Experimental fingerprints of vibrational wave-packet motion during ultrafast heterogeneous electron transfer

Article abstract of DOI:10.1021/jp011106z

By application of 20 fs laser pulses, vibrational wave packets of low-energy modes (mainly 357 and 421 cm^-1) were generated in the perylene chromophore that gave rise to periodic beats that lasted longer than 1 ps in transient absorption signals. Electron transfer from the excited singlet state of the perylene chromophore, attached as molecule DTB-Pe via the -CH₂-phosphonic acid group to anatase TiO₂, was measured in ultrahigh vacuum with a time constant of 75 fs. The vibrational wave packet that was generated in the donor state continued its motion for several hundred femtoseconds in the product state of the reaction, i.e., in the ionized chromophore. This is direct proof for electron transfer occurring from a nonrelaxed vibrational population that was created by the short laser pulse in the donor molecule. The rise of the product state showed a staircase-like time dependence. The steps are attributed to electron transfer that occurs preferentially each time the vibrational wave packet (frequency 480 cm^-1) reaches a crossing point for the potential curves of reactant and product state. Such wave-packet modulation of heterogeneous electron transfer can arise if the density of electronic acceptor states in the electrode is changing strongly over an energy range on the order of the reorganization energy below the excited molecular donor orbital.

Full text of DOI:10.1021/jp011106z

J. Phys. Chem. B 2001, 105, 9245-9253
9245
Experimental Fingerprints of Vibrational Wave-Packet Motion during Ultrafast
Heterogeneous Electron Transfer
C. Zimmermann,† F. Willig,*,† S. Ramakrishna,† B. Burfeindt,† B. Pettinger,‡
R. Eichberger,† and W. Storck‡
Hahn-Meitner-Institut, Glienicker Strasse 100, D-14109 Berlin, Germany, and Fritz-Haber-Institut der MPG,
Faradayweg 4-6, D-14195 Berlin, Germany
ReceiVed: March 22, 2001; In Final Form: June 9, 2001
By application of 20 fs laser pulses, vibrational wave packets of low-energy modes (mainly 357 and 421
cm-1) were generated in the perylene chromophore that gave rise to periodic beats that lasted longer than 1
ps in transient absorption signals. Electron transfer from the excited singlet state of the perylene chromophore,
attached as molecule DTB-Pe via the -CH2-phosphonic acid group to anatase TiO2, was measured in
ultrahigh vacuum with a time constant of 75 fs. The vibrational wave packet that was generated in the donor
state continued its motion for several hundred femtoseconds in the product state of the reaction, i.e., in the
ionized chromophore. This is direct proof for electron transfer occurring from a nonrelaxed vibrational
population that was created by the short laser pulse in the donor molecule. The rise of the product state
showed a staircase-like time dependence. The steps are attributed to electron transfer that occurs preferentially
each time the vibrational wave packet (frequency 480 cm-1) reaches a crossing point for the potential curves
of reactant and product state. Such wave-packet modulation of heterogeneous electron transfer can arise if
the density of electronic acceptor states in the electrode is changing strongly over an energy range on the
order of the reorganization energy below the excited molecular donor orbital.
Introduction
studied in such systems by application of laser pulses of, e.g.,
20 fs duration.6,7,9 A particularly interesting case is the postulated
Recently, time-resolved measurements of photoinduced,
heterogeneous electron-transfer reactions with time constants
considerably shorter than 100 fs have become feasible by
employing transient absorption techniques.1-3,9 The essential
prerequisite for such measurements was the earlier introduction
of a transparent spongelike semiconductor electrode with a high
inner surface area that can accommodate a sufficiently large
number of organic chromophores.4 Ultrafast photoinduced
electron transfer from such large molecular adsorbates into a
semiconductor represents an interesting fundamental case study
of interfacial reactions.5-7 There are two border cases for
ultrafast heterogeneous electron-transfer dynamics. Electronic
coupling can be very strong in the case of direct contact between
atoms of the organic chromophore and surface atoms of the
semiconductor. The corresponding photoinduced electron trans-
fer can be as fast as 1 fs with an energy uncertainty greater
than 0.5 eV. The effect of vibrational excitation of the molecular
donor is virtually washed out in this strong coupling limit.7 In
certain systems, heterogeneous electron transfer may arise as
direct optical charge-transfer transition from the molecular
ground state to the empty electronic states of the semiconduc-
tor.5,8 Electronic coupling can be greatly diminished by inserting
a molecular spacer group with saturated bonds between the
chromophore and the surface atoms of the semiconductor. In
the latter case, typical electron-transfer times are from ten to a
few hundred femtoseconds, depending on the configuration and
length of the spacer group. The influence of vibrational wave
packets on heterogeneous electron-transfer dynamics can be
periodic modulation of electron transfer due to the motion of a
vibrational wave packet in the molecular donor state and the
corresponding periodic curve crossing events.6,7,10-12
In this paper, we present experimental fingerprints of
vibrational wave-packet motion in transient absorption signals
that probe light-induced ultrafast heterogeneous electron transfer.
These fingerprints are periodic oscillations or periodic steps
whose time separation is dictated by the motion of the
vibrational wave packet in the reactant, i.e., excited molecular
donor, and in the product state, i.e., the ionized molecule. The
behavior of the vibrational wave packets was measured first in
the chromophore in the absence of electron transfer. To this
end, the chromophore was immersed in a solvent. Subsequently
the influence of wave-packet motion during heterogeneous
electron transfer was studied with the chromophore attached
via a spacer cum anchor group to the surface of a semiconductor
where it performs ultrafast light-induced electron transfer. In
the latter case, the measurements were carried out in ultrahigh
vacuum, thereby achieving excellent stability and reproduc-
ibility. Laser pulses of 20 fs duration were employed allowing
for coherent excitation of vibrational modes with energies up
to 600 cm-1. Fourier transforms of the periodic oscillations in
the transient absorption signals revealed frequencies of well-
known normal modes of the chromophore perylene. These
frequencies were slightly shifted with respect to the naked
perylene chromophore first due to the side groups covalently
attached to obtain desired properties of the dye molecules and
second due to the neighborhood of the semiconductor surface.
The two most interesting observations are the following. First,
wave-packet motion was found also in the product state of
heterogeneous electron transfer, where the wave packet must
* To whom correspondence should be addressed: E-mail: willig@hmi.de.
† Hahn-Meitner-Institut.
‡ Fritz-Haber-Institut der MPG.
10.1021/jp011106z CCC: $20.00 © 2001 American Chemical Society
Published on Web 09/01/2001

9246 J. Phys. Chem. B, Vol. 105, No. 38, 2001
Zimmermann et al.
have survived electron transfer since the reaction was too slow,
i.e., 75 fs, for its creation in the product state. Similar
observations have been reported already for electron transfer
in molecular donor-acceptor pairs in solution.10,12 Second, the
rise to the product state of electron transfer, ionized perylene
chromophore, showed three distinct steps whose height de-
creased when the plateau that represents complete electron
transfer was approached. This is ascribed to pulsed electron
transfer due to periodic curve crossing of a vibrational wave
packet that is moving back and forth in the potential curve of
the donor molecule. Experimental10,12 and theoretical papers11,13
have addressed this effect for homogeneous electron transfer.
Recently, we have presented a theoretical treatment of the
corresponding photoinduced, wave-packet-modulated hetero-
geneous electron transfer.14 This pulsed electron transfer can
arise in a heterogeneous electron-transfer reaction with the
molecular donor level located high in the conduction band of
the semiconductor if there is a strong energy-dependent change
in the density of electronic states over an energy range on the
order of the reorganization energy of the electron-transfer
reaction. Modulation of electron transfer by a vibrational wave
packet shows directly that the reaction occurs in a vibrational
hot state of the molecule prior to relaxation and transfer of
vibrational energy via anharmonic coupling. A wave packet
surviving in the product state of the reaction also proves this
point. Wave-packet modulation of electron transfer invites
speculations on coherent control scenarios for photoinduced
reactions even in the case of large organic molecules.
Experimental Section
This work became possible through the development of a
high-surface-area semiconductor film, where the inner surface
can accommodate several hundred monolayers of the organic
chromophore.4,15 It would not have been possible to apply
optical pump-probe techniques if a monolayer of organic
molecules had been adsorbed on a flat surface. In the latter case,
the signal-to-noise ratio is totally unsatisfactory. At a film
thickness of 1 µm, the inner surface area of this nanoporous
TiO2 electrode can accommodate about 100 times more dye
molecules in a monomolecular surface layer than the corre-
sponding planar surface. The semiconductor film is transparent
throughout the visible and most of the infrared spectrum. The
electronic levels in the conduction band function as acceptors
for the ultrafast electron injection from the excited electronic
state of the organic chromophore. The spongelike nanostructured
TiO2 electrode with the dye molecules (black dots) attached to
its inner surface is illustrated in part A of Figure 1. Our
preparation methods for growing the crystalline TiO2 nanopar-
ticles and the nanoporous TiO2 film16 followed the procedures
described by Gra¨tzel et al.15 Crystallinity and typical lattice
planes of such an individual anatase TiO2 nanoparticle are
illustrated by the TEM image shown in part B of Figure 1. The
TEM image of a suitably thinned TiO2 film gave direct evidence
of the spongelike film structure. The inner surface of the film
was made up of different crystal surfaces of anatase nanopar-
ticles, with a dominant (101)-surface. Before adsorbing the dye,
the TiO2 film was fired at 450 °C for 45 min in laboratory
ambient. The hot film was transferred quickly from the oven
into an ampule where it cooled to room temperature in a dry
argon atmosphere.
Figure 1. (A) Spongelike nanostructured TiO2 electrode with dye
molecules (black dots) attached to the huge internal surface. (B) TEM
image of a TiO2 nanoparticle. Different crystal surfaces of the anatase
nanoparticle are identified with a dominant (101)-surface.
was prevented here by the covalent attachment of four bulky
side groups, TTB-Pe (2,5,8,11-tetra-tertiary-butyl-perylene), if
the chromophore was to be investigated in a solvent environment
(left-hand side in the upper part of Figure 2). Two of these bulky
side groups and a spacer cum anchor group were covalently
attached, DTB-Pe (2,5-di-tert-butyl-9-perylenyl-methyl-phos-
phonic acid), if the chromophore was employed for electron
injection into TiO2 (right-hand side in part A of Figure 2). A
detailed description of the synthesis of both these compounds
is given in the Supporting Information. A survey over the
synthetic routes appears sufficient at this place. The reaction
sequence started by coupling 1-bromo-3,6-di-tert-butylnaphtha-
lene to 1-naphthalene boronic acid under Suzuki conditions to
yield 3,6-di-tert-butyl-1,1′-binaphthyl which was then anioni-
cally cyclized to yield 2,5-di-tert-butylperylene. This compound
was formulated to yield 2,5-di-tert-butyl-9-formylperylene;
reduction with sodium tetrahydridoborate yielded 2,5-di-tert-
butyl-9-hydroxymethylperylene, and transformation with gas-
eous hydrogen bromide/toluene gave 2,5-di-tert-butyl-9-bromo-
methylperylene. Heating the latter compound with triethyl
phosphite transformed it into (2,5-di-tert-butyl-perylen-9-yl)-
methylphosphonic acid diethylester which upon subsequent
hydrolysis yielded the free acid. Di-tert-butyl-formylperylene
was also reacted with (ethoxycarbonylmethylene)triphenyl-
The dye molecules employed in this work are shown in the
upper part of Figure 2. The perylene chromophore is always
the redox-active part in these dyes. The naked perylene
chromophore is known to dimerize easily, and this dimerization

Experimental Fingerprints of Wave-Packet Motion
J. Phys. Chem. B, Vol. 105, No. 38, 2001 9247
Figure 3. Absorption spectrum of DTB-Pe dissolved in toluene (A)
and attached to the TiO2 surface (B). In the solvent environment the
0-0 transition is dominant whereas the 0-1 transition is the strongest
for the adsorbed perylene chromophore.
of the TiO2 film, the 0-1 transition is strongest. Thus, the part
B of Figure 3 indicates a much stronger shift in the nuclear
equilibrium coordinates upon excitation of the excited singlet
state than seen in part A. The different behavior can be attributed
to the more polar environment in the sponge-type TiO2 electrode
that is interacting much more strongly with the dipole moment
in the excited electronic state of perylene than the toluene
molecules. For the topic of this paper, i.e., the role of vibrational
wave packets in heterogeneous electron transfer, it is helpful
that the vibrational spectra of the perylene chromophore are
available already for the ground state,18-20 the excited singlet
state,18-20 and for the ionized chromophore.21 Through applica-
tion of femtosecond 2-photon-photoemission spectroscopy, the
electronic donor level of the excited singlet state of the perylene
chromophore has been located about 1 eV above the lower edge
of the conduction band in rutile TiO2.22 This should also be
true approximately for the nanocrystallites in the nanoporous
anatase TiO2 film.
Transient absorption and stimulated emission measurements
are illustrated in Figure 4, where all of the different electronic
states of the perylene chromophore are represented whose
absorption spectra have been shown in part B of Figure 2. The
letter P stands for one of the product states, i.e., the ionized
perylene chromophore combined with a specific injected hot
electron whose energy corresponds to the bottom of the parabola
labeled P for the nuclear coordinates of the ionized chro-
mophore. Femtosecond laser pulses had to be generated at
several different wavelengths in order to carry out the measure-
ments illustrated in Figure 4. Appropriate femtosecond laser
pulses were generated utilizing a commercial high repetition
rate femtosecond laser system (Coherent Instruments). A Ti-
sapphire oscillator combined with a regenerative amplifier
provided pulses at 800 nm with an energy of about 7 µJ, 100
kHz repetition rate, and 50 fs pulse width (fwhm). A wide range
of different wavelengths could be generated in the visible and
near-infrared range utilizing suitable commercial OPAs. How-
ever, wavelengths in the spectral range between 400 and 480
nm that are required for preparing the first excited singlet state
of the perylene chromophore (part B of Figure 2) could not be
generated with the commercial instrumentation available to us.
Thus, a tunable wavelength-tripler was built in our laboratory
for generating the third harmonic of suitable wavelengths that
could be generated with the commercial OPA in the infrared
range (Coherent Instruments). This wavelength-tripler turned
Figure 2. (A) Structural scheme of the employed perylene dye
molecules with bulky tertiary-butyl side groups to prevent dimerization
and a phosphonic acid group for bond formation with the TiO2 surface.
(Left) TTB-Pe: 2,5,8,11-tetra-tertiary-butyl-perylene. (Right) DTB-
Pe: 2,5-di-tert-butyl-9-perylenyl-methyl-phosphonic acid. B: Emission
spectrum and absorption spectra of perylene in its ground, first excited
singlet, and ionized state.
phosphorane leading to 3-(2.5-di-tert-butylperylen-9-yl)acrylic
acid ethyl ester which was hydrogenated to yield the corre-
sponding propionic acid ethyl ester and subsequently saponified
to give 3-(2.5-di-tert-butylperylen-9-yl)propionic acid. Purity
and constitution of all of the new compounds were checked
with IR, NMR, MS, TLC, and elemental analysis.
The dye DTB-Pe was adsorbed onto the TiO2 film by
exposing the latter for about 20 min to a 10-4 molar dye solution
(toluene and acetic acid with volume ratio 200:1). The dye-
covered TiO2 electrode was rinsed several times with the solvent,
dried under argon, and afterward quickly transferred either into
an ultrahigh vacuum (UHV) chamber, base pressure 10-10mbar,
via a load-lock valve, or into a quartz ampule that was
evacuated and then flooded with argon prior to inserting the
sample and was sealed after insertion of the sample. Both ways
the sample was protected completely from degradation under
laser irradiation. Degradation can be seen if the sample is kept
in ambient atmosphere and if only traces of water are present
that will lead to irreversible splitting of the aromatic ring in a
slow reaction of the ionized chromophore (radical cation) and
water.17 In the absence of solvent environment, recombination
between the ionized chromophore and its geminate electron
injected into TiO2 was found to be fast enough to allow for a
repetition rate of 100 kHz of the pulse train. After excitation of
the perylene chromophore with the pump laser pulse, recom-
bination was completed before the next pump laser pulse was
impinging on the sample. Some of the advantages of employing
the perylene chromophore for such electron injection studies is
its rigid molecular structure and its spectroscopic properties with
the absorption spectra of the relevant electronic states, i.e.,
ground state, first excited singlet state, and ionized state all
falling into the visible spectral range and at the same time being
well separated from each other (part B of Figure 2). On the
surface of the TiO2 electrode (part B of Figure 3) the absorption
spectrum of compound DTB-Pe changed its shape in com-
parison to the toluene environment (part A of Figure 3). In
toluene, the 0-0 transition is dominant, whereas on the surface

9248 J. Phys. Chem. B, Vol. 105, No. 38, 2001
Zimmermann et al.
Experimental Results
The first task was determining the lifetime of vibrational wave
packets in the perylene chromophore. The influence of a
vibrational wave packet on an electron-transfer reaction can be
measured if the lifetime of the wave packet in the chromophore
is long compared to the electron-transfer time. The electron-
transfer time has been measured as 75 fs for electron injection
from the excited singlet state of the dye DTB-Pe into the
nanocrystals of the spongelike anatase TiO2 film. This value
has been derived from the decay of the reactant state and the
rise of the product state, i.e., the decay of the perylene
chromophore and the rise of the ionized perylene chromophore
(radical cation) if DTB-Pe was attached to TiO2,1,3 and from
the rise of the second product state, i.e., the hot electrons injected
into TiO2.9 The lifetime of the vibrational wave packet is most
conveniently measured with a high concentration of the dye
immersed in a solvent. However, the dye DTB-Pe (see Figure
2) was not the best choice for carrying out this experiment. In
a solvent, this dye is not protected against dimerization since it
loses its preferential orientation that is imposed on the dye if
bonded to a surface via its anchor group. Thus, a differently
modified perylene chromophore, i.e., TTB-Pe (see Figure 2),
was employed for investigating vibrational wave packets with
the perylene chromophore immersed in a solvent. The four bulky
side groups of TTB-Pe keep the perylene chromophores of
two neighboring TTB-Pe molecules at a sufficiently great
distance irrespective of their relative orientation. Thus, the
corresponding excitonic and electronic interactions should
remain negligible if TTB-Pe is immersed in a solvent. Indeed,
the dye TTB-Pe did not show any sign of dimerization either
in toluene or in the form of a dry powder. This was confirmed
by measuring time-resolved and stationary fluorescence and
excitation of fluorescence spectra in solution and by measuring
high-resolution spectra of the powder at 1.5 K.20
Figure 4. Scheme illustrating the preparation of a vibrational wave
packet by a short pump pulse and the probing by femtosecond transient
spectroscopy of wave-packet motion in either the reactant (excited-
state absorption, stimulated emission) or the product state (cation
absorption) of the electron-transfer reaction.
out to be a convenient tool for generating tunable wavelengths
between 425 and 455 nm. The signal wave of the infrared OPA
was the input beam for the wavelength-tripler. The infrared OPA
was pumped with 90% power of the pulse train from the Ti-
sapphire laser system. Generation of the second harmonic and
frequency mixing for obtaining the third harmonic were carried
out with BBO crystals that were cut for type-I phase matching.
A zero-order half wave plate changed the polarization of the
frequency-doubled pulse. Spatial overlap between the ground
wave and the frequency-doubled wave was achieved in the
mixing crystal by employing special dichroic mirrors. A
conversion efficiency of about 9% was achieved for third
harmonic generation. The energy of the pump pulse in the blue
wavelength region was about 10 nJ. The remaining 10% power
of the pulse train from the Ti-sapphire laser system was used
for the generation of white light by focusing the beam into a
sapphire plate. Probe pulses were derived from this white light
by cutting out the appropriate range of wavelengths. Both pump
and probe pulse were recompressed by applying a prism
sequence. Thus, the bandwidth limitation of the pulse width
was approached. With this procedure, the temporal width of
the autocorrelation function for the pump pulse was reduced to
about 30 fs. This was essential for being able to generate in the
excited singlet state of the perylene chromophore wave packets
of vibrational modes (compare Figure 4). The instrumental
response function was identified with the measured sum
frequency signal generated from the pump and the probe pulse
in a BBO crystal of 100 µm thickness. It was different in
different spectral ranges and will be indicated below in the
respective figures or text. As in our earlier work in this field,1-3,9
lock-in techniques were employed here for measuring the time-
resolved transient absorption signals. Other experimental details
were also similar to our work reported earlier. In particular, all
of the optical elements, mainly windows where the laser beam
had to pass through before reaching the sample, e.g. in the
ultrahigh-vacuum chamber, were doubled outside of the vacuum
chamber and the laser pulses appropriately shaped such that
minimum pulse width was achieved at the position of the
sample.
Detection of rapid oscillations in a transient optical spectrum
due to vibrational wave-packet motion requires a high time
resolution and thus very short laser pulses. The absorption path
has to be short in order to minimize the influence of group
velocity dispersion. Thus, a highly concentrated dye solution
(about 10-3 M) was employed. The available pump pulse of
about 20 fs corresponded to an energy spread over about 700
cm-1. Stimulated emission from TTB-Pe dissolved in toluene
was generated with a laser pulse centered around 435 nm and
was probed with a pulse centered at 470 nm. A clear beating
pattern can be seen in part A of Figure 5, which is superimposed
on the slow excited-state population decay. Such oscillations
were found to last for more than 2 ps. The oscillatory part of
the signal was determined by subtracting a smooth fit that
connects the peak values of the oscillations. The rationale for
choosing this fit in contrast to a least-squares deviation fit will
become clear in the Discussion below. The inset of part B of
Figure 5 gives the oscillatory part of the experimental curve
shown in part A of Figure 5. A Fourier Transform of this
oscillatory part is shown in the center part B of Figure 5. Three
peaks can be clearly identified, i.e. at 280, 360, and 420 cm-1
.
They are labeled a, b, and c, respectively. The Raman spectrum
of TTB-Pe (in dry powder form) was also measured (part C
of Figure 5) to facilitate a comparison with the frequencies of
the totally symmetric modes of the dye TTB-Pe. The peaks in
parts B and C of Figure 5 show fair agreement up to frequencies
beyond 600 cm-1. A theoretical normal-mode analysis for the
chromophore perylene23 has assigned frequencies at 357 and
421 cm-1 to totally symmetric in- and out-of-plane C-C-C-
bend vibrations. A mode with frequency around 280 cm-1 has

Experimental Fingerprints of Wave-Packet Motion
J. Phys. Chem. B, Vol. 105, No. 38, 2001 9249
Figure 6. Decay of the excited-state absorption at 715 nm of the
perylene chromophore attached to the TiO2 surface (DTB-Pe, λEX
)
429 nm). There is only one significant step in the falling part of the
curve. The latter is perhaps due to curve crossing during wave-packet
motion. The small inset shows a calculated decay curve neglecting a
contribution from the absorption of the cation at the probe wavelength.
dye, and afterward even in the absence of the TiO2 film, etc.
We have shown before3 that a quantitative fit can be made to
the decay curve of the excited singlet state of the chromophore
if the partial spectral overlap with the absorption curve of the
ionized perylene chromophore (compare part B of Figure 2) is
taken into account. The corresponding fit curve is not shown
again in Figure 6 since wave-packet dynamics are the focus in
this paper, and the electron-transfer kinetics has already been
established. The inset of Figure 6 shows a calculated decay curve
neglecting the superimposed contribution from the ionized
chromophore. The initial magnitude of the beat pattern (two
frequencies, 360 and 420 cm-1) was chosen in accordance with
the amplitude seen in the plateau range of the curve shown
below in part A of Figure 7. It is qualitatively clear from this
simulation that the rapid decrease in the amplitude of the signal
renders the oscillatory pattern hardly discernible. A similarly
inconclusive result concerning the oscillatory behavior has been
seen in the decay of transient stimulated emission of the same
sample observed at 470 nm. In contrast, the beat pattern was
easily detected in the plateau range of the electron-transfer
product state, i.e., in the ionized perylene chromophore. Beat
patterns due to wave-packet motion have been observed before
in the plateau range of electron-transfer product states in the
case of homogeneous electron-transfer reactions.10,12 It is known
for other aromatic molecules that differences in vibrational
frequencies are often small between neutral and ionized
molecules.24-26 The transient absorption curve of the ionized
perylene chromophore in the DTB-Pe molecule attached to
TiO2 was recorded at 575 nm (part A of Figure 7). Strong
oscillations appeared toward the plateau of the curve. Subtracting
a smooth curve that joins the peak positions of the oscillatory
part (compare the Discussion below for the rationale) resulted
in the oscillatory residual shown as inset of part B of Figure 7.
It should be noted that this oscillatory behavior was recorded
over a time span of more than 1 ps in accordance with the
behavior of the perylene chromophore of the TTB-Pe molecule
in solution (see Figure 5). A Fourier Transform of the oscillatory
part is shown in part B of Figure 7. It revealed two pronounced
frequencies, i.e., at 290 and 380 cm-1, and a weak shoulder at
430 cm-1. It appeared necessary to obtain a reference spectrum.
The investigation of the TTB-Pe molecule had revealed shifts
in the vibrational frequencies and even the possible occurrence
of an additional vibrational mode due to the molecular groups
covalently attached to the perylene chromophore. Thus, transient
absorption of the excited singlet state of the molecule DTB-
Figure 5. (A) Strong oscillations in the stimulated emission signal at
470 nm due to wave-packet motion in the excited state of perylene
(TTB-Pe, λEX ) 435 nm, measured in toluene). The thin line gives a
smooth fit connecting the upper peak values of the oscillations. (B)
Fourier Transform of the oscillatory part of the emission signal shown
in the small inset. (C) Raman spectrum of the perylene dye (dry
powder).
not been found, neither for the IR nor the Raman spectrum.
The 280 cm-1 vibrational mode, clearly seen in parts B and C
of Figure 5, is attributed therefore to the presence of the bulky
side groups that distinguish the dye TTB-Pe from the naked
perylene chromophore. Our calculations of beat patterns due to
wave-packet motion showed also the possibility of assigning
this frequency in part B to a difference frequency. However,
the peak also showed up prominently in the Raman spectrum,
and this latter assumption appeared less likely. Thus, the
occurrence of a beat pattern due to vibrational wave-packet
motion and a lifetime of the wave packet in the range of 2 ps
was established for the perylene chromophore.
The next important task was the search for the beat pattern
in the transient absorption spectra of the reactant and product
states of the electron-transfer reaction, i.e., the first excited
singlet state and the ionized state of the perylene chromophore
bonded in the form of the dye DTB-Pe to the surface of TiO2
(compare part A of Figure 2). The electron-transfer time in the
range of 75 fs had already been established for this experimental
system.1,3,9 As shown next, the attempt to identify the beat
pattern in the decay of the donor state did not yield a satisfactory
result. The transient absorption spectrum of the excited singlet
state of DTB-Pe attached to the spongelike TiO2 film is shown
in Figure 6. The excitation pulse was centered around 429 nm
and the probe pulse around 715 nm (compare part B of Figure
2). Only one clearly discernible step appeared in the falling part
of the curve shown in Figure 6. The small oscillatory feature at
the foot of the rising part of the curve is the remnant of a
coherent artifact. These coherent artifacts were studied carefully
with the same experimental system also in the absence of the

9250 J. Phys. Chem. B, Vol. 105, No. 38, 2001
Zimmermann et al.
Figure 8. Time-resolved formation of ionized perylene on TiO2
(DTB-Pe, 585 nm). The steps are ascribed to the modulation of electron
transfer as a result of curve crossing during the periodic motion of a
vibrational wave packet in the donor state (λEX ) 432 nm).
part resulted in the curves shown in Figure 8. The excited singlet
state of DTB-Pe attached to TiO2 via its anchor cum spacer
group was generated with a pulse centered around 432 nm and
the rise of the product state was time-resolved with a probe
pulse at 585 nm. Three distinct steps can be recognized in Figure
8 with the step height strongly decreasing toward the plateau
of the curve. The temporal separation corresponds to about 70
fs. The steps can reflect periodic electron transfer caused by
the motion of a vibrational wave packet in the potential curve
of the donor molecule resulting in periodic curve crossings. This
important effect of a vibrational wave packet on time-dependent
electron transfer will be discussed below.
Figure 7. (A) Transient absorption at 575 nm of ionized perylene as
product state of electron transfer to TiO2 (DTB-Pe, λEX ) 430 nm).
The thin line gives a smooth fit connecting the upper peak values of
the oscillations. (B) Fourier Transform of the oscillatory part of the
absorption signal shown in the small inset. (C) Fourier Transform of
the oscillatory part in the transient excited-state absorption at 715 nm
of the same dye DTB-Pe in toluene.
Discussion
The experimental results shown in Figure 5 prove that
vibrational wave packets are created in the excited singlet state
of the perylene chromophore via excitation from the electronic
ground state with a laser pulse of about 20 fs duration. The
vibrational wave packet is generated via instantaneous promotion
of some of the population in the vibrational levels of the
electronic ground state to higher vibrational levels in the excited
electronic state (compare scheme in Figure 4). The nuclear
equilibrium coordinates of the latter are shifted against those
in the electronic ground state. The 20 fs duration of the laser
Pe was measured at not too high a concentration in a thin layer
of toluene (about 10-4 M). At the identical observation
wavelength of 715 nm, an oscillatory behavior was observed.
A Fourier Transform of the oscillatory residual resulted in the
spectrum shown in part C of Figure 7. It revealed three
frequencies at 280, 375, and 430 cm-1. In part C, they are
labeled a, b, and c, respectively. The additional peak labeled
LM in part C of Figure 7 is most likely due to a solvent mode.
It appears reasonable to identify the peaks labeled a, b, and c
in part B for the ionized molecule with the corresponding peaks
in part C for the excited singlet state of the perylene chro-
mophore (Figure 7). The corresponding slight differences in the
vibrational frequencies are quite reasonable in view of the
available data for other aromatic molecules.24-26 Thus, motion
of a vibrational wave packet in the product state of this ultrafast
heterogeneous electron-transfer reaction is clearly borne out by
the data shown in Figure 7. It should be noted that the vibrational
wave packet moves in the potential of the product state long
after electron transfer has been completed. Oscillations in this
time range cannot be related in any direct way to periodic
electron transfer controlled by the motion of a vibrational wave
packet in the potential of the donor state. They demonstrate
only that a vibrational wave packet is surviving in the product
state after electron transfer.
pulse corresponds to an energy uncertainty of about 600 cm-1
.
Thus, this laser pulse can excite coherently at least two adjacent
vibrational levels of oscillators with an energy spacing of 600
cm-1 or less. The vibrational wave packet oscillates in the upper
potential energy curve similar to a classical particle (illustrated
in Figure 4). However, there is spread in the temporal and spatial
position, and the shape of the wave packet changes periodically
when it moves between the two turning points of the potential
curve. Dephasing processes and population decay via anhar-
monic vibrational coupling in the large molecule will destroy
the vibrational wave packet. However, the lifetime of the wave
packet is longer than 1 ps for the low-energy vibrations with
frequencies below 600 cm-1 in the perylene chromophore (see
Figures 5 and 7). Thus, upon excitation of vibrationally excited
states, at least for excitation energies below 600 cm-1, electron
transfer will proceed from the originally prepared excited
vibrational levels if electron transfer is completed within 1 ps.
An earlier approach is not valid in this case where photoinduced,
heterogeneous electron transfer was modeled by assuming
thermalized molecules as reactants.27 The latter assumption
requires averaging over a molecular ensemble to which a
temperature can be ascribed. The corresponding equilibrium
Boltzmann population over the vibrational energy levels of the
donor molecules is not established in the above case of fast
photoinduced, heterogeneous electron transfer originating from
a vibrational wave packet.
The last task was the search for a modulation of the electron-
transfer rate due to vibrational wave-packet motion in the
molecular donor state. Closer inspection of signals that probe
the product state, compare the curve shown in part A of Figure
7, revealed in the rising part a few steplike deviations from the
smooth fit. A more focused effort in time resolving the rising

Experimental Fingerprints of Wave-Packet Motion
J. Phys. Chem. B, Vol. 105, No. 38, 2001 9251
Figure 9. Simulated oscillatory behavior in the transient absorption
signal of ionized perylene illustrating the behavior seen in Figure 7.
For comparison, the smooth curve shows the rise in the product state
absorption for a thermalized population of the vibrational states. Also
for comparison, the inset shows the beating of the two assumed modes,
i.e., 360 and 420 cm-1, without the effect of a rise that is starting from
zero population.
Oscillations in the decay of the excited state of the chro-
mophore are obscured if this decay is controlled by electron
transfer with a time constant of 75 fs. This is born out by the
experimental result shown in Figure 6 and by the corresponding
simulated curve shown in the inset of Figure 6. In contrast,
Figure 7 shows clearly beats due to periodic wave-packet motion
corresponding to normal modes of the perylene chromophore.
This occurrence of a vibrational wave packet in the already
completely formed product state of photoinduced electron
transfer (compare oscillations in the plateau range of the curve
in part A of Figure 7) can have two different origins. First, the
vibrational wave packet could be surviving the electron-transfer
reaction. This requires similar vibrational frequencies in both
the reactant and the product state. This requirement is fulfilled
in the present system, as can be seen from a comparison of
parts B and C in Figure 7; i.e., the frequencies for the ionized
state on TiO2 (part B) are shifted by only about 20-30 cm-1 to
higher energies compared to those of the excited state in toluene
(part C). Second, in principle a vibrational wave packet can be
generated in the ionized molecule via an extremely fast electron-
transfer reaction. This mechanism would require a very short
electron-transfer time corresponding to an energy uncertainty
covering the vibrational frequencies of the observed wave
packet, i.e., 290, 410, and 450 cm-1 in the ionized chromophore
(see Figure 7). However, in the present system, electron transfer
was slowed with the spacer cum anchor group to 75 fs (rise of
the curve in part A of Figure 7 and references1,3,9). The cor-
responding energy uncertainty is much smaller than the above
energies of the vibrational frequencies observed in the wave
packet. Thus, the second possibility can be ruled out as an
explanation for the oscillatory beats seen in the upper curve in
Figure 7. It can be concluded for the experimental system under
study that the vibrational wave packet is surviving in the product
state of the heterogeneous electron-transfer reaction. Our group
has calculated the effect of wave-packet motion on transient
absorption spectra during heterogeneous electron transfer.6 The
calculations were carried out for a simple harmonic oscillator
model. A corresponding calculation is shown in Figure 9 for
the rise of the product state monitored by a transient absorption
measurement, where quite arbitrarily two frequencies, 360 and
420 cm-1, of the naked perylene chromophore were assumed
to be active in the vibrational wave packet. Recombination and
dephasing was neglected. The solid curve shows for comparison
the absorption behavior for the same frequencies and the same
Figure 10. Scheme illustrating photoinduced, heterogeneous electron
transfer from the excited donor molecule into the continuum of empty
electronic acceptor states in the conduction band of a semiconductor.
Two different densities of states (DOS) are shown in part A. Constant
DOS gives a smooth rise in the formation of the product state (upper
curve in part C), strongly energy dependent DOS leads to a stepwise
increase (lower curve in part C) indicating pulsed electron transfer due
to curve crossing effects during the periodic motion of the vibrational
wave packet in the donor state (part B).
potential curves in the absence of a vibrational wave packet.
The same qualitative trend can be seen in Figure 9 and in the
curves shown in part A of Figure 7. There are some additional
structures in the rising part of the experimental curve in Figure
7 that do not show up in the same way in Figure 9. Measuring
this buildup of the product state population is of particular
interest if one wants to observe the effect of vibrational wave-
packet motion on the rate of electron transfer. This effect will
be discussed next.
Figure 10 helps in understanding the measured stepwise rise
of the ionized state of the DTB-Pe molecules as displayed in
Figure 8. This stepwise rise of the product curve is a fingerprint
of the second role that a vibrational wave packet can play in
the electron-transfer reaction. Part B in Figure 10 shows the
periodic motion of the vibrational wave packet in the potential
curve of the donor molecule (reactant) and the resulting periodic
curve crossing events with the product states potentials. The
nuclear configurations of reactant and product state coincide at
the crossing point of two potential curves. This gives rise to
the highest probability for electron transfer. Thus, periodic wave-
packet motion in the molecular donor state leads to periodic
modulation of electron transfer. Integration over the product
state population, as is carried out in the transient absorption
measurement of the ionized chromophore, should thus display
consecutive steps whose height decreases with ongoing electron

9252 J. Phys. Chem. B, Vol. 105, No. 38, 2001
Zimmermann et al.
transfer and should vanish at the plateau of the signal where
electron transfer is complete (compare the lower curve in part
C of Figure 10). This expectation is in agreement with the
experimental result shown in Figure 8. Experimental10,12 and
theoretical papers11,13 have addressed this effect for homoge-
neous electron transfer. Recently, our group has developed a
theory of photoinduced, heterogeneous electron transfer from
a molecule into a continuum of electronic states in the
conduction band of a semiconductor, where the electron transfer
is modulated by the periodic motion of a vibrational wave packet
in the molecular donor state.14 Electron transfer to specific
vibrational excited levels of the ionized molecule or to specific
electronic levels in the semiconductor is modulated according
to the periodic motion of the vibrational wave packet in the
potential curve of the donor state.7,14 The phase differences
between population transfer to electronic states with different
energies in the semiconductor and to the corresponding different
vibrational states in the ionized molecule (energy conservation)
depend on the specific positions of the wave packet, where it
reaches the respective crossing point with the specific nuclear
configuration of the electronic product state.7 Calculated curves
for the buildup of the electronic and vibrational populations in
the product states are given in the theoretical paper.7 All of the
Franck-Condon factors and the corresponding different crossing
points can be realized sequentially by the moving wave packet
(part B in Figure 10), provided the molecular donor state is
located high enough above the bottom of the conduction band.
This is the case in the present experimental system.22 There is
an ideal border case, the so-called wide band limit, where the
density of states in the conduction band of the semiconductor
(DOS on the upper left-hand side of Figure 10) is constant over
an energy range spanning about twice the reorganization energy
in the conduction band below the donor orbital. This constant
DOS leads to complete cancellation of all of the individual phase
differences in the population of the molecular product states if
integrated over all of the vibrational levels. In the fictitious case
of a constant DOS, there will be a smooth rise toward complete
electron transfer (smooth upper curve in part C of Figure 10)
since all of the cross terms of individual contributions cancel
each other and all of the Franck-Condon factors are utilized
with their usual weight factors.14 In any real semiconductor,
e.g. in TiO2, the density of electronic band states (DOS) is not
that the separation between the steps seen in Figure 8 suggest
a slightly higher frequency, i.e., about 480 cm-1, than the highest
frequency seen in Figure 7, shoulder c at 450 cm-1 in part B.
However, there is a totally symmetric mode (out of plane -C-
C-C- bend) in the naked perylene chromophore at 452 cm-1
23 that could appear at 480 cm-1 in DTB-Pe on the TiO2
surface, considering the blue shift of about 30 cm-1 seen in the
frequencies in part B of Figure 7 compared to the nearest
frequencies in the naked perylene chromophore. A wave packet
of this mode could be seen in Figure 8 to make a periodic
contribution to electron transfer. Figure 10 illustrates the
feasibility of this interpretation.
It can be assumed that the molecular reorganization energy
for the heterogeneous electron-transfer reaction is on the order
of 0.3 eV. It is therefore much larger than the energies of the
vibrational modes that contribute to the wave packet generated
by the laser pulse of 20 fs duration (Figure 7). Considering that
the maximum Franck-Condon factor occurs in the range of
the reorganization energy, i.e., for the population of the
electronic donor level that is located in the conduction band by
about 0.3 eV below the electronic donor level of the molecule,5,7
it is very likely that several totally symmetric vibrational modes
with higher frequencies, i.e., in the range of 1000 cm-1 and
higher,23 must be populated in an incoherent fashion in the
ionized chromophore via the electron-transfer reaction. It appears
plausible that this incoherent population of vibrational levels
in the product states of the electron-transfer reaction is providing
a smooth background against which the stepwise behavior is
seen in Figure 8.
Summary
By application of transient absorption and stimulated emission
measurements, vibrational wave packets of low-energy modes
(mainly 357 and 421 cm-1) were found to give rise to periodic
beats over a time span longer than 1 ps in derivatized perylene
compounds in toluene. In ultrahigh vacuum, electron transfer
from the excited singlet state of the perylene chromophore
attached in the form of the DTB-Pe molecule via the -CH2-
phosphonic acid group to anatase TiO2 was found to be
monoexponential with a time constant of 75 fs, in agreement
with our earlier measurements. The transient absorption signal
from the ionized perylene chromophore that was formed in the
above heterogeneous electron-transfer reaction also showed
periodic beats. The corresponding frequencies were blue-shifted
by about 30 cm-1 compared to those known for the naked
perylene chromophore. The beats also continued in the ionized
chromophore, i.e., the product state of electron transfer, for up
to 1 ps. The vibrational wave packet survived with a lifetime
that was long compared to the electron-transfer time of 75 fs.
Thus, electron transfer has occurred with the molecule in a hot
vibrational state. Moreover, a stepwise increase toward complete
product state formation with decreasing step heights showed
directly a modulation of the rate of heterogeneous electron
transfer due to periodic wave-packet motion. This effect can
arise not only in an electronic two-level system but also for a
molecular donor state that can access a continuum of empty
electronic states over a wide energy range. In the latter case,
vibrational wave-packet modulation of electron transfer becomes
effective if the density of electronic states is strongly energy
dependent and thereby certain Franck-Condon factors are being
favored over others.
constant over the energy levels of the conduction band. A more
28,29
realistic energy-dependent density of states for TiO2
is
illustrated by the curved solid line in part A of Figure 10. The
corresponding calculated curve for electron transfer originating
from the motion of a vibrational wave packet in the molecular
donor state does not show the behavior of the wide band limit.
Instead, the product state rises in a stepwise fashion toward the
plateau, where the steps begin to vanish. A theoretical calcula-
tion for this more realistic case is shown as the lower curve in
part C of Figure 10. The stepwise increase toward the plateau,
corresponding to a complete formation of the product states,
resembles the behavior of an electronic two-level system. Since
the DOS is not a constant, the contribution of certain Franck-
Condon factors to electron transfer is enhanced where the DOS
is high. The behavior of the heterogeneous system begins to
resemble that of an electronic two-level system. Stepwise
formation of product states has been discussed before by other
groups in conjunction with experiments on homogeneous
electron transfer10,12 and in related theoretical papers.11,13 To
our knowledge, an earlier experimental observation of a clearly
stepwise formation of the product state (Figure 8) has not been
reported for an electron-transfer reaction. It should be noted
Acknowledgment. We are grateful to the Volkswagen
Foundation (electron transfer) and to the German Science
Foundation (SFB 450) for financial support. It is a pleasure to

Experimental Fingerprints of Wave-Packet Motion
J. Phys. Chem. B, Vol. 105, No. 38, 2001 9253
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staff of the Organic Chemistry Institute (Free University of
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the organic compounds.
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Supporting Information Available: Detailed description
of the synthesis of the employed perylene derivatives. This
material is available free of charge via the Internet at http://
pubs.acs.org.
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