J. Phys. Chem. B 2001, 105, 9245-9253
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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 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 transfer 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 semiconductor.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 * To whom correspondence should be addressed: E-mail:
[email protected]. † Hahn-Meitner-Institut. ‡ Fritz-Haber-Institut der MPG.
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 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 reproducibility. 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 wellknown 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
10.1021/jp011106z CCC: $20.00 © 2001 American Chemical Society Published on Web 09/01/2001
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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 decreased 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 heterogeneous 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 corresponding 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 nanoparticles 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 nanoparticles, 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. 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
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-phosphonic 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-butylnaphthalene to 1-naphthalene boronic acid under Suzuki conditions to yield 3,6-di-tert-butyl-1,1′-binaphthyl which was then anionically 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-tertbutyl-9-hydroxymethylperylene, and transformation with gaseous hydrogen bromide/toluene gave 2,5-di-tert-butyl-9-bromomethylperylene. 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-
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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. 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) DTBPe: 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 corresponding 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 dyecovered 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, recombination 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 comparison to the toluene environment (part A of Figure 3). In toluene, the 0-0 transition is dominant, whereas on the surface
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 application 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 chromophore. Femtosecond laser pulses had to be generated at several different wavelengths in order to carry out the measurements illustrated in Figure 4. Appropriate femtosecond laser pulses were generated utilizing a commercial high repetition rate femtosecond laser system (Coherent Instruments). A Tisapphire 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. However, 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
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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 (excitedstate 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 Tisapphire 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 timeresolved 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.
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 electrontransfer 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 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-Cbend vibrations. A mode with frequency around 280 cm-1 has
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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.
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
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-
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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.
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 chromophore (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. The last task was the search for a modulation of the electrontransfer 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
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 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 anharmonic 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.
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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 chromophore 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 electrontransfer 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 corresponding 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 wavepacket 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 wavepacket 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 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 homogeneous 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 constant over the energy levels of the conduction band. A more realistic energy-dependent density of states for TiO228,29 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 calculation 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 FranckCondon 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
Zimmermann et al. 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 -CC-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 -CH2phosphonic 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. 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 thank Mr. Schubert-Bischoff, Ms. Bloeck, and Dr. S. Su for supplying the TEM images of the nanoparticles. We thank the staff of the Organic Chemistry Institute (Free University of Berlin) for carrying out elemental analysis (Ms. Vasak), MS analysis (Ms. Hube), and NMR analysis (Dr. A. Scha¨fer) of the organic compounds. 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. References and Notes (1) Burfeindt, B.; Hannappel, T.; Storck, W.; Willig, F. J. Phys. Chem. 1996, 100, 16463. (2) Hannappel, T.; Burfeindt, B.; Storck, W.; Willig, F. J. Phys. Chem. B 1997, 101, 6799. (3) Burfeindt, B.; Zimmermann, C.; Ramakrishna, S.; Hannappel, T.; Meissner, B.; Storck, W.; Willig, F. Z. Phys. Chem. 1999, 212, 67. (4) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (5) Miller, R. D.; McLendon, G. L.; Nozik, A. J.; Schmickler, W.; Willig, F. Surface Electron-Transfer Processes; VCH Publishers: New York, 1995; chapter 5. (6) Ramakrishna, S.; Willig, F. J. Phys. Chem. B 2000, 104, 68. (7) Ramakrishna, S.; Willig, F.; May, V. Phys. ReV. B 2000, 62, R16330. (8) Persson, P.; Bergstro¨m, R.; Lunell, S. J. Phys. Chem. B 2000, 104, 10348. (9) Willig, F.; Zimmermann, C.; Ramakrishna, S.; Storck, W. Electrochim. Acta 2000, 45, 4565.
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