1. A density functional study on polymerization processes catalyzed by Pd(II) complexes Artur Michalak and Tom Ziegler* University of Calgary; Calgary, Alberta, Canada Artur Michalak and Tom Ziegler* University of Calgary; Calgary, Alberta, Canada

2. Introduction The Pd(II)-based catalysts due to Brookhart (JACS 1995, 117,6414; 1996,118,11664; 1996,118,267,1998, 120, 888) are not only able to polymerize  -olefins, but also exhibit substantial tolerance towards polar functional groups on the monomer. By modification of the catalyst structure one can potentially control the properties of the resulting polymer. Therefore, it is important to understand the factors that determine the relationship between catalyst structure and polymer properties. The main purpose of the present investigation was to conduct a computational study of the relative stability of the different species present in the catalytic cycle and the activation barriers of the elementary steps in the Pd-catalyzed ethene and propene polymerization, as well as their co-polymerization with methyl acrylate.We studied the ethene and propene insertions into Pd-alkyl bond involving primary, secondary, and tertiary carbon atom, as well as the isomerization reactions following the olefin insertions; influence of the substituents on the insertion barriers and the relative stabilities of isomer alkyl  -agostic and olefin  -complexes complexes; acrylate insertion into the Pd-alkyl bond, and the stability of insertion products, including alternative chelate structures; chelate opening by ethene - stabilities of ethene complexes and the insertion barriers. The Pd(II)-based catalysts due to Brookhart (JACS 1995, 117,6414; 1996,118,11664; 1996,118,267,1998, 120, 888) are not only able to polymerize  -olefins, but also exhibit substantial tolerance towards polar functional groups on the monomer. By modification of the catalyst structure one can potentially control the properties of the resulting polymer. Therefore, it is important to understand the factors that determine the relationship between catalyst structure and polymer properties. The main purpose of the present investigation was to conduct a computational study of the relative stability of the different species present in the catalytic cycle and the activation barriers of the elementary steps in the Pd-catalyzed ethene and propene polymerization, as well as their co-polymerization with methyl acrylate.We studied the ethene and propene insertions into Pd-alkyl bond involving primary, secondary, and tertiary carbon atom, as well as the isomerization reactions following the olefin insertions; influence of the substituents on the insertion barriers and the relative stabilities of isomer alkyl  -agostic and olefin  -complexes complexes; acrylate insertion into the Pd-alkyl bond, and the stability of insertion products, including alternative chelate structures; chelate opening by ethene - stabilities of ethene complexes and the insertion barriers.

3. Propene polymerization: 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. 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. Models for the catalyst: 1) generic system: R = H; Ar = H 2) a variety of systems with different substituents: R = H; Ar = Ph R = H; Ar = Ph (Me) 2 R = H; Ar = Ph (i-Pr) 2 R = Me; Ar = H R = Me; Ar = Ph (Me) 2 R = Me; Ar = Ph (i-Pr) 2 R 2 = An; Ar = H R 2 = An; Ar = Ph (i-Pr) 2 1) generic system: R = H; Ar = H 2) a variety of systems with different substituents: R = H; Ar = Ph R = H; Ar = Ph (Me) 2 R = H; Ar = Ph (i-Pr) 2 R = Me; Ar = H R = Me; Ar = Ph (Me) 2 R = Me; Ar = Ph (i-Pr) 2 R 2 = An; Ar = H R 2 = An; Ar = Ph (i-Pr) 2 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. 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.

5. Propene insertion - calculations for a generic system: Complexes with primary, secondary, and tertiary alkyl (modeled by n-propyl, iso-propyl, and tert-butyl, respectively): propene  -complexes; 1,2- and 2,1-ins. TS; 1,2- and 2,1-ins. products (  - and  - agostic) Complexes with primary, secondary, and tertiary alkyl (modeled by n-propyl, iso-propyl, and tert-butyl, respectively): propene  -complexes; 1,2- and 2,1-ins. TS; 1,2- and 2,1-ins. products (  - and  - agostic) Propene insertion - calculations for real systems: propene  -complexes with n- and iso- propyl alkyl chain; n- and iso- propyl  -agostic complexes; 1,2- and 2,1- insertion TS (with n-propyl alkyl); propene  -complexes with n- and iso- propyl alkyl chain; n- and iso- propyl  -agostic complexes; 1,2- and 2,1- insertion TS (with n-propyl alkyl);

6. Isomerization reactions - calculations for a generic system: Mechanism of both isomerisation reactions involves hydrogen abstraction, formation of hydride-olefin  -complex, olefin rotation, and re-insertion of hydrogen. Butyl groups were used in our calculations. Mechanism of both isomerisation reactions involves hydrogen abstraction, formation of hydride-olefin  -complex, olefin rotation, and re-insertion of hydrogen. Butyl groups were used in our calculations.

7. generic system -  -complex stabilization energies: OlefinAlkyl primarysecondarytertiary propene-20.85-20.08-14.13 ethene-18.82-18.18-12.45 in kcal/mol OlefinAlkyl primarysecondarytertiary propene-20.85-20.08-14.13 ethene-18.82-18.18-12.45 in kcal/mol generic system -  insertion barriers  OlefinAlkyl primarysecondarytertiary propene - 1,2 ins.22.7226.0229.31 - 2,1 ins.20.6721.9525.65 ethene18.8320.1523.78 in kcal/mol OlefinAlkyl primarysecondarytertiary propene - 1,2 ins.22.7226.0229.31 - 2,1 ins.20.6721.9525.65 ethene18.8320.1523.78 in kcal/mol

8. 2,1-insertion preference (generic system): In the TS geometry the C-H or C-C bonds of the propene carbon atom which forms the C-C bond are bent more than those of C forming C-Pd bond. Therefore, the preferred TS has a methyl group attached to the carbon atom interacting with Pd. Propene distortion energy - c.a. 76% of the activation barrier. For the same reason ethene insertion barriers are lower than those of propene - the difference in propene and ethene distortion energies (1.7 kcal/mol) corresponds to the difference in their insertion barriers (1.9 kcal/mol). For the same reason ethene insertion barriers are lower than those of propene - the difference in propene and ethene distortion energies (1.7 kcal/mol) corresponds to the difference in their insertion barriers (1.9 kcal/mol).

9. Generic system - stability of insertion products: OlefinStructureAlkyl primarysecondarytertiary propene  -agostic- 1,2 ins. +5.21+6.85-1.55 - 2,1 ins.+4.05+4.37-2.97 ethene  -agostic+1.97+2.71-6.17 propene  -agostic -1,2 ins.-2.17-1.63-3.46 -2,1 ins.-4.06-4.18-7.18 ethene-5.65-5.06-8.42 in kcal/mol, with respect to corresponding olefin  -complexes OlefinStructureAlkyl primarysecondarytertiary propene  -agostic- 1,2 ins. +5.21+6.85-1.55 - 2,1 ins.+4.05+4.37-2.97 ethene  -agostic+1.97+2.71-6.17 propene  -agostic -1,2 ins.-2.17-1.63-3.46 -2,1 ins.-4.06-4.18-7.18 ethene-5.65-5.06-8.42 in kcal/mol, with respect to corresponding olefin  -complexes In all the cases the 2,1- insertion products have lower energies than the complexes formed after 1,2-insertions. In all the cases the 2,1- insertion products have lower energies than the complexes formed after 1,2-insertions.

10. Generic system - isomerization reactions: ReactionStructures / Relative Energies 1  -agosticTS 2  -agostic (3)10 0.0013 +4.5614 -3.42 (4)15 0.0016 +5.8419 +1.59 1 in kcal/mol, with respect to corresponding b-agostic insertion product 2 the highest energy TS along the preferred reaction path ReactionStructures / Relative Energies 1  -agosticTS 2  -agostic (3)10 0.0013 +4.5614 -3.42 (4)15 0.0016 +5.8419 +1.59 1 in kcal/mol, with respect to corresponding b-agostic insertion product 2 the highest energy TS along the preferred reaction path Generic system - relative stabilities of isomers: Alkylalkyl  -agostic propene radicalcomplex  -complex n-butyl6.724.95 0.53 iso-butyl5.483.42 1.01 sec-butyl3.832.12, 3.36 0.00 tert-butyl0.000.00 1.82 in kcal/mol, with respect to the most stable complex Alkylalkyl  -agostic propene radicalcomplex  -complex n-butyl6.724.95 0.53 iso-butyl5.483.42 1.01 sec-butyl3.832.12, 3.36 0.00 tert-butyl0.000.00 1.82 in kcal/mol, with respect to the most stable complex The chain straightening isomerization reaction (4) leads to the less stable  -agostic complex. The chain straightening isomerization reaction (4) leads to the less stable  -agostic complex. The stability of  -agostic complexes follows the trend for alkyl radicals. The steric repulsion between olefin and alkyl changes this trend for the olefin complexes. The stability of  -agostic complexes follows the trend for alkyl radicals. The steric repulsion between olefin and alkyl changes this trend for the olefin complexes.

11.  -complex stabilization energies:  -complex stabilization energies: Catalyst Alkyl R Arprimarysecondary HH-20.85-20.08 HPh-19.69-15.23 HPh(Me) 2 -21.25-16.86 HPh(i-Pr) 2 -20.48-15.78 MeH -20.22-19.48 MePh(Me) 2 -20.88-15.97 MePh(i-Pr) 2 -16.34-10.68 AnH-21.03-20.30 AnPh(i-Pr) 2 -16.82-12.23 in kcal/mol Catalyst Alkyl R Arprimarysecondary HH-20.85-20.08 HPh-19.69-15.23 HPh(Me) 2 -21.25-16.86 HPh(i-Pr) 2 -20.48-15.78 MeH -20.22-19.48 MePh(Me) 2 -20.88-15.97 MePh(i-Pr) 2 -16.34-10.68 AnH-21.03-20.30 AnPh(i-Pr) 2 -16.82-12.23 in kcal/mol Catalyst  E(iPr - nPr) 1 R Ar  -agostic  -complex HH-1.96 -1.20 HPh-2.47 +1.97 HPh(Me) 2 -3.11 +1.28 HPh(i-Pr) 2 -3.21 +1.50 MeH -1.75 -1.02 MePh(Me) 2 -2.76 +2.15 MePh(i-Pr) 2 -2.36 +3.31 AnH-1.87 -1.14 AnPh(i-Pr) 2 -2.65 +1.94 1 energy difference between complexes with iso- and n-propyl alkyl; in kcal/mol Catalyst  E(iPr - nPr) 1 R Ar  -agostic  -complex HH-1.96 -1.20 HPh-2.47 +1.97 HPh(Me) 2 -3.11 +1.28 HPh(i-Pr) 2 -3.21 +1.50 MeH -1.75 -1.02 MePh(Me) 2 -2.76 +2.15 MePh(i-Pr) 2 -2.36 +3.31 AnH-1.87 -1.14 AnPh(i-Pr) 2 -2.65 +1.94 1 energy difference between complexes with iso- and n-propyl alkyl; in kcal/mol Relative stability of isomers : With an increase of the aryl substituents size the difference in stabilization energies for primary and secondary system increases. With an increase of the aryl substituents size the difference in stabilization energies for primary and secondary system increases. While the preference of iso-propyl  -agostic complexes increases with an increase in steric bulk, the  -complexes with n-propyl become more stable.

12. Propene insertion barriers: CatalystInsertion RAr 1,2- 2,1-  HH 22.7220.67-2.05 HPh 23.3822.99-0.39 HPh(Me) 2 22.2820.99-1.29 HPh(i-Pr) 2 21.8520.05-1.80 MeH 23.1821.42-1.77 MePh(Me) 2 21.5819.92-1.66 MePh(i-Pr) 2 18.3018.83+0.53 AnH 23.5922.31-1.28 AnPh(i-Pr) 2 17.4816.90-0.58 in kcal/mol CatalystInsertion RAr 1,2- 2,1-  HH 22.7220.67-2.05 HPh 23.3822.99-0.39 HPh(Me) 2 22.2820.99-1.29 HPh(i-Pr) 2 21.8520.05-1.80 MeH 23.1821.42-1.77 MePh(Me) 2 21.5819.92-1.66 MePh(i-Pr) 2 18.3018.83+0.53 AnH 23.5922.31-1.28 AnPh(i-Pr) 2 17.4816.90-0.58 in kcal/mol With an increase in the aryl ortho- substituents size the preference of the 2,1- insertion decreases; for the system with R=Me and Ar=Ph(i-Pr) 2 the 1,2insertion becomes slightly preferred. With an increase in the aryl ortho- substituents size the preference of the 2,1- insertion decreases; for the system with R=Me and Ar=Ph(i-Pr) 2 the 1,2insertion becomes slightly preferred.

13. Insertion barriers - steric effect: Increased steric repulsion for 2,1-insertion TS - 2,1-insertion becomes less preferred with increase of R’. Increased steric repulsion for 2,1-insertion TS - 2,1-insertion becomes less preferred with increase of R’. Stability of  -complexes - steric effect: Increased steric repulsion for a complex with iso - propyl alkyl -n - propyl system becomes more preferred with increase of R’. Increased steric repulsion for a complex with iso - propyl alkyl -n - propyl system becomes more preferred with increase of R’.

14. Olefin - methyl acrylate co-polymerization 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; 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;

15. Olefin - methyl acrylate co-polymerization - calculations: 1,2- and 2,1-acrylate insertion:  complexes; insertion TS,  - and  -agostic complexes; generic system, with n-propyl alkyl 1,2- and 2,1-acrylate insertion:  complexes; insertion TS,  - and  -agostic complexes; generic system, with n-propyl alkyl alternative chelates formed after 1,2- and 2,1-insertion; alternative chelates formed after 1,2- and 2,1-insertion; 4-, 5-, and 6-member chelate opening by ethene: ethene  -complexes and insertion TS. 4-, 5-, and 6-member chelate opening by ethene: ethene  -complexes and insertion TS.

16. Acrylate complexes -20.7 kcal/mol -17.2 kcal/mol The complexes with acrylate bound by C=C bond are more stabilized than the complexes with acrylate bound by oxygen atom. The arrangement of acrylate in the most stable complex is similar to the propene case. The complexes with acrylate bound by C=C bond are more stabilized than the complexes with acrylate bound by oxygen atom. The arrangement of acrylate in the most stable complex is similar to the propene case.

17. Acrylate insertion: System Insertion 1,2- 2,1- TS +23.9 +19.4  -agostic +5.2 +0.9  -agostic +0.4 -4.7 chelates: 5-memb. -18.7 4-memb. -12.9 5-memb. -19.0 6-memb. -20.1 in kcal/mol, with respect to the acrylate  -complex System Insertion 1,2- 2,1- TS +23.9 +19.4  -agostic +5.2 +0.9  -agostic +0.4 -4.7 chelates: 5-memb. -18.7 4-memb. -12.9 5-memb. -19.0 6-memb. -20.1 in kcal/mol, with respect to the acrylate  -complex strong preference of the 2,1-insertion; strong stabilization of chelates, increasing from 4-member structure to 6-member one. strong preference of the 2,1-insertion; strong stabilization of chelates, increasing from 4-member structure to 6-member one. Chelates (after 2,1-ins.) : 4-memb. 5-memb. 6-memb.

18. Chelate opening - ethene  complexes  memb.:  kcal/mol  memb.:  kcal/mol  memb.:  kcal/mol In all the cases the Pd-O bond is still present in the olefin  -complexes; in olefin complexes, the chelate ring is rotated, with oxygen atom in axial position. In all the cases the Pd-O bond is still present in the olefin  -complexes; in olefin complexes, the chelate ring is rotated, with oxygen atom in axial position.

19. Chelate opening - ethene insertion TS:  memb.:  kcal/mol  memb.:  kcal/mol  memb.:  kcal/mol In all the TS geometries the Pd-O bond is broken; ethene insertion barriers are much higher than those for the insertion into the Pd-alkyl bond; the insertion barrier increases dramatically in the 6-memb. chelate case. In all the TS geometries the Pd-O bond is broken; ethene insertion barriers are much higher than those for the insertion into the Pd-alkyl bond; the insertion barrier increases dramatically in the 6-memb. chelate case.

20. Conclusions A strong preference of the 2,1-propene insertion in generic system is decreased in real systems as a result of steric repulsion. The chain straightening isomerization reaction leads to the less stable  -agostic complex, and becomes even less favourable in real systems. On the other hand, with the increase of the substituent size, the  -complexes involving primary alkyl become more stable than those with secondary alkyl. In the case of acrylate insertion, the 2,1-regioselectivity is preferred even stronger. In the ethene  -complexes the Pd-O bond is still present, and is broken in the TS The chelate opening is the easiest in the 4-member case, and becomes more difficult for 5- and 6-member chelates. A strong preference of the 2,1-propene insertion in generic system is decreased in real systems as a result of steric repulsion. The chain straightening isomerization reaction leads to the less stable  -agostic complex, and becomes even less favourable in real systems. On the other hand, with the increase of the substituent size, the  -complexes involving primary alkyl become more stable than those with secondary alkyl. In the case of acrylate insertion, the 2,1-regioselectivity is preferred even stronger. In the ethene  -complexes the Pd-O bond is still present, and is broken in the TS The chelate opening is the easiest in the 4-member case, and becomes more difficult for 5- and 6-member chelates.