Delocalization of excitons in dimers
Electronic excited states of interacting molecular systems has been an active
research area since early work by Frenkel. The concept of collective delocalized
excitations, excitons, was developed. Phenomena like Davydov splitting in
molecular crystals, motional narrowing and superradiant decay in molecular
aggregates have been explained by using the exciton theory. Particularly the
excitons in photosynthetic light-harvesting antenna systems are in the focus of
active research. Such issues as exciton relaxation, excitation delocalization
versus localization, and the resulting spectroscopic signatures has been
addressed. Already Frenkel recognized the important role of the nuclear motions
in the concept of excitons. First of all, even a weak coupling between the
electronic and nuclear degrees of freedom causes dephasing and population
relaxation among exciton levels. For strong electron-phonon coupling, further
phenomena like self-trapping of the exciton, also called polaron formation,
occur. Various theoretical approaches addressing different aspects of exciton
dynamics in antenna systems have recently appeared. For example Redfield
relaxation theory, has been applied using model functions as well as
experimental data for the spectral density to describe exciton relaxation and
corresponding experimental observables in different antenna systems.
In order to describe simultaneously different stages of exciton
dynamics we have recently developed a method based on nuclear dynamics
for explicit vibrational modes combined with the surface hopping
approach. In this method the complete dynamic process from dephasing
and exciton relaxation to polaron formation (self-trapping), and
eventually diffusion of the polaron can be described. This approach
seems to be appropriate for application on excitonically coupled
systems of arbitrary size, from the simple dimer to the extended
photosynthetic antenna complexes.
There exists a large variety of dimeric molecular systems from
interacting pair of guest molecules in a molecular mixed crystal to
dimeric pigment complexes in biological systems e.g. the so called
B820 antenna complex from purple bacteria or the special pair in the
photosynthetic reaction center. Excited states and their dynamics in
molecular dimers has been studied experimentally and theoretically by
numerous authors. In the present work we calculate the potential
surfaces more generally including also the heterodimer, where the
transition energies of the two molecular sites are different.
Potential Surfaces
Using the model of two excitonically coupled electronic two-level
systems with one-dimensional potential surfaces of the monomers given
as displaced harmonic oscilators (see above) one obtains two excitonic
states with adiabatic potential surfaces given by
The resulting potential surfaces depend on two parameters: v which
represents the strength of the excitonic coupling and Δ which
represents the difference in the transition energies of the monomers,
both in units of the Stokes shift of the monomers. For several
combinations of these parameters the potential surfaces of the lower
(U-) and the upper (U+) one exciton state has
been calculated. (point to parameter combinations assigned by red
bullets for a look on the lower exciton's potential surfaces).
Potential surfaces for the lower exciton (U- ) in dependence
of excitonic coupling v and transition energy difference .
Nuclear motion
In order to describe the nuclear motion on the potential surfaces in a
dissipative surrounding we use the classical Langevin equation
The fluctuating forces fi(t), and the damping rate
g are connected by the dissipation fluctuation theorem as
We have performed Monte-Carlo simulations of the nuclear motion to
determine the time evolution of the statistical distribution of nuclear
coordinates (see below).
Delocalization Length
To define the delocalization length L± of the
excitonic state |±> over the dimer we use the participation ratio
which depends on the nuclear coordinates as well as on the parameters
v and Δ (point to the assigned parameter combination below).
Averaged over a statistical distribution of nuclear coordinates
one obtains an effective delocalization length Leff± , which
are shown below for the following cases
Surface hopping
The non-adiabatic coupling between the two potential surfaces is
taken into account by a surface hopping with rate
The back transfer will be ignored. This results in a decay of the
initially excited upper exciton to the lower one and a corresponding
change in the time evolution of the nuclear coordinates and the
delocalization length.
References
- W. J. D. Beenken, M. Dahlbom, P. Kjellberg, T. Pullerits, Potential surfaces and delocalization of excitons in dimers, J. Chem. Phys. 117 (12),
5810-5820 (2002)
[Details]
- M. Dahlbom, W. Beenken, V. Sundström, T. Pullerits, Collective excitation dynamics and polaron formation in molecular aggregates, Chem. Phys. Lett. 364 (5-6),
556-561 (2002)
[Details]
- M. Dahlbom, W. Beenken, V. Sundström, T. Pullerits, Collective excitation dynamics in molecular aggregates: Exciton relaxation, self-trapping and polaron formation., Roy. Soc. Ch. (283),
118-135 (2002)
[Details]
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