PC VIII: Femtochemistry and/or Photochemistry - …ffffffff-cd8c-9a46-0000... · 2016-10-04 · Femtochemistry and Photochemistry Examples gas-phase chemistry vision natural and artifiicial

PC VIII: Femtochemistryand/or Photochemistry

Organization

Physikalische Chemie VIII: Spektroskopie II• Some exercises with Mathematica• Exercises 2 weeks• Debriefing: Thursday 8.00-10.00 in room 34-K-01 or 13K24

(through 13 K 26), every second week, start Oct. 4• Return exercises Wednesday before 12.00• Computer-Exam• Script (password PCseven7)Tutor: Fivos Perakis 34 K 30

Femtochemistry: Basic Concepts

Examples of Photochemical Reactions Experimental Methods Motion in Quantum Mechanics: Wavepackets Franck-Condon Transition Jablonski Diagram, Fermi Golden Rule, Energy Gap Law Prototype Potential Energy Surfaces Non-Crossing Rule, Avoided Crossings, Conical Intersections Born Oppenheimer Approximation and its Breakdown Adiabatic and Diabatic Surfaces Mixed Quantum-Classical Methods, Landau Zener Theory Solvation Electron Transfer Theory Excitation Transfer: Exciton- and Förster Transfer

ConceptsFemtochemistry and Photochemistry

Examples

gas-phase chemistry vision natural and artifiicial photosynthesis coherent ind incoherent excitation transfer

motion in quantum mechanics

Free

Ene

rgy

R

D*AD+A-ED(R)

EA(R)

E

E

Ea

R0(D) R0

(A)

Free

Ene

rgy

R

D*AD+A-ED(R)

EA(R)

E

E

Ea

R0(D) R0

(A)

HOMO

LUMO

A*BAB*

HOMO

LUMO

A*BAB*

S0

S1

S2

kf kIC

kIS C

T1

kp kIS C10ns(dipoleallowed)

200fs –100ns

fast (Kasha‘s Rule)

1-10 pskIVR Period 2: slowHeavy elements: fast

100ns

Franck-Condontransition

Jablonski diagramand energy gap rule

Adiabatic and diabatic surfaces, non-crossing rule, Landau-Zener theory

conical intersections solution phase dynamics

Solvation Coordinate

Free

Ene

rgy

S0

S1

solvation

electron transfer

excitation transfer

FemtochemistryNobel Prize 1999

Ahmed Zewail

http://www.rleggat.com/photohistory/history/daguerr.htm

Louis Jacques Mande Daguerre, 1839Exposure Time: 10-20 min

The First Time-Resolved Photo

Stroboskop

Zeitauflösung: 1 msca. 1880

1 s 1 ms 1 ps1 ns1 s 1 fs

100 s 10-3 s 10-9 s10-6 s 10-15 s10-12 s

MechanikComputer

Radiowellen

Schall

Schwingungs-bewegung

Photochemie

Energierelaxation

Proteindynamik

Diffusionskontrollierte Chemie

Zeitpfeil

100 Femtosekunden

Lichtgeschwindigkeit: 300.000 km/s

1 s: Erde → Mond8 min: Erde → Sonne

100 fs: Dicke eines dünnen Blatt Papiers

Short Pulses with Lasers

1960 1970 1980 1990 2000

1E-15

1E-12

1E-9

1E-6

1E-3

?Compression

CPM Laser

Mode Locking

Q-Switching

Pu

lsew

idth

[sec

]

Year

Femtosecond Lasers

CPM Laser 1980

Pump-Probe Spectroscopy






Photochemical Reactions in Nature: Isomerization of Bacteriorhodopsin

Wikipedia, Halobacteria in the salt lake Chokrak (Ukraine)


http://www.biochem.mpg.de/oesterhelt/photobiology/br.html


Dobler, W. Zinth, W. Kaiser, D. Oesterhelt Excited-state reaction dynamics of Bacteriorhodopsin studied by femtosecond spectroscopy. Chem. Phys. Lett. 144 (Feb. 1988) 215


Dobler, W. Zinth, W. Kaiser, D. OesterheltExcited-state reaction dynamics of Bacteriorhodopsin studied by femtosecond spectroscopy. Chem. Phys. Lett. 144 (Feb. 1988) 215


Vision: Isomerization in Rhodopsin

movie

Photochemical Reactions in Nature: Isomerization of Rhodopsin

Q. Wang, R. W. Schoenlein, L. A. Peteanu, R. A. Mathies, C. V. Shank, Science 266 (1994) 422

Photochemical Reactions in Nature: Electron Transfer in Photosynthesis

Photochemical Reactions in Nature: Photosynthesis in Green Plants

Photochemical Reactions in Nature: Bacterial Photosynthesis


Nobel Prize in Chemistry 1988 The structure of a photosynthetic reaction center, Johann Deisenhofer, Robert Huber and Hartmut Michel


W. Zinth, J. Wachtveitl ChemPhysChem 2005, 6, 871 – 880



Photochemical Reactions in Nature: Myoglobin

Friedrich Schotte, Manho Lim, Timothy A. Jackson, leksandr V. Smirnov, Jayashree Soman, John S. Olson, George N. Phillips Jr., Michael Wulff, Philip A. Anfinrud Watching a Protein as it Functions with 150-ps Time-Resolved X-ray Crystallography, Science, 300 1944 (2003)

Prototype Photochemical Reactions in Chemistry

Prototype Photochemical Reaction: ICN

M. Dantus, M. J. Rosker, A. H. Zewail, J. Chem. Phys. 87 (1987) 2395A. H. Zewail, J. Phys. Chem. A 104 (2000) 5660

1 2 3 4

-2

-1

1

2

3

4

R/Å

eV

Photochemie: H2+-Molekül

pum

ppr

obe

prob

e

Prototype Photochemical Reaction: NaI

T. S. Rose, M. J. Rosker, A. H. Zewail, J. Chem. Phys. 91 (1989) 7415A. H. Zewail, J. Phys. Chem. A 104 (2000) 5660

Motion in Quantum Mechanics: I2

M. Gruebele, A. H. Zewail, J. Chem. Phys. 98 (1993) 883

Ring Opening of 1-3-Cyclohexadien

W. Fuß, W. E. Schmid, and S. A. Trushin, Time-resolved dissociative intense-laser field ionization for probing dynamics: Femtosecond photochemical ring opening of 1,3-cyclohexadiene, J. Chem. Phys. 112 (2000) 8347

H. Tamuraa S. Nanbu T. Ishida H. Nakamura Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization J Chem. Phys. 124, 084313 2006


H. Tamuraa S. Nanbu T. Ishida H. Nakamura Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization J Chem. Phys. 124, 084313 2006





The Laser Lab

IR-OPATi:S

Amplifier

Ti:SOscillator Vis-OPA

Experiment

h

Absorption

h

spontaneousEmission

stimulatedEmission

h

Interaction of Light with Matter

hoptic

alpu

mp

4-Level System

Laser Medium Output Coupler

Laser

Short Pulses:- Broad Gain Medium (organic Dyes, Ti:S) - Mode Locking- Dispersion Control

Laser Medium

l

Gain Profilec/2l

n n+1n-1

Output Coupler

Laser

Re(E(t))

Re(E(t))

-1 -0.5 0.5 1

-6 -4 -2 2 4 6

t

t

n

tl

cni

neEtE 22

)(

E(t)

-6 -4 -2 2 4 6

-10

-5

5

10

n

tl

cniin eeEtE n 2

2)(

Random Phase

High IntensityMode

Low IntensityMode

Aperture

Kerr Medium

d0

z

20)( nInIn

Kerr Effect:

n()

Visible Range

Dispersion

ddn

cncv

ncv

gr

ph

)(

)(

A

B

C

D

E

F L

Prism-Compressor

Ti:S Laser

- 10-100 fs- 750-900 nm- 100 MHz- 1 W (average)- 10 nJ/pulse

Nd-YAG Laser

Output Coupler

Ti:S

Ti:S Laser


The Laser Lab

IR-OPATi:S

Amplifier


Experiment

Regenerative Amplifier

- 10-100 fs- 760-850 nm- 1-10 kHz- 1-10 W (average)- 1-10 mJ/pulse

Nd-YAG LaserTi:S

PockelsCell

PockelsCell

in

out

Chirped Pulse Amplification

Ti:S Laser

Stretcher

Amplifier

Compressor

100 fs10 nJ/pulse 105 W100 MHz

100 ps10 nJ/pulse 102 W100 MHz

100 ps1 mJ/pulse 107 W1 kHz

100 fs1 mJ/pulse 1010 W1 kHz

Grating-Stretcher

f 2f fleff<0

l

Grating-Compressor


The Laser Lab

IR-OPATi:S

Amplifier


Experiment

Nonlinear Optics

tEE cos0

)cos(011 tEP

EEEP 21

)2cos(1202

2 tEP

Second Harmonic Generation

Nonlinear Crystal

12=21

Nonlinear Optics

EEEP 21

tEtEE 2010 coscos

ttEP )cos()cos( 21212

022

Sum Frequency Generation

Nonlinear Crystal

1

2

3=1+2

Difference Frequency Mixing

Nonlinear Crystal

1

2

3=2-1

Signal

Idler

1

Optical Parametrical Process

Nonlinear Crystal

1

2

3=2-1

Signal

Idler

200 µJ

3.5 µJ

2 µJ

f=50 cm

f=10 cm f=3 cm

f=20 cm

f=-5 cmR=50 cm

R=1 m

R=1m

BBOTyp II4 mm

AgGaS2Typ I

1.5 mm

Sapphire DM1DM1

DM2

DM2

M2: Delay I-IITi

:Sap

phire

:80

0 nm

, 90

fs M1: Delay p-s

200 µJ

3.5 µJ

2 µJ

f=50 cm

f=10 cm f=3 cm

f=20 cm

f=-5 cmR=50 cm

R=1 m

R=1m

BBOTyp II4 mm

AgGaS2Typ I

1.5 mm

Sapphire DM1DM1

DM2

DM2

M2: Delay I-IITi

:Sap

phire

:80

0 nm

, 90

fs M1: Delay p-s

IR Light Source

IR Pulses:• 100 fs• 200 cm-1

• 1-2 J• 1000-3500 cm-1

P. Hamm et al. Opt. Lett. 25 (2000) 1798

White-light Generation






Prototype Photochemical Reaction: NaI


J. Phys. Chem.; 1991; 95; 2022.

Licht*

J. Chem. Phys. 127, 241101 (2007)

Inversion Tunneling in Ammonia (in He droplets)

0

11 cm-1

x

x

resonance structuresChemical equilibrium

Time-propagating Wavepackets

tEi

ii

i

ett

)0()(

- in an eigenstate basis:

- direct propagation

)0()(ˆ

tettHi

2

2

2ˆ ˆˆ1 tHtHie

tHi

with

- simple numerical scheme by discretizing time

ttHitttt )(ˆ

2)()(



Wavepackets: I2


Classical Wavepacket





h

S0

S1

Vertical Franck Condon Transition



S0

S1

S2

kf kIC

kIS C

T1


200fs –100ns



100ns

Jablonski Diagram

kIVR: IntramolecularVibrational Energy Relaxation

kf: Fluorescencekp: PhosphorescencekIC: Internal conversion

(non-radiadivedecay)

kISC: Intersystem Crossing

Fermi Golden Rule: Derivation

i fk?

with

propagating the time-dependent SEQ:

same for non-resonant states:

with V<<E t/Vp(

t)

1 2 3 4 5 6

0.2

0.4

0.6

0.8

1 E=0

E=2V

E=4V

-10 -5 5 10

1

2

3

4

i fk?

relaxation into a continuum of states:

E

Fermi Golden Rule: Derivation

Fermi Golden Rule

fiif VV

)(2 2 EVk ifif

)(2 2 EVk ifif

or

with

S0

S1

S2

kf kIC

kIS C

T1


200fs –100ns



100ns

Jablonski Diagram

kIVR: IntramolecularVibrational Energy Relaxation

kf: Fluorescencekp: PhosphorescencekIC: Internal conversion

(non-radiadivedecay)

kISC: Intersystem Crossing

Energy Gap Law

Energy gap

kisc for T1S0 for several species

Internal Conversion orNon-Radiative Decay

)(2 2 EVk ifif

fiif VV

)();(),( RRrrR nucel

electronic nuclear

fifeliif VV

Franck-Condon Factor

kIVR kISC

kIVR

T1

S0

=0=1

·

·

=0=1

·

·



)()( 01 Sf

TiFC

)( 0Sf

)( 1Ti


Poor overlap Better overlap

Energy Gap Law

The vibrational frequency of deuterium substituted compounds is lower than unsubstituted

Thus higher quantum numbers (more nodes) involved in final state for same energy gap – poorer overlap.

Rates of T1 – S0 intersystem crossing

Energy Gap Law

• Rate of intramolecular energy transfer decreases with increasing energy gap

• Usually S1-T1 < T1-S0 < S1-S0

• Thus this factor tends to make ISC faster than IC

Kasha‘s Rule

• Emission from the lowest excited state S1.• Consequence of energy gap law (FC factor)• In general E(S2)-E(S1) << E(S1)-E(S0)

S3

S2

S1

S0

Thus fast internal conversion between higher singlet states





0° 90° 180°

ba 0°

90°

180°

Ethylene: MO picture

Ethylene: Large Scale CI

E (k

cal/m

ol)

Symmetric case: {coupleAsymmetric case: {couple 33 CI Model

)2()1( spatialpart

spinpart )1()2()2()1(

symmetricunder particle

exchangesymmetric antisymmetric symmetric

)1()2()2()1( )1()2()2()1(

)1()2()2()1()2()1()2()1(

bb

Singlet11

Triplet3

Singlet12

Singlet11

1 2 3 4

)1(*)2()2(*)1(

)1(*)2()2(*)1(

)2(*)1(*

Prototype Isomerization: Ethylene

Breaking the Symmetry

Charge 1.85 Å away along the C=C axis

Prototype Isomerization: Ethylene

CH2=NH2+


Examples of Photochemical Reactions Experimental Methods Motion in Quantum Mechanics: Wavepackets Franck-Condon Transition Jablonski Diagram, Fermi Golden Rule, Energy Gap Law Prototype Potential Energy Surfaces Non-Crossing Rule, Avoided Crossings, Conical

Intersections Born Oppenheimer Approximation and its Breakdown Adiabatic and Diabatic Surfaces Mixed Quantum-Classical Methods, Landau Zener Theory Solvation Electron Transfer Theory Excitation Transfer: Exciton- and Förster Transfer

Na+I-

NaI

bNa+I-

NaI

a

R

Na+I-

NaI

bNa+I-

NaI

a

R

Ionic Bond

Avoided Crossing, Non-crossing Rule

)()()()(

)(2221

1211

RHRHRHRH

RH

Two surfaces cross when:

0)()()(

12

2211

RHRHRH

In 1D: Avoided Crossing

Avoided Crossing in NaI


Avoided Crossing, Non-crossing Rule

)()()()(

)(2221

1211

RHRHRHRH

RH

Two surfaces cross when:

0)()()(

12

2211

RHRHRH

In 2D: 0D-Conical Intersection C. Woywod, W. Domcke, A. L. Sobolewski, H.-J. Werner J. Chem. Phys. 100, 1400 (1994)

S1 and S2 in pyrazine in the Q6a and Q10a subspace



Avoided Crossing in NaI


Born Oppenheimer Expansion

Na+I-

NaI

bNa+I-

NaI

a

R

Na+I-

NaI

bNa+I-

NaI

a

R

Ionic Bond

2

1)(

2

)(1

12

12

2

1

00

ad

ad

nuc

nuc

EE

TFFT

ti

Adiabatic Representation

2

1)(

2)(

12

)(12

)(1

2

1

00

diadia

diadia

nuc

nuc

EEEE

TT

ti

Diabatic Representation

with: 2112

R

F

-2 -1 1 2

-1000

1000

2000

3000

10 20 30 40 50 60

0.05

0.1

0.15

0.2

10 20 30 40 50 60

0.05

0.1

0.15

0.2

-2 -1 1 2

-1000

1000

2000

3000a b

c d

Wavepacket on Coupled Surfaces

Adiabatic Representation

+Output of quantum chemistry programs

+Born Oppenheimer approximation- Discontinuous at CI- Breaks down in avoided crossing

- Useless for numerical wavepacketpropagation


+ renders or small

+closer to chemical intuition+continuous even in CI+ Better description in avoided

crossing region+Useful for numerical purposes- Requires additional couplingsurface E12

- Not calculated by quantum chemistry programs

- Not unique in more than 1D

0/ )( elR

222

2112

222

2111

)5.0(

)5.0(

xkxkV

xkxkV

21212 xkV

212

121

VVVV

H

V1, V2 V12

S1 and S2 in pyrazine in the Q6a and Q10a subspace

Domcke et al. JCP 100 (1994) 1400



S. Hahn, G. Stock, J. Phys. Chem. B, Vol. 104, 2000, 1146

Model RhodopsinS1 (adiabatic)

S0 (adiabatic)

Model Rhodopsin

S. Hahn, G. Stock, J. Phys. Chem. B, Vol. 104, 2000, 1146

500 nm

570 nm



h

Reaction Coordinate

h

Barrier

Reaction Coordinate

h

Barrier

Reaction Coordinate

a bc

h

Reaction Coordinate

h

Barrier

h

Barrier

Reaction Coordinate

h

Barrier

Reaction Coordinate

a bc



2

1)(

2)(

12

)(12

)(1

2

1

00

diadia

diadia

nuc

nuc

HHHH

TT

ti


Semiclassical Approximation:

tvtR )(

2

1)(

2)(

12

)(12

)(1

2

1

))(())(())(())((

cc

tRHtRHtRHtRH

cc

ti diadia

diadia

H12 small

H12 large

velocity small

velocity large

d/dR(H11-H22)small

d/dR(H11-H22)large

2211

212

24exp1HHR

Hhv

P dia

Landau Zener: Velocity Dependence

pump=300 nm

pump=295 nm

pump=290 nm

pump=284 nm

Mean-Field Approach

Equation of motion of classical subsystem

Equation of motion of quantum subsystem

Hellmann-Feynmann force

Energy conservation

0.1 0.2 0.3 0.4 0.5

0.2

0.4

0.6

0.8

1

0.1 0.2 0.3 0.4 0.5

-1

1

2

-2 -1 1 2

-1000

1000

2000

3000

-2 -1 1 2

-1000

1000

2000

3000a b

c d

tt

R(t)

Popu

latio

n

Mean-Field Approach

-2 -1 1 2

-1000

1000

2000

3000

10 20 30 40 50 60

0.05

0.1

0.15

0.2

10 20 30 40 50 60

0.05

0.1

0.15

0.2

-2 -1 1 2

-1000

1000

2000

3000a b

c d

Wavepacket on Coupled Surfaces

R

a b

R

pad

1-pad

Mean-Field versus Surface Hopping



+-+-

+-+

-

+-

+-

+- +-+- +-

+- +-

+-+-

+-+

-

+-

+-

+- +-

+- +-

+- +-

+-+

-

+ -+ -+ -+ -

+ -+ -

+ -+ -

+- +-

- Solute +

+-

+-

+-

+-

+ -+ -+ -+ -

+ -+ -

+ -+ -

+-

+-

+-

+-

+ -+ - + -+ -

+ -+ - + -+ -

+-

+-+- +-

+- +-+- +-

+-

+-

+ -+ - + Solute -

h

Solvation

23)12(

)1(

rE

Onsager‘s Reaction Field Model

Solvation


Free

Ene

rgy

S0

S1

Solvation of Coumarin in Ploar Solvents

M. L. Horng, J. A. Gardecki, A. Papazyan, M. Maroncelli, SubpicosecondMeasurements of Polar Solvation Dynamics: Coumarin 153 Revisited J. Phys. Chem.; 1995; 99(48); 17311-17337.

50 fsFormamide

50 ps

Solvation of Coumarin in Polar Solvents

M. L. Horng, J. A. Gardecki, A. Papazyan, M. Maroncelli, SubpicosecondMeasurements of Polar Solvation Dynamics: Coumarin 153 Revisited J. Phys. Chem.; 1995; 99(48); 17311-17337.

Solvation


Free

Ene

rgy

S0

S1

Central Limit Theorem

When a random property is the sum of many random properties, e.g.:

N

izP

1

then, the sum (P) is Gaussian distributed (in the limit N), regardless what the distribution of the individual terms (z) is. The mean of the sum is:

zNP

and the variance:

22zzNPP

Polarisation around a dipole

+-+-

+-+

-+

-+

-

+- +-+- +-

+- +-

+-+-

+-+

-

+-

+-

+- +-

+- +-

+- +-

+-+

-

+ -+ -+ -+ -

+ -+ -

+ -+ -

+- +-

- Solute +

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+ -

+ -+ -

+ -

+ -

+-

Polarisation in a Plate Capacitor

Energy of a single solute molecule

-2 2 4 6 8 100

-2 2 4 6 8 100

-2 2 4 6 8 100

N=1

N=2

N=15

prob

abilit

y

P/



Polarisation P

Free

Ene

rgy

F

P)

Ene

rgy

E

a b

0Polarisation P

Free

Ene

rgy

F

P)

Ene

rgy

E

0

-TS

Field =0 Field >0

time

posi

tion

x

- 3- 2- 1

123

Langevin Dynamics

with

Fluctuation-Dissipation Theorem

Ensemble of Particles

thermal equilibrium non-equilibrium

Solvation


Free

Ene

rgy

S0

S1

Onsager Regresssion Hypothesis

2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1

time

x(t)

x(0)

Correlation Function

2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1

time

x(t)

x(0) critically

damped

=2

2 4 6 8 10 12 14

-0.4-0.2

0.20.40.60.8

1

time

under-damped

=0.5

2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1

x(t)x

(0)

=5

over-damped

Kramers Theory of Reaction Kinetics

reactant

product

FB

R

B

Kramers Theory of Reaction Kinetics

criticallydamped

stronglyoverdamped

under-damped

Tk

ER

BB

RB

b

ek

2421 2

2

TkE

RBR

B

b

ek

2

TkE

R

B

bR

B

B

eTk

EIpk

2

)(

R

P. Hänggi et al., Rev. Mod. Physics, 62 (1990) 251

G. R. Fleming, S. H. Courtney, M. W. Balk, J. Stat. Phys. 42 (1986) 83

a b

Photoisomerisation of Stilbene: Dependence on Solvent Viscosity






Artificial Photosynthesis: Grätzel Cell

DonorHOMO

LUMO Conduction Band

Valence Band

I

e-

e-

Light

TiO2

M. Grätzel, Nature 2001, 414, 338−344.

Donor AcceptorHOMO

LUMO

Light

Donor Acceptor

ET ?

Donor Acceptor

DA D*A D+A-

Donor Acceptor

DA

r

Donor Acceptor

VD(r)VA(r)

D,EDA,EA

Distance Dependence of ElectronTransfer

F. D. Lewis,* T. Wu, Y. Zhang, R. L. Letsinger, S. R. Greenfield, M. R. Wasielewski, Distance-DependentElectron Transfer in DNA Hairpins Science 277 (1997) 673

Rek 1 Å-1

D A

+-

+-

+-

+-

+-+-

+-

+-

+-

+-

+-

+-

+ -

+-

+ -

+ -

+ -

+-

D+ A- +-

+-

+-

+-

+-

+-+-

+-

+-

+-

+-+

- + -

+-

+ -+ -

+ -

+-

Solvation of a Charge Transfer Complex

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+ -

+ -+ -

+ -

+ -

+-


Energy of a single solute molecule


Polarisation P

Free

Ene

rgy

F

P)

Ene

rgy

E

a b

0Polarisation P

Free

Ene

rgy

F

P)

Ene

rgy

E

0

-TS

Field =0 Field >0

Marcus Theory of Electron Transfer

TkF

TFkVk

B

a

BDAET exp2

2

Free

Ene

rgy

R

D*AD+A-

F

F

Fa

R0(DA) R0

(D+A-)

F DA(R)

F D+A-(R)


TkFFF

TFkVk

BBDAET

4

exp2

22

Free

Ene

rgy

R

D*AD+A-

F

F

Fa

R0(DA) R0

(D+A-)

F DA(R)

F D+A-(R)



Rek 1 Å-1


TkFFF

TFkVk

BBDAET

4

exp2

22

Free

Ene

rgy

R

D*AD+A-

F

F

Fa

R0(DA) R0

(D+A-)

F DA(R)

F D+A-(R)

Marcus Theory of Electron TransferFr

ee E

nerg

y

R R R

FFFFFF

Normal RegimeInverted Regime Barrier Less

TkFFF

TFkVk

BBDAET

4

exp2

22

Marcus Parabola

J. R. Miller, L. T. Calcaterra, G. L. Closs Intramolecular long-distance electron transfer in radical anions. The effects of free energy and solvent on the reaction rates J. Am. Chem. Soc.; 1984; 106(10); 3047-3049.


Marcus Parabola

P. Huppman,* T. Arlt,* H. Penzkofer,* S. Schmidt,* M. Bibikova, B. Dohse, D. Oesterhelt, J. Wachtveit,* and W. Zinth* Kinetics, Energetics, and Electronic Coupling of the Primary Electron Transfer Reactions in Mutated Reaction Centers of Blastochloris viridis Biophys J, 2002, 3186 82


Marcus Parabola

Donor AcceptorHOMO

LUMO

Light

Donor Acceptor

ET ?

Donor Acceptor

DA D*A D+A-

Donor Acceptor

DA

Supressing Back Electron Transfer

Forward ET: F=Fand small barrier less

R

Backward ET: F>>F and large strongly in the inverted regimeh


3 ps

500 ps

Zinth et al. Spectrochimica Acta Part A 51 (1995) 1565-1578 andFeher at al. J. Phys. Chem. 1994,98, 3417-3423

1 ms

0.9 ps

200 ps


TkFFF

TFkVk

BBDAET

4

exp2

22

Free

Ene

rgy

R

D*AD+A-

F

F

Fa

R0(DA) R0

(D+A-)

F DA(R)

F D+A-(R)

Marcus Parabola

J. R. Miller, L. T. Calcaterra, G. L. Closs Intramolecular long-distance electron transfer in radical anions. The effects of free energy and solvent on the reaction rates J. Am. Chem. Soc.; 1984; 106(10); 3047-3049.

F=F


Marcus Parabola

F=F

Solvation Energy

23)12(

)1(

rE

Onsager‘s Reaction Field Model

+-+-

+-+

-

+-

+-

+- +-+- +-

+- +-

+-+-

+-+

-

+-

+-

+- +-

+- +-

+- +-

+-+

-

+ -+ -+ -+ -

+ -+ -

+ -+ -

+- +-

- Solute +

D A

+-

+-

+-

+-

+-+-

+-

+-

+-

+-

+-

+-

+ -

+-

+ -

+ -

+ -

+-

D+ A- +-

+-

+-

+-

+-

+-+-

+-

+-

+-

+-+

- + -

+-

+ -+ -

+ -

+-

Solvation of a Charge Transfer Complex

DAADr re

Re

ReE

222

2211

81

in analogy to Onsager‘s Reaction Field Model



Rek 1 Å-1

Bridged Electron Transfer

DA

Superexchange

DA

Hopping


W. B. Davis, W. A. Svec, M. A. Ratner, M. R., Nature 396, 60 - 63 (1998)


k ET(

ps-1

)


Distance [Å]

0.04 Å-1



Superexchange in Reaction Center?

Wachtveitl and Zinth, ChemPhysChem 2005, 6, 871




Special Pair in Reaction Center

LH II Antenna Complex



J-Aggregates

H2OMethanol

J. Moll, S. Daehne, J. R. Durrant and D. A. Wiersma, Optical dynamics of excitons in J aggregates of a carbocyanine dye, JCP 102, (1995) 6362

HOMO

LUMO

A*B AB*

Excitation (Exciton) Transfer

Excitonic Coupling

1 2

R12

1 2

R12

1

2

R12

1

2

R12

1 2

R12


Photosynthesis


Excitons in a Ring

j=0 j=N-1

NjJJ

2cos2cos2 00

a b

c

Ener

gy

Excitons in a Ring

Coherent Transfer of Excitation Energy?

Fleming et al., Nature 434 (2005) 625 and Nature 446 (2007) 782

FMO Complex

Coherent versus Incoherent Transfer

DA

DA


DA

Superexchange

DA

Hopping

HOMO

LUMO

A*B AB*

Exciton Transfer: Coherent

HOMO

LUMO

A*B AB*

Förster Transfer: Incoherent

k

k

Förster Transfer

Fermi Golden Rule

Absorption and Emission Spectra

Förster Transfer

Förster Efficiency

h krad

kDA

Förster Transfer

Schuler B, Single-molecule fluorescence spectroscopy of protein folding, ChemPhysChem 6 (2005) 1206-1220

Protein Folding: Single Molecule Spectroscopy

Two-State Folding Observed in Individual Protein MoleculesRhoades, E.; Cohen, M.; Schuler, B.; Haran, G.; J. Am. Chem. Soc.; 2004; 126; 14686-14687

Documents

PC VIII: Femtochemistry and/or Photochemistry - …ffffffff-cd8c-9a46-0000... · 2016-10-04 · Femtochemistry and Photochemistry Examples gas-phase chemistry vision natural and artifiicial