ELECTRONIC STRUCTURE
THEORY
Navigating Chemical Compound Space
for Materials and Bio Design:
Tutorials
K. N. Houk
Department of Chemistry and Biochemistry
UCLA
March 16, 2011
Navigating Chemical Compound Space for Materials
and Bio Design: Tutorials
Electronic Structure Theory
Generalities and history
Wavefunction electronic structure theory
Benchmarking, accuracies
General programs for quantum mechanics calculations
Some applications from our group
Thanks to six great postdocs in my group:
Peng Liu
Gonzalo Jimenez
Silvia Osuna
Nihan Celebi
Steven Wheeler
Arik Cohen
Quantum Mechanics
Heisenberg–Schrödinger
WFT
Reproduce and Predict Chemistry?
Post-HF
Methods
Møller–
Plesset: MP2,
MP3, ...
CI, MCSCF,
GVB,
CCT
Born–Oppenheimer
Orbital Approximation
Hartree–Fock
Complete
Basis Set
Ab initio
Kohn–Sham
LCAO
LCAO
Roothaan–Hall
KS-LDA Methods
LSDA, Xa
SVWN
Semiempirical
Hybrid Methods
HMO, PPP
EH, CNDO, INDO
MNDO, AM1, PM3, PM6
Half & Half
KS Methods
Non LDA
Local Density
Approximation
(LDA)
Hartree–Fock–Slater
Approximate
Hamiltonian
Parametrization
Thomas–Fermi–Dirac
Hohenberg–Kohn
Schrödinger Eq.
?
DFT
Relativistic Effects (Dirac)
BLYP
BP86
BPW91
Generalized
Gradient
Approximation
(GGA)
B3LYP
B3P86
B3PW91
The underlying physical laws necessary for the
mathematical theory of a large part of physics
and the whole of chemistry are thus completely
known, and the difficulty is only that the exact
application of these laws leads to equations
much too complicated to be soluble. It
therefore
becomes
desirable
that
approximate
It
therefore
becomes
desirable
that
practical methods
of applying
approximate
practical
methodsquantum
of applying
mechanics
should beshould
developed,
which can lead
quantum
mechanics
be developed,
to an explanation
main features
which
can lead to of
an the
explanation
of theof
main
complex of
atomic
systems
without
toowithout
much
features
complex
atomic
systems
computation.
too
much computation.
Paul A. M. Dirac
Proceedings of the Royal Society of London.
Series A, Containing Papers of a Mathematical
and Physical Character, Vol. 123, No. 792
(1929)
The Nobel Prize in Physics 1933
Erwin Schrödinger, Paul A.M. Dirac
65 years later…..
John Pople
Walter Kohn
The Nobel Prize in Chemistry 1998
The Nobel Prize in Chemistry 1998 was divided equally between Walter Kohn
"for his development of the density-functional theory"
and John A. Pople
"for his development of computational methods in quantum chemistry".
Gaussian, Inc. (since 1987)
Introduction to ab initio Molecular Orbital Theory
Ĥ   E 
Hˆ  Hˆ N  Hˆ e
Born-Oppenheimer Approximation
   e N
Electronic Schrödinger Equation
Hˆ e e  Ee e
2

Hˆ e 
2m
electrons

 
i
Kinetic energy
2
i
electrons nuclei
 
i
A
electrons
ZA
1
 
ri  R A
ri  r j
i j
Coulomb attraction
(nuclei-electrons)
Electronic repulsion
Ab Initio Molecular Orbital theory consists of a family of methods to solve approximately
the Electronic Schrödinger Equation without parameterization
Eelec 


0
*
elec
Hˆ elec elec dr


0
Eelec   elec Hˆ elec  elec
*
elec
 elec dr = 1 (normalization)
Dirac
“bra-ket”
notation
for
integrals
The Schrödinger equation can be solved analytically (‘exactly’) only for the simplest
systems (H, He+).
Variational Principle:
E'(F’')
Approximate energies,
trial wavefunctions
E'' (F'')
E'''(F''')
Exact energy,
real wavefunction
Eelec (elec)
Hartree-Fock Theory
Assume e as a single antisymmetric product of one-electron functions
(molecular orbitals)
 e  r1 , r2  
1
1  r1  2  r2   2  r1  1  r2    e  r2 , r1 
2
For a general N-electron system, we can write this antisymmetric product as a
Slater Determinant
Linear Combination of Atomic Orbitals
Expansion of orbitals in terms of some basis functions centered
on the nuclei:
Unoccupied
(virt)
c
coefficients
b
a
 i   cia a
a
basis functions
k
j
Linear Combination of Atomic Orbitals (LCAO)
i
Occupied
(occ)
Hartree-Fock equations (eigenvalue equations) for each molecular orbital:
Fˆi   ii
orbital
energy
Fock operator

1 2 M Z A occ ˆ
ˆ
F   i     2 J j 1  Kˆ j 1
2
A riA
j
Coulomb
operator

Exchange
operator
i  1, 2, ..., N
molecular
orbital
1
Jˆ j 1 i (1)  i (1) j (2)
i (1) j (2)  ij ij
r12
1
Kˆ j 1 i (1)  i (1) j (2)
 j (1)i (2)  ij ji
r12
Substituting this expansion in the Schrödinger equation solution:
*

 ˆ


c

H
c




*

ia a
ia a  r
 Hˆ elec  r 0  

a
  a

E 0 


*
*

0    r 0   ciaa     ciaa  r
 a
  a


H a  E  S a   0

a
1
1

  H na  E  S na   0
a
c a c  H a

a 
c a c  Sa

a 
i
i
i
i
H11  E  S11
H12  E  S12

H1n  E  S1n
H 21  E  S 21
H 22  E  S 22 
H 2n  E  S2n

H n1  E  S n1
cia and E are unknown


Minimum

0
Roothaan-Hall
equations
H n 2  E  S n 2  H nm  E  S nm
solved by an iterative numerical method:
self-consistent field (SCF)
Solution yields N “occupied” orbitals and (M – N) “unoccupied” orbitals
The SCF Procedure
occ
D  2 ci c i
i
Adapted from Cramer, C. J., Essentials of Computational Chemistry, Theories and Models. Second ed.; Wiley: 2004.
The SCF Procedure and Geometry Optimization
occ
D  2 ci c i
i
Density matrix D
describes how much
each basis function
contributes to elec.
Adapted from Cramer, C. J., Essentials of Computational Chemistry, Theories and Models. Second ed.; Wiley: 2004.
The Hartree-Fock approximation can be applied with or without restrictions on
the spins of the MOs.
Restricted (RHF)
Closed shell
E
a/
RHF
singlet
The Hartree-Fock approximation can be applied with or without restrictions on
the spins of the MOs.
Restricted (RHF, ROHF) and unrestricted (UHF) solutions:
Closed shell
E
Open shell
a/
a/
RHF
singlet
ROHF
doublet
a

UHF
singlet
a

UHF
doublet
What molecular properties can be calculated?
R:
F:
B:
I:
Nuclear positions
External electric field
External magnetic field
Internal magnetic field
¶2 E
¶ R2
Harmonic vibrational frequencies (IR)
¶2 E
¶F2
Electric polarizability
Magnetic susceptibility
¶E
¶R
Energy gradient (Forces)
¶2 E
¶ B2
¶E
¶F
Electric dipole moment
¶2 E
¶I 2
¶E
¶B
Magnetic dipole moment
¶E
¶I
Hyperfine coupling constants
(EPR)
Spin-spin coupling (J)
¶2 E
¶R¶E
IR absorption intensities
¶2 E
¶B¶I
Nuclear magnetic shielding (d)
¶2 E
¶B¶F
Circular dichroism
… and many others
Potential Energy
Surface (PES)
E
r1
r2
Nuclear coordinates
Basis Sets
1.0
STO
GTO
0.8
0.8
0.6
0.6
Radial part
Radial part
1.0
0.4
0.4
0.2
0.2
0.0
0.0
0.0
0.5
1.0
1.5
2.0
r
Slater type orbitals (STOs)
STO
GTOs
STO-3G
0.0
0.5
1.0
1.5
2.0
r
Gaussian type orbitals (GTOs)
STO
The analytical form of the two-electron
integrals is computationally expensive.
The quadratic dependence on r makes the
analytical form of the two-electron integrals quite
easy.
Linear combination of GTOs
Classification of Basis Sets
Minimal
Basis Sets
Every occupied atomic orbital is represented using a single basis function,
which corresponds to the smallest set that one could consider.
First row elements: two s-functions (1s and 2s) and one set of p-functions (2px, 2py,
2pz)
Double
Zeta (DZ)
A better representation can be obtained combining 2 GTOs in a different
proportion to represent every atomic orbital.
Triple Zeta
(DZ)
First row elements: four s-functions (1s, 1s’, 2s, 2s’) and two sets of p-functions
(2px, 2py, 2pz and 2px’, 2py’, 2pz’)
Quadruple
Zeta (DZ)
split valence
Calculations are usually simplified applying a DZ only for the valenceorbitals, and a single GTO is used to represent the inner-shell orbitals.
Examples of Basis sets
STO-3G, 3-21G, 6-31G, 6-311G, cc-pVDZ, cc-pVTZ, …
Effective Core
Potential (ECP)
Valence electrons
EXPLICITLY
Core electrons
POTENTIAL
Coulomb repulsion
effects
Pauli principle
Relativistic effects
Semi-empirical Methods: Overview
INDO/S
ZINDO/S
SAM1
Ridley, Zerner
Dewar, Jie, Yu
MINDO/3
Bingham, Dewar, Lo
Methods restricted to π-electrons:
Rocha
Stewart
PPP
CNDO
SINDO1
Hückel
Pople
Pople
Nanda, Jug
1930
1953
1965
HMO
RM1
PM3
1973
1963
1980
1977
AM1/d
1989
1993
Voityuk
Rosch
Stewart
2000 2006
1996 2002 2007
1985
EHT
MNDO
MNDO/d
PM6
Hoffmann
Dewar, Thiel
Thiel, Voityuk
Stewart
AM1
Dewar,Stewart
Methods restricted to all valence electrons:
PDDG/PM3
PDDG/MNDO
Jorgensen
CNDO (Complete Neglect of Differential Overlap)
INDO (Intermediate Neglect of Differential Overlap)
NDDO (Neglect of Diatomic Differential Overlap)
Semi-empirical Methods: Overview
Methods restricted to π-electrons
Methods restricted to all valence electrons:
1963 1965
1930
1977
1980
CNDO (Complete
Neglect of Differential
Overlap)
INDO (Intermediate
Neglect of Differential
Overlap)
INDO
NDDO
+
+
All integrals involving
different atomic
orbitals
IGNORED
All 2-center 2e- integrals
(not Coulomb)
NEGLECTED
ELECTRON
CORRELATION
EFFECTS INCLUDED
Use of empirical
parameters
2007
NDDO (Neglect of Diatomic
Differential Overlap)
Overlap matrix:
UNIT matrix
1e- integrals involving 3 centers
= ZERO
3- and 4-center 2e- integrals
NEGLECTED
Remaining integrals:
PARAMETERIZED
Semi-empirical Methods: Benchmarks
Activation Barriers (kcal/mol)
PDDG-PM3
PDDG-MNDO
PM3
AM1
MNDO
Exp
49,8
45,6
44,8
42,8 41,8
41,1
41,4
36,3
33,3
30,0
27,1
23,8
39,8
39,7
37,9
41,3
35,1
32,0
34,1
40,6
40,2
35,3
39,0
32,9
25,7
25,1
22,1
18,5
4,5
1
2
3
4
Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. J. Comp. Chem. 2002, 23, 1601.
5
Semi-empirical Methods: Benchmarks
Overall MAEs for Isomerization Energies (kcal/mol)
PDDG-PM3
PDDG-MNDO
3,7
PM3
AM1
MNDO
4,0
2,9
2,1
2,3
Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. J. Comp. Chem. 2002, 23, 1601.
Electron Correlation
monodeterminantal
approximation
treated the average Coulombic
interaction of the electrons
neglected instantaneous
electron-electron interactions
(electron correlation)
Ab initio
HF limit
Correlation
Energy
Roothaan–Hall
Hartree–Fock
(not a physical entity)
Exact solution
overestimated energy
Limitations of HF Theory
Schrödinger Eq.
The Correlation Energy
E
H · + H·
“exact”
at HF level
H–H
Hartree-Fock
calculations recover ~99%
of total energy
HF underestimated
binding energy
HF energy
Exact (correlated) energy
Why is the correlation
energy so important?
Due to the absence of correlation energy, HF calculations usually lead to:
- too large stretching bond energies
- too short bonds
- too large vibrational frequencies
- wavefunctions with a too ionic character.
too large activation energies for bond formation
reactions.
Electron Correlation Methods
To go beyond HF,
• must include electron-electron interaction explicitly (Electron Correlation)
• must also move beyond the single-determinant picture
Electron Correlation
Methods
Configuration Interaction
(CI)
CISD
CISD(T)
CISDT
CISDTQ
……
Coupled Cluster
(CC)
CCSD
CCSD(T)
CCSDT
QCISD
QCIST(T)
……
Many Body Perturbation Theory
(MBPT)
MP2
MP3
MP4
……
Configuration Interaction (CI)
Unoccupied
(vir)
c
c
c
b
b
b
a
a
a
Occupied
(occ)
CI: wavefunction expansion of Slater determinants in which electrons are “excited” to
unoccupied orbitals.
k
k
k
j
j
j
i
i
i
0
S-type: i
HF:
D-type:  ij
ab
a
…
Full CI: include all possible Slater determinants
 CI   cI I  c0 0   cia ia 
I
i ,a
ab ab
c
 ij  ij  
i  j , a b
Solving CI Secular Equations
Solving the set of CI secular equations == diagonalizing the CI matrix
Hij is evaluated by expanding it in a sum product of MO’s
MO’s are expanded in AO’s
Combinatorial Issues with CI Calculations
Number of electronic configurations grows factorially with the basis-set size
Excitation
Level (n)
Method
Total Electronic
Configurationsa
1
CIS
71
2
CISD
2556
3
CISDT
42,596
4
CISDTQ
391,126
5
CISDTQ5
2,114,666
…
……
……
Ne
Full CI
30,046,752
a
Number of singlet configurations for H2O with 6-31G(d) basis set (19 basis functions)
R. J. Harrison and N. C. Handy, Chem. Phys. Lett. 95, 386 (1983).
c N = number of electrons
e
b
Truncated CI Methods
In Practice, we truncate the N-particle expansion:
Excitation
Level (n)
Method
Total Electronic
Configurationsa
% Corr. Enery
Recoveredb
1
CIS
71
0
2
CISD
2556
94.7
Applied to a large variety of
systems
3
CISDT
42,596
95.5
T contributions are relatively
small
4
CISDTQ
391,126
99.8
Results close to full CI
5
CISDTQ5
2,114,666
-
…
……
……
Ne
Full CI
30,046,752
a
100
ECIS = EHF (Brillouin’s theorem)
Excitations above Q-type are
not important
Only feasible to very small
molecule and basis set
Number of singlet configurations for H2O with 6-31G(d) basis set (19 basis functions)
R. J. Harrison and N. C. Handy, Chem. Phys. Lett. 95, 386 (1983).
c N = number of electrons
e
b
Coupled Cluster (CC) Theory
Alternatively, the CI wavefunction can be described as
Tˆ
 CC  e  0
The excitation operator
TˆI
Tˆ  Tˆ1  Tˆ2 TˆN
generate all possible determinants
having I excitations from the reference
occ vir
Tˆ1 0   tia ia
i
a
occ vir
Tˆ2 0   tijab ijab
i  j a b
Truncated Coupled Cluster theory:
CCSD:
CCSD(T):
Tˆ  Tˆ1  Tˆ2
Tˆ1 Tˆ2
 CCSD  e
0
CCSD with perturbative triples corrections
CCSD(T) with large basis-set is the “gold standard” for a single ground state calculation.
CCSD(T) Procedure
Perturbation Theory
basic idea: Treat correlation into a series of corrections to an
unperturbed starting point
•
Start with a system with known Hamiltonian,
and eigenfunctions,
.
•
Calculate the changes in these eigenvalues and eigenfunctions that
result from a small change, or perturbation, in the Hamiltonian for
the system.
total Hamiltonian
0
Hˆ  Hˆ    Vˆ
unperturbed system
, eigenvalues,
perturbation
,
Møller-Plesset Perturbation Theory
Second order Møller-Plesset Perturbation Theory (MP2)
E0   
2
 0* ˆ  0
 0* ˆ  0 

V

d


0
 i
 0 V i d
i 0
E0   Ei
0
0
N 1 N
N N
1
Vˆ      J i  Ki 
i 1 j i rij
i 1 j 1
Third order Møller-Plesset Perturbation Theory (MP3) additionally includes the third
order correction to the energy.
Nth order Møller-Plesset Perturbation Theory is called MPn.
Calculations up to MP4 are common.
Møller-Plesset Perturbation Theory
Advantages of MP methods:
• MP2 captures ~ 90% of electron correlation
Disadvantages of MP methods:
• MP methods are not variational
E
HF
MP3
SCS-MP2
MP4
MP2
Extrapolation Methods
Exact Solution to
the Schrödinger
Equation
Basis Set
complete
basis set
…
TZ2P
DZP
DZ
SZ
HF/
minimal
BS
HF
MP2
QCISD
CCSD
CCSD(T)
…
Electron Correlation
Full CI
A Simple Example of Extrapolation Method
Basis Set
complete
basis set
…
 Ecorr
HF
large BS
CCSD(T)
large BS
TZ2P
DZP
EBS
DZ
SZ
Ecorr
HF
small BS
HF
 EBS
MP2
QCISD
CCSD(T)
small BS
CCSD
CCSD(T)
…
Electron Correlation
Full CI
Extrapolation Methods
Common Extrapolation Methods:
• Gaussian-n (G2, G2(MP2), G3, etc.)
• Complete basis set (CBS-Q, CBS-QB3, CBS-RAD, etc.)
• Weizmann-n (W1, W2, etc.)
• HEAT (thermochemistry calculations)
• Focal point methods
G2 Theory
• Geometry optimized at the HF and MP2/6-31G(d) level.
MP4 with a relatively
small basis set
zero-point
vibrational
energy at the
HF/6-31G(d)
level
basis set corrections to the
6-311+G(3df,2p) basis set
higher-level
correction
correlation energy
corrections to the
QCISD(T) level
L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys., 94 (1991) 7221-30.
MAE / kcal mol-1
Performance of G2 and DFT for Enthalpies of Formation
Curtiss, L. A. et al., J. Chem. Phys. 1997, 106, 1063.
Test Set: G2/97
(148 Hf)
G3 and G4 Theories
• G3
–
–
–
–
new basis sets for single point energies
spin–orbit correction and correction for core correlation
MAD for G2/97 set: 1.01 kcal/mol
requires less computational time than G2
• G3(MP2)
– use MP2 instead of MP4 in single point energy calculations
– increase MAD to 1.30 kcal/mol
• G3B3: G3 using B3LYP geometries
– MAD for G2/97 set: 0.99 kcal/mol
• G4
–
–
–
–
for molecules with 1st, 2nd, and 3rd row main group atoms
use CCSD(T) instead of QCISD(T) for correlation corrections
B3LYP geometries
Larger basis sets for single point energy calculations
G3: a) Curtiss, L. A. et al., J. Chem. Phys. 1998, 109, 7764. b) Curtiss, L. A. et al., J. Chem. Phys. 1999, 110, 4703.
c) Baboul, A. G. et al., J. Chem. Phys. 1999, 110, 7650.
G4: Curtiss, L. A. et al., J. Chem. Phys. 2007, 126, 084108.
MAE / kcal mol-1
Performance of G3, G4, versus DFT
Test Set: G3/05
(454 energies)
a) Curtiss, L. A. et al., J. Chem. Phys. 2005, 123, 124107. b) Curtiss, L. A. et al., J. Chem. Phys. 2007, 126, 084108.
Complete Basis Set (CBS) Methods
a) J. W. Ochterski, G. A. Petersson, and J. A. Montgomery Jr., J. Chem. Phys., 104 (1996) 2598.
b) J. A. Montgomery Jr., M. J. Frisch, J. W. Ochterski, and G. A. Petersson, J. Chem. Phys., 110 (1999) 2822.
Weizmann-n Theory: W1, W2, W3, W4
• Compute energies of small molecules to within 1 kJ/mol (0.3 kcal/mol)
accuracy.
• More accurate and computationally demanding than G2, G3, and CBS-QB3.
W1
W2
geometry optimization
B3LYP/cc-pVTZ+1
CCSD(T)/VQZ+1
ZPE
B3LYP/VTZ+1 scaled by 0.985
CCSD(T)/VQZ+1
single point energies
CCSD(T)/AVDZ+2d,
CCSD(T)/AVTZ+2d1f, and
CCSD/AVQZ+2d1f
CCSD(T)/AVTZ+2d1f,
CCSD(T)/AVQZ+2d1f, and
CCSD/AV5Z+2d1f
core correlation
CCSD(T)/Mtsmall
CCSD(T)/MTsmall
relativistic and spinorbit corrections
ACPF/MT
ACPF/MT
empirical parameters
1 (molecule-independent)
0
mean absolute error
0.30 kcal/mol
0.23 kcal/mol
applicability
up to 10 heavy atoms
up to 5 heavy atoms
Martin, J. M. L.; de Oliveira, G., J. Chem. Phys. 1999, 111, 1843.
HEAT:
High accuracy extrapolated ab initio thermochemistry
Tajti, A.; Szalay, P. G.; Csaszar, A. G.; Kallay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vazquez, J.; Stanton, J. F.,
J. Chem. Phys. 2004, 121, 11599-11613.
Mean Absolute Error with the G2/97 Data Set
Exp. Uncertainty 0,54
W2
0,5
W1
0,6
CBS-Q
1,0
G3
1,1
G2
1,2
CCSD(T)/aug-cc-pV5Z
1,2
G2(MP2)
1,5
CBS-4
2,0
CCSD(T)/aug-cc-pVQZ
2,2
B3LYP/6-311+G(3df,2df,2p)//B3LYP/6-31G(d)
2,7
B3LYP/6-31+G(d,p)//B3LYP/6-31G(d)
4,0
B3LYP/6-31G(d)//B3LYP/6-31G(d)
7,9
MP2/6-311+G(2d,p)//MP2/6-311+G(2d,p)
8,9
MP2/6-311+G(2d,p)//HF/6-31G(d)
11,8
PM3
17,2
SWVN5/6-311+G(2d,p)//SWVN5/6-311+G(2d,p)
18,1
AM1
18,8
HF/6-311+G(2d,p)//HF/6-31G(d)
HF/6-31G(d)//HF/6-31G(d)
MAE / kcal mol-1
0,0
10,0
20,0
46,1
51,0
30,0
40,0
50,0
60,0
a) Curtiss, L. A. et al., J. Chem. Phys. 1997, 106, 1063. b) Curtiss, L. A. et al., J. Chem. Phys. 1998, 109, 7764. c) Martin, J. M.
L. et al., J. Chem. Phys. 2001, 114, 6014.
Timings of QM Calculations
NO2
H 2N
NH2
O 2N
NO2
Single-point energy calculation
HF/6-31G(d,p) Gaussian
NH2
7
10
Mainframes
Supercomputers
Workstations
PC
200 years
6
1 week
10
1 day
10
5
1 hour
4
10
1000
1 minute
100
< 30 seconds
10
1965 1970 1975 1980 1985 1990 1995 2000 2005-present
Timings of QM Calculations
Computation times with DFT/DZ on a modern workstation
K. N. Houk and Paul Ha-Yeon Cheong
"Computational Prediction of Small-Molecule Catalysts,”
Nature, 455, 309-313 (2008).
Cost Comparison of Common Computational Methods
Method
Applicability
(max atoms)
Computational
Cost
Scale
Accuracy
100,000
ȼ
N1
(for organic
molecules only)
5,000
ȼȼȼ
N1~2
(for organic
molecules only)
Hartree-Fock
500
$
N3~4
DFT
200
$$
N3~4
MP2
100
$$$
N5
MP4
20 heavy
atoms
$$$$
N6
Composite methods
(e.g. CBS-QB3, G2, G3)
20 heavy
atoms
$$$$
N7
CCSD(T)/cc-pVTZ
10 heavy
atoms
$$$$$
N7
W1/W2
5 heavy
atoms
$$$$$$
N7
Molecular mechanics
(e.g. AMBER, OPLS)
Semi-empirical methods
(e.g. AM1, PM3, PM6)
Cost Comparison of Common Computational Methods
methane
t (s)
(serial computing)
maximum age
of the Universe
benzene
tryptophan
ATP
N10 MP7, CISDTQ
N! Full CI
1020
lactose
6-31G* basis set
N9 MP6
1018
N8
MP5, CISDT, CCSDT
N7
MP4, CCSD(T)
N6
MP3, CCSD, CISD
N5
MP2
1016
1014
1012
millenia
1010
impossible
years
108
dangerous
N4
106
hours
minutes
HF, DFT
feasible
104
N3
100
N2
0
0
100
200
300
400
500
600
N (primitive basis functions)
700
800
900
Semi-empirical
1000
Commercial QM Software
Gaussian 09
$$$$$$
$ = 1,000 US dollars
(unlimited cores, 5 years license)
Molpro7
$$$$
http://www.gaussian.com
http://www.molpro.net
General purpose, easy interface
Accurate correlated ab initio methods
ADF 2010
$$$$$$$$$$$$$$$$$$$$$$$$$
Molcas 7
$$$$$$$$
http://www.scm.com
http://www.teokem.lu.se/molcas
General purpose, DFT-oriented
Excited states (CASSCF, RASSCF, CASPT2)
Jaguar 2010
$$$$$$$$$$$$$$$$$$$$$$$$$
Spartan’10
$$
http://www.schrodinger.com/products/14/7
http://www.wavefun.com/products/spartan.html
General purpose, fast DFT
General purpose, GUI included
Turbomole 6.2 $$
HyperChem 8.0
$
http://www.turbomole.com
http://www.hyper.com
Extra-fast RI-DFT
General purpose, GUI included
Q-Chem 3.2
$$$$
Crystal 09
$
http://www.q-chem.com
http://www.crystal.unito.it
General purpose, fast DFT and post-HF
Solid state and physics, periodic conditions
Non-Commercial QM Software
 GAMESS Oct1, 2010
 Abinit 6.6
http://www.msg.ameslab.gov/gamess
http://www.abinit.org
General purpose and highly scalable
Light and portable DFT code
 NWChem 6.0
http://www.nwchem-sw.org
General purpose and intensively parallelized
 Orca 2.8
 Dirac 6.6
http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program
Properties using relativistic calculations
 Siesta 3.0
http://www.thch.uni-bonn.de/tc/orca
http://www.icmab.es/siesta
General purpose, extra-fast RI-DFT and RI-CC
Simulations of materials
 Dalton 2.0
 CPMD 3.13
http://www.kjemi.uio.no/software/dalton
http://www.cpmd.org
General purpose, multi-reference calculations
Carr-Parrinello Molecular Dynamics
 Mopac 2009
 CP2K
http://openmopac.net/MOPAC2009.html
http://cp2k.berlios.de
Semiempirical methods (PM3, PM6)
Solid state, liquids and biological simulations
 SAPT 2008
 Octopus 3.2
http://www.physics.udel.edu/~szalewic/SAPT
http://www.tddft.org/programs/octopus/wiki
Symmetry-Adapted Perturbation Theory
TDDFT
Reactivity of 2 Components in Rh-catalyzed Cycloadditions
MeO
Rh-VCP
Complex
CO
Rh
Cl
MeO
CO
2π Insertion
Rh
Cl
CO
Cl Rh
MeO
Cl(CO)
Catalyst
Rh
Transfer
Reductive
Elimination
Rh-VCP
Complex
+
MeO
MeO
∆G‡ = 29.3 (slow)
∆G‡ = 22.4 (fast)
∆G‡ = 21.3 (fast)
Substantial differences in reductive elimination
barriers determine the 2π substrate selectivity.
B3LYP/LANL2DZ-6-31G*
(1) Yu, Z. X.; Wender, P. A.; Houk, K. N. J. Am. Chem. Soc. 2004, 126, 9154. (2) Yu, Z.-X.; Cheong, P. H.-Y.; Liu, P.; Legault, C. Y.;
Wender, P. A.; Houk, K. N., J. Am. Chem. Soc. 2008, 130, 2378.
Reactivity of 2 Components in Rh-catalyzed Cycloadditions
Ethylene Reductive Elimination TS
MeO
Rh-VCP
Complex
CO
Rh
Cl
MeO
CO
2π Insertion
Rh
Cl
CO
Cl Rh
MeO
Cl(CO)
Catalyst
Rh
Transfer
Reductive
Elimination
Rh-VCP
Complex
+
MeO
MeO
∆G‡ = 14.8
Acetylene Reductive Elimination TS
∆G‡ = –18.8
B3LYP/LANL2DZ-6-31G*
(1) Yu, Z. X.; Wender, P. A.; Houk, K. N. J. Am. Chem. Soc. 2004, 126, 9154. (2) Yu, Z.-X.; Cheong, P. H.-Y.; Liu, P.; Legault, C. Y.;
Wender, P. A.; Houk, K. N., J. Am. Chem. Soc. 2008, 130, 2378.
QM Applications
Calculation of weak C-H/ van der Waals interactions in water in the recognition of antibiotic
aminoglycosides by proteins SCS-MP2/6-311G(2d,p) // PCM/M06-2X/TZVP (Gaussian/Gamess/Orca)
Conformational analysis of small glycopeptides in explicit water
B3LYP/6-31G(d) (Gaussian)
Calculation of time and temperaturedependent NMR properties of hostguest complexes (H2@C60)
M06-2X/6-31+G(d) (Gaussian)
Calculation of populationally-averaged VCD spectra of
flexible chiral compounds B3LYP/TZVP (Gaussian)
Cu(I)-Box carbene
complex supported
onto clay
RI-BLYP/def2-SV(P)
(Turbomole)
Focal Point Calculations of Free Energies of a 1,3-Dipolar Cycloaddition
Method
1cpx
2TS
3prod
4cpx
5TS
6prod
CBS-QB3
5.6
13.5
-51.3
7.5
10.5
-43.9
G3
4.8
21.8
-48.2
5.9
10.4
-40.4
G3B3
6.1
16.8
-47.8
8.2
12.6
-40.5
G4
5.9
18.0
-47.9
7.5
14.4
-40.0
Focal point
4.4
18.8
-44.4
4.5
13.7
-36.0
Exploring the Reactivity of Large Systems
╪
H
CH2
N
O
O
CH2
N
CH
+
ΔE╪ = 8.8
ΔER=-15.8
╪
H
H
N
H2C
CH2
N
O
CH2
O
N
CH
+
ΔE╪= 4.3
ΔER=-26.3
Osuna, S.; Houk, K. N. Chem. Eur. J.. 2009, 15, 13219.
HDA
69
Reaction Mechanisms:
competing pathways
TS1a
DA
TS2
TS1b
HDA
DA
HDA
Reaction Mechanisms:
competing pathways
DA
TS1
TS2
HDA
DA
TWO-STEP NO INTERMEDIATE
HDA
Reaction Mechanisms:
two-step no-intermediate
TS1
TS2
P2
Reactants
P1
Stereoselectivities
Quinidine=
R:S
Experimental 74 : 26
Computed
76 : 24
G [H] in kcal/mol
Stereoselectivities
TS-R
0.0 [0.0]
TS-S
1.9 [2.8]
G [H] in kcal/mol
ELECTRONIC STRUCTURE
THEORY
Navigating Chemical Compound Space
for Materials and Bio Design:
Tutorials
K. N. Houk
March 16, 2011