Mixed Quantum-Classical Description
of Electronic Excitation Energy Transfer
in Supramolecular Complexes
Volkhard May, Institute of Physics
Humboldt-University at Berlin
- electronic excitation energy
transfer (EET) in supramolecular
chromophore complexes (CC)
- Frenkel-exciton model
- mixed quantum-classical
description of EET
- computation of the absorbance,
of energy transfer dynamics,
and of the emission spectrum
light harvesting complex Lh2
of the photosynthetic apparatus
of purple bacteria
application of standard
density matrix theory
pheophorbide-a molecules
covalently linked to a
butanediamine dendrimer
and dissolved in ethanol
use of a mixed quantumclassical description
energy
Electronic
Excitation Energy Transfer
in Supramolecular
Chromophore Complexes
UDe
UAe
LUMO
UDg
QD
UAg
QA
HOMO
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Schemes of Excitation Energy Transfer
E
P
coherent
excitation
energy
motion
incoherent
excitation
energy
motion
Frenkel-Excitons in
Molecular Systems
excitons in DNA
E. Emanuele, K. Zakrzewska, D. Markovitsi,
R. Lavery, and P. Millie,
J. Phys. Chem. B 109, 16109
(2005).
excitation energy transfer
in complex artificial structures
H. Zhu, M. Fujitsuka, A. Okada, S. Tojo,
F. Takei, K. Onitsuka, S. Takahashi, and
T. Majima, Rapid Exciton Migration and
Fluorescent Energy Transfer in Helical
Polyisocyanides with Regularly Arranged
Porphyrin Pendants,
J. Phys. Chem. B 108, 11935 (2004).
Y.-Z. Ma, R. A. Miller, G. R. Fleming, and M. B. Francis,
Energy Transfer Dynamics in Light-Harvesting Assemblies
Templated by Tobacco Mosaic Virus Coat Protein,
J. Phys. Chem. B 112, 6887 (2008).
A. M. Dennis and G. Bao, Quantum
Dot-Fluorescent Protein Pairs as Novel
Fluorescence Resonance Energy
Transfer Probes,
NanoLett. 8, 1439 (2008).
Pheophorbide-a
Complexes
in Ethanol
(-> PN)
H. Zhu, V. May, B. Röder,
and Th. Renger,
J. Chem. Phys. 128, 154905 (2008).
H. Zhu, V. May, and B. Röder,
Chem. Phys. 351, 117 (2008).
H. Zhu, B. Röder, and V. May,
Chem. Phys. 362, 19 (2009).
H. Zhu and V. May,
Springer Series in Chemical Physics 93
(Springer-Verlag, 2009).
single pheophorbide-a molecule
PN=16
- tetrapyrrole type molecules
- Qy-absorption at 666 nm
- linked to dendrimeric structures
- formation of flexible
supramolecular complexes
- excitation energy transfer
proceeds on a strongly
fluctuating structure
16 pheophorbide-a molecules covalently
linked to a butanediamine dendrimer
The Frenkel-Exciton Model
delocalized state
representation
localized state representation
J’mn
E(b2)
Ef
Jmn
m
Ee
n
E(a1)
Extended Frenkel-Exciton Model
- account for the permanent charge
distribution in the ground and
excited state
- coupling to solvent molecules
- introduction of atomic
centered partial charges
(permanent and transition
charges)
excitonic coupling beyond dipole-dipole approximation
Adiabatic (instantaneous) excitons of P4
energies, oscillator strengths, and expansion coefficients
(coupling to solvent molecules has been neglected)
4
3
2
1
adiabatic exciton energies and oscillator
strengths (data have been computed every
0.5 ps within a single 1 ns MD run)
square of adiabatic exciton expansion
coefficients, taken at every 0.5 ps
Mixed Quantum-Classical Description
of Excitation Energy Transfer
MD simulations of the
solvent-solute system
Ehrenfest dynamics
->exact account for exciton
vibrational coupling
-> atomic resolution of
vibrational dynamics
snapshots of P4 in ethanol along
a 1 ns room–temperature MD run
->back reaction of the electron
dynamics on the nuclear motion
-> high-temperature limit
Energy Transfer Dynamics
without time averaging
averaged with respect to a 10 ps time slice
P1
P2
P3
P3
P1
P4
The modulation of the
single chromophore
excitation energy by
the solvent molecules
is neglected.
The modulation of the
single chromophore
excitation energy by
the solvent molecules
is included.
P2
P4
Spectra of Linear Absorption
full quantum expression for the absorption cross section
1
translation of the cross section to a
mixed quantum-classical version
Room temperature steady state absorption of P4 dissolved in
ethanol using different approximations.
averaging with respect to 40 different 1 ns MD runs,
spectra have been normalized to their maxima,
LRT
inclusion of intra
chromophore
vibrations
adiabatic
excitons
LRT
adiabatic
excitons
measured
data
The modulation of the single chromophore
excitation energy by the solvent molecules is neglected.
The modulation of the single chromophore
excitation energy by the solvent molecules is included.
H. Zhu, V. May, B. Röder, and Th. Renger, J. Chem. Phys. 128, 154905 (2008).
Time and Frequency Resolved Emission
full quantum expression for the spontaneous emission spectrum
density operator has been
reduced with respect to
photon states
ideal time and frequency resolved emission spectrum of P4
Normalized by its maximum
and averaged by 10 MD runs
as well as a dephasing time of 20 fs.
The initial excitation corresponds to
an equal distribution of population
and the absence of inter
chromophore correlations.
mixed quantum classical
approximation
account for
radiative
decay
F11
F22
F33
Time resolved emission of P4 taken at
the photon energy of 15015 cm-1.
Red line: emission convoluted with an
apparatus function (see insert).
F44
P4 time resolved emission separated with
respect to the different partial spectra Fmm
Acknowledgment
Ben Brüggemann
Jörg Megow
Zheng-Wang Qu
Thomas Renger
Beate Röder
Hui Zhu
DFG
Thanks
for your
attention
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Appendix
singly
excited state
Hamiltonian
ground and excited state PES account for electrostatic couplings
single chromophore PES
in a harmonic
approximation
Coulomb
matrix
element
introduction of atomic centered partial charges
(permanent and transition charges)
excitonic coupling beyond dipole-dipole approximation
single chromophore excitation energies
and excitonic couplings
120 ps
440 ps
- use of DFT and HF-CIS methods
- determination of the atomic centred
partial charges by a fit of the ab initio
electrostatic potentials
influence of inter-chromophore couplings
4 pheophorbide-a molecules
covalently linked to a
butanediamine dendrimer
influence of intra-chromophore
and solvent-solute couplings
Linear Absorption Spectra
The modulation of the single chromophore excitation energy by the solvent molecules is neglected.
The modulation of the single chromophore excitation energy by the solvent molecules is included.