-based system. Further, the origin of this difference has mainly electrostatic character. Thus, use of the neutral catalysts in co-polymerization processes seems to be promising. Indeed, in the case of Grubbs ligand, the p-complex is strongly preferred already in Ni-system; this preference is enhanced for Pd catalyst
Studies on the elementary reactions in olefin-acrylate co-polymerization provide the information about the stability of the reaction intermediates. The energetic order of the chelates in Brookhart and Grubbs systems is opposite. As a result of less oxophilic character of the Grubbs complex, formation of the ethylene complex after acrylate insertion is easier than in the Pd-diimine case.
Acknowledgements
This work has been supported by the Novacor Research and Technology Corporation,as well as by the NSERC. A.M. acknowledges the University of Calgary Postdoctoral Fellowhip. Important part of the calculations has been performed with the UofC MACI cluster. 20