Choose start coefficients for MO’s
2.
Construct Fock Matrix with coefficients
3.
Solve Hartree-Fock-Roothaan equations
4.
Repeat 2 and 3 until ingoing and outgoing
coefficients are the same
Self-Consistent-Field
(SCF)
(SCF)
S
F
i
i
i
c
c

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25
Semi-empirical methods
(MNDO, AM1, PM3,
etc.)
Semi-empirical methods
(MNDO, AM1, PM3,
etc.)
Full CI
Full CI
perturbational
hierarchy
(CASPT2, CASPT3)
perturbational
hierarchy
(CASPT2, CASPT3)
perturbational
hierarchy
(MP2, MP3, MP4, …)
perturbational
hierarchy
(MP2, MP3, MP4, …)
excitation
hierarchy
(MR-CISD)
excitation
hierarchy
(MR-CISD)
excitation
hierarchy
(CIS,CISD,CISDT,...)
(CCS, CCSD, CCSDT,...)
excitation
hierarchy
(CIS,CISD,CISDT,...)
(CCS, CCSD, CCSDT,...)
Multiconfigurational HF
(MCSCF, CASSCF)
Multiconfigurational HF
(MCSCF, CASSCF)
Hartree-Fock
(HF-SCF)
Hartree-Fock
(HF-SCF)
Ab Initio
Methods
Ab Initio
Methods

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Who’s Who

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27
Size vs Accuracy
Size vs Accuracy
Number of atoms
0.1
1
10
1
10
100
1000
Accuracy (kcal/mol)
Coupled-cluster,
Multireference
Nonlocal density functional,
Perturbation theory
Local density functional,
Hartree-Fock
Semiempirical Methods
Full CI

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28
R
OO,e
= 291.2 pm
96.4 pm
95.7 pm
95.8 pm
symmetry: C
s
Equilibrium structure of (H
Equilibrium structure of (H
2
O)
O)
2
W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and
W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and
F.B. van Duijneveldt,
F.B. van Duijneveldt,
Phys. Chem. Chem. Phys.
Phys. Chem. Chem. Phys.
2
, 2227 (2000).
, 2227 (2000).
Experimental [J.A. Odutola and T.R. Dyke,
J. Chem. Phys
72
, 5062
(1980)]:
R
OO
2
½
= 297.6 ± 0.4 pm
SAPT-5s potential [E.M. Mas
et al
.,
J. Chem. Phys.
113
, 6687 (2000)
]:
R
OO
2
½
–
R
OO,e
= 6.3 pm
R
OO,e
(exptl.) = 291.3 pm
AN EXAMPLE

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29
Experimental and Computed
Enthalpy Changes
H
e
in
kJ/mol
Enthalpy Changes
H
e
in
kJ/mol
Exptl.
CCSD(T)
SCF
G2
DFT
CH
4
CH
2
+ H
2
544(2)
542
492
534
543
C
2
H
4
C
2
H
2
+ H
2
203(2)
204
214
202
208
H
2
CO
CO + H
2
21(1)
22
3
17
34
2 NH
3
N
2
+ 3 H
2
164(1)
162
149
147
166
2 H
2
O
H
2
O
2
+ H
2
365(2)
365
391
360
346
2 HF
F
2
+ H
2
563(1)
562
619
564
540
Gaussian-2 (G2)
method of Pople and co-workers is a combination of MP2 and QCISD(T)

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30
LCAO
Basis Functions
LCAO
Basis Functions
’s, which are atomic orbitals, are called basis
functions
usually centered on atoms
can be more general and more flexible than
atomic orbital functions
larger number of well chosen basis functions
yields more accurate approximations to the
molecular orbitals
c

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31
Basis Functions
Basis Functions
Slaters (STO)
Gaussians (GTO)
Angular part *
Better behaved than Gaussians
2-electron integrals hard
2-electron integrals simpler
Wrong behavior at nucleus
Decrease too fast with
r
r)
exp(
2
n
m
l
r
exp
*
z
y
x

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32
Contracted Gaussian Basis
Set
Contracted Gaussian Basis
Set
Minimal
STO-nG
Split Valence: 3-
21G,4-31G,6-
31G
•
Each atom optimized STO is fit with
n
GTO’s
•
Minimum number of AO’s needed
•
Each atom optimized STO is fit with
n
GTO’s
•
Minimum number of AO’s needed
•
Contracted GTO’s optimized per atom
•
Doubling of the number of valence AO’s
•
Contracted GTO’s optimized per atom
•
Doubling of the number of valence AO’s

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33

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