Title: Modeling of the Counterion, B(C6F5)3CH3-, with the QM/MM Method and its Application to Olefin Polymerization
1Modeling of the Counterion, B(C6F5)3CH3-, with
the QM/MM Method and its Application to Olefin
Polymerization
- Kumar Vanka and Tom Ziegler
- University of Calgary
2Introduction
- Inclusion of solvent and counterion effects are
important in theoretical studies of single site
olefin polymerisation catalyst systems. - The large size of the activators and counterions
B(C6F5)3CH3-, B(C6F5)4- etc. used, makes full
quantum chemical studies of these systems time
consuming and expensive. - The present study attempts to solve the problem
by modeling the counterion B(C6F5)3CH3- using the
QM/MM (Quantum mechanics - Molecular Mechanics)
method. - The model used is tested by comparison of full QM
to QM/MM calculations for ion-pair systems of the
type L1L2MMe B(C6F5)3CH3- L1, L2 NPH3,
NCMe2 etc. M Zr, Ti Me CH3. - The developed QM/MM model is then employed in
studies of olefin uptake and insertion processes
for the different ion-pair systems.
3Computational Details
- The density functional theory calculations were
carried out using the Amsterdam Density
Functional (ADF) program version 2000.01.1
Geometry optimizations were carried out using the
local exchange-correlation potential of Vosko et
al.2 A triple-zeta basis set was used to describe
the outermost valence orbitals for the titanium
and zirconium atoms, whereas a double-zeta basis
set was used for the non-metals. The frozen core
approximation was used to treat the core orbitals
of all atoms. The gas phase energy differences
between stationary points were calculated by
augmenting the LDA energy with Perdew and Wangs
non-local correlations and exchange corrections.3
The energy differences in solution was corrected
from the gas phase energies by accounting for the
solvation calculated by the Conductor-like
Screening Model (COSMO).4 The solvation energy
calculations were carried out with a dielectric
constant of 2.023 to represent cyclohexane as the
solvent. The code for QM/MM has been incorporated
into ADF by Woo et al.5
1. (a) Baerends, E. J. Ellis,D.E. Ros, P. Chem.
Phys. 1973, 2, 41. (b) Baerends, E. J. Ros, P.
Chem. Phys. 1973, 2,52. 2. Vosko, S. H. Wilk,
L. Nusair, M. Can. J. Phys. 1980,58, 1200. 3.
Perdew, J. P. Phys. Rev. B 1992, 46, 6671. 4.
Pye, C. C. Ziegler, T. Theor. Chem. Acc. 1999 V
101, 396. 5. Woo. T. K. Cavallo, L. Ziegler,
T. Theor. Chim. Acta 1998, 100,307.
4Model Investigated
B(C6F5)3CH3- was substituted with BCl3CH3- in the
QM portion and the phenyl groups modeled with MM
atoms.
5Testing Model on Different Titanium Based
Catalyst Systems
- Catalyst DHipfQM
DHipfQMMM DHipsQM DHipsQMMM - kcal/mol
kcal/mol kcal/mol kcal/mol - (NPH3)2TiMe -22.3
-21.0 81.8 93.6 - (Cp)OSiH3TiMe -10.4
-10.2 93.6 105.3 - (Cp)SiMe2NMeTiMe -13.3 -15.1
90.4 102.6 - (Cp)NCMe2TiMe -24.1
-21.9 87.4 97.6 - (Cp)TiMe2 -12.9
-11.0 95.3
107.8 - (Cp)SiH2(NH)TiMe -13.9
-11.2 94.4 105.0 - (Cp)2TiMe -15.5
-15.4 79.5
94.1
The model was tested by comparing the gas phase
DHipf (enthalpy of ion-pair formation) and DHips
(enthalpy of ion-pair separation) for full QM
calculations on ion-pairs of the type
L1L2TiMe B(C6F5)3CH3- and calculations done
using the QM/MM model for the counterion. While
the DHipf values were quite similar, the
corresponding DHips were higher in the QM/MM
case by 15-20 kcal/mol
6Testing Model on Different Zirconium Based
Catalyst Systems
- Catalyst DHipfQM
DHipfQMMM DHipsQM DHipsQMMM - kcal/mol
kcal/mol kcal/mol kcal/mol - (1,2Me2Cp)2ZrMe -22.8
-24.8 80.5 95.6 - (Cp)2ZrMe -19.1
-18.7 88.5
99.5 - (Cp)ZrMe2 -15.7
-13.3 93.3
103.3 - (Cp)SiH2(NH)ZiMe -16.6
-13.1 92.4 106.2
The corresponding calculations for DHipf and
DHips were done with zirconium based catalyst
systems. Results, similar to the titanium based
systems were obtained.
7Inclusion of Solvent Effects
- Catalyst DHipsQM DHipsQMMM
- kcal/mol kcal/mol
- (NPH3)2TiMe 45.8
48.9 - (Cp)OSiH3TiMe 56.3
61.9 - (Cp)SiMe2NMeTiMe 55.4 61.7
- (Cp)NCMe2TiMe 52.4
55.6 - (Cp)TiMe2
58.2 62.8 - (Cp)SiH2(NH)TiMe 54.6
61.0 - (Cp)2TiMe
47.1 52.3
The difference in the gas phase values for DHips
between the full QM and the QM/MM calculations
was reduced when solvent effects were considered.
On doing single point calculations with
cyclohexane as the solvent, the differences in
DHips between the QM and QM/MM systems was
reduced to about 5 kcal/mol.
8Inclusion of Solvent Effects
- Catalyst DHipsQM DHipsQMMM
- kcal/mol kcal/mol
- (1,2Me2Cp)2ZrMe 49.6 54.1
- (Cp)2ZrMe 50.2 56.8
- (Cp)SiH2NHZrMe 51.8 58.4
- (Cp) ZrMe2 51.6
59.7
The corresponding calculations with the zirconium
based catalyst systems gave analogous results.
The inclusion of solvent effects reduced
the difference between full QM and QM/MM
calculations to about 5-7 kcal/mol.
9Comparison in the Insertion region
DHits
DHc
Insertion Transition State
Ethylene p complex
For the modeling to be considered successful, the
QM/MM model has to perform satisfactorily in the
insertion region, i.e., it has to compare
favourably with full QM calculations for the
momomer (ethylene) complexation and insertion
into the metal alkyl bond. The enthalpies of
ethylene complexation and for the insertion
transition state were termed DHc and DHits
respectively.
10Comparison in the Insertion region
DHc
DHits
Comparative calculations in the insertion region
were done for the (NPH3)2TiMe B(C6F5)3CH3-
system. The QM/MM calculations compared
favourably with the corresponding calculations
for the full QM system.
Full QM Calculation 1.51 kcal/mol
DHc
QMMM Calculation -0.73 kcal/mol
Full QM Calculation 5.90 kcal/mol
DHits
QMMM Calculation 4.00 kcal/mol
11Catalyst Systems Studied with QMMM Model
(NPR3)2TiMe B(C6F5)3CH3- R Hydrogens,
tert-butyl groups
CpNCR2TiMeB(C6F5)3CH3- R hydrogens,
tert-butyl groups
The validated QM/MM model was then employed to
study ethylene complexation and insertion
processes in different catalyst systems, shown
above. The tertiary butyl groups on the cation
were modeled with MM atoms. Results are discussed
in the next few slides.
12Cis Attack of Ethylene for the (NPR3)2TiMe
System
(NPR3)2TiMe B(C6F5)3CH3- R
tert-butyl groups
(NPR3)2TiMe B(C6F5)3CH3- R
Hydrogens
DHc 1.79 kcal/mol
DHc 8.41kcal/mol
DHits 3.24 kcal/mol
DHits 1.93 kcal/mol
The approach of the ethylene cis to the methide
bridge of the titanium to the counterion, was
considered for complexation and insertion studies
on the (NPR3)2TiMe B(C6F5)3CH3- system, with
different R groups. Results indicated that
increasing steric bulk on the cation increased
the total barrier to the ethylene insertion into
the Ti-alkyl bond.
13Trans Attack of Ethylene for the (NPR3)2TiMe
System
(NPR3)2TiMe B(C6F5)3CH3- R
Hydrogens
(NPR3)2TiMe B(C6F5)3CH3- R
tert-butyl groups
DHc -0.73 kcal/mol
DHc 11.26 kcal/mol
DHits 3.99 kcal/mol
DHits 3.43 kcal/mol
The approach of the ethylene trans to the methide
bridge of the titanium to the counterion, was
considered next, for complexation and insertion
studies on the (NPR3)2TiMe B(C6F5)3CH3-
system, with different R groups. Results analogus
to the cis case were obtained. For the case of
the cation with bulky groups, the ethylene
preferred the cis pathway over the trans, the net
barrier to insertion being 4.35 kcal/mol less.
14Cis Attack of Ethylene for the CpNCR2TiMe
System
CpNCR2TiMeB(C6F5)3CH3- R
hydrogens
CpNCR2TiMeB(C6F5)3CH3- R
tert-butyl groups
DHc 5.25 kcal/mol
DHc 10.18 kcal/mol
DHits 7.04 kcal/mol
DHits 3.16 kcal/mol
Calculations for the cis approach of the ethylene
was considered next for the CpNCR2TiMeB(C6F5)
3CH3- system. Analogous to the previous case,
increasing steric bulk on the cation increased
the barrier to insertion.
15Trans Attack of Ethylene for the CpNCR2TiMe
System
CpNCR2TiMeB(C6F5)3CH3- R
tert-butyl groups
CpNCR2TiMeB(C6F5)3CH3- R
hydrogens
DHc 11.36 kcal/mol
DHc 9.38 kcal/mol
DHits 4.99 kcal/mol
DHits 3.45 kcal/mol
The corresponding trans attack of the ethylene
monomer was also considered for the
CpNCR2TiMeB(C6F5)3CH3- system. As before,
increasing the steric bulk increased the barrier
to insertion. For the case of the cation with
bulky groups, the ethylene preferred the cis
pathway over the trans, the net barrier to
insertion being 3.01 kcal/mol less.
16Conclusions
- The counterion, B(C6F5)3CH3-,was modeled with the
QM/MM method - The model was successfully validated with
calculations comparing full QM and QM/MM
calculations - The validated model was then used in ethylene
complexation and insertion studies of different
catalyst systems
Acknowledgements
This research was supported by the Natural
Sciences and Engineering Research Council of
Canada (NSERC) and Novacor Research and
Technology Corporation.