Thursday Februar 22, 2007
19.00 - 21.00 pm.
Prof. Tom Ziegler - Department of Chemistry
University of Calgary-Calgary,Alberta,Canada T2N 1N4
Density Functional Theory. Approaching Chemistry
from First Principle
Early Atomic Theory
400 b.c.
John Dalton
(1766 - 1844 )
Joseph Louis Gay-Lussac,
Memoires de la Societe
d'Arcueil 2:207 (1808)
"We are perhaps not far removed from
the time when we shall be able to
submit the bulk of chemical phenomena
to calculation."
-
- A. Comte,
Philosophie Positive,
1830.
"Every attempt to employ
mathematical methods in the study of
chemical questions must be considered
profoundly irrational and contrary to
the spirit of chemistry.
Atomic Theory
Nield Bohr
(1885-1962)
Ernest
Rutherford
(1871-1937)
Quantum Wave-Mechanics
1926
H(ri)ψ(ri)= Eψ(ri)
i=1,3N
Erwin Rudolf
Josef Alexander
Schrödinger
1887-1961
Werner
Karl
Heisenberg
1901-1976
H(ri)!(ri)= E!(ri)
i=1,3N
`P.A.M. Dirac
(1929)
"The underlying physical laws necessary
for the mathematical theory of..the whole
of chemistry are thus completely known,
and the difficulty is only that the exact
application of these laws leads to
equations much to complicated to solve."
n! Exact Quantum
H(ri)!(ri)= E!(ri)
Wave-Mechanics
C6H6 (2000)
i=1,3N
H2 (1956)
Time required
n! with
H2+ (1929) number of
electrons
n
H (1926)
He (1930)
Development
Electron Correlation ?
Exchange-correlation hole ?
? ?
Approximate Quantum Wave-Mechanics
Some theories are too
true to be good
Hartree
Atomic Theory
R.K.Mullikan
Molecular Orbital theory
Some too good
to be true
L.Pauling
Valence Bond theory
J. Pople
Systematic Improvements
Approximate Wave mechanics
log(t)
Dead End
Quadratic CI ( 10 atoms)
4
2
Møller-Plesset (100 atoms)
Hartree Fock (2000 atoms)
Density Functional theory
Thomas-Fermi-Dirac (1929)
Model expression of total energy in
terms of electron density
Fermi
E(ρ)
Kohn-Hohenberg-Sham
(1964)
Exact relationship between electron
density and molecular energy ..
..but, form of relationship not known
W. Kohn
E(ρ)
Exchange-correlation hole ?
? ?
Approximate density
functional theories
for exchange and correlation
HFS
Local exchange
LSD
Local exchange +
Local correlation
LSD/NL
Local exchange +
Local correlation
+ Nonlocal corrections
Exchange energy
from electron gas
Exchange+correlation
from electron gas
Nonlocal Exchange:
Becke,A.D. Phys.Rev. 1988,A38
Nonlocal Correlaion
Perdew,J. Phys.Rev. 1986,B33
Program Implementations for first
generation DFT
1973-1983
DFT Underground
Calgary
Montreal
A'dam
Florida
Excellent Molecular geometries and electronic properties
Poor bond and atomization energies
Second generation Gradient Corrected Functionals
Axel Becke
Queens
University
1983-1992
John
Perdew
Tulane
Implementations for second
generation DFT 1983-1993
DFT-underground
Calgary
Montreal
Chicago
San Diego
A'dam
Zurich
Florida
Excellent Molecular geometries and electronic properties
Good bond and atomization energies
Many properties
Nobel Prizes in Chemistry
1998
Walter Kohn
E(ρ)
John Pople
E = <ψ|Η|ψ>
JACOBS LADDER OF DFT
Rung 5
H" = E"
QUANTUM
MECHANICAL
HEAVEN
2
Rung 4
E( ",#",# ")
+HF
2
Hyper-GGA
Meta-GGA
Rung 3
E( ",#",# ")
Rung 2
E( ",#")
GGA
E( ")
LDA
! 1
Rung
!
CO
Fe
OC
OC
Cr
CO
CO
CO
Relativity and Structure
Method
LDA
NL-SCF
NLSCF+QR
MP2
CCSD(T)
Exp
Cr(CO)6
M-C
C-O
1.866
1.910
1.910
1.883
1.939
1.918
1.145
1.153
1.153
Mo(CO)6
M-C
C-O
W(CO)6
M-C
C-O
2.035
2.077
2.060
2.116
2.076
1.144
1.152
1.153
2.049
1.144
1.154
1.155
1.168
1.178
2.066
1.164
2.054
1.166
1.141
2.063
1.145
2.058
1.148
H(ri)!(ri)= E!(ri)
i=1,3N
`P.A.M. Dirac
(1929)
"..that relativistic effects are “of no
importance in the consideration of atomic and
molecular structure and ordinary chemical
reactions.”
"
that relativistic effects are “of no importance in
the consideration of atomic and molecular
structure and ordinary chemical reactions.”
[P.A.M. Dirac, Proc. R. Soc., London Ser. A
1929, 123, 714.]
O
O
C
O
77.7°
77.6°
C
96.0°
96.1°
Fe
116.8
117.6
C
O
C
252.3
252.3
C
Fe
C
O
C
C
O
201.1
201.6
O
O
182.5
183.6
C
114.8
115.6
O
NL - SCF
Experiment
Biological
BiologicalMolecules
molecules
Metal
MetalSurfaces
Surfaces
Solids
Solids
Calculated and Experimental First Bond
Dissociation Energies (kcal/mol) for M(CO) 6
.
Cr(CO)6
Mo(CO) 6
W(CO) 6
LDA
NL-SCF
NL-SCF+QR
MP2
CCSD(T)
62.1
45.9
46.2
58.0
45.8
52.7
38.2
39.7
46.1
40.4
48.4
38.8
43.7
54.9
48.0
Exp
43.8 ±2
40.5 ±2
46.0 ±2
H(ri)!(ri)= E!(ri)
i=1,3N
`P.A.M. Dirac
(1929)
"..that relativistic effects are “of no
importance in the consideration of atomic and
molecular structure and ordinary chemical
reactions.”
"
that relativistic effects are “of no importance in
the consideration of atomic and molecular
structure and ordinary chemical reactions.”
[P.A.M. Dirac, Proc. R. Soc., London Ser. A
1929, 123, 714.]
Biological molecules
( Hydrogen Bond Strength)
Metal Surfaces
(Adsorption Energies)
Solids
(Cohesive Energy)
Excitations
Electronic Spectrum of Permanganate
Exp
Calc
Baerends et al. J.C.P 2005
Vibrations
Spin-flip
NMR/ESR
Spin-spin coupling
NMR/ESR
Results I : scalar ZORA
Tungsten
compounds
W(CO)6
W(CO)5PF3
W(CO)5PCl3
W(CO)5WI3
cp-W(CO)3H
WF6
J.Autschbach , T. Ziegler,
JCP (2000), 113.9410
C om p ou n d C ou p l i n g
W (CO)6
W -C
W (CO)5PF3
W -P
W (CO)5PCl 3 W -P
W (CO)5PCI 3 W -P
CpW (CO )3H W -H
W F6
W -F
K (N R ,G G A)
K (Z o r a, LD A ) K (Z o r a, G G A ) K (Ex p )
603
1726
985
2383
1997
1688
103
-96
1126
972
26
151
1001
2435
997
2380
2041
1745
96
-94
2090
1639
73
87
Biological molecules
( ESR of metallo-proteins)
Metal Surfaces
(Ir of absorbed molecules)
Solids
(NMR of Solids)
Astronomy
(Molecules in out-space)
Static DFT:
Walking on the potential energy surface
Energy
E
TS
A+B
C+D
Reaction Coordinate
RC
SN2 reaction: Cl- + CH3Cl → Cl-CH3 + Cl-
Cl- + CH3Cl
Thermolized canonical
molecular dynamics.
Constant T,V,N.
T=O
TS
Cl-CH3 + Cl-
SN2 reaction: Cl- + CH3Cl → Cl-CH3 + Cl-
Cl- + CH3Cl
IRC-MD (P → TS → P):
Thermolized canonical
molecular dynamics.
Constant T,V,N.
T>O
TS
Cl-CH3 + Cl-
Brookhart Polymerization Catalyst
C&EN Feb. 5, 1996:
iPr
“Polymer Catalyst System:
Dupont Eyes New Polyolefin
Business”
R
R
N
+
iPr
N
Ni
iPr
R
iPr
Brookhart
catalyst
highly linear to moderately branched
• high MWs
• good activities
•
temperature: Temp ↑ branching ↑
•
monomer pressure: [Et] ↑ branching ↓
•
bulk of substituents: bulk ↑ branching ↑ MW ↑
Johnson, L. K.; Killian, C. M.; Brookhart, M. J. Am. Chem. Soc. 1995, 117, 2343.
Including Steric Bulk and Solvation :
Typical Polymerization System
Cl
H
H
Cl
Cl
H
H
Cl
Cl Cl
H
H
Cl
iPr
H
Cl
Cl
H
H
Cl H
H
Cl
Cl
H
iPr
Cl
C
N
+
N
Cl
Ni
iPr
H
H
H
C
BCl
Cl
iPr
Cl
Cl
Cl
H
Cl H
Cl
H
H
Cl H
Cl
HH
H
Cl
H
Cl
Cl
H
Cl
Cl
H
H Cl
H
Cl
H
H
Cl Cl
H
H
Polar copolymerization – diimine catalysts
Including Steric Bulk and Solvation
Traditional Computational Models
no substituents
no counter-ion
H N
+
N H
Ni
gas phase
model system
no solvent
0 K simulation
(static)
L. Deng, T. K. Woo, L. Cavallo,
P. Margl and T. Ziegler,
Jacs 1997, 119, 6177-6186.
Including Steric Bulk and Solvation
Continuum Model
_
+
+
+
+
_
+
+
+
+
_
+
_
_
QM solute
_
+
+
+
_
+
_
_
+
+
QM solute
+
+
+
+
_
_
_
_
+
+
+
_
+
continuum
_
+
b
_
a
explicit solvent
+ +
+
_
_
+
_
+
+
1. COSMO : Klamt, A.; Schuurmann, G. J. Chem. Soc. Perkin
Trans. 1993, 2, 799.
2. PCM : Tomasi, J. Chem. Rev. 1994, 94, 2027.
A QM/MM study of Monomer Capture in Brookhart’s Catalyst
Ni
Ni
R=Me
R=H
indirect steric effect
R’ substituent effect found to be both electronic and steric effect
Woo,Ziegler J,Phys.Chem. A,1997
PRF
Mitsui
Moving to Calgary Canada
Calgary Skyline
University of Calgary
Banff Rocky Mountain National Park
Full Simulated CD Spectrum for [Os(phen)3]2+
Autschbach et al. J. Phys.Chem. A 2005, 109, 4836