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Quantum chemical molecular modelling
Dr. hab. Artur Michalak
Department of Theoretical Chemistry
Faculty of Chemistry
Jagiellonian University
Kraków, Poland
http://www.chemia.uj.edu.pl/~michalak/mmod/
http://www.chemia.uj.edu.pl/~michalak/mmod2008/
In Polish: http://www.chemia.uj.edu.pl/~michalak/mmod2007/
Ck08
Lecture 12
• Basic ideas and methods of quantum chemistry:
Wave-function; Electron density; Schrodinger equation; Density Functional theory; Born-Oppenheimer
approximation; Variational principles in wave-function mechanics and DFT; One-electron approximation; HF
method; Electron correlation; KS method; Wave-function-based electron correlation methods;
• Input data for QM calculations, GAMESS:
Molecular geometry, Z-Matrix, Basis sets in ab initio calculations;, input, output;
Geometry of molecular systems:
Geometry optimization; Constrained optimization; Conformational analysis; Global minimum problem
Electronic structure of molecular systems:
Population analysis; Bond-orders; Molecular orbitals (KS orbitals); Chemical bond; Deformation density;
Localized orbitals;
•Molecular vibrations, Thermodynamics; Chemical Reactivity:
Vibrational analysis; Thermodynamic properties; Modeling chemical
reactions; Trantition state optimization and validation; Intrinsic Reaction
Coordinate; Chemical reactivity indices; Molecular Electrostatic Potential;
Fukui Functions; Single- and Two-Reactant Reactivity Indices
• Other Topics:Modelling of complex chemical processes – examples from catalysis; Molecular spectroscopy from ab initio calculations; Advanced
methods for electron correlation;Molecular dynamics; Modelling of large systems – hybrid approaches (QM/MM); Solvation
models
Example:
Theoretical studies on the polymerisation
and co-polymerisation processes catalyzed
by the late-transition metal complexes
Example:
Theoretical studies on the polymerisation
and co-polymerisation processes catalyzed
by the late-transition metal complexes
PolyethylenePolyethylene
Annual consumption (in 2000)
- 165 M tons
19 000 tons during 1 hour lecture
PolyethylenePolyethylene
Annual consumption (in 2000)
- 165 M tons
Various classes of polyethylenes:
HDPE, LDPE, LLDPE
- size of macromolecules: molecular weight, molecular weight distribution
19 000 tons during 1 hour lecture
n
Etylene:
...
PolyethylenePolyethylene
Annual consumption (in 2000)
- 165 M tons
Various classes of polyethylenes:
HDPE, LDPE, LLDPE
- size of macromolecules: molecular weight, molecular weight distribution
- architecture of macromolecules: degree of branching, topology of branches
19 000 tons during 1 hour lecture
1) Influence of catalyst structure
and reaction conditions (T, p)
on the polyolefin mictrostructure
1) Influence of catalyst structure
and reaction conditions (T, p)
on the polyolefin mictrostructure
• Static DFT calculations; Ab initio MD (CP-MD); Stochastic simulations• Static DFT calculations; Ab initio MD (CP-MD); Stochastic simulations
Theoretical studies - methodology :
1) Influence of catalyst structure
and reaction conditions (T, p)
on the polyolefin mictrostructure
1) Influence of catalyst structure
and reaction conditions (T, p)
on the polyolefin mictrostructure
2) Copolymerization of αααα-olefins
with polar monomers
– factors determining catalyst activity
2) Copolymerization of αααα-olefins
with polar monomers
– factors determining catalyst activity
Ethylene polymerizationEthylene polymerization
n
n
TiCl4/MgCl2
• Ziegler, K.; Holtzkamp, E.; Martin, H.; Breil, H. Angew. Chem. 1955, 67, 541. (Das Mülheimer
Normaldruck-Polyäthylen-Verfahren)
• Ziegler, K.; Holtzkamp, E..; Breil, H.; Martin, H Angew. Chem. 1955, 67, 426. (Polymerisation
Äthylen und Anderen Olefinen)
• Natta, G. J. Polym. Sci. 1955, 16, 143. (Une Nouvelle Classe de Polymeres d’α-Olefines ayant
une Regularite de Structure Exceptionelle)
• Natta, G. Angew. Chem. 1956, 68, 393. (Stereospezifische Katalysen und isotaktische
Polymere)
1950’s : K. Ziegler, G. Natta
-heterogenous catalyst
Ethylene polymerizationEthylene polymerization
• Sinn, H.; Kaminsky, W.; Vollmer H.J.; Woldt, R. Angew. Chem. Int. Ed. Engl. 1980, 19, 380. (“Living Polymers”:
On Polymerization with Extremely Productive Zigler Catalysts)
• Sinn, H.; Kaminsky, W. Adv. Organomet. Chem. 1980, 18, 99. (Ziegler-Natta Catalysis)
• Wild, F.R.W.P.; Zsolnai, L.; Huttner, G.; Brintzinger, H.H. J. Organomet. Chem. 1982, 232, 233. (ansa-Metallocene
Derivatives IV. Synthesis and Molecular Structures of Chiral ansa-Titanocene Derivatives with Bridged
Tetrahydroindenyl Ligands)
• Kaminsky, W.; Kulper, K.; Brintzinger, H.H.; Wild, F.R.W.P. Angew. Chem. Int. Ed. Engl. 1985, 24, 507.
(Polymerization of Propene and Butene with a Chiral Zirconocene and Methyl Aluminoxane as Cocatalyst)
1980:
‘Metallocene revolution’
homogeneous catalysts
- metallocenes (Zr, Ti)
Ethylene polymerizationEthylene polymerization
1990’s:
Non-metallocene
homogeneous catalysts
(various metals and ligands)
ACS Symp.Ser. 857 (2003)
AcAcRaRaFrFr7
RnRnAtAtPoPoBiBiPbPbTlTlHgHgAuAuPtPtIrIrOsOsReReWWTaTaHfHfLaLaBaBaCsCs6
XeXeIITeTeSbSbSnSnInInCdCdAgAgPdPdRhRhRuRuTcTcMoMoNbNbZrZrYYSrSrRbRb5
KrKrBrBrSeSeAsAsGeGeGaGaZnZnCuCuNiNiCoCoFeFeMnMnCrCrVVTiTiScScCaCaKK4
ArArClClSSPPSiSiAlAl
XIIXIVIII IX XVIIVIVIVIII
MgMgNaNa3
NeNeFFOONNCCBBBeBeLiLi2
HeHeHH1
XVIII
XVIIXVIXVXIVXIIIII
I
Ethylene polymerization catalystsEthylene polymerization catalysts
LuLuYbYbTmTmErErHoHoDyDyTbTbGdGdEuEuSmSmPmPmNdNdPrPrCeCe6
Neutral ligands in the Ni (II) and Pd (II) complexes
Anionic ligands in the Ni (II) and Pd (II) complexes
CC
NN
Pd
R R
Ar Ar
+
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
M. Brookhart, 1995
Diimine catalysts; Ni, PdDiimine catalysts; Ni, Pd
CC
NN
Pd
R R
Ar Ar
+
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
• Mw: 30 000 – 1 000 000;
controlled by catalyst, temperature and pressure;
• Mw/ Mn: ca. 1.1-2.0;
• number of branches controlled by catalyst, temperature and pressure;
• microstructure controlled by catalyst, temperature and pressure;
• active in copolymerization of ethylene with polar monomers
• Mw: 30 000 – 1 000 000;
controlled by catalyst, temperature and pressure;
• Mw/ Mn: ca. 1.1-2.0;
• number of branches controlled by catalyst, temperature and pressure;
• microstructure controlled by catalyst, temperature and pressure;
• active in copolymerization of ethylene with polar monomers
Katalizatory diiminowe; Ni, PdKatalizatory diiminowe; Ni, Pd
Diimine catalystsDiimine catalysts
n
Propylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
Observed: up to 130 branches / 1000 C
Observed: 210 - 333 branches / 1000 C
n
Propylene:
n
Propylene:
n
Etylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
Observed: up to 130 branches / 1000 C
Observed: 210 - 333 branches / 1000 C
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
Diimine catalystsDiimine catalysts
Influence of olefin pressure on the polymer structure
high p - ‘linear structures’
low p - hyperbranched structures
Pd – No. of branches independent of p
Ni – No. of branches influenced by p
n
Propylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
Observed: up to 130 branches / 1000 C
Observed: 210 - 333 branches / 1000 C
n
Propylene:
n
Propylene:
n
Etylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
Observed: up to 130 branches / 1000 C
Observed: 210 - 333 branches / 1000 C
β-agostic
π-complex
+ ethylene
β-agostic
γ-agostic
insertion
Ethylene polymerization mechanismEthylene polymerization mechanism
n
Propylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
α-olefin polymerization mechanismα-olefin polymerization mechanism
n
Propylene:
n
Etylene:
333 methyl branches / 1000 C atoms
Linear chain
Observed: up to 130 branches / 1000 C
Observed: 210 - 333 branches / 1000 C
α-olefin polymerization mechanismα-olefin polymerization mechanism
Chain isomerization
α-olefin polymerization mechanismα-olefin polymerization mechanism
α-olefin polymerization mechanismα-olefin polymerization mechanism
•Relative stability of isomeric alkyl complexes
•Relative stability of isomeric olefin ππππ-complexes
•Relative insertion barriers
•Relative rates of insertion vs. isomerization
•Relative stability of isomeric alkyl complexes
•Relative stability of isomeric olefin ππππ-complexes
•Relative insertion barriers
•Relative rates of insertion vs. isomerization
α-olefin polymerization mechanismα-olefin polymerization mechanism
Theoretical modelingTheoretical modeling
• Schrödinger Equation →→→→ wave function; Kohn-Sham eq. →→→→ density
• Born-Oppenheimer approximation
• Potential energy surface (PES): reactants, products, TS
TS
minimum
reaction cooridinate
E
Quantum chemical modelling of chemical processes
• Computational methods: ab initio and semi-empirical
• Reactions involving transition metals:
ab initio methods that account for electron correlation
- success of the density functional theory (DFT)
•DFT calculations possible for relatively large systems (up to 100-200
atoms; 1000 electrons)
Quantum-chemical modelling of TM-complexes and reactions:
•Niu, S.; Hall, M.B. Chem. Rev. 2000, 100, 353.
•Frenking G., Frohlich, N. Chem. Rev. 2000, 100, 717.
•Cundari, T.R. Chem. Rev. 2000, 100, 807.
•Dedieu, A. Chem. Rev. 2000, 100, 543.
polymerization processes:
•Rappe, A.K.; Skiff, W.M.; Casewit, C.J. Chem. Rev. 2000, 100, 1435.
•Angermund, K.; Fink, G.; Jensen, V.R.; Kleinschmidt, R. Chem.Rev.2000, 100, 1457.
Quantum-chemical modelling of TM-complexes and reactions:
•Niu, S.; Hall, M.B. Chem. Rev. 2000, 100, 353.
•Frenking G., Frohlich, N. Chem. Rev. 2000, 100, 717.
•Cundari, T.R. Chem. Rev. 2000, 100, 807.
•Dedieu, A. Chem. Rev. 2000, 100, 543.
polymerization processes:
•Rappe, A.K.; Skiff, W.M.; Casewit, C.J. Chem. Rev. 2000, 100, 1435.
•Angermund, K.; Fink, G.; Jensen, V.R.; Kleinschmidt, R. Chem.Rev.2000, 100, 1457.
Theoretical modelingTheoretical modeling
Assumption: energetics independent of polymer length ( P )
6 propagation reactions
(2,1- i 1,2-; 1o, 2o, 3o)
3 termination reactions
(1o, 2o, 3o )
9 isomerizations
(from: 1o, 2o, 3o
to: 1o, 2o, 3o )
DFT calculations:DFT calculations:
Chain growth:
Chain isomerization:
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
NN
Pd
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
CCCC
CNN CCC
CCC C
Pd
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
C
CC
C
CCCC
CNN CCC
CCC C
C
Pd
C
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
C
CC
C
CC
C
CC
C
C
CNN CCC
CC
C
C C
CC
Pd
CC
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
CC
NN
Pd
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
C
CC
C
CC
CC
CNN CCC
CCC C
C
Pd
C
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
CC
C
CC
C
CC
CC
NN
Pd
Models for the catalyst:Models for the catalyst:
1) generic system: R = H; Ar = H1) 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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
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
• R2 = An; Ar = H
• R2 = An; Ar = Ph (i-Pr)2
CC
NN
Pd
R R
Ar Ar
+
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
DFT calculations:DFT calculations:
���� A. Michalak, T. Ziegler, "Pd-catalyzed Polymerization of Propene - DFT Model Studies", Organometallics, 18, 1999, 3998-4004.
���� A. Michalak, T. Ziegler, "DFT studies on substituent effects in Pd-catalyzed olefin polymerization", Organometallics, 19, 2000, 1850-1858.
Examples of results:
Ethylene insertion barrier:
DFT: 16.7 kcal/mol
exp.: 17.4 kcal/mol
Isomerization barrier:
DFT: 5.8 (6.8) kcal/mol
exp: 7.2 kcal/molC
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
DFT calculations (ethylene):DFT calculations (ethylene):
���� A. Michalak, T. Ziegler, "Pd-catalyzed Polymerization of Propene - DFT Model Studies", Organometallics, 18, 1999, 3998-4004.
���� A. Michalak, T. Ziegler, "DFT studies on substituent effects in Pd-catalyzed olefin polymerization", Organometallics, 19, 2000, 1850-1858.
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
Exp.
(theoret.)
Isomerization reactionsIsomerization reactions
0.000.00
+4.56+4.56
-3.42-3.42
0.000.00+5.84+5.84
+1.59+1.59
following
1,2-insertion
following
2,1-insertion
Isomerization reactionsIsomerization reactions
0.000.00
+4.56+4.56
-3.42-3.42
0.000.00+5.84+5.84
+1.59+1.59
following
1,2-insertion
following
2,1-insertion
Isomerization reactionsIsomerization reactions
0.000.00
+4.56+4.56
-3.42-3.42
0.000.00+5.84+5.84
+1.59+1.59
following
1,2-insertion
following
2,1-insertion
1 C atom attached to the catalyst:
olefin capture
followed by
1,2- or 2,1-
insertion
Stochastic simulation - how it worksStochastic simulation - how it works
���� A. Michalak, T. Ziegler, „Stochastic modelling of the propylene polymerization catalyzed by thePd-based diimine catalyst: influence of the catalyst structure and the reaction conditions on the polymermicrostructure”, J. Am. Chem. Soc, 2002, 124, 7519-7528.
1 C atom attached to the catalyst:
olefin capture
followed by
1,2- or 2,1-
insertion
Stochastic simulation - how it worksStochastic simulation - how it works
Primary C attached to the catalyst:
1) 1 possible isomerization
2) olefin capture and 1,2- insertion
3) olefin capture and 2,1- insertion
4) termination
Stochastic simulation - how it worksStochastic simulation - how it works
1
2
3
4
Secondary C attached to the catalyst:
1) isomerization to primary C
2) isomerisation to secondary C
3) olefin capture and 1,2- insertion
4) olefin capture and 2,1- insertion
5) termination
Stochastic simulation - how it worksStochastic simulation - how it works
Secondary C attached to the catalyst:
1) isomerization to secondary C
2) isomerisation to secondary C
3) olefin capture and 1,2- insertion
4) olefin capture and 2,1- insertion
5) termination
Stochastic simulation - how it worksStochastic simulation - how it works
Secondary C attached to the catalyst:
1) isomerization to primary C
2) isomerisation to secondary C
3) olefin capture and 1,2- insertion
4) olefin capture and 2,1- insertion
5) termination
Stochastic simulation - how it worksStochastic simulation - how it works
Primary C attached to the catalyst:
1) isomerization to secondary C
2) olefin capture and 1,2- insertion
3) olefin capture and 2,1- insertion
4) termination
Stochastic simulation - how it worksStochastic simulation - how it works
Primary C attached to the catalyst:
1) isomerization to tertiary C
2) olefin capture and 1,2- insertion
3) olefin capture and 2,1- insertion
4) termination
Stochastic simulation - how it worksStochastic simulation - how it works
Stochastic simulation - how it worksStochastic simulation - how it works
Stochastic simulation - how it worksStochastic simulation - how it works
Stochastic simulation - how it worksStochastic simulation - how it works
Stochastic simulation - how it worksStochastic simulation - how it works
ProbabilitiesProbabilities
][ 01,1 βisokr =
][ 02,2 βisokr =
β0 , β1 , β2 β-agostic complexes
Basic assumption:
Relative probabilities (microscopic)
= relative reaction rates (macroscopic)
Basic assumption:
Relative probabilities (microscopic)
= relative reaction rates (macroscopic)
π i
π j
=r i
r j
πiso.1
π iso.2
=r iso.1
r iso.2
=k iso.1
kiso.2
≈ exp(∆∆G 1 , 2
kT)
πi
i
∑ = 1
Two isomerization
reactions:
β0 , β1 , β2 β-agostic complexes;
π0- olefin π complexes
Insertion vs.
isomerization:
Basic assumption:
Relative probabilities (microscopic)
= relative reaction rates (macroscopic)
Basic assumption:
Relative probabilities (microscopic)
= relative reaction rates (macroscopic)
π i
π j
=r i
r j
πi
i
∑ = 1
πiso.1
π ins. 1, 2
=riso.1
r ins.1, 2
≈kiso.1
k ins.1, 2 Kcompl. polefin
olefincomplins
insins
pKk
kr
][
][
0..
0..
β
π
=
==
][ 01,1 βisokr =
ProbabilitiesProbabilities
R=H; Ar= Ph
CC
CCCC
CNN CCC
CCC C
Pd
Propylene polymerization (theoretical data)Propylene polymerization (theoretical data)
R=An; Ar= Ph(i-Pr)2
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
Propylene polymerization (theoretical data)Propylene polymerization (theoretical data)
Propylene polymerization (theoretical data)Propylene polymerization (theoretical data)
R = H; Ar = H
CC
NN
Pd
���� A. Michalak, T. Ziegler, „Stochastic modelling of the propylene polymerization catalyzed by thePd-based diimine catalyst: influence of the catalyst structure and the reaction conditions on the polymermicrostructure”, J. Am. Chem. Soc, 2002, 124, 7519-7528.
Propylene polymerization - effect of the catalystPropylene polymerization - effect of the catalyst
R=H; Ar=H: 331.6 br.; 66.7% 33.3%; 0
R=H; Ar=Ph: 122.5 br.; 51.7%; 40.1%; 14.2
R=H; Ar=Ph(CH3)2:
269.6 br.;60.9%; 38.1%; 0.89
R=H; Ar=Ph(i-Pr)2:
269.6 br.; 60.9%; 38.1%; 1.37
R=CH3; Ar=Ph(CH3)2:
251.0 br.; 59.7%; 38.7%; 0.93
R=CH3; Ar=Ph(i-Pr)2:
238.2 br.;61.7%; 36.5%; 2.6
R=An; Ar=Ph(i-Pr)2:
255.6 br.; 59.9%; 38.5%; 1.35
The values above the plots denote:
the average number of branches / 1000 C, % of atoms in the
main chain and % in primary branches, and the ratio between
the isomerization and insertion steps.
Colors are used to mark different types of branches (primary,
secondary, etc.).
61
0
30
60
90
120
150
180
0 100 200 300 400 500
T [K]
No. of
bra
nch
es
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
62
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
0
30
60
90
120
150
180
0 100 200 300 400 500
T [K]
No. of
bra
nch
es
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
63
CC
CC
C
CC
C
C
CC
C
CC
C
CC
C
C
CC
C
N CNC CC
C
C
CCC C
CC
Pd
CC
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical data
220
240
260
280
300
320
0 100 200 300 400 500
T [K]
No
. o
f b
ran
ches
/ 1
00
0 C
Propylene polymerization - temperature effectPropylene polymerization - temperature effect
T=98K
T=198K
T=298K
T=398K
T=498K
64
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
220
240
260
280
300
320
0 100 200 300 400 500
T [K]
No
. o
f b
ran
ches
/ 1
00
0 C
Propylene polymerization - temperature effectPropylene polymerization - temperature effect
T=98K
T=198K
T=298K
T=398K
T=498K
65
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
• Two insertion pathways:
1,2- i 2,1-
• Chain straightening follows
2,1-insertion only
•Lower barrier for the 1,2-
insertion (by c.a. 0.6 kcal/mol)
• Practically each 2,1-
insertion is followed by chain
straighening
220
240
260
280
300
320
0.001 0.01 0.1 1
p [ arbitrary units]
No. of
bra
nch
es
Propylene polymerization - pressure effectPropylene polymerization - pressure effect
66
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
���� A. Michalak, T. Ziegler, „Stochastic modelling of the propylene polymerization catalyzed by thePd-based diimine catalyst: influence of the catalyst structure and the reaction conditions on the polymermicrostructure”, J. Am. Chem. Soc, 2002, 124, 7519-7528.
220
240
260
280
300
320
0.001 0.01 0.1 1
p [ arbitrary units]
No. of
bra
nch
es
Propylene polymerization - pressure effectPropylene polymerization - pressure effect
67
C
CC
C
C
CC
C
CC
C
CC
C
C
N CNC CC
CC
C
C C
CC
Pd
CC
Exp.: 213br. / 1000 C
„Ideal” – no chain straighening333.3
���� A. Michalak, T. Ziegler, „Stochastic modelling of the propylene polymerization catalyzed by thePd-based diimine catalyst: influence of the catalyst structure and the reaction conditions on the polymermicrostructure”, J. Am. Chem. Soc, 2002, 124, 7519-7528.
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
68
p
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from experimental data
69
p
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
Ethylene polymerization by Pd-based diimine catalyst
Simulations from theoretical and experimental data
70
���� Michalak, A.; Ziegler, T.; Macromolecules 2003, 36, 928-933 („Exploring the Scope ofPossible Microstructures from Polymerization of Ethylene by Late Transition Metal Single-SiteCatalysts. A Theoretical Study.”)
Ethylene polymerization - model studies on the effects of catalyst
(elementary reaction barriers), temperature, and pressure on the
microstructure of polymers
Ethylene polymerization - model studies on the effects of catalyst
(elementary reaction barriers), temperature, and pressure on the
microstructure of polymers
0
50
100
150
200
250
300
350
400
450
0.0001 0.001 0.01 0.1 1
∆∆∆∆E1=2.0 kcal/mol
0
50
100
150
200
250
300
350
400
450
500
0.0001 0.001 0.01 0.1 1
∆∆∆∆E1=3.0 kcal/mol
0
100
200
300
400
500
600
0.0001 0.001 0.01 0.1 1
∆∆∆∆E1=4.0 kcal/mol
0
100
200
300
400
500
600
0.0001 0.001 0.01 0.1 1
∆∆∆∆E1=6.0 kcal/mol
p
∆∆∆∆E2=1
∆∆∆∆E2=9
∆∆∆∆E1 =1; ∆∆∆∆E2=2 kcal/mol
∆∆∆∆E1 =1; ∆∆∆∆E2=5 kcal/mol
∆∆∆∆E1 =1; ∆∆∆∆E2=7 kcal/mol
∆∆∆∆E1 =2; ∆∆∆∆E2=5 kcal/mol
∆∆∆∆E1 =4; ∆∆∆∆E2=5 kcal/mol
p=0.0001; T=298 K
The polyethylene galleryThe polyethylene gallery
0
20
40
60
80
100
120
140
160
0 0.0038 0.0076 0.0114 0.0152 0.019 0.0228
p [arb.u.]
br./
10
00
C
14 50 100 200 400 600p [psig]
theor.
exp.
EthyleneEthylene polymerizationpolymerization catalyzedcatalyzed by by NiNi--basedbased BrookhartBrookhart--HicksHicks complexcomplex
� A. Michalak, T. Ziegler, Organometallics 2003, 22, 2069-2079 „Polymerization of
Ethylene Catalyzed by a Ni(+2) Anilinotropone-based catalyst: DFT and Stochastic Studies on the
Elementary Reactions and the Mechanism of Polyethylene Branching”
Experimental data: Hicks, F.A., Brookhart M.Organometallics 2001, 20, 3217.Experimental data: Hicks, F.A., Brookhart M.Organometallics 2001, 20, 3217.
NNi
O
P
0
10
20
30
40
50
60
70
80
90
100
40 50 60 70 80 90 100
T [C]
br./
10
00
C
p = 0.011 arb.u. / p = 400 psig
theor.
exp.
EthyleneEthylene polymerizationpolymerization catalyzedcatalyzed by by NiNi--basedbased BrookhartBrookhart--HicksHicks complexcomplex
� A. Michalak, T. Ziegler, Organometallics 2003, 22, 2069-2079 „Polymerization of
Ethylene Catalyzed by a Ni(+2) Anilinotropone-based catalyst: DFT and Stochastic Studies on the
Elementary Reactions and the Mechanism of Polyethylene Branching”
Experimental data: Hicks, F.A., Brookhart M.Organometallics 2001, 20, 3217.Experimental data: Hicks, F.A., Brookhart M.Organometallics 2001, 20, 3217.
NNi
O
P
p 600 psig
200 psig
50 psig
14 psig
EthyleneEthylene polymerizationpolymerization catalyzedcatalyzed by by NiNi--basedbased BrookhartBrookhart--HicksHicks complexcomplex
0
20000
40000
60000
80000
100000
120000
140000
0 100 200 300 400 500 600 700
p
Mn
N O
Ni
Ph(iPr)2
P(Ph)3
Ph
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
500000
0 200 400 600 800 1000
p
Mn
N O
Ni
Ph(iPr)2
P(Ph)3
Ph
Experimental data: Brookhart M. , Hicks F.A. Organometallics 2001, 20, 3218;
Brookhart, M., Jenkins J. C., J.Am.Chem.Soc., 2004, 126, 582.
Ni(II)-anilinotropone
catalyst
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
Pressure dependence of molecular weight
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
propagation:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
propagation:
BHT termination:Ni
L L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
nterminatio
npropagatio
r
rR =
Molecular weight of polymer
can be estimated from
the average number of insertions
that happen before termination,
ie. relative rates
of propagarion and termination
propagation:
BHT termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
BHT
ins
BHT
ins
k
k
EtKk
EtKk
r
rR ===
]][[
]][[
nterminatio
npropagatio
β
β
No pressure dependence:
propagation:
BHT termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSBHE
R+
Ni
L L
H
kBHE
NiL L
R
H
Ni
L L
H
R
propagation:BHE termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSBHE
R+
Ni
L L
H
kBHE
NiL L
R
H
Ni
L L
H
R
pk
Kk
k
EtKk
r
rR
BHE
ins
BHE
ins ===][
]][[
nterminatio
npropagatio
β
β
Pressure dependence:
propagation:BHE termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
Rys. Regina Szeliga
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSBHE
R+
Ni
L L
H
kBHE
NiL L
R
H
Ni
L L
H
R
JACS, 2004, 126, 5827JACS, 2004, 126, 5827
pk
Kk
k
EtKk
r
rR
BHE
ins
BHE
ins ===][
]][[
nterminatio
npropagatio
β
β
Pressure dependence:
propagation:BHE termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSBHE
R+
Ni
L L
H
kBHE
NiL L
R
H
Ni
L L
H
R
∆∆∆∆EBHE≈≈≈≈ 40 kcal/mol
pk
Kk
k
EtKk
r
rR
BHE
ins
BHE
ins ===][
]][[
nterminatio
npropagatio
β
β
Pressure dependence:
propagation:BHE termination:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
propagation:
NiL L
H
R
isomerization:
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TS
primary propagation
NiL L
H
R
isomerization:
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INS
secondary propagation
TS
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSNi
L L
H
R
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INSTS
BHT’ BHT
primary propagation
isomerization:
secondary propagation
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSNi
L L
H
R
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INSTS
BHT’ BHT
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
primary propagation
isomerization:
secondary propagation
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSNi
L L
H
R
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INSTS
BHT’ BHT
Ni
L L
H
+
R
NiL L
H
R
Ni
L L
H
R NiL L
H
R
k’BHT
primary propagation
isomerization:
secondary propagation
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSNi
L L
H
R
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INSTS
BHT’ BHT
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
Ni
L L
H
+
R
NiL L
H
R
Ni
L L
H
R NiL L
H
R
k’BHT
primary propagation
isomerization:
secondary propagation
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
kINS
K
TSNi
L L
H
R
NiL L
H
R
+
CH2
CH2
K’
NiL L
R
NiL L
R
k’INSTS
BHT’ BHT
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
kBHT
Ni
L L
H
+
R
NiL L
H
R
Ni
L L
H
R NiL L
H
R
k’BHT
Pressure
dependence:1
'
3
'
13
'
23
1
'
2
'
12
'
22
kkkkpkk
kkkkpkkR
++
++=
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
1
'
3
'
13
'
23
1
'
2
'
12
'
22
kkkkpkk
kkkkpkkR
++
++=
3
1
'
3
'
1
'
3
'
2
3
1
'
3
'
2
'
3
'
1
3
2
'
3
'
2
3
2
k
k
k
kp
k
k
k
k
k
k
k
k
k
kp
k
k
k
k
R
++
++
=
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
� R. Szeliga, A. Michalak, manuscript in preparation
1
'
3
'
13
'
23
1
'
2
'
12
'
22
kkkkpkk
kkkkpkkR
++
++=
- no isomerization : k1 = k’1 = 0- no pressure dependence
3
2
k
kR =
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
- very fast isomerization : k1 , k’1 >> k2 ,k3 , k’2 ,k’3
- no pressure dependence
'
3
1
'
13
1
'
23
'
2
1
'
12
1
'
22
kk
kkp
k
kk
kk
kkp
k
kk
R
++
++
=
'
33
'
22
kKk
kKkR
isom
isom
+
+=
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
1
'
3
'
13
'
23
1
'
2
'
12
'
22
kkkkpkk
kkkkpkkR
++
++=
- only one propagation mechanism,
(no secondary propagation):
k’2 = 0- no pressure dependence
1
'
3
'
13
'
12
kkkk
kkR
+=
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
- identical primary and secondary
insertion:termination relative rates: k2 /k3 = k’2 /k’3
- no pressure dependence
3
1
'
3
'
1
'
3
'
2
3
1
'
3
'
2
'
3
'
1
3
2
'
3
'
2
3
2
k
k
k
kp
k
k
k
k
k
k
k
k
k
kp
k
k
k
k
R
++
++
=
3
2
3
1
'
3
'
1
3
2
3
1
'
3
'
1
3
2
3
2
k
k
k
k
k
kp
k
k
k
k
k
kp
k
k
k
k
R =
++
++
=
∆∆∆∆E= ∆∆∆∆E’
E
TSins
TSterm
TSins
TStermI rz. II rz.
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
1
'
3
'
13
'
23
1
'
2
'
12
'
22
kkkkpkk
kkkkpkkR
++
++=
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
k1, k1’ - isomerizationk2, k2’ - propagationk3, k3’ - BHT
(primary and secondary)
Pressure dependence exist if:
-there are two propagation mechanisms (primary and secondary)
-the relative propagation/termination rates are different
for primary and secondary cycles: k2 /k3 ≠≠≠≠ k’2 /k’3
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
0
20000
40000
60000
80000
100000
120000
140000
160000
0 100 200 300 400 500 600 700
p [psig]
Mn
iBHTiBHTINSBHT
iINSiINSINSINS
kkkkpkk
kkkkpkkR
'''
'''
++
++=
Pressure dependence of molecular weight:
kINS / kBHT → E#BHT - E#
INS = 6,1[kcal/mol]
k’INS / k’BHT → E#BHT’ - E#
INS’ = 5,0[kcal/mol]
ki / kBHT → E#BHT - E#
i = 6,1 [kcal/mol]
k’i / k’BHT → E#BHT’ - E#
i’ = 3,4 [kcal/mol]
experimental fitted
‘Experimental’ energy differences:
� R. Szeliga, A. Michalak, manuscript in preparation
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
NiL L
H
R
+CH2
CH2
NiL L
R
NiL L
R
BHTBHT
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
NiL L
H
R
Ni
L L
H
R
NiL L
H
R
NiL L
R
H
Ni
L L
H
R
NiL L
HR
1a1b
2a
3a
2b
3b
5a
Propagation
6
9a
11a
13a14
9b
11b
13a
5b
R
+
Ni
L L
H
7
Propagation
Isomerization
CH2
CH2
CH2
CH2
++
BHE
BHTBHT
� R. Szeliga, A. Michalak, manuscript in preparation
NiL L
R
H
CH2
CH2
NiL L
R
NiL L
R
+
NiL L
H
R
+CH2
CH2
NiL L
R
NiL L
R
BHTBHT
NiL L
H
R
Ni
L L
H
R
NiL L
HR
Ni
L L
H
+
R
NiL L
H
R
Ni
L L
H
R
NiL L
H
R
NiL L
R
H
Ni
L L
H
R
NiL L
HR
1a1b
2a
3a
2b
3b
5a6
9a
11a
13a14
9b
11b
13a
5b
R
+
Ni
L L
H
7
CH2
CH2
CH2
CH2
++
BHE
BHTBHT
PropagationPropagation
Isomerization
� R. Szeliga, A. Michalak, manuscript in preparation
∆E
0
10
-10
-20,0
1,73
7,05
-20.89
0.65
TS
TSTS
TS
TSTS
n - propyl iso - propyl
β, n β, izoπ,ag, p
π,ag, et π,ag, et
π,ag, p π,2H
π,2H
π π
-5.01 -5.01
β, et β, et
Insertion, isomerization, BHT – real system:Insertion, isomerization, BHT – real system:
10.38
6.696,49
6.73
14.77
0.01,03
Isomerization
π,H -1,46
-2,54
TS
-19,03
Propagation
secondary
BHT
secondary
BHT
primary
Propagation
primary
TS
-1,7
-18,43
β β
∆E = 9,03
Mn= 10 900 000
highly
overestimated
4,73 3,37
kINS / kBHT → E#BHT - E#
INS = 8,43 [kcal/mol]
k’INS / k’BHT → E#BHT’ - E#
INS’ = 9,03[kcal/mol]
ki / kBHT → E#BHT - E#
i = 2,07 [kcal/mol]
k’i / k’BHT → E#BHT’ - E#
i’ = 1,83 [kcal/mol]
Modelling molecular weight and termination mechanismsModelling molecular weight and termination mechanisms
Calculated energy differences:
kINS / kBHT → E#BHT - E#
INS = 6,1[kcal/mol]
k’INS / k’BHT → E#BHT’ - E#
INS’ = 5,0[kcal/mol]
ki / kBHT → E#BHT - E#
i = 6,1 [kcal/mol]
k’i / k’BHT → E#BHT’ - E#
i’ = 3,4 [kcal/mol]
‘Experimental’ energy differences:
Calculations prove the existence of two different
propagation and termination mechanisms
(qualitatively justify pressure dependence)
but the accuracy of the energy differences is insufficient to
quantitatively model the molecular weight
Polar copolymerization – diimine catalysts
Copolymerization of α-olefins with methyl acrylate
N^N-Pd+ - active
N^N-Ni+ - inactive
Diimine catalystsDiimine catalysts
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
Copolymerization of ethylene with methyl acrylate
N^N-Pd+ - active
N^N-Ni+ - inactive
(active in higher T)
Diimine catalystsDiimine catalysts
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
O OMe
MeO O
OMeO
MeO
O
OMeO
Ni-diimine catalyst:
Pd-diimine catalyst:
Copolymerization mechanism – acrylate insertionCopolymerization mechanism – acrylate insertion
� A. Michalak, T. Ziegler, „DFT Studies on the Copolymerization of a-Olefins with Polar Monomers: Ethylene-Methyl Acrylate Copolymerization Catalyzed by a Pd-based Diimine Catalyst”,
J. Am. Chem. Soc, 123, 2001, 12266-12278.
0
-10
-5
-15
-20
-25
-30
-35
-40
alkyl agostic
+acrylate
acrylate
ππππ complex
insertion TS
γγγγ−−−−agostic
ββββ-agostic
-20.7
+19.4
-18.5
-5.3
-20.7
CC
C
NN
O
O
C
Pd
C
CC
C
C
C C
N N
Pd
C
C
O
C
C
C
C
C
O
C C
N N
Pd
O
C
C
C
C
C
O
C
C
CC
NN
Pd
C C
C
O
CC
C
C
O
kcal/mol
Acrylate insertion (2,1-) – Pd catalystAcrylate insertion (2,1-) – Pd catalyst
� A. Michalak, T. Ziegler, J. Am. Chem. Soc, 123, 2001, 12266-12278.
0
-10
-5
-15
-20
-25
-30
-35
-40
alkyl agostic
+acrylate
acrylate
ππππ complex
insertion TS
γγγγ−−−−agostic
ββββ-agostic
-20.7
+19.4
-18.5
-5.3
-20.7
CC
C
NN
O
O
C
Pd
C
CC
C
C
C C
N N
Pd
C
C
O
C
C
C
C
C
O
C C
N N
Pd
O
C
C
C
C
C
O
C
C
CC
NN
Pd
C C
C
O
CC
C
C
O
kcal/mol
Acrylate insertion (2,1-) – Pd catalystAcrylate insertion (2,1-) – Pd catalyst
� A. Michalak, T. Ziegler, J. Am. Chem. Soc, 123, 2001, 12266-12278.
Real catalyst:
insertion barrier 12.4 kcal/mol
exp. ins. barrier 12.1 ± 1.4
0
-10
-5
-15
-20
-25
-30
-35
-40
alkyl agostic
+acrylate
acrylate
ππππ complex
insertion TS
γγγγ−−−−agostic
ββββ-agostic
4-memb.
chelate
5-memb.
chelate6-memb.
chelate
-20.7
+19.4
-18.5
-5.3
-8.5
-6.1
-1.1
-20.7
CC
C
NN
O
O
C
Pd
C
CC
C
C
C C
N N
Pd
CO
C
C
C
C
C
O
C
C C
C
N N
C
Pd
C
CO
C
C
C
O
C C
N N
Pd
CO
C
C
C
C
C
C
O
C C
N N
Pd
C
C
O
C
C
C
C
C
O
C C
N N
Pd
O
C
C
C
C
C
O
C
C
CC
NN
Pd
C C
C
O
CC
C
C
O
kcal/mol
Acrylate insertion (2,1-) – Pd catalystAcrylate insertion (2,1-) – Pd catalyst
� A. Michalak, T. Ziegler, J. Am. Chem. Soc, 123, 2001, 12266-12278.
0
-10
-5
-15
-20
-25
-30
-35
-40
alkyl agostic+acrylate
acrylate
ππππ complex
insertion TS
γγγγ-agostic
ββββ-agostic
4-memb. chelate
5-memb. chelate
6-memb. chelate
CC
C
NN
O
O
C
Pd
C
CC
C
C
C C
N N
Pd
CO
C
C
C
C
C
OC
C C
C
N N
C
Pd
C
CO
C
C
C
O
C C
N N
Pd
CO
C
C
C
C
C
C
O
C C
N N
Pd
C
C
O
C
C
C
C
C
O
C C
N N
Pd
O
C
C
C
CC
O
C
C
CC
NN
Pd
C C
C
O
CC
C
C
O
kcal/mol
Acrylate insertion (2,1-) - Pd and Ni catalystsAcrylate insertion (2,1-) - Pd and Ni catalysts
� A. Michalak, T. Ziegler, J. Am. Chem. Soc, 123, 2001, 12266-12278; Organometallics, 22 (2003), 2660-2669.
Two-step chelate openingTwo-step chelate opening
very high insertion barriers
lower for Ni-catalyst
low insertion barriers,
lower for Ni-catalyst
� A. Michalak, T. Ziegler, Organometallics, 22, 2003, 2660-2669. „A comparison of Ni- and Pd-diimine complexes as catalysts for Et / MA copolymerization. A static and dynamic density functional theory study”
Two-step chelate openingTwo-step chelate opening
very high insertion barriers
lower for Ni-catalyst
� A. Michalak, T. Ziegler, „DFT Studies on the Copolymerization of a-Olefins with Polar Monomers: Ethylene-Methyl Acrylate Copolymerization Catalyzed by a Pd-based Diimine Catalyst”,
J. Am. Chem. Soc, 123, 2001, 12266-12278.
� A. Michalak, T. Ziegler, „A comparison of Ni- and Pd-diimine complexes as catalysts for ethylene / methyl acrylate copolymerization. A static and dynamic density functional theory study”,
Organometallics, 22, 2003, 2660-2669.
� A. Michalak, T. Ziegler, „DFT Studies on the Copolymerization of a-Olefins with Polar Monomers: Ethylene-Methyl Acrylate Copolymerization Catalyzed by a Pd-based Diimine Catalyst”,
J. Am. Chem. Soc, 123, 2001, 12266-12278.
� A. Michalak, T. Ziegler, „A comparison of Ni- and Pd-diimine complexes as catalysts for ethylene / methyl acrylate copolymerization. A static and dynamic density functional theory study”,
Organometallics, 22, 2003, 2660-2669.
low insertion barriers,
lower for Ni-catalyst
Copolymerization mechanism
– catalyst-monomer complexes
Copolymerization mechanism
– catalyst-monomer complexes
� A. Michalak, T. Ziegler, „DFT Studies on the Copolymerization of a-Olefins with Polar Monomers: Comonomer Binding by Nickel- and Palladium-Based Catalysts with Brookhart and GrubbsLigands”, Organometallics, 20, 2001, 1521-1532.
� A. Michalak “Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
� A. Michalak, T. Ziegler, „DFT Studies on the Copolymerization of a-Olefins with Polar Monomers: Comonomer Binding by Nickel- and Palladium-Based Catalysts with Brookhart and GrubbsLigands”, Organometallics, 20, 2001, 1521-1532.
� A. Michalak “Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
Ni- (inactive):
σ−complex preferred
Pd- (active)
π−complex preferred
Preference of the π− / σ− complex
- theoretical catalyst screening test
π− / σ− complexesπ− / σ− complexes
ππππ−−−− / σ/ σ/ σ/ σ−−−− complexes: two reactant Fukui functionππππ−−−− / σ/ σ/ σ/ σ−−−− complexes: two reactant Fukui function
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
π− / σ− complexesπ− / σ− complexes
Methyl acrylate: molecular electrostatic potential
Electrostatic origin of the σσσσ−−−−complex preference for Ni-system
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
π− / σ− complexesπ− / σ− complexes
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
� A. Michalak „“Two-reactant Fukui function and molecular electrostatic potential analysis of the methyl acrylate binding mode in the complexes with the Ni- and Pd-diimine catalysts”, Chem. Phys.
Lett., 386, 2004, 346-350.
Electrostatic origin of the σσσσ−−−−complex preference for Ni-system
Copolymerization of ethylene with methyl acrylate
N^N-Pd+ - active
N^N-Ni+ - inactive
(active in higher T)
Diimine catalystsDiimine catalysts
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
Experimental data:
• Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267.
• Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888.
O OMe
MeO O
OMeO
MeO
O
OMeO
Ni-diimine catalyst:
Pd-diimine catalyst:
Chain isomerization
α−olefin polymerization mechanismα−olefin polymerization mechanism
Isomerization reactions in polar copolymerizationIsomerization reactions in polar copolymerization
O OMe
MeO O
influence on microstructure:
no isomerizations
O OMe
MeO Oisomerizations
after ethylene insertion
OMeO
MeO
O
isomerizations
after acrylate insertion
OMeO
MeO
O
OMeO
isomerizations after both, MA and Et insertion
RC
7.8
12.9
E [kcal/mol]
14A-Pd
14A-Ni
6A,6E-Ni, Pd Pd
Ni
non-polarpolar
10.4
14E-Pd
4.2
14E-Ni
8A,8E-Ni, Pd
The energy of hydride olefin complexes (isomerization’s intermediates)
with Pd- and Ni-catalysts.
Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005
TheThe profile profile ofof isomerizationisomerization for for NiNi--catalystcatalyst::
Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005
TheThe profile profile ofof isomerizationisomerization for for PdPd--catalystcatalyst::
Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005Mariusz Mitoraj, Artur Michalak, J. Mol. Model. , 2005, published on web, May 2005
ConclusionsConclusions
DFT:• understanding mechanistic details of the process;
• energetics in reasonable agreement with experimental data;
• understanding of the electronic and steric influence of the
catalysts substituents;
• relationship between the catalyst structure and the energetics
of the process
Stochastic (mesoscopic) simulations:• provide a link between the microscopic and macroscopic level
• identify the factors controlling of the polyolefin branching and
their microstructure
• demonstrates that a huge range of polyolefin materials with
specific microstructures can be rationally designed by
modification of the catalysts
• relationship between the energetics of the process, p, T, and
the polymer branching and microstructure
DFT:• understanding mechanistic details of the process;
• energetics in reasonable agreement with experimental data;
• understanding of the electronic and steric influence of the
catalysts substituents;
• relationship between the catalyst structure and the energetics
of the process
Stochastic (mesoscopic) simulations:• provide a link between the microscopic and macroscopic level
• identify the factors controlling of the polyolefin branching and
their microstructure
• demonstrates that a huge range of polyolefin materials with
specific microstructures can be rationally designed by
modification of the catalysts
• relationship between the energetics of the process, p, T, and
the polymer branching and microstructure
To be continued…
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