Kloster Banz (near Bamberg), Germany

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Dalton Discussion 4
Kloster Banz (near Bamberg), Germany 10-13
January 2002
INORGANIC REACTION MECHANISMS INSIGHT
INTO CHEMICAL CHALLENGES
Friday Morning, January 11, 2002.
T.Ziegler, Department of Chemistry University of
Calgary,Alberta, Canada T2N 1N4
TOOLS OF THE TRADE IN MODELING INORGANIC
REACTIONS. FROM BALLS AND STICKS TO HOMOs AND
LUMOs
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Elementary Reaction Steps
Inorganic reaction mechanisms describe
processes as a sequence of elementary reaction
steps
Each step connects by a minimum energy path
reactants (AB) with products ( CD). The maximum
energy point along the path is the transition
state TS.
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Experimental Work in Inorganic Reaction Mechanisms
Experimental work in inorganic reaction
mechanisms starting after WWII ( 1945 )
Fred Basolo
Ralph Pearson
Henry Taube
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Early Theoretical Work in Inorganic Reaction
Mechanisms
M.Dewar
R. Hoffmann
Van Vleck/Hartmann
Perturbational molecular orbital theory
Extended Hückel theory
Crystal-field stabilization energy
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Outline of Talk

• Generating a potential energy surface (PES) from
  quantum mechanical methods
• Walking on the PES
• Including solvation and steric bulk
• Excited state PESs

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Outline of Talk

• The determination of reaction rates from PESs
  by dynamical approaches based on trajectories
• The determination of reaction rates from PESs
  by statistical approaches

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Electronic Structure Theory and Potential Energy
Surfaces
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Electronic Structure Theory and Potential Energy
Surfaces, Wavefunction methods
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Electronic Structure Theory and Potential Energy
Surfaces Wave function methods
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Electronic Structure Theory and Potential Energy
Surfaces Kohn-Sham Density functional theory
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Electronic Structure Theory and Potential Energy
Surfaces Kohn-Sham Density functional theory
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Electronic Structure Theory and Potential Energy
Surfaces Geometries
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Modern Exc functionals
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Electronic Structure Theory and Potential Energy
Surfaces Bond Energies
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Electronic Structure Theory and Potential Energy
Surfaces Relativistic Effects
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Walking on the potential energy surfac
At minima (AB) and (CD) dE/dqi 0 d2E/dqi2 gt
0 qi i 1,3N-6 normal modes
Local minimum located by descending in
direction of forces Fqi -dE/dqi to
minimum energy
Forces Fqi -dE/dqi calculated analytically
(Pulay)
Locating global minimum difficult
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Walking on the potential energy surface
At minima TS dE/dqi 0 d2E/dqi2 gt 0 qi i
1,3N-5 normal modes d2E/dqRC2 lt 0
Locating TS still an art
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Brookhart Polymerization Catalyst

CEN Feb. 5, 1996
Polymer Catalyst System Dupont Eyes New
Polyolefin Business
Brookhart catalyst
highly linear to moderately branched

• temperature Temp ? branching ?
• monomer pressure Et ? branching ?
• bulk of substituents bulk ? branching ? MW ?

• high MWs
• good activities

Johnson, L. K. Killian, C. M. Brookhart, M. J.
Am. Chem. Soc. 1995, 117, 2343.
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Including Steric Bulk and Solvation Typical
Polymerization System
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Including Steric Bulk and SolvationTraditional
Computational Models
gas phase model system
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Linear Scaling and Combined Methods
1. Large region (white balls) lover level theory
(Molecular mechanics, Semi-emperical, low level
ab initio
2. Smaller region (colored balls) higher level
theory (DFT or wave function methods)
(a)A.Warshel, M.Levitt, J.Mol.Biol. 1976,103,227.
(b) U.C. Singh, P.A.Kollman J.Comput.Chem.
1986,7,718. (c) M.Field, P.A.Bash, M.Karplus,
J.Cimput. Chem. 1990,11,700.
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Linear Scaling and Combined Methods
1. Combining QM and MM
(d) F.Maseras, K.Morokuma J.Comput.Chem 1995,
16, 1170. (e)T.K.Woo, L.Cavello, T.Ziegler.
Theor.Chem.Acc. 1998,100, 307 D.Bakowies,
W.Thiel, J.Phys.Chem. 1996, 100, 10580.
2. Combining QM and QM
M.Svensson, S.Humbel, R.D.J.Froese, T.
Matsubara, S.Sieber, K.Morokuma J.Phys. Chem.
1996, 100, 19357
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L. Deng, P. M. Margl and T. Ziegler, Jacs 1997,
119, 1094-1100.
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L. Deng, T. K. Woo, L. Cavallo, P. Margl and T.
Ziegler, Jacs 1997, 119, 6177-6186.
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Experiment M. Brookhart, Jacs 1999 121
10634
Theory L. Deng, Jacs 1997, 119, 6177-6186.
Insertion Barrier Exp 13.5 kcal/mol QMMM 12
kcal/mol
Exp 13.5 kcal/mol
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Including Steric Bulk and SolvationContinuum
Model
1. COSMO Klamt, A. Schuurmann, G. J. Chem.
Soc. Perkin Trans. 1993, 2, 799. 2. PCM
Tomasi, J. Chem. Rev. 1994, 94, 2027.
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Including Steric Bulk and Solvation Explicit
Solvent Model
Molecular-dynamics Or Monte-Carlo
1. Allen, M. P. Tildesley, D. J. Computer
Simulation of Liquids Oxford University Press
Oxford, 1987. 2. Gao, J. in Reviews in
Computational Chemistry K. B. Lipkowitz and D.
B. Boyd, Ed. VCH New York, 1996 Vol. 7.
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Including Steric Bulk and Solvation Explicit
Solvent Model
Ornstein-Zernike Equation
Ornstein and Zernike
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1. Crystal Field Theory 1950 2 HF ab initio
theory 1972 Hillier Saunders
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Exited States
1. TD-DFT M.Petersilka, U.J.Grossmann,E.K.U.Gro
ss Phys.Rev.Lett, 1996,
2. D-SCF DFT (Geometry optimization
possible) T.Ziegler, A.Rauk, E.J.Baerends, Theor.
Chim. Acta. 1977, 43, 261.
3. Symmetry-adapted Cluster Configuration
Interaction (SAC-CI) H.Nakai, Y.Ohmori,
H.Nakatsuji, J.Chem.Phys. 1991, 95. 8287
4.Complete Active Space Second-order Perturbation
Theory (CASPT2). K.Andersson,P.Å.
Malmqvist,B.O.Ross. J.Chem.Phys. 1992,96,1218.
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Exited States
Excitation Energies for Ni(CO)4 (eV)
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Determination of Reaction Rates from the
Potential Energy Surface
1. Reaction rates are macroscopic averages over
a large number of "chemically identical systems"
passing with different initial velocities from
the reactant valley to the product valley.
2 In order to determine the rates one must
either perform a large number of trajectories in
a dynamic approach or introduce statistical
theories based on ensamble distributions.
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Determination of Reaction Rates from the
Potential Energy Surface Classical trajectories
with empirical or first principle PES's.
In classical trajectory calculations the nuclei
are allowed to move on the potential surface
according to Newton's classical laws of motion
Thus, the position of particle i at time can be
deduced from the position, velocity and force at
as
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Determination of Reaction Rates from the
Potential Energy Surface Classical trajectories
with empirical or first principle PES's.
1. This method has not been used much for
inorganic systems where empirical PES are
unreliable in the transition state region of
reactions involving bond making and bond
breaking.
2.Use could have been made of PES's from
electronic structure calculation. However,
fitting multi-dimensional functions with more
than two nuclei is a formidable and in practice
intractable task.
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Conventional QM Molecular Dynamics
Car-Parrinello Molecular Dynamics
Time
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Conventional QM Molecular Dynamics
Car-Parrinello Molecular Dynamics
Time
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First Principle Molecular Dynamics
Full Dynamics
Along IRC
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Quantum Dynamics with Fitted or Empirical
PES's..
Quantum dynamics makes use of the
time-dependent Schrödinger equation for a system
of N nuclei with the potential energy E.
The method is only feasible for up to 3 nuclei.
However, for larger molecules the remaining
degrees of freedom can be treated as
'background'"
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Quantum Dynamics with Fitted or Empirical
PES's..
1. Absorption of H2 on metal surfaces. E. Pijper,
G.J. Kroes, R.A. Olsen ,E.J. Baerends J. Chem.
Phys. 2000,113,8300
2. Exchange of hydrogen between hydride and
di-hydrogen ligands A.Jarid, M.Moreno, A.Lledos,
J.M.Lluch, J.Bertran J.Am.Chem.Soc.
1993,115,5861.
3. Photo-dissociation of H2 or H from metal
complexes (c) M.-C. Heitz, C. Daniel
J.Am.Chem.Soc. 1997 119 8269
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Statistical Approach to the Calculation of
Reaction Rates Eyring Transition State Theory
The most well known statistical approach to the
calculation of reaction rates is the transition
state theory by Eyring in which the degrees of
freedom perpendicular to the reaction coordinate
at the transition state are assumed to be in
thermal equilibrium with degrees of freedom of
reactants and products.
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Statistical Approach to the Calculation of
Reaction Rates Eyring Transition State Theory
In conventional transition state theory is
evaluateda at the saddle point of the PES of
the reaction using standard expressions from
statistical mechanics based on the relative
energies, vibrational frequencies, total masses
and moment of inertia of reactants, transition
states, and products. (a) W.J.Hehre, L.Radom,
P.v.R. Schleyer, J.A.Pople, Ab Initio Molecular
Orbital Theory, Wiley, New York, 1986.
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Statistical Approach to the Calculation of
Reaction Rates Variational Transition State
Theory
In the variational transition state theory
(VTST) by Truhlar is taken at the top of a
minimum free energy path (MFEP) that connects
reactants and products rather than at the top of
the MEP.
B.C.Garrett, D.G.Truhlar J.Chem.Phys.
1979,70,1593
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Statistical Approach to the Calculation of
Reaction Rates Eyring Transition Theory.
Evaluation
Many applications to transition metal chemistry.
No systematic validation 1. Ligand
substitution reactions, 2. insertion reactions
3. Oxidative addition 4. nucleophilic and
electrophilic attack 5. Metallacycle formation
and surface chemistry.
Higher accuracy than 5 kcal/mol for reaction
barrier requires CCSD(T) or GGC DFT
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Reaction free energies
assumed reaction coordinate dynamics with
constraint for points on assumed RP free
energy change obtained by integration of the
force on constraint (thermodynamic integration)
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Intrinsic reaction path (IRP)
Steepest descent path in mass-weighted coordinates
Fukui, K. Acc. Chem. Res. 1981, 14, 363.
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Slow growth simulations
TS
the reaction coordinate l is changed in a
continuous manner
min.
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A QM/MM study of Monomer Capture in Brookharts
Catalyst
RH
RMe
indirect steric effect
R substituent effect found to be both electronic
and steric effect
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Concluding remarks about potential energy surfaces
1. It is possible to describe the potential
energy surface of a gas phase molecule
containing up to 10 atoms with great accuracy
using high level wave function methods such as
CCSD(T) (ground state) or CASSPT2/SAC-CI (excited
states)
2. For larger systems acceptable accuracy can be
obtained by DFT (ground state) or
TD-DFT/DSCF-DFT (excited states)
3. Steric bulk can be introduced by combining QM
and MM
4. No accurate solvation method. Continuum model
best choice
5. Relativistic methods makes it possible to
treat all elements
6. Excited State Dynamics Emerging
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Concluding remarks about rate determination
from Knowledge of the PES
1. The majority of cases will be determined with
the help of Eyring's transition state method. To
this end, locating saddle points on the PES is
still time consuming in terms of manpower, and
more systematic and automated procedures would be
welcome
2. Standard applications will not be possible for
reactions without an enthalpic barrier (most
radical recombination processes and acid base
reactions or for reactions with many low
frequency modes (such as processes in solution
with several explicit solvent molecules
included, nucleation and folding of large
molecules). In those cases the free energy of
activation will have to be determined from
methods based on thermodynamic integration
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Collaborators
Peter Margl
Rochus Schmid
Artur Michalak
Tom Woo