ch 41.2.2-kadosh - Chemistry

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autocorrelation function with a substantial amplitude is
indicative of a correlated evolution of the dye excited
state. The Fourier transform of the autocorrelation function
shown in Fig. 3c peaks at 1600 cm –1 . This frequency
is within the range associated with a carbon stretch,
immediately revealing the origin of the oscillation.
Since the first excited state of the chromophore is a
π-state localized on the ring carbons, an oscillation of
the ring carbons should modulate the energy of the state.
In order to establish the types of ion motions available
at the 1600 cm –1 frequency, Fourier transforms of
velocity autocorrelation functions of all atoms in the
combined system have been computed. The result is
shown in Fig. 3d on a logarithmic scale. Only chromophore
carbon and nitrogen atoms exhibit motions with
frequencies near 1600 cm –1 , with the peak at 1600 cm –1
dominated by the three middle carbons. The first excited
state of the dye is localized on the four middle carbons:
The persistent oscillation of the dye excited state energy
shown in Fig. 3a is indeed due to a C–C-stretching
mode.
In the combined dye–TiO 2 system, the dye excited
state interacts with the TiO 2 conduction band. As a
result, the adiabatic states represented in the one-electron
picture by the Kohn–Sham orbitals of the combined
system are, generally, delocalized between the chromophore
and the semiconductor. It is assumed in the
current simulation that photoexcitation promotes an
electron into the adiabatic state with the largest localization
on the dye. This is expected with strong excited
state selection rules with transition dipole moments
favoring excitation of the dye fragment, or with relatively
long laser pulses that by the time–energy uncertainty
relationship can select a state with a stationary,
adiabatic state of a given energy. The opposite limit is
the diabatic excitation, where the laser excites a superposition
of adiabatic states that best corresponds to the
dye excited state in the absence of a semiconductor. The
details of the photoexcitation realized in experiments
depend on both properties of the dye–semiconductor
system, such as transition dipole moments between
ground and excited states, and properties of the laser
pulse, such as its shape, duration, and polarization. Investigation
of the photoexcitation details extends beyond
the scope of the present study, which takes the
adiabatic excitation limit. Figure 4a shows localization
L p of the photoexcited state φ p
Israel Journal of Chemistry 42 2002
(9)
on the chromophore along the production run. The
photoexcited state is defined in the adiabatic limit as the
state with the largest localization on the dye, chosen
within a range of states of the combined system at the
energies corresponding to the excited state energy of the
isolated chromophore, Fig. 2c. The degree to which the
photoexcited state is localized on the dye varies substantially
along the trajectory. In many instances the
photoexcited state is localized on the dye 80% or more,
similar to our previous low temperature simulation. 34
Very often, the photoexcited state is less than 50%
localized on the dye. In such cases, the excited state of
the isolated chromophore, the diabatic state, contributes
to several, typically 2 or 3, adiabatic states of the combined
system; see Fig. 5a below.
A closer look at the data of Figs. 3a and 4a reveals
that the localization of the photoexcited state on the dye
has the same fluctuation as the energy of the photoexcited
state. The autocorrelation function
(10)
of the localization of the initial state, Fig. 4b, and its
Fourier transform, Fig. 4c, are very similar to those of
the state energy, Figs. 3b and 3c. The localization oscillates
with the same frequency as the energy. This result
can be expected, since the density of states in the conduction
band grows with energy, Fig. 5b, increasing the
likelihood of interaction and mixing between the dye
and semiconductor states. The localization varies with
energy, and thereby oscillates with the same frequency
as the energy.
The correlation between the energy of the photoexcited
state and its localization on the chromophore
fragment is illustrated in Fig. 4d, which shows the data
for the 100 randomly chosen initial conditions. The
correlation is far from perfect; however, a general trend
can be seen very clearly. A higher density of semiconductor
states does not always imply that more states will
be coupled to the dye excited state. The coupling relies
not only on energy resonance, but also on other characteristics
of semiconductor states, such as their localization
at the surface. Fluctuations in the surface structure
cause changes in the localization and coupling. The
effect of fluctuations in the surface structure is further
emphasized by a finite depth of the TiO 2 slab. The
simulation represents the conduction band continuum
by a finite number of states. Consequently, the coupling
and mixing of the dye excited state with the surface and
bulk states of the substrate is more discretized than it
may be in reality. Although there will be on average a
greater amount of mixing and coupling when the energy
of the dye excited state is high, there will always be
cases where the mixing and localization are more or less