DFT studies on the Co-monomer Binding in the Copolymerization of  -Olefins with Polar Monomers Catalyzed by Late Transition Metal Complexes Artur Michalak a,b and Tom Ziegler a a Department of Chemistry, University of Calgary, Calgary, Alberta, Canada b Department of Theoretical Chemistry Jagiellonian University Cracow, Poland Artur Michalak a,b and Tom Ziegler a a Department of Chemistry, University of Calgary, Calgary, Alberta, Canada b Department of Theoretical Chemistry Jagiellonian University Cracow, Poland

A new emerging frontier in olefin polymerization is the controlled copolymerization of  -olefins with monomers bearing a polar functional group. Of particular interest are the copolymers of monomers with oxygen-containing polar groups. In order to incorporate polar monomers into a polymer chain in random copolymerization process, it is required that its insertion follows the same reaction mechanism, as that of  ‑ olefin Ziegler-Natta polymerization. Thus, the polar monomer must also be initially bound to the metal center by its double C=C bond rather than by the oxygen atom of the polar group. Therefore, it seems to be important, that the stabilization energy of the  -complex is larger than that of complexes in which the monomer is bound by polar group. Introduction Scheme 1. Initial steps in the copolymeryzation of  -olefins with methyl acrylate. 2

In the present study we have computationally investigated the binding mode of the oxygen-containing monomers (methyl acrylate, vinyl acetate, and their fluorinated analogues) in the complexes involving cationic and neutral Ni- and Pd- based catalysts with the Brookhart and Grubbs ligands. The static, gradient corrected DFT calculations have been performed for two binding modes: the  -complexes in which a polar monomer is bound by its olefinic fnctionality, and the O-complexes with a monomer bound by its carbonyl oxygen. The role of the electronic and the steric effects has been investigated, by considering the simplified (generic) models and the examples of the real catalysts. An energy decomposition of the contributions to the binding energies has been performed in order to understand the origin of the differences between Brookhart Pd- and Ni-based system (active and inactive copolymerization catalyst). Also discussed are the effects of the reduced basicity of the carbonyl oxygen on the monomer (in the fluorinated compounds) as well as of the reduced oxophilicity of the catalyst (in the neutral Grubbs system). Further, the ab initio Molecular Dynamics simulations have been performed to explore the free enegy surface of the acrylate complexes with Pd- and Ni-based diimine catalysts. The stability of both types of complexes at finite temperatures has been studied by free (unconstrained) MD simulation. Also, the slow-growth MD simulations for the inter-conversion between the two acrylate binding modes (  - and O- complexes)have been performed. In the present study we have computationally investigated the binding mode of the oxygen-containing monomers (methyl acrylate, vinyl acetate, and their fluorinated analogues) in the complexes involving cationic and neutral Ni- and Pd- based catalysts with the Brookhart and Grubbs ligands. The static, gradient corrected DFT calculations have been performed for two binding modes: the  -complexes in which a polar monomer is bound by its olefinic fnctionality, and the O-complexes with a monomer bound by its carbonyl oxygen. The role of the electronic and the steric effects has been investigated, by considering the simplified (generic) models and the examples of the real catalysts. An energy decomposition of the contributions to the binding energies has been performed in order to understand the origin of the differences between Brookhart Pd- and Ni-based system (active and inactive copolymerization catalyst). Also discussed are the effects of the reduced basicity of the carbonyl oxygen on the monomer (in the fluorinated compounds) as well as of the reduced oxophilicity of the catalyst (in the neutral Grubbs system). Further, the ab initio Molecular Dynamics simulations have been performed to explore the free enegy surface of the acrylate complexes with Pd- and Ni-based diimine catalysts. The stability of both types of complexes at finite temperatures has been studied by free (unconstrained) MD simulation. Also, the slow-growth MD simulations for the inter-conversion between the two acrylate binding modes (  - and O- complexes)have been performed. 3

DFT calculations (ADF program) with Becke-Perdew XC functional; triple-zeta STO basis set for Pd, double-zeta with polarization function for C, N, O, F,H; frozen core: 1s for C,N,O, F, 1s-2p for Ni, 1s-3d for Pd; energies with the first-order scalar relativistic correction. DFT calculations (ADF program) with Becke-Perdew XC functional; triple-zeta STO basis set for Pd, double-zeta with polarization function for C, N, O, F,H; frozen core: 1s for C,N,O, F, 1s-2p for Ni, 1s-3d for Pd; energies with the first-order scalar relativistic correction. 4 PART I. Static DFT calculations for the  -complexes and O-complexes PART I. Static DFT calculations for the  -complexes and O-complexes

3b 1b Catalyst Models: 4a 5a 6a 2b 5

Table 1. The monomer binding energies for the generic models for the Ni- and Pd-based Brookhart and Grubbs catalysts. CatalystMonomer  E (C=C) 1  E (O) 2 E(C=C) - E(O) 2 1a. Brookhart/NiMA b. Brokhart/PdMA a. Brookhart/NiVA b. Brokhart/PdVA a. Brookhart/NiFMA b. Brokhart/PdFMA a. Brookhart/NiFVA b. Brokhart/PdFVA a. Grubbs/NiMA b. Grubbs/PdMA a. Grubbs/NiVA b. Grubbs/PdVA  -complex stabilization energy, in kcal/mol; 2 stabilization energy of the O-complex, in kcal/mol; 3 the difference in the energies of the  -complex and O-complex; Table 1. The monomer binding energies for the generic models for the Ni- and Pd-based Brookhart and Grubbs catalysts. CatalystMonomer  E (C=C) 1  E (O) 2 E(C=C) - E(O) 2 1a. Brookhart/NiMA b. Brokhart/PdMA a. Brookhart/NiVA b. Brokhart/PdVA a. Brookhart/NiFMA b. Brokhart/PdFMA a. Brookhart/NiFVA b. Brokhart/PdFVA a. Grubbs/NiMA b. Grubbs/PdMA a. Grubbs/NiVA b. Grubbs/PdVA  -complex stabilization energy, in kcal/mol; 2 stabilization energy of the O-complex, in kcal/mol; 3 the difference in the energies of the  -complex and O-complex; 6 1a (Ni) 1b (Pd)   Fig 1. MA  - and O-complexes with diimine catalysts  

7 The results of Table 1 show: A preference of the MA and VA O-complexes in the case of the Ni-diimine catalyst (inactive in copolymerization). A preference of the MA aqnd VA  -complexes for Pd-diimine system (active copolymerization catalyst). A decrease in the preference of the O-complex or/and increase in the preference of the  - complexes for the fluorinated monomers (with reduced basicity of their carbonyl oxygen). This is accompanied by the substantial decrease of the absolute binding energies for both, O- and  -complexes, that would result in substantially lower incorporation of the polar monomer in a prospective copolymerization. A strong increase in the preference of the  -binding mode for the complexes involving the neutral Grubbs catalysts based on both, Ni and Pd. Here, unlike for the fluorinated monomers, the absolute stabilization energies of the  -complexes are not decreased, compared to the cationic diimine catalysts. A decomposition of the binding energies (Fig. 3) indicates that the difference between the Ni- and Pd- diimine catalyst has mainly {electrostatic + Pauli repulsion} origin. Concerning a comparison between the two binding modes, there is practically no difference in the orbital interaction terms. This confirms, that use of the nutral catalysts with the reduced electrophilicity of the metal can be promising. The results of Table 1 show: A preference of the MA and VA O-complexes in the case of the Ni-diimine catalyst (inactive in copolymerization). A preference of the MA aqnd VA  -complexes for Pd-diimine system (active copolymerization catalyst). A decrease in the preference of the O-complex or/and increase in the preference of the  - complexes for the fluorinated monomers (with reduced basicity of their carbonyl oxygen). This is accompanied by the substantial decrease of the absolute binding energies for both, O- and  -complexes, that would result in substantially lower incorporation of the polar monomer in a prospective copolymerization. A strong increase in the preference of the  -binding mode for the complexes involving the neutral Grubbs catalysts based on both, Ni and Pd. Here, unlike for the fluorinated monomers, the absolute stabilization energies of the  -complexes are not decreased, compared to the cationic diimine catalysts. A decomposition of the binding energies (Fig. 3) indicates that the difference between the Ni- and Pd- diimine catalyst has mainly {electrostatic + Pauli repulsion} origin. Concerning a comparison between the two binding modes, there is practically no difference in the orbital interaction terms. This confirms, that use of the nutral catalysts with the reduced electrophilicity of the metal can be promising.

Table 2. Key catalyst-monomer interatomic distances in the  - and O-complexes with the generic catalyst models. CatalystMonomer  C 1 M-O 2 1a. Brookhart/NiMA2.06, b. Brokhart/PdMA2.21, a. Brookhart/NiVA2.03, b. Brokhart/PdVA2.19, a. Brookhart/NiFMA2.05, b. Brokhart/PdFMA2.21, a. Brookhart/NiFVA2.03, b. Brokhart/PdFVA2.20, a. Grubbs/NiMA2.02, b. Grubbs/PdMA2.17, a. Grubbs/NiVA2.03, b. Grubbs/PdVA2.19, metal-carbon distances in the  -complex; in A; 2 metal-oxygen distance in the  -complex; in A. Table 2. Key catalyst-monomer interatomic distances in the  - and O-complexes with the generic catalyst models. CatalystMonomer  C 1 M-O 2 1a. Brookhart/NiMA2.06, b. Brokhart/PdMA2.21, a. Brookhart/NiVA2.03, b. Brokhart/PdVA2.19, a. Brookhart/NiFMA2.05, b. Brokhart/PdFMA2.21, a. Brookhart/NiFVA2.03, b. Brokhart/PdFVA2.20, a. Grubbs/NiMA2.02, b. Grubbs/PdMA2.17, a. Grubbs/NiVA2.03, b. Grubbs/PdVA2.19, metal-carbon distances in the  -complex; in A; 2 metal-oxygen distance in the  -complex; in A. 8 3a (Ni)    Fig 2. The alternative, cis- (left) and trans- (right) MA  - (top) and O-complexes (bottom) with the generic model for the Grubbs catalysts. In the case of the  -complexes the cis-isomer is preferred, while the trans-O-complex is more stable.

Binding Energy Decomposition  E =  E geom. +  E tot. =  E geom. + [  E steric +  E orb.int. ] =  E geom. + [ (  E el. +  E Pauli ) +  E orb.int. ] where  E geom. is a geometry distortion term,  E tot. is a total interaction energy between the distorted reactants. The latter can be further decomposed into the orbital interaction term (stabilizing, two-orbital, two-electron interactions),  E orb.int., and the steric contribution consisting of the electrostatic interaction (stabilizing or destabilizing) and the Pauli repulsion (destabilizing, two orbital, four- electrons interaction),  E steric =  E el. +  E Pauli. Fig. 3. A schematic representation of the differences in the contributions to the bonding energies between the O- and p- complexes of the methyl acrylate and vinyl acetate with the Ni- and Pd- based Brookhart catalysts. Panels a-e display the differences in the orbital interaction, steric, electrostatic, Pauli repulsion and geometry distortion contributions, respectively. The arrows point the preferred complex of the respective pair. The numbers correspond to the differences in respective contributions (for vinyl acatate in parantheses). 9

Table 3. The binding energies for MA complexes with the real Brookhart and Grubbs catalysts. Catalyst  E (C=C) 1  E (O) 2 E(C=C) - E(O) 3 2a. Brookhart/Ni b. Brokhart/Pd a. Grubbs/Ni a. Grubbs/Ni a. Grubbs/Ni  -complex stabilization energy, in kcal/mol; 2 stabilization energy of the O-complex, in kcal/mol; 3 the difference in the energies of the  -complex and O-complex, in kcal/mol; Table 3. The binding energies for MA complexes with the real Brookhart and Grubbs catalysts. Catalyst  E (C=C) 1  E (O) 2 E(C=C) - E(O) 3 2a. Brookhart/Ni b. Brokhart/Pd a. Grubbs/Ni a. Grubbs/Ni a. Grubbs/Ni  -complex stabilization energy, in kcal/mol; 2 stabilization energy of the O-complex, in kcal/mol; 3 the difference in the energies of the  -complex and O-complex, in kcal/mol; 2b (Pd) 2a (Ni) 6a (Ni) 10 Fig 4. The most stable MA complexes with the real catalysts.    The results of Table 3 show that: The steric bulk of the real catalysts results in decrease of the absolute binding energies for both, O- and  -binding modes (compare with Table 1). There is practically no steric effect on the preference of the binding mode. In the case of the real Ni-diimine catalyst the O-complex stays preferred, while for the Pd- diimine and Grubbs Ni-based catalysts the  -complex is substantially more stable. The results of Table 3 show that: The steric bulk of the real catalysts results in decrease of the absolute binding energies for both, O- and  -binding modes (compare with Table 1). There is practically no steric effect on the preference of the binding mode. In the case of the real Ni-diimine catalyst the O-complex stays preferred, while for the Pd- diimine and Grubbs Ni-based catalysts the  -complex is substantially more stable.

11 Pd-  Pd-  Ni-  Ni-  PART II. MD studies on the stability of the  - and O-complexes and the interconversion pathways PART II. MD studies on the stability of the  - and O-complexes and the interconversion pathways 1) For the  - and O-complexes with the Ni- and Pd-diimine catalysts the free (unconstrained) molecular dynamics simulations at 300 K were performed. In addition, for the local minima (Pd/O- and Ni-  ) similar simulations at 700 K were performed. 2) For all four possible inter-conversion reactions (Pd: O  Pd:  O; Ni: O  Ni:  O) the slow-growth MD simulation (300K) with the substitution constraint, R(Me-O)-R(Me-C)=const., changing between the values characterizing the respective initial (O/  )and the final (  /O) complexes. The constrained MD were followed by the relaxation simulations (300 K free dynamics), starting from the final stage of the slow-growth MD. 1) For the  - and O-complexes with the Ni- and Pd-diimine catalysts the free (unconstrained) molecular dynamics simulations at 300 K were performed. In addition, for the local minima (Pd/O- and Ni-  ) similar simulations at 700 K were performed. 2) For all four possible inter-conversion reactions (Pd: O  Pd:  O; Ni: O  Ni:  O) the slow-growth MD simulation (300K) with the substitution constraint, R(Me-O)-R(Me-C)=const., changing between the values characterizing the respective initial (O/  )and the final (  /O) complexes. The constrained MD were followed by the relaxation simulations (300 K free dynamics), starting from the final stage of the slow-growth MD.

Ni:  Pd: O Ni: O Pd:  timestep R [A] R Pd-C (300K) R Pd-O (300K) timestep R [A] timestep R [A] timestep R [A] R Ni-C (300K) R Ni-O (300K) R Ni-C (300K) R Ni-C (700K) R Ni-O (300K) R Ni-O (700K) R Pd-C (300K) R Pd-C (700K) R Pd-O (300K) R Pd-O (700K) 12 Fig 5. The two M-C(  ) and the M-O distances from the unconstrained MD simulations for the MA O- and  - complexes with the Ni- and Pd-diimine catalysts.

13 The free MD simulations (Fig.5) indicate that both, O- and  - complexes for both, Ni- and Pd-based catalysts form stable minima on the free-energy surfaces and are are separated by non-negligible barriers. All the complexes at 300K stay in a relatively rigid geometries and they do not inter-convert spontaniously. The higher energy complexes (local minima; Pd/O, and Ni/  ) stay in their geometries at 700K, and do not evolve toward the global minima (Pd/  and Ni/O). The free MD simulations (Fig.5) indicate that both, O- and  - complexes for both, Ni- and Pd-based catalysts form stable minima on the free-energy surfaces and are are separated by non-negligible barriers. All the complexes at 300K stay in a relatively rigid geometries and they do not inter-convert spontaniously. The higher energy complexes (local minima; Pd/O, and Ni/  ) stay in their geometries at 700K, and do not evolve toward the global minima (Pd/  and Ni/O). Stability of the O- and  -complexes on the free-energy surfaces Stability of the O- and  -complexes on the free-energy surfaces

Inter-conversion: Pd catalyst;  -complex toward O-complex R Pd-C -R Pd-O [A] R[A] R Pd-C R Pd-O timestep constrained dynamics relaxation 14 Fig. 6. The MA  -complex with Pd-diimine catalyst does not directly inter-convert toward the O-complex. The MD simulation reveals a dissociative pathway; it leads to the  -agostic alkyl complex (see also Fig. 10) with the acrylate molecule attached to the NH group of the catalyst with a hydrogen bond.

Inter-conversion: Pd catalyst;  O-complex  toward  -complex R Pd-C -R Pd-O [A] R[A] R Pd-C R Pd-O timestep constrained dynamics relaxation 15 Fig. 7. During the constrained MD simulation, the MA  -complex with Pd-diimine catalyst directly converts into one of the possible  -complexes, that can be easily transformed into the global minimum complex by a rotation of MA and/or alkyl. Figs Top: the geometries from the constrained MD simulation at s=0.0, 0.25, 0.5, 0.75, 1.0 (s- reaction progress variable). Bottom: theM-C(  ) and M-O distances from the constrained MD and the relaxation (unconstrained) simulations.

Inter-conversion: Ni catalyst;  -complex toward O-complex R Ni-C -R Ni-O [A] R[A] R Ni-C R Ni-O timestep constrained dynamics relaxation 16 Fig. 8. Similarly to the Pd-case, the  -complex with the Ni-based catalyst dissociates before going toward the O-complex. However, the relaxation run leads to the structure with  -agostic (not the  - agostic, as in the Pd-case; see also Fig. 10). It may be expected that this  - agostic complex can easily lead to the O-complex.

Inter-conversion:  Ni-catalyst O-complex  toward  -complex R Ni-C -R Ni-O [A] R[A] R Ni-C R Ni-O timestep constrained dynamics relaxation 17 Fig. 9. Unlike for the Pd-catalyst, in the Ni-case the O-complex does not inter-convert into the  -complex. The structure formed here is the ‘mixed’ O-  -complex (1,4- arrangement). Although it is a higher- energy intermediate, it forms stable minimum at the potential energy- and the free energy surfaces. In the Pd-case such intermediate either does not exist, or forms an extremely shallow minimum.

18 Fig. 10. Final products of the four inter-conversion simulations (after a relaxation simulations). Top-left: Pd-catalyst; an alkyl  -agostic complex with hydrogen-bonded MA molecule (from  O simulation). Top-right: Ni-catalyst; an  -agostic complex (from  O simulation). Bottom-left: Pd- catalyst; the  -complex (from  O  simulation  Bottom-right: Ni-catalyst; the 1,4-MA complex (from O  simulation  Fig. 10. Final products of the four inter-conversion simulations (after a relaxation simulations). Top-left: Pd-catalyst; an alkyl  -agostic complex with hydrogen-bonded MA molecule (from  O simulation). Top-right: Ni-catalyst; an  -agostic complex (from  O simulation). Bottom-left: Pd- catalyst; the  -complex (from  O  simulation  Bottom-right: Ni-catalyst; the 1,4-MA complex (from O  simulation 

E [kcal/mol] timestep constrained dynamics relaxation timestep Pd: O   Pd:   O Ni:   O Ni: O   19 Energetics of the inter-conversion reactions Fig. 11. The average potential energy (running average with a window of 200 timsteps) from the constrained and unconstrained MD simulations. An zero value for the energy corresponds to the preferred complexes (  -complex in the Pd-, and to the O-complex in the Ni-case)

Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No AC3). A.M. acknowledges a University of Calgary Postdoctoral Fellowship. Important parts of the calculations was performed using the UofC MACI cluster. Conclusions A comparison of the binding mode of polar monomers for the Ni- and Pd-based diimine complexes (inactive and active co-polymerization catalysts) shows that the preference of the O- bound complex in Ni case is reversed in Pd-based system. Further, the difference between the two catalysts has mainly {electrostatic + Pauli repulson} origin. Thus, use of the neutral catalysts in co-polymerization processes seems to be promising. Indeed, in the case of Grubbs ligand, the  -complex is strongly preferred already in the Ni-system; this preference is enhanced for Pd catalyst. The absolute  -complexation energies for the Grubbs catalyst are comparable with those of the diimine systems. In the complexes with fluorinated monomers, the preference of the O-binding mode is decreased, but with a price of decreased absolute complexation energies. This would lead to a low incorporation of the fluorinated monomer in the co-polymerization. The presence of the steric bulk in the real catalysts does not affect the preference of the binding mode. The MD simulations show that all the complexes are stable on the free-energy surfaces and do not exhibit ant tendency toward a spontaneous inter-conversion. Further, the complexes are separated by relatively large barriers. In the Ni-case the O   inter-conversion reaction is difficult and leads first to another ‘inactive’ intermediate, the 1,4-MA complex. Thus, an analysis of the polar monomer binding mode can be used as a screening test in a search for the active co-polymnerization catalyst: the systems with a strong preference of the O-binding mode can be excluded from further studies. Conclusions A comparison of the binding mode of polar monomers for the Ni- and Pd-based diimine complexes (inactive and active co-polymerization catalysts) shows that the preference of the O- bound complex in Ni case is reversed in Pd-based system. Further, the difference between the two catalysts has mainly {electrostatic + Pauli repulson} origin. Thus, use of the neutral catalysts in co-polymerization processes seems to be promising. Indeed, in the case of Grubbs ligand, the  -complex is strongly preferred already in the Ni-system; this preference is enhanced for Pd catalyst. The absolute  -complexation energies for the Grubbs catalyst are comparable with those of the diimine systems. In the complexes with fluorinated monomers, the preference of the O-binding mode is decreased, but with a price of decreased absolute complexation energies. This would lead to a low incorporation of the fluorinated monomer in the co-polymerization. The presence of the steric bulk in the real catalysts does not affect the preference of the binding mode. The MD simulations show that all the complexes are stable on the free-energy surfaces and do not exhibit ant tendency toward a spontaneous inter-conversion. Further, the complexes are separated by relatively large barriers. In the Ni-case the O   inter-conversion reaction is difficult and leads first to another ‘inactive’ intermediate, the 1,4-MA complex. Thus, an analysis of the polar monomer binding mode can be used as a screening test in a search for the active co-polymnerization catalyst: the systems with a strong preference of the O-binding mode can be excluded from further studies. 20