Organic quantum chemistry

Trygve Helgaker

Department of Chemistry, University of Oslo

November 25, 2009

1

Chemistry and computation

“Every attempt to employ mathematical methods in the study of

chemical questions must be considered profoundly irrational. If

mathematical analysis should ever hold a prominent place in chemistry—an

aberration which is happily impossible—it would occasion a rapid and

widespread degradation of that science.”

August Comte, 1748–1857

“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.”

P. A. M. Dirac, 1902–1984

2

Quantum mechanics and the many-body problem

3

The electronic computer—the quantum chemist’s tool

• The solution came in an unexpected manner, with the emergence of the computer

• ENIAC (Electronic Numerical Integrator and Computer) (1946)

– the first large-scale electronic digital reprogramable computer

– 30-ton collection of 19 000 vacuum tubes (357 multiplies per second)

– four of the six main programmers of ENIAC

4

The electronic computer—the quantum chemist’s tool

• Over the last 50 years, computers have developed in a spectacular fashion,

– Moore’s law: the capacity of computers double every two years, at no extra cost

– computers are now 10000 more powerful than one generation ago

• With this amazing tool at their disposal, chemists have diligently developed new

computational techniques: quantum chemistry

– the development of refined models of chemical electronic systems

– their solution using advanced methods of numerical analysis

– their implementation on the latest computer hardware

• The exact solution is beyond reach but can be approached systematically

– the “insoluble” problem is being solved every day—by nonspecialists!

5

Atomization energies (kJ/mol)

-200 200

HFDZ

-200 200 -200 200

HFTZ

-200 200 -200 200

HFQZ

-200 200 -200 200

HF5Z

-200 200 -200 200

HF6Z

-200 200

-200 200

MP2DZ

-200 200 -200 200

MP2TZ

-200 200 -200 200

MP2QZ

-200 200 -200 200

MP25Z

-200 200 -200 200

MP26Z

-200 200

-200 200

CCSDDZ

-200 200 -200 200

CCSDTZ

-200 200 -200 200

CCSDQZ

-200 200 -200 200

CCSD5Z

-200 200 -200 200

CCSD6Z

-200 200

-200 200

CCSD(T)DZ

-200 200 -200 200

CCSD(T)TZ

-200 200 -200 200

CCSD(T)QZ

-200 200 -200 200

CCSD(T)5Z

-200 200 -200 200

CCSD(T)6Z

-200 200

6

The emergence of DFT

• The traditional methods of quantum chemistry are capable of high accuracy

– nevertheless, most calculations are performed using density-functional theory (DFT)

• What is the reason for the poularity of DFT?

– the standard methods are (at least for high accuracy) very expensive

7

Reaction Enthalpies (kJ/mol)

B3LYP CCSD(T) exp.

CH2 + H2 → CH4 −543 1 −543 1 −544(2)

C2H2 + H2 → C2H4 −208 −5 −206 −3 −203(2)

C2H2 + 3H2 → 2CH4 −450 −4 −447 −1 −446(2)

CO + H2 → CH2O −34 −13 −23 −2 −21(1)

N2 + 3H2 → 2NH2 −166 −2 −165 −1 −164(1)

F2 + H2 → 2HF −540 23 −564 −1 −563(1)

O3 + 3H2 → 3H2O −909 24 −946 −13 −933(2)

CH2O + 2H2 → CH4 + H2O −234 17 −250 1 −251(1)

H2O2 + H2 → 2H2O −346 19 −362 3 −365(2)

CO + 3H2 → CH4 + H2O −268 4 −273 −1 −272(1)

HCN + 3H2 → CH4 + NH2 −320 0 −321 −1 −320(3)

HNO + 2H2 → H2O + NH2 −429 15 −446 −2 −444(1)

CO2 + 4H2 → CH4 + 2H2O −211 33 −244 0 −244(1)

2CH2 → C2H4 −845 −1 −845 −1 −844(3)

8

NMR spectra: nuclear magnetic spin transitions

• Effective NMR spin Hamiltonian

H = −

X

i

BT(I − σi)Miz +

X

i<j

KijMi · Mj

σi = d2E/dBdMi, Kij = d2E/dMidMj

• Simulated 200 MHz NMR spectra of vinyllithium (C2H3Li)

0 100 200

MCSCF

0 100 200 0 100 200

B3LYP

0 100 200

0 100 200

experiment

0 100 200 0 100 200

RHF

0 100 200

9

Valinomycin C54H90N8O18

• DFT can be applied to large molecular systems such as valinomycin (168 atoms)

– there are a total of 7587 spin–spin couplings to the carbon atoms in valinomycin

– below, we have plotted the magnitude of the reduced LDA/6-31G coupling constants

on a logarithmic scale, as a function of the internuclear distance:

500 1000 1500

1019

1016

1013

– the coupling constants decay in characteristic fashion, which we shall examine

– most of the indirect couplings beyond 500 pm are small and cannot be detected

10

New Challenges

• Today quantum chemistry has become an integral part of modern chemistry

– used by specialists and nonspecialists alike

– for prediction, elucidation, explanation and confirmation

– Computational Science has become an important area of modern science

• But, chemistry itself is in constant change

– biochemistry

– materials science

• This development provides ever new challenges to quantum chemistry

– we must prepare ourselves for tomorrow’s important problems

• Quantum chemistry is an interdisciplinary science

– theory, experiment, computation

– chemistry, physics, mathematics, computer technology

• The future of quantum chemistry requires knowledge of all these areas!

11

QSD & CTCC, Department of Chemistry, University of Oslo

•! Centre for Theoretical and Computational Chemistry (CTCC)

–! centre of excellence established in 2007 for a period of 5 (10) years

–! shared equally with the University of Tromsø

–! 10 (5+5) senior researchers

–! 30 people connected to CTCC in Oslo

•! Experimental activities organized around a core of quantum chemistry

12

13

Courses in Theoretical Chemistry

• KJM 2600

– Kvantekjemi og spektroskopi (Quantum Chemistry and Spectroscopy)

– Atkins and de Paula: ‘Elements of Physical Chemistry’

– 10 study points (spring term)

• KJM 4600

– Molekylmodellering (Molecular Modelling)

– Cramer: ‘Essentials of Computational Chemistry’

– 10 study points (spring term)

• KJM 5600

– Kvantekjemi (Quantum Chemistry)

– Atkins: ‘Molecular Quantum Mechanics’

– 10 study points (every third term)

• KJM 5610

– Molekylegenskaper (Molecular Properties)

– Atkins: ‘Molecular Quantum Mechanics’

– 10 study points (every third term)

14

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