quantum chemical molecular modellingmichalak/mmod2008/l12.pdf · 2009. 1. 13. · quantum chemical...

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



- 165 M tons

Various classes of polyethylenes:

HDPE, LDPE, LLDPE

- size of macromolecules: molecular weight, molecular weight distribution


n

Etylene:

...



- 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


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 :







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


• 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)


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:


Linear chain



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


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:


Linear chain



n

Propylene:

n

Propylene:

n

Etylene:

n

Etylene:


Linear chain



β-agostic

π-complex

+ ethylene

β-agostic

γ-agostic

insertion

Ethylene polymerization mechanismEthylene polymerization mechanism

n

Propylene:

n

Etylene:


Linear chain

α-olefin polymerization mechanismα-olefin polymerization mechanism

n

Propylene:

n

Etylene:


Linear chain




Chain isomerization


•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


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



• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2

CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2

CC

NN

Pd

R R

Ar Ar

+

CC

CC

NN

Pd





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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





• 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


• R2 = An; Ar = H

• R2 = An; Ar = Ph (i-Pr)2



• 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


• 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

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


Primary C attached to the catalyst:

1) 1 possible isomerization

2) olefin capture and 1,2- insertion


4) termination


1

2

3

4

Secondary C attached to the catalyst:

1) isomerization to primary C

2) isomerisation to secondary C



5) termination



1) isomerization to secondary C




5) termination



1) isomerization to primary C




5) termination



1) isomerization to secondary C



4) termination



1) isomerization to tertiary C



4) termination


ProbabilitiesProbabilities

][ 01,1 βisokr =

][ 02,2 βisokr =

β0 , β1 , β2 β-agostic complexes

Basic assumption:

Relative probabilities (microscopic)

= relative reaction rates (macroscopic)

Basic assumption:



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:



Basic assumption:



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



R = H; Ar = H

CC

NN

Pd


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



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


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





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


Simulations from theoretical data


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


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






68

p









69

p





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


0

100

200

300

400

500

600

0.0001 0.001 0.01 0.1 1


0

100

200

300

400

500

600

0.0001 0.001 0.01 0.1 1


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.


� 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


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:


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


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:


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:


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:


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:



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




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




NiL L

R

H

CH2

CH2

NiL L

R

NiL L

R

+

kINS

K

TS

propagation:

NiL L

H

R

isomerization:


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


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:



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:



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:



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:



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)




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

++

++

=






� 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 =






- 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

+

+=






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

+=






- 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.






1

'

3

'

13

'

23

1

'

2

'

12

'

22

kkkkpkk

kkkkpkkR

++

++=





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


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:


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


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


∆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


INS = 8,43 [kcal/mol]




i = 2,07 [kcal/mol]




Calculated energy differences:


INS = 6,1[kcal/mol]




i = 6,1 [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


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:



Copolymerization of ethylene with methyl acrylate

N^N-Pd+ - active

N^N-Ni+ - inactive

(active in higher T)


Experimental data:



Experimental data:



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


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



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


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



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,


� 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



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.


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,


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.


Lett., 386, 2004, 346-350.


Methyl acrylate: molecular electrostatic potential

Electrostatic origin of the σσσσ−−−−complex preference for Ni-system


Lett., 386, 2004, 346-350.


Lett., 386, 2004, 346-350.



Lett., 386, 2004, 346-350.


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)


Experimental data:



Experimental data:



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::


TheThe profile profile ofof isomerizationisomerization for for PdPd--catalystcatalyst::


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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