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Dynamique Quantique des Systemes ComplexesVers les Nanostructures et les Environnements Biologiques

Irene Burghardt

Pole Theorie, Departement de Chimie, UMR 8640, Ecole Normale Superieure, Paris

Journee Annuelle de la Chimie 2009-2010UFR de Chimie UPMC

Concepts/Models/SystemsMethods

Perspectives

Agenda

1 Concepts/Models/Systems: From Polyatomics to Extended SystemsExciton Dissociation at Organic Semiconductor JunctionsExcitation Energy Transfer (EET)Photobiological Systems

2 Methods: Quantum & Quantum-Classical Dynamics in Many DimensionsMulticonfigurational MethodsEffective-Mode ModelsQuantum-Classical Phase-Space & Density Functional Methods

3 Perspectives - Towards Quantum and Classical TransportExciton DynamicsProcesses at InterfacesClassical Transport Phenomena

Irene Burghardt Dynamique Quantique des Systemes Complexes


Perspectives

Exciton Dissociation at Organic Semiconductor JunctionsExcitation Energy Transfer (EET)Photobiological Systems

Goals in a Nutshell

Charge TransferEnergy & Non−Equilibrium

Transport& Nuclear DynamicsElectronic Structure

Microscopic

Extended, Nano−Structured

Biological & Material Systems

e.g. for PhotovoltaicsCoherent Control

Photo−Excitation, Dissipation,

Decoherence

& Optimization

Understanding



Perspectives


Can We Put to Use Our Knowledge of Reactivity &Photochemistry?

A. Piryatinski, http://cnls.lanl.gov/External/people/AndreiPiryatinski.php

Many processes require (non-adiabatic) quantum dynamics



Perspectives


Landmark Topology: Conical Intersections (CoIn’s)

CoIn = photochemical funnel

Schultz et al., J. Am. Chem. Soc. 125, 8098 (2003)

• CoIn topology highly anharmonic

• Extreme breakdown of theBorn-Oppenheimer approximation

• Ultrafast decay (fs to ps scale)

• CoIn’s are ubiquitous(Truhlar/Mead:“Principle ofnon-rareness of CoIn’s”)

• Polyatomic molecules; Jahn-Tellereffect in solids

Koppel, Domcke, Cederbaum, Adv. Chem. Phys. 57, 59 (1984)

Conical Intersections, Eds. Yarkony, Koppel, Domcke (2004)



Perspectives


Photochemistry of “Complex” Systems

• polyatomic molecules

• solute-solvent systems

• biological chromophores & photoswitches

• extended systems, e.g., semiconducting polymers

• molecular nano-scale assemblies

• ultrafast processes (fs–ps)

• quantum coherence & decoherence

• special topologies, e.g., CoIn’s



Perspectives


Methods for “Large” Systems

Approximate Potentials

& Approximate Dynamics

On−The−Fly Electronic Structure

& Classical / Semiclassical Dynamics

Parametrized Model Hamiltonians

& Accurate Quantum Dynamics

Accurate Potentials

& Accurate Quantum Dynamics

Vibronic Coupling & Lattice Models;

Accurate Multiconfigurational

Techniques (MCTDH)

High−Level or Semi−Empirical

Electronic Structure Methods;

Surface Hopping,

Gaussian Wavepackets

Dyn

am

ics A

ccu

racy

Electronic Structure Accuracy



Perspectives


Example 1: How Do Excitons Dissociate at aPolymer Interface (Heterojunction)?

exciton = electron + hole

photovoltaic devices, organic light-emitting diodes (OLED’s), . . .

Peumans, Uchida, Forrest, Nature 125, 8098 (2003)

F8BT:

TFB:

NNS

NN

RR

R

R

RR

N

SN

R

R

molecular-level understanding of interactions & dynamicsat the polymer interface is required

collaboration with Eric R. Bittner (Univ. Houston)Irene Burghardt Dynamique Quantique des Systemes Complexes


Perspectives


Zeroth-Order Picture of a Heterojunction

Kar

ab

un

arliev

&B

ittn

er,

J.C

hem

.P

hys

.1

18

,4

29

1(2

00

3)

polymer/polymer interface:

F8BT

1.92eV

-3.54eV

3.16 eV

PFB/TFB

-2.75 eV (PFB)

-2.98eV (TFB)

• HOMO/LUMO valence/conduction band• 1st bound excited state: singlet exciton (1B−u in PPV); Frenkel type exciton• @junction: compare band offset vs. exciton binding energy (εB ∼ 0.5 eV)



Perspectives


Objective: Molecular-Level Perspective of Exciton Dissociation

TFB:F8BTheterojunction

exciton

-2.98 eV

1.92 eV

h

Ground state

Exciton state

Charge transfer

state

hole

+-

(A)

(C) F8BT (e-acceptor)

Lattice

distortion

h

0

(B)

e-donore-acceptor

-3.54 eV

3.16 eV

TFB (e-donor)

Ta

mu

ra,

Bit

tner

,B

urg

har

dt,

JCP

12

6,

02

11

03

(20

07

)

• initial photogeneration of an exciton state (XT, bright state)

• exciton decay to an interfacial charge transfer state (CT, exciplex)

• the XT CT transition is mediated by electron-phonon coupling



Perspectives


3-State Electron-Phonon Coupling Model

2.0

2.2

2.4

2.6

2.8

3.0

displacement

Energy@eVD

XT

IS

CT

parameterization for TFB:F8BT:polymer lattice model based on dimer;TDDFT and semi-empirical (PM3) calculations+ Wannier-function representation

Bittner et al., JCP 122, 214719 (2005)

H =N∼30

∑i

Hi = ∑i

ωi

2

(p2

i + x2i

)+V lin

i

V lini =

κ(1)i xi λ

(12)i xi λ

(13)i xi

λ(12)i xi κ

(2)i xi λ

(23)i xi

λ(13)i xi λ

(23)i xi κ

(3)i xi

state 1 = exciton (XT) statestate 2 = charge transfer (CT) statestate 3 = intermediate (IS) state

phonons = C=C stretch + ring torsions

Tamura, Ramon, Bittner, Burghardt, J. Phys. Chem. B 112, 10269 (2008)



Perspectives


Quantum Dynamics of Exciton Dissociation

3-state

2-state

• 3-state 28-mode model

• MCTDH calculations

• sample over relevantinterface configurations

• intermediate statesplay a key role

• qualitative agreementwith time-resolvedphotoluminescence

Tamura, Ramon, Bittner, Burghardt,

Phys. Rev. Lett. 100, 107402 (2008)



Perspectives


Interface Configurations: Role of Stacking

eclipsed: π-stacked F8 units

staggered: F8 units displaced

Note: F8’s electro-positive in F8BT but electro-negative in TFB



Perspectives


Example 2: Excitation Energy Transfer (EET)

photosynthesis, (artificial) light-harvesting systems

Tamura, Burghardt, in preparation

H = ∑i

ωi

2

(p2

i + x2i

)+

(κ

(1)i x(1)

i VCoulomb12

VCoulomb12 κ

(2)i x(2)

i

)

VCoulomb12 =

∫drD drA

ρ(eg)D (rD)ρ

(ge)A (rA)

|rD− rA|• inter-monomer couplings via transition densities• generalization of Forster rate theory & transition dipole approximation



Perspectives


Ultrafast, Coherent Regime:Excitation Transfer Coupled to Porphyrin Effective Mode(s)

Tamura, Burghardt, in preparation 0

0.2

0.4

0.6

0.8

1

0 500 1000 1500

site

pop

ulat

ion

time [fs]

site 1: initial excitation

23 4 5 6 7 8 9

• significantly different from non-coherent, Forster (FRET) type transfer



Perspectives


EET in Functionalized Assemblies

e.g., carbon nanotubes (CNT) or quantum dots (QD) as donor/acceptor species

ANR project “Experimental and theoretical study of energy andcharge transfer in nanotube/chromophore compounds”, submitted

Tamura, Mallet, Oheim, Burghardt, J. Phys. Chem. C, 113, 7548 (2009)

• FRET1 labeling in biological/medical applications; photovoltaics

• again, pronounced non-Forster effects, esp. for elongated nano-objects

1FRET = Fluorescence Resonance Energy TransferIrene Burghardt Dynamique Quantique des Systemes Complexes


Perspectives


Example 3: Biological Switches, e.g., PYPPYP = Photoactive Yellow Protein

isomerisation constrained by “protein nanospace”

Tyr98

P h e 96

A rg 5 2

C h ro m o p h o re

C ys 6 9

P h e 6 2V a l6 6

Th r5 0

G lu 4 6

Tyr4 2

(a)

O

S

O

CNRS/DFG collaboration ENS/Heidelberg; Gromov, Burghardt, Koppel, Cederbaum, JACS 129, 6798 (2007)

• excited-state lifetime ∼ 700 fs (in solution ∼ 10 ps)

• the local amino acid environment is of key importance

• how is the chromophore’s quantum dynamics concerted with theenvironmental dynamics/fluctuations?



Perspectives


A Complicated Photo-Switch . . . Two Isomerisation Pathways

O O

H

H

O

H

H

O

S CH3

a

b

Phenol part

Alkene part

• two S1 minima; β min. near a CoIn

• charge distributions inverted atthese two minima

0.0

1.0

2.0

3.0

En

erg

y(e

V)

-0.53/-0.47-0.25/-0.75 -0.76/-0.24

-0.39/-0.61

-0.87/-0.13

-0.71/-0.29

S 0,eqS 1,mina

S 1,minb

S1

S1

S0

S0

S1

S0

Gromov, Burghardt, Koppel, Cederbaum, JACS 129, 6798 (2007)



Perspectives


The Amino Acid Environment “Tunes” the Chromophore

CC2supermolecularcalculations

Impact of Impact of the active site amino acidsthe active site amino acids

E.V. Gromov, I. Burghardt, H. Köppel, L.S. Cederbaum, JACS 129 (2007) 6798

2.8

3.2

3.6

4.0

4.4

4.8

En

erg

y(e

V)

IP

IP� -� 2

*

� -� 1*

n - � 1*

� -� 1*

nPh-

� 1*

� - � 2*

�-Arg52 � -� 1*

nPh-

� 1*

nPh-

� 1*

� -� 1*

�-Arg52

nPh-

� 1*

� - � 1*

� - � 1*

� - � 1*

�-Arg52

� - � 2* � - � 2

*

n - � 1*

� - � 1*

n - � 1*

nPh-

� 1*

�-Arg52

� - � 1*

n -� 1*

nPh-

� 1*

� -� 2*

Arg

52

Phe96

Tyr98

Glu46 Tyr42

SC

H3

O

HO

Arg

52

Arg

52

Phe6

2

Arg

52

Thr50

Va

l66

Arg

52

Arg

52

Va

l66

Tyr98

Thr50

Glu46 Tyr42

Arg

52

Va

l66

Tyr98

Thr50

Glu46 Tyr42

pCTM pCTM I II III IV V VI VII�

n -� 1*

SC

H3

O

O

SC

H3

O

O

Cy

s69

SOO

SC

H3

O

O

SC

H3

O

O

SC

H3

O

O

SC

H3

O

O

Cy

s69

SO

O

Gromov, Burghardt, Koppel, Cederbaum, J. Am. Chem. Soc. 129, 6798 (2007)



Perspectives


Hierarchical Treatment of Complex, Structured Systems

Hybrid methods for quantum dynamics & electronic structure

Primary zone:

• dominant modes in many-atomsystems

• chromophore (in solution,protein)

Secondary zone:

• intramolecular “bath”

• first solvent shell (microscopicor mesoscopic description)

modes

}{ϕ(κ)

primary

modes

}{χ(n)

dissipative

secondary

modes

{g(f)}



Perspectives


Just Appeared

› springer.com

isbn 978-3-642-02305-7

123

Energy Transfer Dynamics in Biom

aterial Systems

! is book presents a collection of 14 review articles that cover the key topics addressed in the workshop Energy Flow Dynamics in Biomaterial Systems which was held in October 2007 in Paris. ! ese reviews illustrate the many facets of today’s theoretical picture of electronic and vibronic dynamics and transport phenomena in biological, biomimetic, and molecular electronic systems. Part I focuses on excitation energy transfer in photosynthetic re-action centers and other multichromophoric systems, part II gives a tour d’horizon of DNA research, and part III addresses molecular electronics and quantum transport in organic materials. Finally, parts IV and V cover recent methodological developments in open system dynamics and hybrid quantum-classical methods. ! e scope of the book is deliberately broad in terms of physical systems studied and yet uni( ed in the use of quantum dynamical methods to describe transient and o) en ultrafast energy and charge transfer events in complex systems.

Burghardt · May · M

icha Bittner Ed

s.

Springer Series in Chemical Physics 93

Irene BurghardtVolkhard MayDavid A. MichaEric R. BittnerEditors

Energy Transfer Dynamics in Biomaterial Systems

1

SPRINGER SERIES IN CHEMICAL PHYSICS 93

Energy Transfer Dynamics in Biomaterial Systems

Irene BurghardtVolkhard MayDavid A. MichaEric R. BittnerEditors



Perspectives


Acknowledgments & Collaborations

• E. R. Bittner (University of Houston)

• L. Cederbaum, H. Koppel, E. Gromov, E. Gindensperger(University of Heidelberg)

• G. A. Worth (University of Birmingham, UK)

• K. H. Hughes (University of Bangor, UK)

• H. Tamura (ENS Paris, now Tohoku University)

• S. Zhao, P. Ramanathan, F. Martelli (Group ENS)

Thanks to: CNRS, ANR (France) for financial support


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