Department of Chemistry

Woche Datum Dozent

1 20.02.2015 Ernst

2 27.02.2015 Ernst

3 06.03.2015 Helbing

4 13.03.2015 Helbing

5 20.03.2015 Helbing

6 27.03.2015 Helbing

Chirality Lecture

6 27.03.2015 Helbing

7 03.04.2015 Ostern

8 10.04.2015 Ostern

9 17.04.2015 Ernst

10 24.04.2015 Helbing

11 01.05.2015 01. Mai

12 08.05.2015 Ernst

13 15.05.2015 Ernst?

14 22.05.2015 Ernst

15 29.05.2015 Helbing

Department of Chemistry

Natural Optical Activity

Rotation of linear polarization - independent of initial orientation

http://www.quartzpage.de/gen_phys.html

“Natural optical activity is the difference in the interaction of a

chiral molecule with left versus right circularly polarized radiation” (L. Nafie)

Department of Chemistry

OA with linear and circularpolarized light

L

R

L

R

Circular Birefringence Circular Dichroism

Department of Chemistry

Chapter 1

Description of Polarized Light

Department of Chemistry

z

x

y

x

Left handed

Time profile at z=0(looking toward source)

t=0t>0

Left and Right-Handed Light

±

=

nc

z-tsin

nc

z-tcos),(E LR, ωω yx eetz

rrr

z

x

y

z

y

Right handed

t=0 t>0

CDF-Animation FieldPolarizations!Linear (x)

Department of Chemistry

Left or Right?Definitions

Opt.

RotationDefinition Grund

+

dextro (D)α > 0

Clockwise (looking towards

source)

nL > nR

vL < vR

-

laevo (L)α < 0

Anti-Clockwise (looking towards

source)

nL < nR

vL > vRlaevo (L) source) vL > vR

Light Definition

RFieldvector rotates clockwise (looking

towards source)

LFieldvector rotates anti-clockwise

(looking towards source)

)](sin[

)](cos[

nc

zte

nc

zte

y

x

−+

−

ω

ω

r

r

)](sin[

)](cos[

nc

zte

nc

zte

y

x

−−

−

ω

ω

r

r

Department of Chemistry

Generation of Polarized LightReflection

a

α

a

ααα

αα222

222

sincos

sincos

aba

abas

r

nnn

nnnE

−+

−−=

s-polarization

sticking out of the plane of light propagation

p-polarizatoin, polarization

b

a

β β

α

cos

cos=

a

b

b

a

β β

α

cos

cos=

a

bαα

αα2222

2222

sincos

sincos

abab

ababp

r

nnnn

nnnnE

−+

−−=

p-polarizatoin, polarizationin plane of light propagation

Department of Chemistry

Generation of Polarized LightReflection

αα

αα222

222

sincos

sincos

aba

abas

r

nnn

nnnE

−+

−−=

s-polarization

sticking out of the plane of light propagation

p-polarizatoin, polarization

N1

1

N2

2.41

Brewster Angel: 67.4646normal to planein plane

αα

αα2222

2222

sincos

sincos

abab

ababp

r

nnnn

nnnnE

−+

−−=

p-polarizatoin, polarizationin plane of light propagation

in plane

0 20 40 60 800

20

40

60

80

100

angle of incidence H°L

refl

ecti

onH%

L

CDF-Animation FresnelReflection!

Department of Chemistry

Generation of Polarized LightLinear birefringence

Different refractive indexof x- and y-polarized light

Normal incidence:Change in polarization

stateIncidence at an angle:Separation of beamsCDF-Animation: SummingLinearPolarizedFields

http://www.webelements.com/compounds/magnesium/magnesium_difluoride.html

Department of Chemistry

Polarizers use Reflection andLinear birefringence

© 2013 - B.Halle Nachfl. GmbH / Subject to change and correction.

Department of Chemistry

Polarizers use Reflection andLinear birefringence

© 2013 - B.Halle Nachfl. GmbH / Subject to change and correction.http://www.b-halle.de/EN/Catalog/Polarizers/Different_Types_of_Polarizing_Prisms.php

Department of Chemistry

Natural Optical Activity

Rotation of linear polarization - independent of initial orientation

http://www.quartzpage.de/gen_phys.html

“Natural optical activity is the difference in the interaction of a

chiral molecule with left versus right circularly polarized radiation” (L. Nafie)

Department of Chemistry

Optical activity andCircular birefringence

Different refractive indexfor L- and R-polarized

light

Normal incidence:Change in polarizationstateIncidence at an angle:Separation of beams

CDF-Animation: SummingLinearPolarizedFields

Computer model of Quartz lattice structure(Steven Dutch, Univ. of Wisconsin-Green Bay)

Department of Chemistry

Chirality and index of refraction

Ghosh, A.; Fischer, P., Chiral Molecules Split Light: Reflection and

Refraction in a Chiral Liquid. Physical Review Letters 2006, 97, (17),

173002.

Original

experiment with

optically activequartz

A. Fresnel, Ann.

Chim. Phys. 28, 147 (1825).

Department of Chemistry

Description of Polarized Light

We assume plane waves, propagating in the z-direction

The electric field vectors then lie in the xy-plane and can be written as a linear combination of unit vectors in x and y direction:

±

=

nc

z-tsin

nc

z-tcos),(E LR, ωω yx eetz

rrr

We neglect the z-dependence (z=0) and write

The column vector completely describes the polarization state and theamplitude of the field and we need not write the basis vectors and the time dependence.

( ) ( )

( )( )

=

±=

±=

ti

yxyx

yx

ei

eeee

eetz

ω

ω

ω

ωω

m

rrrr

rrr

1Re),(

tsin

tcos),(

tsintcos),(E LR,

Department of Chemistry

Jones Vectors

yxL

y

x

iEEE

E

E

+=

+=

=

=

1

1

0

0

1

inout Ebd

caE

=

Matrix describing sample (CD,

ORD, Absorption,LD…)

yxR

yxL

iEEi

E

iEEi

E

−=

−=

+=

+

=

1

Jones, R. C., A new calculus for the treatment of optical systems I. Description and discussion of the calculus. J. Opt. Soc. Am. 1941, 31 (7), 488-493.

(and 6 further papers II-VII)

inout Ebd

E

=

Field before

sampleField after

sample

Department of Chemistry

Jones Calculus

inout Ee

eE

=

−

−

2/

2/

0

0α

α

Absorption

ininoutout IeIEI')10ln('2

10αα −− ===

Circular dichroism

in

L

in

L

out

L IeIeI L )( ααα ∆+−− ==

in

R

in

R

out

R IeIeI R )( ααα ∆−−− ==

in

R

L

out

R

L

a

a

e

ee

a

a

=

∆

∆−−

2/

2/

2/

0

0α

αα

−=

y

x

R

L

a

a

i

i

a

a

1

1New Basis: Amplitude of left and

right handed fields

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Jones Calculus

in

R

L

out

R

L

a

a

e

ee

a

a

=

∆

∆−−

2/

2/

2/

0

0α

αα

=

−=

y

x

y

x

R

L

a

aU

a

a

i

i

a

a

1

1

in

R

L

out

R

L

a

aUU

e

eUe

a

aU

=

−

∆

∆−−

0

0 1

2/

2/

2/

α

αα

43421444 3444 2143421

in

y

x

in

y

x

out

y

x

a

a

i

ie

a

a

eeieie

ieieeee

a

a

∆∆

∆−

∆

=

++−

−+=

−

∆∆−

∆∆−

∆∆−

∆∆−−

2cosh

2sinh

2sinh

2cosh

2

2/

2222

22222/

αα

αα

α

αααα

ααααα

43421444 3444 2143421

Department of Chemistry

Jones Calculus

∆∆

∆−

∆

=

2cosh

2sinh

2sinh

2cosh

αα

αα

i

iM CD

)10ln(2 α∆=CD

Phase shift (circular birefringence): replace byα∆ φ∆i

∆∆−

∆∆

=

2cos

2sin

2sin

2cos

φφ

φφ

ORDM )10ln(2 φ∆=ORD

Department of Chemistry

Chapter 2

Overview: Optical Activity and Chiral Spectroscopy

Department of Chemistry

First Observations

Optical Rotation:

- Arago, 1811 in quartz

- Biot, 1815 in organic liquids

Circular Dichroism:

- Haidinger, 1847 in amethyst form of quartz

- Cotton, 1895 in solution of tartrate metal complexes

Vibrational:

- Katzin, 1964 indication of band in the mid-IR (a-Quartz) from NIR ORD

- Holzwarth, 1975 (VCD, C-H stretch of neat 2,2,2-trifluoromethyl-1-phenylethanol), confirmed by Nafie and Stephens

- First VORD 2009!

Department of Chemistry

First Observations

X-Rays:

- Alagana et al. 1998

Microwave:

- Tinoco, Freedman, 1957 copper helices

Radiowaves (NMR)?

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Related Phenomena (additional fields)

Raman Optical Activity

- Barron and Buckingham 1973, Werner Hug 1975

Time-resolved CD

- Several groups, 1970s (ms)

-Xie, 1990 (ps, vis)

-Hache (fs, UV)

Non-linear Optical Activity (wave mixing)

- R. Shen…(past 15 years)

Magnetic Circular Dichroism (MCD and MVCD)

- Also observed for achiral molecules

Department of Chemistry

ORD and CD

δ δδ δ

Circular Birefringence Circular Dichroism

ηδ

VORD ∼ δ

VCD ∼ η

δδ

frequency

δ

Department of Chemistry

φ

ER

EL

Why is CD measured as an angle?

θ

aa

ee

ee

EE

EE

RL

RL

aa

aa

RL

RL

∆=∆≈°

+

−=

+

−=≈

−−

−−

98.324

10ln180][

tan2/2/

2/2/

πθ

θθ rr

rr

E = ER

EL

+

Department of Chemistry

Circular Dichroism Basics

L

R

L

R

Circular Birefringence Circular Dichroism

Measure smallintensity difference

Measure small

phase difference

Find intensityminimum

Measure smallintensity ratio

Department of Chemistry

Source

Measurement ORD

DetectorWavelength

selectionSampleModulator

Polarizer Analyzer

Department of Chemistry

Experiment PCP I

Light Intensity

Modulation

Transmission

Light source Sample Detector

AnalyzerPolarizer

Modulatorλ-Selection

Analyzer angle90°

Indicated Voltage= ÛM(t)I(t)dt

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Source

L

R

Measurement CD

DetectorRotating

gratingSampleModulator

Polarizer

Department of Chemistry

Source

(globar)

L

R

Measurement VCD

Detector

(MCT)

Fixed mirror

Moving mirror SampleModulator

Polarizer

Department of Chemistry

Spectrometer

Polarizer SampleModulator

Detector

L R

Commercial (V)CD Spectrometer

Source: R.Dukor, BioTools

L R

Lock-in

Absorption

VCD AC

DC

Department of Chemistry

[CO(en)3]3+ – Experiment

350 400 450 500 550 600 650

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Ab

sorp

tion

0.2

0.3

Optical ro

tation(°

)

Λ

Co

N

N NN

NN

I

3+

3

350 400 450 500 550 600 650

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3350 400 450 500 550 600 650

-0.3

-0.2

-0.1

0.0

0.1

Optical ro

tation(°

)C

ircula

r D

ichro

ism

(°)

wavelength (nm)

Λ

∆

Department of Chemistry

600 550 500 450 400 350 300

0

50

100

150

ε (M

-1 c

m-1)

[CO(en)3]3+ – Theorie

Mark Rudolph , Tom Ziegler , Jochen Autschbach. Time-dependent density functional theory applied to ligand-field

excitations and their circular dichroism in some transition metal complexes. Chemical Physics, 391 (2011) 92 – 100.

http://dx.doi.org/10.1016/j.chemphys.2011.03.022

600 550 500 450 400 350 300

600 550 500 450 400 350 300

-300

-200

-100

0

100

200

300 m

deg

∆-(-) [Co(en)3]3+

wavelength (nm)

Λ-(+) [Co(en)3]3+

600 550 500 450 400 350 300

-2

-1

0

1

2

∆ε

(M-1 c

m-1)

Department of Chemistry

Vibrations-Zirkulardichroismus(VCD)

400

-5-4-3-2-10123

6456

VC

D x

10

5

VCD(1)-VCD(2)

900 1000 1100 1200 1300 1400 1500 1600 1700

-400

-200

0

200

Frequency [cm-1]

B3LYP 6-31**, scaled 0.97

64

71

9146

40,4155

56

5761

63

66

7285

7877

∆ε

x10

4

•Enantiomers from chiral column, poor crystal structure

•Absolute configuration determined•VCD Spectrometer ordered…

Department of Chemistry

VCD - Konformationsanalyse

Experiment

Polavarapu et al.

Department of Chemistry

CD Peptides and Proteins

UV: Konformationsanalyse (Proteine, DNA)

Source: http://cnx.org/content/m38277/latest/

Original caption: Figure 4: CD spectra of samples with

representative conformaitons. Adapted by permission from

N. Greenfield, Nat. Proto., 2006, 1, 6.

Department of Chemistry

(LKKL)n

(LK)n

α-helix

(β-sheet)

VCD Peptides and Proteins

(K)n coil

T. A. Keiderling, J. Kubelka and J. Hilario in Vibrational Circular Dichroism of

Biopolymers. Summary of Methods and Applications, Vol. Eds.: M. Brainman and V.

Gregoriou), Marcel Dekker, New York, 2005, p. 253.

K=Lysine

L=LeucineN

O

N

O

N