Femtochemistry And/Or Photochemistry Organization

PC VIII: Femtochemistry and/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 S2 conical intersections solution phase dynamics fast (Kasha‘s Rule)

kIVR 1-10 ps Period 2: slow Heavy elements: fast

S1 kISC

T 1

100ns

kf kIC kp kISC 10ns 200fs –100ns (dipole allowed)

Jablonski diagram Energy Free and energy gap rule

electron transfer S Franck-Condon 0 transition D*A ED(R) + - D A Solvation Coordinate E (R) A solvation

E FreeFree Energy Energy Ea

E

AB* A*B Adiabatic and diabatic surfaces, non- A*B R (D) R (A) R

crossing rule, Landau-Zener theory 0 0 HOMO Concepts HOMO

excitation transfer LUMO motion in quantum mechanics Femtochemistry and Photochemistry LUMO Examples

gas-phase chemistry vision natural and artifiicial photosynthesis coherent ind incoherent excitation transfer Femtochemistry Nobel Prize 1999 Ahmed Zewail The First Time-Resolved Photo

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

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

Zeitauflösung: 1 ms ca. 1880 Zeitpfeil

Radiowellen Mechanik Schall Computer 100 s10-3 s1010-6 s10-9 s 10-12 s -15 s

1 s 1 ms1 s 1 ns 1 ps 1 fs Proteindynamik Schwingungs- bewegung Diffusionskontrollierte Chemie Photochemie Energierelaxation 100 Femtosekunden

Lichtgeschwindigkeit: 300.000 km/s

1 s: Erde → Mond 8 min: Erde → Sonne

100 fs: Dicke eines dünnen Blatt Papiers Short Pulses with Lasers

1E-3

1E-6 Q-Switching

1E-9 Mode Locking

CPM Laser 1E-12 Compression

Pulsewidth [sec] Pulsewidth 1E-15 ?

1960 1970 1980 1990 2000 Year Femtosecond Lasers

CPM Laser 1980 Pump-Probe Spectroscopy Pump-Probe Spectroscopy Pump-Probe Spectroscopy Pump-Probe Spectroscopy 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 Photochemical Reactions in Nature: Isomerization of Bacteriorhodopsin

Wikipedia, Halobacteria in the salt lake Chokrak (Ukraine) Photochemical Reactions in Nature: Isomerization of Bacteriorhodopsin Photochemical Reactions in Nature: Isomerization of Bacteriorhodopsin

http://www.biochem.mpg.de/oesterhelt/photobiology/br.html Photochemical Reactions in Nature: Isomerization of Bacteriorhodopsin

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

Dobler, W. Zinth, W. Kaiser, D. Oesterhelt Excited-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 Photochemical Reactions in Nature: Bacterial Photosynthesis 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 Photochemical Reactions in Nature: Electron Transfer in Photosynthesis

W. Zinth, J. Wachtveitl ChemPhysChem 2005, 6, 871 – 880 Photochemical Reactions in Nature: Electron Transfer in Photosynthesis 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) 2395 A. H. Zewail, J. Phys. Chem. A 104 (2000) 5660 + Photochemie: H2 -Molekül probe eV 4 3 2 probe 1 pump

1 2 3 4 R/Å -1 -2 Prototype Photochemical Reaction: NaI

T. S. Rose, M. J. Rosker, A. H. Zewail, J. Chem. Phys. 91 (1989) 7415 A. 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 Ring Opening of 1-3-Cyclohexadien

H. Tamuraa S. Nanbu T. Ishida H. Nakamura Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization J Chem. Phys. 124, 084313 2006 Ring Opening of 1-3-Cyclohexadien

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

Ti:S Ti:S Oscillator Vis-OPA Amplifier IR-OPA Experiment Interaction of Light with Matter

spontaneous stimulated Absorption Emission Emission h h h 4-Level System

h optical pump Laser

Laser Medium Output Coupler

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

Laser Medium Output Coupler

c/2l Gain Profile

n-1 nn+1  Re(E(t))

-1 -0.5 0.5 1 t

Re(E(t))

-6 -4 -2 2 4 6 t

c i2n t 2l E(t)   Ene n Random Phase

E(t)

-6 -4 -2 2 4 6

-5

-10

c  i2n t i n 2l E(t)   Ene e n Kerr Medium High Intensity Mode

Low Intensity z Mode Aperture

Kerr Effect:

n(I)  n0  I  n2 n() iil Range Visible v v gr ph   n n (

(

Dispersion

c c   ) )

 c 

d dn

  Prism-Compressor

A F  L

C E

B D Ti:S Laser

Ti:S Nd-YAG Laser

Output Coupler - 10-100 fs - 750-900 nm - 100 MHz - 1 W (average) - 10 nJ/pulse Ti:S Laser Pump-Probe Spectroscopy The Laser Lab

Ti:S Ti:S Oscillator Vis-OPA Amplifier IR-OPA Experiment Regenerative Amplifier

in Pockels Cell

Ti:S Nd-YAG Laser

out - 10-100 fs - 760-850 nm Pockels - 1-10 kHz Cell - 1-10 W (average) - 1-10 mJ/pulse Chirped Pulse Amplification

Ti:S Laser 100 fs 10 nJ/pulse  105 W 100 MHz Stretcher 100 ps 10 nJ/pulse  102 W 100 MHz Amplifier 100 ps 1 mJ/pulse  107 W 1 kHz Compressor 100 fs 1 mJ/pulse  1010 W 1 kHz Grating-Stretcher

f 2ff leff<0 Grating-Compressor

l 

Pump-Probe Spectroscopy The Laser Lab

Ti:S Ti:S Oscillator Vis-OPA Amplifier IR-OPA Experiment Nonlinear Optics

P  1  E  2  E  E  E  E cost 0 1 P  1  E0 cos(t)

2 2 P  2  E0 1 cos(2t) Second Harmonic Generation

Nonlinear Crystal

 =2 1 2 1 Nonlinear Optics

P  1 E  2  E  E   E  E0 cos1t  E0 cos2t

2 2  P  2  E0 cos( 1  2 )t  cos( 1 2 )t Sum Frequency Generation

Nonlinear Crystal

2

3=1+2

1 Difference Frequency Mixing

Nonlinear Crystal

3=2-1 1 Idler

2 1 Signal Optical Parametrical Process

Nonlinear Crystal  = - 3 2 1 Idler

2 1 Signal IR Light Source

IR Pulses: R=1 m M2: Delay  • 100 fs I-II AgGaS2 -1 R=1m Typ I •200 cm 1.5 mm •1-2 J DM2 • 1000-3500 cm-1 200 µJ M1: Delay  f=50 cm f=20 cm p-s 3.5 µJ R=50 cm f=-5 cm f=10 cm f=3 cm Ti:Sapphire:Ti:Sapphire:

800 nm, 90 fs 90 fs nm, nm, 800 800 2 µJ

Sapphire DM1 BBO DM1 DM2 Typ II 4 mm P. Hamm et al. Opt. Lett. 25 (2000) 1798 White-light Generation Pump-Probe Spectroscopy 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 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 Prototype Photochemical Reaction: NaI

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

J. Phys. Chem.; 1991; 95; 2022. Inversion Tunneling in Ammonia (in He droplets)

Chemicalresonance equilibrium structures x

1 1 cm-1

0 x

J. Chem. Phys. 127, 241101 (2007) Time-propagating Wavepackets

- in an eigenstate basis: E i i t   (t)   (t  0) i ie

- direct propagation

Hˆ i t (t)  e  (t  0)

with Hˆ 2 i t ˆ ˆ H H 2  e 1 i t  2 t    - simple numerical scheme by discretizing time Hˆ (t  t)  (t  t)  2i (t)t  Motion in Quantum Mechanics: I2

M. Gruebele, A. H. Zewail, J. Chem. Phys. 98 (1993) 883 Wavepackets: I2

Classical Wavepacket

M. Gruebele, A. H. Zewail, J. Chem. Phys. 98 (1993) 883 Motion in Quantum Mechanics: I2

M. Gruebele, A. H. Zewail, J. Chem. Phys. 98 (1993) 883 Femtochemistry: Basic Concepts

h

S0 Femtochemistry: Basic Concepts

S2 fast (Kasha‘s Rule)

kIVR 1-10 ps Period 2: slow Heavy elements: fast kIVR: Intramolecular S k Vibrational Energy 1 ISC Relaxation k : Fluorescence T 1 f kp: Phosphorescence

100ns kIC: Internal conversion k k k k (non-radiadive f IC p ISC decay) 10ns 200fs –100ns (dipole kISC: Intersystem allowed) Crossing

S0 Fermi Golden Rule: Derivation

i k?  f

with

propagating the time-dependent SEQ: 1 E=0

0.8

0.6 E=2V same for non-resonant states: p(t) 0.4 E=4V 0.2

1 2 3 4 5 6 with V<<E t/V Fermi Golden Rule: Derivation

 f i k?

relaxation into a continuum of states:

-10 -5 5 10 E Fermi Golden Rule

2 2 kif  Vif  (E) 

2 2 or kif  Vif (E)  with Vif  i V  f Jablonski Diagram

S2 fast (Kasha‘s Rule)

kIVR 1-10 ps Period 2: slow Heavy elements: fast kIVR: Intramolecular S k Vibrational Energy 1 ISC Relaxation k : Fluorescence T 1 f kp: Phosphorescence

100ns kIC: Internal conversion k k k k (non-radiadive f IC p ISC decay) 10ns 200fs –100ns (dipole kISC: Intersystem allowed) Crossing

S0 Energy Gap Law

kisc for T1S0 for several species

Energy gap Internal Conversion or Non-Radiative Decay

2 2 kif  Vif  (E) 

Vif  i V  f

(R,r)  el (r; R)nuc (R)

electronic nuclear  Vif  i Vel f i  f

Franck-Condon Factor Internal Conversion or Non-Radiative Decay

· · k IVR =1 kISC =0 T1

kIVR · · =1 =0 S0 Internal Conversion or Non-Radiative Decay

(T1 ) i

(S0 )  f  (T1 ) (S0 ) FC  i  f Internal Conversion or Non-Radiative Decay

Poor overlap Better overlap Energy Gap Law

Rates of T1 –S0 intersystem crossing

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. 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 Thus fast internal S2 conversion S 1 between higher singlet states S0 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 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 Ethylene: MO picture a b 0°  

90°  

180° 0° 90° 180° Ethylene: Large Scale CI E (kcal/mol) 1 2 3 4



 spatial  (1) (2)  (1) *(2)   (1) *(2)   *(1) *(2) part   symmetric (2) *(1) (2) *(1) under particle symmetric antisymmetric symmetric exchange (1)(2) spin  (1) (2) (2) (1) (1) (2) (2) (1)  b(1)b(2) (1) (2) (2) (1) part  (1) (2)  (2) (1)

Singlet Singlet Triplet Singlet 1 1 3 1 1 2  1

Symmetric case: {couple

Asymmetric case: {couple 33 CI Model Prototype Isomerization: Ethylene Breaking the Symmetry Charge 1.85 Å away along the C=C axis Prototype Isomerization: Ethylene + CH2=NH2 Femtochemistry: Basic Concepts

a b Na+I- Na+I- NaI NaI

R Avoided Crossing, Non-crossing Rule

 H11(R) H12 (R) H (R)     H 21(R) H 22 (R)

Two surfaces cross when:

H11(R)  H 22 (R)

H12 (R)  0

In 1D: Avoided Crossing AvoidedCrossingin NaI

T. S. Rose, M. J. Rosker, A. H. Zewail, J. Chem. Phys. 91 (1989) 7415 A. H. Zewail, J. Phys. Chem. A 104 (2000) 5660 Avoided Crossing, Non-crossing Rule

S1 and S2 in pyrazine in the Q6a and Q10a subspace

 H11(R) H12 (R) H (R)     H 21(R) H 22 (R)

Two surfaces cross when:

H11(R)  H 22 (R)

H12 (R)  0

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

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

a b Na+I- Na+I- NaI NaI

R   Adiabatic Representation

(ad )    1  Tnuc F12   E 0  1  i        1    t    F T   (ad )       2   12 nuc   0 E2  2 

 with: F     12 1 R 2  Diabatic Representation

(dia) (dia)    1  Tnuc 0   E E  1  i        1 12    t    0 T   (dia) (dia)       2   nuc   E12 E2  2  Wavepacket on Coupled Surfaces

ab3000 3000

2000 2000

1000 1000

-2 -1 1 2 -2 -1 1 2

-1000 -1000

0.2 cd0.2 0.15 0.15

0.1 0.1

0.05 0.05

10 20 30 40 50 60 10 20 30 40 50 60 Adiabatic Representation Diabatic Representation

+Output of quantum chemistry + renders  /  R  (el )  0 or small programs +Born Oppenheimer approximation +closer to chemical intuition - Discontinuous at CI +continuous even in CI - Breaks down in avoided crossing + Better description in avoided crossing region - Useless for numerical wavepacket +Useful for numerical purposes propagation - Requires additional coupling

surface E12 - Not calculated by quantum chemistry programs - Not unique in more than 1D V1, V2 V12

2 2 V1  k1 (x1  0.5)  k2 x2 2 2 V2  k1 (x1  0.5)  k2 x2

V12  k12 x2

 V1 V12  H    V12 V2  S1 and S2 in pyrazine in the Q6a and Q10a subspace

Domcke et al. JCP 100 (1994) 1400 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 Model Rhodopsin

S1 (adiabatic)

S0 (adiabatic)

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

500 nm

570 nm

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

h h h

Reaction Coordinate Reaction Coordinate Reaction Coordinate Femtochemistry: Basic Concepts

(dia) (dia)    1  Tnuc 0   H H  1  i        1 12    t    0 T   (dia) (dia)       2   nuc   H12 H 2  2 

Semiclassical Approximation:

R(t)  vt

(dia) (dia)   c1   H (R(t)) H (R(t)) c1  i     1 12    t c   (dia) (dia)  c    2   H12 (R(t)) H 2 (R(t)) 2   4 2 H 2  Pdia 1 exp 12   hv  R H11  H 22  d/dR(H -H ) H small 11 22 12 velocity small small

H large d/dR(H -H ) 12 velocity large 11 22 large 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 Mean-Field Approach

ab3000 3000

2000 2000

1000 1000

-2 -1 1 2 -2 -1 1 2

-1000 -1000

0.8 2 cd

R(t) 0.6 1 0.4

0.1 0.2 0.3 0.4 0.5 0.2 Population -1 t 0.1 0.2 0.3 0.4 0.5 t Wavepacket on Coupled Surfaces

ab3000 3000

2000 2000

1000 1000

-2 -1 1 2 -2 -1 1 2

-1000 -1000

0.2 cd0.2 0.15 0.15

0.1 0.1

0.05 0.05

10 20 30 40 50 60 10 20 30 40 50 60 Mean-Field versus Surface Hopping ab

1-pad

pad

R R Femtochemistry: Basic Concepts

- -

+ +

- -

+ +

- -

+ + + + + +

- -

+ + + -

- - +

+ + - +

+ Solute - + -

- - - - -

- - + +

+ +

+ + - -

+ 2

- -

+ +

- 

+ + 3 r ) ) 1 1    h  Solvation  ( 2 ( + + - - +  + + + - E - - + - Onsager‘s Reaction Field Model

- 

- - - -

+ +

- -

+ +

- -

+ +

+ - Solute + +

+ + + - - - + + - -

+ - Solvation

S1 Free Energy

Solvation Coordinate Solvation of Coumarin in Ploar Solvents

50 fs Formamide

50 ps

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

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

S1 Free Energy

Solvation Coordinate Central Limit Theorem

When a random property is the sum of many random properties, e.g.: N P   z i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:

P  N z

and the variance:

2  2 P  P  N  z  z  Polarisation around a dipole

+ -

+ - - - -

+ + + + - + -

+ +

- - - +

+ - - + -Solute+ +

- -

+ -

+ +

- - -

+ - +

+ +

- -

+ +

- -

+ - + + - + -

- + -

+ -

- +

- - +

- + + +

+ +   + - - + + - - + + - + + - - - + + - + + - - + - -

+ - Polarisation in a Plate Capacitor +- Energy of a single solute molecule Polarisation in a Plate Capacitor

N=1

-2 0 2 4 6 8 10

N=2 probability

-2 0 2 4 6 8 10 N=15

-2 0 2 4 6 8 10 P/ Polarisation in a Plate Capacitor

Field =0 Field >0 a b F F -TS E E P) P) Energy Energy Free Energy Free Energy Free Energy 0 0 Polarisation P Polarisation P Langevin Dynamics

3 2 1

position x -1 -2 time -3

with

Fluctuation-Dissipation Theorem Ensemble of Particles

thermal equilibrium non-equilibrium Solvation

S1 Free Energy

Solvation Coordinate Onsager Regresssion Hypothesis

 0.8

0.6

0.4 x(t)x(0)  0.2

2 4 6 8 10 12 14 time Correlation Function

1 critically  0.8 damped 0.6 =2 0.4 x(t)x(0)  0.2

2 4 6 8 10 12 14 time 1 1 over- under- 0.8 0.8 damped damped 0.6 0.6 =5 0.4 =0.5 0.4 0.2 x(t)x(0) 0.2 2 4 6 8 10 12 14 -0.2 -0.4 time 2 4 6 8 10 12 14 Kramers Theory of Reaction Kinetics

B

R reactant

product Kramers Theory of Reaction Kinetics

  R E strongly    b B R kBT overdamped k R  e 2

  

E critically  2    b  1 2     R kBT damped k R     B  e   2 4  2 B   

under-  E I(E )   B  damped b R kBT k R  p  e  k T 2 B  

P. Hänggi et al., Rev. Mod. Physics, 62 (1990) 251 Photoisomerisation of Stilbene: Dependence on Solvent Viscosity

G. R. Fleming, S. H. Courtney, M. W. Balk, J. Stat. Phys. 42 (1986) 83 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 Photochemical Reactions in Nature: Electron Transfer in Photosynthesis Photochemical Reactions in Nature: Electron Transfer in Photosynthesis Photochemical Reactions in Nature: Electron Transfer in Photosynthesis Artificial Photosynthesis: Grätzel Cell

TiO2

LUMO e- Conduction Band

Light e- HOMO Valence Band Donor

M. Grätzel, Nature 2001, 414, 338−344. DA D*A D+A-

LUMO Light

HOMO Donor Acceptor Donor Acceptor Donor Acceptor

ET ?

Donor Acceptor Donor Acceptor

D,ED A,EA

VD(r) VA(r) Distance Dependence of Electron Transfer

k  eR 1 Å-1

F. D. Lewis,* T. Wu, Y. Zhang, R. L. Letsinger, S. R. Greenfield, M. R. Wasielewski, Distance-Dependent Electron Transfer in DNA Hairpins Science 277 (1997) 673 Solvation of a Charge Transfer Complex

- +

+ - - +

- + -

- +

- + + + -

+ -

- +

- - +

- +

+ -

- +

- + -

D A +

+ + -

+ +

- - D A

+ +

+ - -

- -

- - - - +

+ +

+ + + - + - + - + + - + -

- + -

+ -

- +

- - +

- + + +

+ +   + - - + + - - + + - + + - - - + + - + + - - + - -

+ - Polarisation in a Plate Capacitor +- Energy of a single solute molecule Polarisation in a Plate Capacitor

Field =0 Field >0 a b F F -TS E E P) P) Energy Energy Free Energy Free Energy Free Energy 0 0 Polarisation P Polarisation P Marcus Theory of Electron Transfer

D*A F (R) DA D+A-

F D+A-(R)

Free Energy 

Fa F

(DA) (D+A-) R0 R0 R

  F  k  V 2 exp a  ET DA 2    kBTF  kBT  Marcus Theory of Electron Transfer

D*A F (R) DA D+A-

F D+A-(R)

Free Energy 

Fa F

(DA) (D+A-) R0 R0 R

2 2    F  F   k  V exp   ET DA 2    kBTF  4F kBT  Distance Dependence of Electron Transfer

k  eR 1 Å-1

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

D*A F (R) DA D+A-

F D+A-(R)

Free Energy 

Fa F

(DA) (D+A-) R0 R0 R

2 2    F  F   k  V exp   ET DA 2    kBTF  4F kBT  Marcus Theory of Electron Transfer

Inverted Regime Barrier Less Normal Regime Free Energy

FF FF FF R R R

2 2    F  F   k  V exp   ET DA 2    kBTF  4F kBT  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. Photochemical Reactions in Nature: Electron Transfer in Photosynthesis 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

LUMO Light

HOMO Donor Acceptor Donor Acceptor Donor Acceptor

ET ?

Donor Acceptor Supressing Back Electron Transfer

Forward ET: F=Fand small  barrier less

Backward ET: F>>F and large h   strongly in the inverted regime

R Photochemical Reactions in Nature: Electron Transfer in Photosynthesis

3 ps 0.9 ps 200 ps

500 ps 1 ms

Zinth et al. Spectrochimica Acta Part A 51 (1995) 1565-1578 and Feher at al. J. Phys. Chem. 1994,98, 3417-3423 Marcus Theory of Electron Transfer

D*A F (R) DA D+A-

F D+A-(R)

Free Energy 

Fa F

(DA) (D+A-) R0 R0 R

2 2    F  F   k  V exp   ET DA 2    kBTF  4F kBT  Marcus Parabola

F=F

+ -

+ - - - -

+ + + + - + -

+ +

- - - +

+ - - + -Solute+ +

- -

+ -

+ +

- - -

+ - +

+ +

- -

+ +

- -

+ - ( 1) E    2 (2 1)r 3

Onsager‘s Reaction Field Model Solvation of a Charge Transfer Complex

- +

+ - - +

- + -

- +

- + + + -

+ -

- +

- - +

- +

+ -

- +

- + -

D A +

+ + -

+ +

- - D A

+ +

+ - -

- -

- - - - +

+ +

+ + + - + - + -

1  1 1  e2 e2 e2      E         8    r  2RD 2RA rDA  in analogy to Onsager‘s Reaction Field Model Distance Dependence of Electron Transfer

k  eR 1 Å-1

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

Superexchange

D A

Hopping

D A Bridged Electron Transfer

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

0.04 Å-1 ) -1 (ps ET k

Distance [Å]

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

W. B. Davis, W. A. Svec, M. A. Ratner, M. R., Nature 396, 60 - 63 (1998) Superexchange in Reaction Center?

Wachtveitl and Zinth, ChemPhysChem 2005, 6, 871 Femtochemistry: Basic Concepts

W. Zinth, J. Wachtveitl ChemPhysChem 2005, 6, 871 – 880 LH II Antenna Complex LH II Antenna Complex LH II Antenna Complex J-Aggregates

Methanol H2O

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 Excitation (Exciton) Transfer

A*B AB*

LUMO

HOMO Excitonic Coupling

R12  1 2 2 2

1 2 R12 R12 R12 R  12 1 2 1 1

   Photosynthesis

W. Zinth, J. Wachtveitl ChemPhysChem 2005, 6, 871 – 880 LH II Antenna Complex Excitons in a Ring

   2j   2J cos    2J cos  0 0 N

j=0 j=N-1 Excitons in a Ring

a b Energy

c Coherent Transfer of Excitation Energy?

FMO Complex

Fleming et al., Nature 434 (2005) 625 and Nature 446 (2007) 782 Coherent versus Incoherent Transfer

D A

D A Bridged Electron Transfer

Superexchange

D A

Hopping

D A Exciton Transfer: Coherent

A*B AB*

LUMO

HOMO Förster Transfer: Incoherent

A*B AB*

LUMO k

k HOMO Förster Transfer

Fermi Golden Rule



Absorption and Emission Spectra Förster Transfer

kDA

h krad Förster Efficiency 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 Molecules Rhoades, E.; Cohen, M.; Schuler, B.; Haran, G.; J. Am. Chem. Soc.; 2004; 126; 14686-14687