Navigating Chemical Compound Space for Materials and Bio Design: Tutorials K. N. Houk Department of Chemistry and Biochemistry UCLA March 16, 2011.

ELECTRONIC STRUCTURETHEORY

Navigating Chemical Compound Space for Materials and Bio Design:

Tutorials

K. N. HoukDepartment of Chemistry and Biochemistry

UCLAMarch 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 LiuGonzalo Jimenez

Silvia OsunaNihan Celebi

Steven WheelerArik Cohen

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

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…..

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

Gaussian, Inc. (since 1987)

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

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

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

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

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

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

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

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.

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

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

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

Potential EnergySurface (PES)

Nuclear coordinates

r1

r2

E

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

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

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

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

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

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.

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

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

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……

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:

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

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

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

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

CCSD(T) Procedure

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.

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

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

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

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

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

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

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)

• 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.

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

•

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.

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

•

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.

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.

TIMING ISSUES

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

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

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

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

AVAILABLE PROGRAMS

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

$$$$

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

SOME APPLICATIONS

Mechanisms of reactions and

Origins of reactivity differences

(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

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.

Magnitudes and originsof

nonbonded interactionsbetween

molecules

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

Conformationsand

properties

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

High-accuracyactivation barriers

andthermodynamics

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

Reactions of large molecules

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.

69

HDA

Reaction Mechanism:Exploring the potential energy surface

Reaction Mechanisms: competing pathways

DA

HDA

TS1b

TS1a DA

HDA

TS2

Reaction Mechanisms: competing pathways

DA

HDA

TS1

TWO-STEP NO INTERMEDIATE

DA

HDA

TS2

Reaction Mechanisms: two-step no-intermediate

TS1

Reactants

TS2

P1

P2

Stereoselectivitiesof

useful reactions

R : SExperimental 74 : 26Computed 76 : 24

Stereoselectivities

Quinidine=

G [H] in kcal/mol

Stereoselectivities

0.0 [0.0] 1.9 [2.8]

TS-R TS-S

G [H] in kcal/mol

ELECTRONIC STRUCTURETHEORY

Navigating Chemical Compound Space for Materials and Bio Design:

Tutorials

K. N. HoukMarch 16, 2011