ELECTRONIC STRUCTURE THEORY
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Transcript of ELECTRONIC STRUCTURE THEORY
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ELECTRONIC STRUCTURETHEORY
Navigating Chemical Compound Space for Materials and Bio Design:
Tutorials
K. N. HoukDepartment of Chemistry and Biochemistry
UCLAMarch 16, 2011
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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 LiuGonzalo Jimenez
Silvia OsunaNihan Celebi
Steven WheelerArik Cohen
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Reproduce and Predict Chemistry?
Schrödinger Eq.
Quantum Mechanics
Heisenberg–Schrödinger
Hartree–Fock
Thomas–Fermi–DiracRelativistic Effects (Dirac)WFT DFT
Born–Oppenheimer
Orbital Approximation
Roothaan–Hall
LCAO
Ab initio
Semiempirical
ApproximateHamiltonian
HMO, PPPEH, CNDO, INDOMNDO, AM1, PM3, PM6
CompleteBasis Set
Post-HFMethods
Parametrization
? Møller–Plesset: MP2, MP3, ...CI, MCSCF, GVB,CCT Hartree–Fock–Slater
Hohenberg–Kohn
Kohn–Sham
KS-LDA Methods LSDA, Xa
Local Density Approximation(LDA)
LCAO
KS Methods Non LDA
Hartree–Fock–Slater
Generalized Gradient Approximation (GGA)
BLYPBP86BPW91
B3LYPB3P86B3PW91
Hybrid Methods
Half & Half
SVWN
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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 practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without 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)
It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.
The Nobel Prize in Physics 1933Erwin Schrödinger, Paul A.M. Dirac
65 years later…..
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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".
Walter KohnJohn Pople
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Gaussian, Inc. (since 1987)
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H E
eeee EH ˆ
eN HHH ˆˆˆ
Ne
Born-Oppenheimer Approximation
Electronic Schrödinger Equation
22 1ˆ
2
electrons electrons nuclei electronsA
e ii i A i ji A i j
ZH
m
r R r r
Ab Initio Molecular Orbital theory consists of a family of methods to solve approximately the Electronic Schrödinger Equation without parameterization
Kinetic energy Coulomb attraction(nuclei-electrons)
Electronic repulsion
Introduction to ab initio Molecular Orbital Theory
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0
*
0
* ˆ
r
r
d
dHE
elecelec
elecelecelec
elec
The Schrödinger equation can be solved analytically (‘exactly’) only for the simplest systems (H, He+).
ˆelec elec elec elecE H
Dirac “bra-ket” notation for integrals
= 1 (normalization)
Variational Principle:
Eelec (Yelec)
E'''(F''')
E'' (F'')
E'(F’')
Exact energy,real wavefunction
Approximate energies,trial wavefunctions
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1 2 1 1 2 2 2 1 1 2 2 1
1, ,
2e e r r r r r r r r
Assume Ye as a single antisymmetric product of one-electron functions (molecular orbitals)
For a general N-electron system, we can write this antisymmetric product as a Slater Determinant
Hartree-Fock Theory
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Linear Combination of Atomic Orbitals
i ic
Linear Combination of Atomic Orbitals (LCAO)
basis functions
Expansion of orbitals in terms of some basis functions centered on the nuclei:
i
j
k
a
b
c
Occupied(occ)
Unoccupied(virt)
coefficients
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ˆi i iF
molecular orbitalorbital
energy
Hartree-Fock equations (eigenvalue equations) for each molecular orbital:
1, 2, ..., i N
21ˆ ˆ ˆ2 1 12
M occA
i j jA jiA
ZF J K
r
Fock operator
Coulomboperator
Exchangeoperator
12
1ˆ 1 (1) (1) (2) (1) (2)j i i j i jJ ij ijr
12
1ˆ 1 (1) (1) (2) (1) (2)j i i j j iK ij jir
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Substituting this expansion in the Schrödinger equation solution:
Scc
Hcc
rcc
rcHc
r
rHE
ii
ii
ii
iielec
0
*
0
*
0
*
0
* ˆˆMinimum
Roothaan-Hallequations
0
011
nn SEH
SEH
ci and E are unknown solved by an iterative numerical method: self-consistent field (SCF)
Solution yields N “occupied” orbitals and (M – N) “unoccupied” orbitals
0
2211
2222222121
1112121111
nmnmnnnn
nn
nn
SEHSEHSEH
SEHSEHSEH
SEHSEHSEH
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The SCF Procedure
Adapted from Cramer, C. J., Essentials of Computational Chemistry, Theories and Models. Second ed.; Wiley: 2004.
2occ
i ii
D c c
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The SCF Procedure and Geometry Optimization
Adapted from Cramer, C. J., Essentials of Computational Chemistry, Theories and Models. Second ed.; Wiley: 2004.
2occ
i ii
D c c Density matrix D
describes how much each basis function contributes to elec.
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The Hartree-Fock approximation can be applied with or without restrictions on the spins of the MOs.
E
Closed shell
RHFsinglet
Restricted (RHF)
/a b
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The Hartree-Fock approximation can be applied with or without restrictions on the spins of the MOs.
E
Closed shell Open shell
RHFsinglet
ROHFdoublet
UHFdoublet
UHFsinglet
Restricted (RHF, ROHF) and unrestricted (UHF) solutions:
a b a b/a b/a b
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What molecular properties can be calculated?
R: Nuclear positionsF: External electric fieldB: External magnetic fieldI: Internal magnetic field
Harmonic vibrational frequencies (IR)
Electric polarizability
Energy gradient (Forces)
Electric dipole moment
Magnetic dipole moment
Hyperfine coupling constants (EPR)
Magnetic susceptibility
Spin-spin coupling (J)
IR absorption intensities
Nuclear magnetic shielding (d)
Circular dichroism
… and many others
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Potential EnergySurface (PES)
Nuclear coordinates
r1
r2
E
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0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
STO GTOs STO-3G
Rad
ial p
art
r
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0 STO GTO
Rad
ial p
art
r
Slater type orbitals (STOs) Gaussian type orbitals (GTOs)
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
STO
Basis Sets
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Every occupied atomic orbital is represented using a single basis function, which corresponds to the smallest set that one could consider.
MinimalBasis Sets
DoubleZeta (DZ)
A better representation can be obtained combining 2 GTOs in a different proportion to represent every atomic orbital.
First row elements: two s-functions (1s and 2s) and one set of p-functions (2px, 2py, 2pz)
First row elements: four s-functions (1s, 1s’, 2s, 2s’) and two sets of p-functions (2px, 2py, 2pz and 2px’, 2py’, 2pz’)
Calculations are usually simplified applying a DZ only for the valence-orbitals, and a single GTO is used to represent the inner-shell orbitals.
split valence
Classification of Basis Sets
Triple Zeta (DZ)
Quadruple Zeta (DZ)
STO-3G, 3-21G, 6-31G, 6-311G, cc-pVDZ, cc-pVTZ, …
Examples of Basis sets
Effective Core Potential (ECP)
Valence electronsEXPLICITLY
Core electronsPOTENTIAL
Coulomb repulsion effects
Pauli principleRelativistic effects
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1930 1953
1963
1965 1973 1980
1977 1985
1989
1993
1996
2000 2006
2007
HMOHückel
PPPPople
EHTHoffmann
CNDOPople
INDO/SZINDO/SRidley, ZernerMINDO/3Bingham, Dewar, Lo
NDDO (Neglect of Diatomic Differential Overlap)
MNDODewar, Thiel
SINDO1Nanda, Jug
AM1Dewar,Stewart
PM3Stewart
SAM1 Dewar, Jie, Yu
MNDO/dThiel, Voityuk
AM1/dVoityukRosch
RM1Rocha
Stewart
PM6Stewart
CNDO (Complete Neglect of Differential Overlap)
INDO (Intermediate Neglect of Differential Overlap)
Methods restricted to all valence electrons:
Methods restricted to π-electrons:
2002
PDDG/PM3PDDG/MNDOJorgensen
Semi-empirical Methods: Overview
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1930 1963 1965 19801977 2007
NDDO (Neglect of Diatomic Differential Overlap)
CNDO (Complete Neglect of Differential Overlap)
INDO (Intermediate Neglect of Differential Overlap)
Methods restricted to all valence electrons:Methods restricted to π-electrons
Semi-empirical Methods: Overview
Overlap matrix: UNIT matrix
All 2-center 2e- integrals (not Coulomb)NEGLECTED
All integrals involving different atomic
orbitalsIGNORED
Remaining integrals:PARAMETERIZED
1e- integrals involving 3 centers = ZERO
3- and 4-center 2e- integrals NEGLECTED
NDDO
+INDO
+
Use of empirical parameters
ELECTRON CORRELATION
EFFECTS INCLUDED
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1 2 3 4 5
30.0
45.6
39.741.3
18.5
41.142.8
36.3
44.8
40.2
27.1
41.8
35.1
40.6
25.723.8
37.9
32.035.3
22.125.1
33.3 34.1 32.9
4.5
41.439.8
49.8
39.0
Activation Barriers (kcal/mol)
PDDG-PM3 PDDG-MNDO PM3 AM1 MNDO Exp
Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. J. Comp. Chem. 2002, 23, 1601.
Semi-empirical Methods: Benchmarks
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2.1 2.3
3.74.0
2.9
Overall MAEs for Isomerization Energies (kcal/mol)
PDDG-PM3 PDDG-MNDO PM3 AM1 MNDO
Semi-empirical Methods: Benchmarks
Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. J. Comp. Chem. 2002, 23, 1601.
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monodeterminantal approximation
monodeterminantal approximation
treated the average Coulombic interaction of the electrons
treated the average Coulombic interaction of the electrons
neglected instantaneous electron-electron interactions
(electron correlation)
neglected instantaneous electron-electron interactions
(electron correlation)
overestimated energyoverestimated energy
Schrödinger Eq.
Hartree–Fock
Roothaan–HallAb initioAb initio
CorrelationEnergy
(not a physical entity)
HF limit
Exact solution
Electron Correlation
Limitations of HF Theory
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H · + H· H–H Hartree-Fock calculations recover ~99% of total energy
Why is the correlation energy so important?HF energy
Exact (correlated) energy
E
Due to the absence of correlation energy, HF calculations usually lead to:
- too large stretching bond energies too large activation energies for bond formation reactions.
- too short bonds
- too large vibrational frequencies
- wavefunctions with a too ionic character.
“exact”at HF level
HF underestimated binding energy
The Correlation Energy
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To go beyond HF,
•must include electron-electron interaction explicitly (Electron Correlation)
•must also move beyond the single-determinant picture
Electron Correlation Methods
Electron Correlation Methods
Configuration Interaction(CI)
Coupled Cluster(CC)
Many Body Perturbation Theory (MBPT)
CISDCISD(T)CISDTCISDTQ……
CCSDCCSD(T)CCSDTQCISDQCIST(T)……
MP2MP3MP4……
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Configuration Interaction (CI)
CI: wavefunction expansion of Slater determinants in which electrons are “excited” to unoccupied orbitals.
i
j
k
a
b
c
Occ
upie
d(o
cc)
Uno
ccup
ied
(vir)
i
j
k
a
b
c
0
i
j
k
a
b
c
ai ab
ij
Full CI: include all possible Slater determinants
baji
abij
abij
ai
ai
ai
IIICI cccc
,,00
…HF: S-type: D-type:
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Solving the set of CI secular equations == diagonalizing the CI matrix
Solving CI Secular Equations
Hij is evaluated by expanding it in a sum product of MO’s
MO’s are expanded in AO’s
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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
Combinatorial Issues with CI Calculations
a Number of singlet configurations for H2O with 6-31G(d) basis set (19 basis functions)b R. J. Harrison and N. C. Handy, Chem. Phys. Lett. 95, 386 (1983).c Ne = number of electrons
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In Practice, we truncate the N-particle expansion:
Excitation Level (n)
Method Total Electronic Configurationsa
% Corr. Enery Recoveredb
1 CIS 71 0 ECIS = EHF (Brillouin’s theorem)
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 - Excitations above Q-type are not important
… …… ……
Ne Full CI 30,046,752 100 Only feasible to very small molecule and basis set
Truncated CI Methods
a Number of singlet configurations for H2O with 6-31G(d) basis set (19 basis functions)b R. J. Harrison and N. C. Handy, Chem. Phys. Lett. 95, 386 (1983).c Ne = number of electrons
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Coupled Cluster (CC) Theory
Alternatively, the CI wavefunction can be described as
0
ˆ TCC e NTTTT ˆˆˆˆ
21
The excitation operator
having I excitations from the reference
generate all possible determinants
2 0ˆ
occ virab abij ij
i j a b
T t
1 0ˆ
occ vira ai i
i a
T t
Truncated Coupled Cluster theory:
CCSD:
CCSD(T):
CCSD(T) with large basis-set is the “gold standard” for a single ground state calculation.
21ˆˆˆ TTT 0
ˆˆ21 TT
CCSD e
CCSD with perturbative triples corrections
IT
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CCSD(T) Procedure
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Perturbation Theorybasic idea: Treat correlation into a series of corrections to an
unperturbed starting point
0ˆ ˆ ˆH H V total Hamiltonian
unperturbed system
perturbation
• Start with a system with known Hamiltonian, , eigenvalues, , and eigenfunctions, .
• Calculate the changes in these eigenvalues and eigenfunctions that result from a small change, or perturbation, in the Hamiltonian for the system.
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Calculations up to MP4 are common.
Second order Møller-Plesset Perturbation Theory (MP2)
0 * 0 0 * 00 02
0 0 00 0
ˆ ˆi i
i i
V d V dE
E E
Nth order Møller-Plesset Perturbation Theory is called MPn.
Møller-Plesset Perturbation Theory
Third order Møller-Plesset Perturbation Theory (MP3) additionally includes the third order correction to the energy.
1
1 1 1
1ˆN N N N
i ii j i i jij
V J Kr
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Advantages of MP methods:
• MP2 captures ~ 90% of electron correlation
Disadvantages of MP methods:
• MP methods are not variational
Møller-Plesset Perturbation Theory
EHF
MP2
MP3
MP4
SCS-MP2
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Electron Correlation
Exact Solution to the Schrödinger
Equation
Basi
s Se
t
SZ
DZ
DZP
TZ2P
…
completebasis set
HF MP2 QCISD CCSD CCSD(T) Full CI…
HF/minimal
BS
Increase Accuracy
Extrapolation Methods
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Electron Correlation
Basi
s Se
t
SZ
DZ
DZP
TZ2P
…
completebasis set
HF MP2 QCISD CCSD CCSD(T) Full CI…
HFsmall BS
A Simple Example of Extrapolation Method
HFlarge BS
CCSD(T)small BS
CCSD(T) large BS
EBS
Ecorr
Ecorr
EBS
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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
Extrapolation Methods
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L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys., 94 (1991) 7221-30.
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
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Curtiss, L. A. et al., J. Chem. Phys. 1997, 106, 1063.
Performance of G2 and DFT for Enthalpies of FormationM
AE /
kca
l mol
-1
Test Set: G2/97(148 Hf)
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• 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 and G4 Theories
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.
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a) Curtiss, L. A. et al., J. Chem. Phys. 2005, 123, 124107. b) Curtiss, L. A. et al., J. Chem. Phys. 2007, 126, 084108.
Test Set: G3/05(454 energies)
Performance of G3, G4, versus DFTM
AE /
kca
l mol
-1
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•
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.
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W1 W2geometry 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)/MTsmallrelativistic and spin-orbit corrections
ACPF/MT ACPF/MT
empirical parameters 1 (molecule-independent) 0mean absolute error 0.30 kcal/mol 0.23 kcal/mol
applicability up to 10 heavy atoms up to 5 heavy atoms
• 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.
Martin, J. M. L.; de Oliveira, G., J. Chem. Phys. 1999, 111, 1843.
Weizmann-n Theory: W1, W2, W3, W4
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•
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.
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0.0 10.0 20.0 30.0 40.0 50.0 60.0
0.50.50.61.01.11.21.21.52.02.22.74.0
7.98.9
11.817.218.118.8
46.151.0
Exp. UncertaintyW2W1
CBS-QG3G2
CCSD(T)/aug-cc-pV5ZG2(MP2)
CBS-4CCSD(T)/aug-cc-pVQZ
B3LYP/6-311+G(3df,2df,2p)//B3LYP/6-31G(d)B3LYP/6-31+G(d,p)//B3LYP/6-31G(d)
B3LYP/6-31G(d)//B3LYP/6-31G(d)MP2/6-311+G(2d,p)//MP2/6-311+G(2d,p)
MP2/6-311+G(2d,p)//HF/6-31G(d)PM3
SWVN5/6-311+G(2d,p)//SWVN5/6-311+G(2d,p)AM1
HF/6-311+G(2d,p)//HF/6-31G(d)HF/6-31G(d)//HF/6-31G(d)
MAE / kcal mol-1
Mean Absolute Error with the G2/97 Data Set
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.
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TIMING ISSUES
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Single-point energy calculationHF/6-31G(d,p) Gaussian
200 years
1 week
1 day
1 hour
1 minute
< 30 seconds
NO2
NH2
NH2H2N
O2N NO2
10
100
1000
104
105
106
107
1965 1970 1975 1980 1985 1990 1995 2000 2005-present
MainframesSupercomputersWorkstationsPC
Timings of QM Calculations
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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).
Timings of QM Calculations
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Method Applicability(max atoms)
Computational Cost
Scale Accuracy
Molecular mechanics (e.g. AMBER, OPLS)
100,000 ȼ N1 (for organic molecules only)
Semi-empirical methods (e.g. AM1, PM3, PM6)
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
$$$$ N6
Composite methods (e.g. CBS-QB3, G2, G3)
20 heavy atoms
$$$$ N7
CCSD(T)/cc-pVTZ 10 heavy atoms
$$$$$ N7
W1/W2 5 heavy atoms
$$$$$$ N7
Cost Comparison of Common Computational Methods
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0 100 200 300 400 500 600 700 800 900 1000
1020
1018
1016
1014
1012
1010
108
106
104
100
0
millenia
years
hours
minutes
t (s)(serial computing)
N (primitive basis functions)
maximum age of the Universe
N3
methane benzene lactosetryptophan ATP
N2 Semi-empirical
N5 MP2
N6 MP3, CCSD, CISD
N7 MP4, CCSD(T)
N8 MP5, CISDT, CCSDT
N! Full CI
N4
HF, DFT
N10 MP7, CISDTQ N9 MP6
6-31G* basis set
feasible
dangerous
impossible
Cost Comparison of Common Computational Methods
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AVAILABLE PROGRAMS
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Gaussian 09http://www.gaussian.com
General purpose, easy interface
Turbomole 6.2http://www.turbomole.com
Extra-fast RI-DFT
Q-Chem 3.2http://www.q-chem.com
General purpose, fast DFT and post-HF
Molcas 7http://www.teokem.lu.se/molcas
Excited states (CASSCF, RASSCF, CASPT2)
Spartan’10http://www.wavefun.com/products/spartan.html
General purpose, GUI included
HyperChem 8.0http://www.hyper.com
General purpose, GUI included
Jaguar 2010http://www.schrodinger.com/products/14/7
General purpose, fast DFT
ADF 2010http://www.scm.com
General purpose, DFT-oriented
Crystal 09 http://www.crystal.unito.it
Solid state and physics, periodic conditions
$ = 1,000 US dollars(unlimited cores, 5 years license)
$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$
$$$$$$$$
$$
$
$
$$$$$$$$$$$$$$$$$$$$$$$$$
$$
Commercial QM Software
Molpro7http://www.molpro.net
Accurate correlated ab initio methods
$$$$
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GAMESS Oct1, 2010http://www.msg.ameslab.gov/gamess
General purpose and highly scalable
Orca 2.8http://www.thch.uni-bonn.de/tc/orca
General purpose, extra-fast RI-DFT and RI-CC
NWChem 6.0http://www.nwchem-sw.org
General purpose and intensively parallelized
Dalton 2.0http://www.kjemi.uio.no/software/dalton
General purpose, multi-reference calculations
Mopac 2009http://openmopac.net/MOPAC2009.html
Semiempirical methods (PM3, PM6)
SAPT 2008http://www.physics.udel.edu/~szalewic/SAPT
Symmetry-Adapted Perturbation Theory
Abinit 6.6http://www.abinit.org
Light and portable DFT code
CP2Khttp://cp2k.berlios.de
Solid state, liquids and biological simulations
CPMD 3.13http://www.cpmd.org
Carr-Parrinello Molecular Dynamics
Octopus 3.2http://www.tddft.org/programs/octopus/wiki
TDDFT
Siesta 3.0http://www.icmab.es/siesta
Simulations of materials
Non-Commercial QM Software
Dirac 6.6http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program
Properties using relativistic calculations
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SOME APPLICATIONS
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Mechanisms of reactions and
Origins of reactivity differences
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(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.
∆G‡ = 21.3
∆G‡ = 22.4
∆G‡ = 29.3
Substantial differences in reductive elimination barriers determine the 2 substrate selectivity.π
2π InsertionReductive
EliminationCatalystTransfer
Rh
Cl
COMeO
Rh
Cl
COMeO
Cl Rh
CO
MeO
Cl(CO)Rh
MeO
MeO
Rh-VCPComplex
Rh-VCPComplex
+
(fast)
(fast)
(slow)
B3LYP/LANL2DZ-6-31G*
Reactivity of 2 Components in Rh-catalyzed Cycloadditions
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2π InsertionReductive
EliminationCatalystTransfer
Rh
Cl
COMeO
Rh
Cl
COMeO
Cl Rh
CO
MeO
Cl(CO)Rh
MeO
MeO
Rh-VCPComplex
Rh-VCPComplex
+
B3LYP/LANL2DZ-6-31G*
Reactivity of 2 Components in Rh-catalyzed Cycloadditions
∆G‡ = 14.8
Ethylene Reductive Elimination TS
∆G‡ = –18.8
Acetylene Reductive Elimination TS
(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.
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Magnitudes and originsof
nonbonded interactionsbetween
molecules
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Calculation of weak C-H/p 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)
QM Applications
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Conformationsand
properties
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Calculation of time and temperature-dependent NMR properties of host-guest complexes (H2@C60) M06-2X/6-31+G(d) (Gaussian)
Conformational analysis of small glycopeptides in explicit waterB3LYP/6-31G(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)
N
O
Me Me
N
O
Cu
H CO2Me
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High-accuracyactivation barriers
andthermodynamics
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Method 1cpx 2TS 3prod 4cpx 5TS 6prod
CBS-QB3 5.6 13.5 -51.3 7.5 10.5 -43.9G3 4.8 21.8 -48.2 5.9 10.4 -40.4G3B3 6.1 16.8 -47.8 8.2 12.6 -40.5G4 5.9 18.0 -47.9 7.5 14.4 -40.0Focal point 4.4 18.8 -44.4 4.5 13.7 -36.0
Focal Point Calculations of Free Energies of a 1,3-Dipolar Cycloaddition
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Reactions of large molecules
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Exploring the Reactivity of Large Systems
+
╪
╪
+
ΔE╪ = 8.8ΔER=-15.8
ΔE╪= 4.3ΔER=-26.3
Osuna, S.; Houk, K. N. Chem. Eur. J.. 2009, 15, 13219.
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69
HDA
Reaction Mechanism:Exploring the potential energy surface
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Reaction Mechanisms: competing pathways
DA
HDA
TS1b
TS1a DA
HDA
TS2
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Reaction Mechanisms: competing pathways
DA
HDA
TS1
TWO-STEP NO INTERMEDIATE
DA
HDA
TS2
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Reaction Mechanisms: two-step no-intermediate
TS1
Reactants
TS2
P1
P2
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Stereoselectivitiesof
useful reactions
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R : SExperimental 74 : 26Computed 76 : 24
Stereoselectivities
Quinidine=
G [H] in kcal/mol
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Stereoselectivities
0.0 [0.0] 1.9 [2.8]
TS-R TS-S
G [H] in kcal/mol
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ELECTRONIC STRUCTURETHEORY
Navigating Chemical Compound Space for Materials and Bio Design:
Tutorials
K. N. HoukMarch 16, 2011