ch 41.2.2-kadosh - Chemistry

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simulation of ref 34. The NA transfer becomes significantly
faster with a higher initial energy due to access to
a larger density of TiO 2 states. However its contribution
to the total ET is diminished, and the adiabatic mechanism
completely predominates over the NA mechanism
at high initial energies. The adiabatic and NA contributions
are comparable at low energies. Pre-ET by
photoexcitation is more important at higher energies
and is less pronounced at lower energies, where the
excited state dynamics plays a major role. Assuming
that photoexcitation places the system in an adiabatic
excited state, about 50% of ET occurs due to photoexcitation
and 50% by excited state dynamics (Fig. 7c).
4. DISCUSSION AND CONCLUSIONS
The simulated photoinduced ET between the molecular
electron donor and the TiO 2 acceptor typical of the dyesensitized
semiconductor nanomaterials used in solar
cells, photocatalysis, and photoelectrolysis applications
is thermally driven at 350 K. Pronounced thermal effects
are evident both in the equilibrium ground state
fluctuations that define the distribution of initial conditions
for ET, and in the nonequilibrium excited state ET
dynamics that are dominated by the thermally activated
adiabatic mechanism. The rate of NA transfer is nearly
unchanged from 50 to 350 K, while the adiabatic ET rate
is dramatically increased.
A detailed picture of the ET process follows from the
simulation. As should be expected, higher temperatures
increase the likelihood of a fluctuation that can drive the
ET coordinate over the transition state. The adiabatic ET
is thereby enhanced at high temperatures, becoming
much more effective than the NA, predominating both
in magnitude and timescale.
Another, more subtle, effect is also induced by the
thermal fluctuations. Since the photoexcited state is a
π*-state localized on chromophore carbons, thermal
motions of the carbon atoms change the energy of the
state. Although the energy variation is only a fraction of
an electronvolt, which is small relative to the photoexcitation
scale of several electronvolts, it has a significant
impact on the ET process. Since the density of the
semiconductor states increases with energy, the higher
the energy of the electron donor, the more likely it will
interact with an acceptor state. The oscillation of the
photoexcited state energy slows down at the high and
low energy turning points, and the energies tend to
cluster around these points, resulting in a bimodal distribution
of the initial conditions.
The two distinct types of initial conditions observed
in the simulation are responsible for two kinds of ET
events. At lower initial energies the photoexcited state is
localized primarily on the chromophore, and the ET is
Israel Journal of Chemistry 42 2002
largely determined by the excited state dynamics. At
higher initial energies a significant fraction of the ET
has already occurred upon photoexcitation. The photoexcited
state is significantly delocalized onto the semiconductor,
and the excited state dynamics are responsible
for only the last third of the ET. These conclusions
are based on the adiabatic photoexcitation model, where
it is assumed that the laser prepares the combined chromophore–semiconductor
system in an adiabatic excited
state. A diabatic photoexcitation model provides the
opposite limit, where the initial photoexcitation is assumed
fully localized on the chromophore, spanning 2
or 3 adiabatic states. A more detailed analysis of the
interaction between the system and the laser field is
required in a general case.
The ET in question has been proposed to be either an
adiabatic ET in which the donor state is strongly coupled
to a single acceptor state, or a NA process in which the
donor state is weakly coupled to a manifold of acceptor
states (Fig. 1). One may postulate that the reaction coordinate
is an activationless NA direct transition from the dye
state to a continuum of conduction band states. In this
case, the Fermi golden rule would give an estimate of the
reaction rate. If, however, the ET was an adiabatic transfer
between the dye state to a particular conduction band state,
a Marcus theory of ET would be more appropriate (eq 1).
Relatively few (1–3) states of the conduction band initially
couple to the excited state of the chromophore. Often,
especially with the low energy part of distribution of the
chromophore state energies, the acceptor states are higher
in energy than the donor state, such that an activation is
needed. Both activated ET and activationless direct relaxation
are observed in this study.
The timescales and dominant mechanisms of ET
vary, depending on whether the initial state has high or
low energy. At high initial energies ET is extremely fast
and purely adiabatic. At low initial energies barriers to
ET arise, and the contribution of the NA mechanism
approaches that of the adiabatic mechanism. The timescale
of ET by the NA mechanism matches the NA ET
timescale of the low temperature simulation. 34 The large
differences seen in the features of the ET processes
occurring at low (50 K, ref 34) and high (350 K, this
paper) temperatures suggest that a systematic study of
the ET process over the whole temperature range can
produce a Marcus theory description of ET, eq 1, with
adiabatic activation energy, NA transmission factor κ,
and turnover between a quantum NA tunneling regime
and a thermally activated adiabatic ET regime.
For the system under study, ET occurs on a 5-fs
timescale. This is in agreement with the ultrafast experimental
data for the alizarin 18 and bi-isonicotinic acid 25
chromophores that, similarly to our model, are directly