Photoinduced Ultrafast Heterogeneous Electron ... - ACS Publications

Perspective pubs.acs.org/JPCL

Photoinduced Ultrafast Heterogeneous Electron Transfer at Molecule−Semiconductor Interfaces Jesus Nieto-Pescador, Baxter Abraham, and Lars Gundlach* Department of Chemistry & Biochemistry and Department of Physics & Astronomy, University of Delaware, 109 Lammot DuPont, Newark, Delaware 19711, United States ABSTRACT: This Perspective discusses recent developments in ultrafast electron transfer dynamics at interfaces between organic and inorganic materials. Heterogeneous electron transfer (HET) is a key process in important fields like catalysis and solar energy conversion. Furthermore, the solid state nature of the systems gives control over relevant parameters and allows for investigating excited state dynamics and electron transfer processes in unprecedented detail. Progress in synthesis, sample preparation, and instrumentation makes it possible to provide experimental proof of recent prediction from theory concerning the adiabaticity of the reaction and the influence of coherence. A short recapitulation of the field is followed by a discussion of recent experimental efforts that allowed for studying HET, particularly focusing on the influence of energetics and vibrational dynamics.

I

were measured in the early 1990s using pulsed dye lasers.7,8 HET is, in general, faster than intra- or intermolecular ET. Consequently, time-resolved investigations of HET required the development of subpicosecond techniques. The rapid development of ultrafast optics in the late 80s made HET reactions accessible to time-resolved spectroscopic techniques and gave “ultrafast HET” its name. The number of ultrafast timeresolved studies increased shortly after Grätzel’s group published the first papers on solar energy conversion employing Ruthenium sensitized TiO2 nanoparticles9 and again after publication of the first 12% cell in 1991.10 Grätzel’s discovery was made in the same year the first commercial Ti:sapphire lasers became available and femtosecond measurements could be performed on a regular basis more easily compared to pumped dye lasers that were used until then to study interfacial charge transfer in the few picosecond regime. In the late 1990s, a wealth of femtosecond time-resolved measurements of interfacial electron transfer were performed, most of them using TiO2 as the semiconducting electrode.11−15 The present Perspective focuses on fundamental experimental studies of the kinetics of HET. Systems for photoinduced heterogeneous electron transfer consist in general of a light absorber that is photoexcited and an electrode that acts as an acceptor for the excited electron. The photoexcited electron is transferred to the acceptor leaving the absorber in an oxidized state and the electron residing in the electrode. Conventionally, the absorber is an organic or metal− organic molecule, also called dye, that is chemically bound to the electrode with some sort of anchor group. However, other light

n heterogeneous electron transfer (HET) an electron is transferred between a molecular species and a solid state electrode. This process is important for many applications in electrochemistry, chemical sensing, and energy conversion. In particular, photoinduced HET where the electron is donated from an electronic excited state is of great interest because of its importance for solar energy conversion. Earlier applications included xerography and companies like Xerox, Kodak, and Polaroid focused especially on ET between molecules and polymers for application in photocopying machines. This Perspective starts with a short recapitulation of the field that does not claim to be exhaustive. However, many excellent reviews of HET dynamics have been published and are cited here. In the early days, research was focused on revealing if photosensitization results in energy or electron transfer. Photocurrent measurements on merocyanine sensitized CdS suggested that this sensitization is in fact electron transfer and not energy transfer.1 The net result of a photodriven redox reaction gives relative little information about the primary electron transfer reaction and its quantum yield because reverse electron transfer competes with the reaction. However, under certain circumstances the reverse reaction can be minimized in heterogeneous systems. Such systems have been used to investigate photoinduced ET by measuring photo current densities.2 Early research focused mostly on the energetics and the alignment of molecular states and semiconducting bands.3,4 First, time-resolved measurements were performed in the 1970s and 80s using flash photolysis on the μs time scale to measure homogeneous ET between quinones.5 A short time later, electron transfer was reported between an organic molecule and semiconducting TiO2 nanoparticles on the nanosecond time scale.6 Picosecond time-resolved energy transfer between organic molecules and organic molecular and inorganic crystals © 2014 American Chemical Society

Received: July 22, 2014 Accepted: September 25, 2014 Published: September 25, 2014 3498

dx.doi.org/10.1021/jz501541a | J. Phys. Chem. Lett. 2014, 5, 3498−3507

The Journal of Physical Chemistry Letters

Perspective

Figure 1. Schematic alignment of the electronic levels with respect to the semiconductor band structure and reaction pathway for two cases discussed in the text. (a) Representation of the most basic ET reaction for a weakly coupled molecule. In the absence of electronic/vibrational coupling, HET proceeds iso-energetic. (b) In the case of strong coupling between donor and acceptor state, direct ET is possible and in the intermediate regime both pathways can interfere.

scales for a process rather than the exact rate constants. These measurements showed that already in the N3/TiO2 system the fastest processes happen on the sub-100-fs time scale. Despite their long history, Ru dyes are still actively studied and their complex intramolecular energy and electron dynamics and HET behavior still reveal new features like sub-10-fs injection from nonthermalized dye states.20 With the availability of shorter laser pulses HET systems with stronger electronic coupling and shorter ET times could be studied. Because of the stronger interaction between the donor and acceptor state, the influence of inhomogeneities in the systems like nearby surface defects or changes in the composition of the semiconductor are less pronounced.21 In addition, sensitizers like perylene,13 alizarin,22 and bi-isonicotinic acid23 have simple electronic structures compared to Ru dyes with its pronounced metal to ligand charge transfer and highly efficient intersystem crossing. These systems have the additional advantage that they are accessible to ab initio calculations because of the relatively small number of atoms.24,25 Charge transfer complexes formed by enediol/TiO2 systems give rise to very strong donor/acceptor coupling to the point were the excited state is predominantly localized on the Ti 3d states, cf. Figure 1b. Resolving these time scales is still challenging.26 However, such systems are very useful for understanding details of the HET process. An intensively studied model system for this case is catechol bound to TiO2. TiO2 sensitized with catechol shows the same charge transfer band in ground state absorption that has been observed for a catechol/Ti complex in solution,27 indicating the formation of a surface charge-transfer complex.28 In this limiting case, the distinction between excited state and charge separated state is not possible anymore and the reaction can be characterized as photoexcitation in the catechol/Ti complex rather than as adiabatic HET between catechol and TiO2. Enediol sensitizers with slightly weaker coupling to Ti can in principle show a combination of both pathways and can be used for studying electronic coherence in ET by measuring interference between both pathways (Figure 1b). Because the HET pathway is absent for the catechol/TiO2 system, it allows for studying short-lived intermediate states at the surface of the semiconductor without the influence of molecular states.29 Recently, a similar reaction pathway has been proposed for HET from a metal nanoparticle to TiO2.30

absorbing materials like nanoparticles have been employed recently.16 The electrode is usually made from metals or semiconductors. For generating a long-lived charge separated state, a semiconducting electrode is preferable. Usually, a semiconductor with a band gap larger than the absorption of the dye is used for preventing direct photoexcitation of the semiconductor. The most important requirement for HET is that the excited dye state aligns energetically with empty states in the electrode. This situation results in the most basic picture for HET shown in Figure 1a. The gray areas on the left constitute the conduction and valence bands of the semiconducting electrode. On the right-hand side, ground and excited state of the dye molecule are shown. Almost all early time-resolved studies of HET were performed on colloidal semiconductor films for two reasons. First, the most prominent application, that is, the Grätzel cell, employs such films. Second, the optical methods that were used demanded high optical density that can only be achieved by high surface area because the covalent nature of the dye/electrode bond restricts the dye coverage to less than one monolayer. These studies were very successful in explaining the first steps of charge separation that happens in the Grätzel cell, for example, the dynamics of the metal-to-ligand charge transfer state in ruthenium dyes. HET of ruthenium dyes or similar metal−organic sensitizers was intensively studied because these dyes resulted in the highest conversion efficiencies.11,17,18 However, the colloidal films that were used differed greatly in composition and morphology. For example, a commonly used commercial TiO2 nanocrystal (Degussa, P25) is a mixture of anatase and rutile. Also, the results of the most commonly used preparation procedure10 can differ greatly. For example, it has been found that the sodium content of the glass substrate used for depositing the colloidal film influenced electron transfer dynamics considerably.19 In addition to problems related to the colloidal film, the Ru dyes are problematic for fundamental HET studies because they have very broad absorption bands. This makes them well suited for application in solar cells; however, it complicates dynamic measurements tremendously because distinguishing contributions from different species, that is, excited state, triplet state, and cation, is very involved due to the spectral overlap.17 Consequently, measurements of electron transfer kinetics are strongly dependent on specific material properties and experimental conditions and transfer rates often represent time 3499



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unpublished experiments that mainly address energy dependence of HET. Strong focus will also be placed on the vibrationalelectronic coupling. This Perspective gives an outlook of experimental and theoretical challenges that are faced when studying fundamental aspects of HET. The most crucial points that are not well understood in heterogeneous ET to date are 1. the distinction between adiabatic and nonadiabatic HET, including possible electronic coherence between the excited donor and the acceptor state. 2. the influence of vibrational degrees of freedom, including their coherence. 3. the influence of the available density of states for reactant and product that includes short-lived intermediates near the surface. Recent results from our group and collaborators that are addressing points 2 and 3 will be discussed here. Experimental work that addresses the first item is rare. However, there are several theoretical approaches that focus on the transition between the nonadiabatic and the adiabatic regime in ET.44 General properties of HET. When studying the basic properties of HET the parameters for the process have to be defined as well as possible. In general, the observables can be expressed by a simple reaction scheme

The influence of conformational changes, vibrational degrees of freedom, and coherence effects can be studied by following ultrafast photoinduced reactions. Apart from its importance for technological applications, HET constitutes a unique test platform for the intrinsic factors that govern chemical reactions. The influence of conformational changes, vibrational degrees of freedom, and coherence effects can be studied by following ultrafast photoinduced reactions. The solid-state nature of the system allows for a high degree of order and for exclusion of solvation effects. The knowledge gained from these studies is not restricted to photochemistry but gives insight into all processes that involve bond breaking and formation in general chemical reactions. A system that proved to be very suitable for fundamental HET studies using femtosecond time-resolved spectroscopy is the perylene/TiO2 system. First, because absorption of the different intermediate species, that is, excited state and cation, are well separated from the ground state absorption and they are located in the visible region.31 Second, the fluorescence lifetime is on the order of several ns and contributions from triplet states can be neglected. Third, the HOMO−LUMO gap is several 100 meV smaller than the band gap of TiO2 allowing for selective excitation of the dye molecule. And last, the electronic coupling between perylene and TiO2 can be adjusted by employing different bridge/anchor group combinations. Using perylene derivatives as sensitizers for TiO2, a large number of studies have been performed. Among others, HET temperature dependence was measured,13 vibrational wave packet motion has been studied,31 the influence of different bridge groups on HET has been investigated,32 and the influence of the anchor group was studied.33 However, the above investigations were all performed using colloidal films as substrates. As mentioned above, HET in these films has the disadvantage that dynamics is influenced by inhomogeneities, in particular on longer time scales. This has been shown by comparing measurements on colloidal films with those employing single-crystal surfaces of TiO2 as substrates for large weakly coupled perylene derivatives. The electron transfer dynamics was strongly influenced by the presence of adjacent colloids on time scales above 70 fs, and it was concluded that measurements of slow dynamics in these films have to be taken with care.21 To circumvent the sensitivity problem that occurs when studying submonolayer coverage of the dye sensitizer on TiO2 single crystal surfaces, two-photon photoelectron spectroscopy (2PPE) has been employed for these measurements. This approach turned out to be very successful and allowed among others for measuring the electronic coupling dependent HET times,34 the orientation of the molecules on the surface,35 and the ET spectrum of the injected electrons.36 Both systems, the colloidal as well as the single crystal system, were also used as model systems for several theoretical studies on different computational levels, employing parametrized fully quantum mechanical models,37,38 combinations of first principle electronic and time-dependent Hartree calculations,39,40 and DFT/ TDDFT calculations.41−43 After giving an overview of the general properties of HET, we will summarize the experimental work that involved the unique perylene/TiO2 system and discuss them in light of results gained from different theoretical models and proceed with an overview of recent published and

D*(ω) + A(k) ⇒ D+(ω) + (A(k) + e−)

(1)

The reactants are the vibrational distribution of occupied excited donor states D*(ω) and the distribution of empty acceptor states in the semiconductor A(k), the products are the vibrational distribution of the oxidized donor D+(ω), and the distribution of the electron among the available acceptor states, including phonon modes A(k) + e−. It is well established that the strength of the diabatic coupling, that is, the splitting between adiabatic potentials, dictates the applicable model. For weak adiabatic coupling, a nonadiabatic picture is appropriate and perturbative treatment of the adiabatic coupling leads to a Fermi’s golden rule result. For strong adiabatic coupling the non-Born−Oppenheimer coupling is small and can be treated perturbatively.45 Although, a Fermi golden rule expression is only valid in the nonadiabatic limit, the expression helps to define the relevant parameters. Following Nitzan’s notation, the rate can be expressed as46 2

ket =

2π VD , A ℏ

(2)

Where VD,A is the strength of the coupling between donor and acceptor potential energy surface (PES) and - is the Franck− Condon weighted density of states, which includes the reorganization of the nuclear configuration. In case of strong coupling donor and acceptor, PES form a single adiabatic state. The height of the barrier E* (the free energy of activation) between donor and acceptor configuration and the relaxation time from the donor configuration to the acceptor configuration Tr are the factors that are governing the transition rate. Adiabatic HET in general is assumed to show Arrhenius type temperature dependence kET ∝

1 E* exp − Tr kBT

(3)

For nonadiabatic (NA) coupling the kinetics of the reaction are dominated by the electronic coupling between the donor and 3500



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requirements. The perylene/TiO2 system in combination with 2PPE allowed for measuring the transient distribution of electrons in the conduction band just after ET for the first measurement of a complete ET spectrum. The perylene is attached to TiO2 via different bridge/anchor groups that allow for varying the distance and coupling between the molecule and semiconductor and gave rise to HET time between 10 fs and 1 ps.33 Saturated bulky head groups prevent the perylene from dimerization in solution and after absorption on the surface of TiO2.47 The quantum yield of the S1−S0 fluorescence is above 90% with a lifetime of around 5 ns. Considering that HET reactions discussed here take place on the 10 fs to 1 ps time scale, intramolecular transitions can be neglected and it can be assumed that the donor state is the vibrational distribution in the electronic excited state created by photoexcitation. In particular, in case a sufficiently narrow spectrum is used for excitation, the photoexcited state can be prepared in the vibrational ground state, resulting in an exceptional simple donor state that constitutes a single state that is inhomogeneously broadened due to variations in the surrounding, for example, differences in binding sites and binding geometries. By measuring the spectrum of electrons above the Fermi level in the short time window after electron injection from the donor is almost completed and electron relaxation has not yet distorted the electron distribution, a complete ET spectrum can be measured. From the width of the spectrum and the position of the maximum, it can be concluded that high-energy vibrational modes are coupled strongly to the excited state and around four quanta of the dominant 160 meV perylene breathing mode are excited. It should be noted that the vibrational excitation in the cation results from the Franck− Condon factors between the molecular excited state and the cation and not from vibrational excitation of the molecular excited state prior to ET. These results are summarized in Figure 3. On the right-hand side the molecular donor state is depicted. Exclusively the vibrational ground state of the electronic excited state was populated by adjusting the excitation wavelength. On the left-hand side the much wider and down shifted spectrum of

all acceptor states, that is, the overlap of the respective states, and by the density of acceptor states. During one oscillation of the excited state wave packet every crossing point (red circles in Figure 2a) between the reactant PES and all product PES is

Figure 2. PES for the reactant state, that is, the excited molecule, and for the product state composed of the cation molecular state and the electron in in the conduction band in case of nonadiabatic coupling (a) and adiabatic coupling (b).

probed and transitions occur with the respective transmission probability. In the case of adiabatic HET, the distribution of available states is reflected in the barrier height (Figure 2a). In the case the donor is positioned well above the conduction band edge such that the whole ET spectrum can be accommodated in empty states below the donor level (referred to as the wide band limit) for every energy of the donor state, there is in general an acceptor state that upon mixing with the donor state results in a near barrierless transition. Thus, reactant and product state share the same adiabatic PES (Figure 2 b) . In this case, the exponential term in eq 3 approaches unity and the temperature dependence is expected to be negligible. Thus, the temperature dependence of the reaction can not be used to distinguish between nonadiabatic and adiabatic reactions. Because nonadiabatic HET can be ultrafast in the wide band limit because of the large amount of available acceptor states, the rate of ET is also not a sufficient indicator for the adiabaticity of the reaction. One property that can be used to distinguish between both regimes is the excitation of high-energy vibrational modes during ET that indicates the involvement of Franck−Condon factors in the reaction and characterizes a nonadiabatic pathway. To study the influence of the different parameters on the ET dynamics it is necessary, first, to choose a system that allows access to the different distributions and their dynamics. Second, a system is needed that allows for changing the relevant parameters, that is, electronic coupling and distribution of available states, individually. Finally, alternative pathways for the reaction like intramolecular charge transfer, internal conversion, or intersystem crossing have to be excluded. Changing the energetic position of donor and acceptor states, their density, and their coupling individually, without simultaneously changing the surface reconstruction, binding geometry, and coupling between electronic and vibrational (phonon) modes, is very challenging. In addition, the environment of the molecule should be kept as simple as possible. For such measurements, single crystals are preferred over colloidal films, and vacuum environment over solvent. Summary of Earlier Results Gained f rom the Perylene/TiO2 System. Recent approaches for measuring HET rates as a function of electronic coupling and energetic position are discussed next. The combination of a perylene dye anchored to single crystal TiO2 discussed above fulfills most of the above-mentioned

Figure 3. Experimental result (spheres) and graphical illustration according to the QM model (yellow lines) of the energy distribution of an injected electron in the conduction band (left-hand side of the figure). On the right-hand side the ground state spectrum (gray line) and the electronic transition between the vibrational ground states is illustrated. The spectrum of injected electrons is considerably wider and lower in energy reflecting the Franck−Condon overlap between the excited state of the molecule and the cation. Reproduced from ref 36. 3501



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further complicated by the short-lived nature of the distribution that thermalizes very rapidly into a Boltzmann distribution. Subsequently, cooling shifts the hot distribution toward the band edge. The perylene/TiO2 system constitutes a good compromise and allowed for measuring the ET spectrum for the first time. Limited energy resolution obscured details of the Franck− Condon progression in the measurement shown in Figure 3. Although this can be circumvented by employing a higher resolution detector, resolving the quantum beats between different states will be challenging due to the rapid dephasing in most solid state materials.

the injected electron is shown. This spectrum is the ET analogue to an optical absorption or emission spectrum where transition probabilities are modulated by Franck−Condon factors and electronic excitation results in vibrational excitation. The dominant mode that couples to HET is the same mode that is observed in gas phase photoionization measurements. This can be expected because both processes leave the molecule in a cationic state. The fully quantum mechanical (QM) model mentioned above has been employed to relate steady-state absorption spectra of the adsorbed dye to lifetime broadening that results from ultrafast HET. Although the QM model is complete in the sense that it includes vibrational modes, it depends on parameters and does not allow for first principle calculations. However, the general results and predictions are very useful for understanding the influence of vibrational modes on HET. The model has been reviewed recently.48,49 It accounts for coupling between electronic and high-energy vibrational states with energies larger than kBT and predicts a Franck−Condon-like energy distribution for the injected electron that is in agreement with the experimental results shown in Figure 3. Figure 4 shows the

The perylene/TiO2 system constitutes a good compromise and allowed for measuring the ET spectrum for the first time. These measurements demonstrate how important the level alignment between donor states and the electrode is. However, a reliable method for measuring the level alignment with sufficient precision to extract the number of vibrational quanta that can be involved in the ET reaction is often lacking. At the same time, it remains challenging to change the relative position of the donor state and the acceptor state without changing other parameters like the electronic−vibrational coupling in the molecule or the density of surface states of the semiconductor. One approach is to take different electronic or vibrational levels of the same dye molecule as donor states. This approach requires that the ET reaction occurs on a shorter time scale than any intramolecular relaxation processes, like vibrational relaxation, internal conversion, or intersystem crossing. In the case where different electronic levels are chosen as donor states, the tunability of the energy is limited. However, this approach has the advantage that the properties of the electrode and molecule are unaltered. Varying Electron Excess Energy by Employing Dif ferent Sensitizers. Recently, the Piotrowiak group published measurements on azulene attached to TiO2.50 Here, the vibrational ground state of the first excited state is located below the conduction band edge and is not expected to give rise to electron injection. However, when the quantum yield for ET was measured as a function of excess vibrational energy a clear change in quantum yield was observed once sufficient vibrational energy was provided to position the donor state in resonance with the high density of acceptor states in the conduction band. Figure 5 shows a plot of the ET yield as a function of excitation energy. Excitation of the vibrational ground state occurs at 1.8 eV. Higher excitation energies result in a vibrationally excited S1 state. At 2.1 eV the excess vibrational energy is sufficient to shift the donor state above the conduction band edge. These results show that energydependent measurements can be performed by employing hot ET and would benefit from dyes with slow IVR. It is remarkable that even for the case where the donor state is located below the conduction band edge, the quantum yield for ET still reached 0.2. This indicates a high density of near surface states that can act as electron acceptors. The importance of unoccupied states that are close to the surface and distinguished from bulk like states by their amount of localization, and their energy has attracted more attention in recent years. Initially, such states were mainly discussed in the context of defect states that are located in the band gap and act as trap states for injected electrons. However, it is well known that the surface band structure is distinguished from the bulk band structure by breaking of symmetry and

Figure 4. Time-dependent probability distribution versus the energy of a quasicontinuum whose width and spacing are similar to Figure 3. The position of the injecting molecular level in the energy band of the substrate is indicated as “ip”. A single harmonic vibrational mode of energy 0.1 eV and an overall transfer time of around 85 fs are considered in the calculation. Reproduced from ref 49.

calculated time-dependent probability distribution versus energy for an electron injected about 0.9 eV above the band edge into a quasicontinuum of acceptor states. A single vibrational mode with 0.1 eV energy was considered. The spacing of the peaks in the energy dimension accounts for the vibrational mode and the intensity distribution represents the Franck−Condon overlap between the electronic excited molecular state and the cation. Along the time-axis vibrational coherence is observed as the modulation of the rising signal. The phase of these oscillations is given by the distance on the excited state PES along the reaction coordinate between the vertically excited population and the crossing point with the cation PES. The distribution in Figure 3 shows that for the perylene/TiO2 system the wide-band limit is valid. Therefore, this particular system gives little information about coherence between individual levels in an energy integrated measurement because integration over the whole spectrum will eliminate the oscillations in the injection yield. However, an energy and time-resolved measurement can reveal the oscillations shown in Figure 4. The distribution will, in addition, be influenced by a nonconstant density of states (DOS) and by an energydependent coupling. Measurements of the ET spectrum are 3502



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allows for measuring the time scale for the delocalization process due to its inherent surface sensitivity. Such measurements showed that these intermediate near-surface states strongly influence the dynamics. The time scale for the occupancy of these states is around 100 fs.29 This number agrees well with TDDFT simulations for the initial delocalization of injected electrons into TiO2. The influence of such “reaction intermediates” on HET has been observed for various interfaces including ZrO2 electrodes that show a larger band gap when compared to TiO2 and ZnO.51−53

These results show that energydependent measurements can be performed by employing hot ET and would benefit from dyes with slow IVR. Altering the energetic position of the donor state can also be achieved by selectively exciting different electronic states of the same molecule. Recently, our group performed femtosecond− TA measurements after selectively exciting the Soret (S2) and Qbands (S1) of porphyrin derivatives. This situation is illustrated in Figure 6b. Here, we briefly summarize preliminary unpublished results. The S2 state is known to be very short-lived due to rapid internal conversion, which constitutes an effective pathway competing with HET from S2. Consequently, it has been challenging to distinguish between the two pathways in the past.54 In addition, the kinetics of competing intramolecular transitions have to be known in detail. Porphyrins have been extensively studied. Their electronic properties are well known and several time-resolved studies have been published.54,55 Recently, we measured HET from a fluorinated free-base phlorin56 into TiO2 attached via a carboxylic acid group. By comparing solution based measurements of the intramolecular relaxation dynamics and measurements of the molecule attached to TiO2 we were able to distinguish between IC and HET from the S2 state and compare the dynamics with HET from the S1 state. Surprisingly, it turned out that the electron transfer times from both states are very similar (Figure 7). They are not affected by the more than 1 eV difference in energetic position. Unfortunately, a conclusive measurement of the level alignment in these systems is challenging. The major reason is the wide

Figure 5. Dependence of Φinjection, the quantum yield of electron injection, on the energy of the incident photons measured on azulene sensitized TiO2. Reproduced from ref 50.

surface reconstruction even in case of defect free single crystal surfaces. In addition, the covalent bound between the anchor of the molecule and the surface can introduce states that act as acceptor states for ET. Including these states into the ET process leads to a three step model, where the electron is first injected into states that are localized close to the surface followed by a delocalization into bulk-like states. A qualitative diagram for the level alignment in the azulene/TiO2 case is shown in Figure 6a. The black distribution on the right represents the vibrational structure of the donor state with its vibrational ground state located below the conduction band edge. The dark gray area represents the DOS of near surface intermediate states. The population in the intermediate near-surface states is inherently difficult to study with transient absorption (TA) signals because the transient change of absorption of the electrons after injection into semiconductor states is in general generated by transition between many different states that all show different kinetics and does not allow for detailed analysis. One way to study these processes is by employing time-resolved electron spectroscopy that probes the electron in the conduction band directly and

Figure 6. Schematic alignment of the electronic and vibrational levels with respect to the semiconductor band structure. (a) Representation of the case where the vibrational ground state of the donor is located below the band edge as realized in the azulene/TiO2 system. (b) Representation of the case of excitation into higher excited states as realized in the porphyrin/TiO2 system. 3503



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Macromolecular HET System. High resolution measurements in the energy as well as in the time domain on heterogeneous colloidal systems are complicated due to the strong inhomogeneity of the electrode. Employing single crystal surfaces instead of colloidal systems and UHV environment instead of solvent helps reduce these inhomogeneities tremendously. However, even a single crystal surface contains steps and defect states and may give rise to different binding geometries and local electronic structure. Such complications are absent in solution-phase spectroscopies of organic molecules because all molecules are identical and contribute identical signals. Recently it has been possible to synthesize HET systems that are based on molecular polyoxotitanate clusters with well-defined stoichiometry and that can be equipped with dye molecules at well-defined binding sites (Figure 8). These clusters showed a mixture of photophysical

Figure 7. Injection dynamics is reflected in the rise of the cation absorption after S2 excitation (blue shaded area) and in the decay of the excited state after S1 excitation (red shaded area). The long-lived signal present in both cases constitutes absorption of the cation. The HET time is very similar for injection from both states.

range of values the work function of TiO2 can take, ranging from 4.4 to 5.5 eV.57 This introduces significant uncertainty in the level alignment. However, a rough estimate can be gained from cyclic voltametric measurements that suggest that the S1 state is located about 1 eV above the band edge. This level alignment would result in a large difference in bulk DOS for the two states that can act as electron acceptors. Calculations of the anatase (101) surface suggest that the density of empty states peaks at around 700 meV above the conduction band edge and decreases strongly toward higher energies. This maximum in the conduction band DOS results mainly from Ti 3d states and can be observed in bulk and surface DOS calculations for rutile and anatase crystals of all orientations. It can be assumed that the wide band limit is already valid for the S1 state. The similarity in ET rate for states that are in resonance with a significant different DOS can be explained in two ways. One possible explanation is that injection occurs into intermediate surface states that are different from surface states of the clean surface and show a constant DOS over a wide energy range. This assumption would also require that the electronic coupling between these states and the excited state is only weakly energy dependent. On the other hand, it is possible that the electronic coupling compensates for the difference in DOS resulting in a stronger coupling for states higher in energy. However, the latter explanation would require a fine balance between two unrelated properties and is thus less likely. These findings support the hypothesis that initial HET proceeds into intermediate surface acceptor states that are different from the DOS of the clean crystal. They are pointing in a similar direction as recent experimental and theoretical studies that are focusing on molecular intermediate states on the bridge/anchor group and go beyond the assumption that bridge/anchor groups act as simple tunneling barrier, instead treating the bridge as a singlemolecule conductor.58

Figure 8. Ti17 (Ti17(μ4-O)4(μ3-O)16(μ2-O)4(OPri)20) cluster: A molecular view showing the central tetrahedral and the penta-coordinate Ti atoms at the corners of the cluster highlighted in green. Reproduced from ref 59.

properties, including broad band-like absorption features traditionally associated with solid state materials and triplet states traditionally associated with molecules. Measurements suggested that high frequency modes of the isopropoxide capping ligands are essential for stabilizing the excited state in the cluster. Measurements on similar nanosized molecular clusters are still at the very early stage. However, their welldefined structure and limited size make them promising candidates for experimental as well as high-level theoretical work. Summary and Outlook. HET becomes considerably more complicated to study once the vibrational degrees of freedom on the molecular side and the surface induced states on the electrode are included. Consequently, it requires much more effort from the experimental as well as the theoretical side. Until now, no ab initio HET calculations are available that include high-energy vibrational modes. Neither has the vibrational progression in the molecular cation state yet been measured. In particular, the vibrational degrees of freedom are closely connected to the question of how the adiabaticity of the system influences its HET dynamics. In general, a nonadiabatic picture has been adopted for HET systems with the assumption that the ultrafast nature of ET is mainly due to the multitude of acceptor levels and not due to the strength of the donor−acceptor

These findings support the hypothesis that initial HET proceeds into intermediate surface acceptor states that are different from the DOS of the clean crystal.

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separated state. However, this requires a sufficiently strong coupling between the two states, that is, a system that is close to the adiabatic regime. In addition, electronic coherence in general dephases on the sub 10 fs time scale in solid state materials. Therefore, very short-lived intermediates have to be measured with high enough precision for revealing any effect of electronic coherence in HET. In order to study electronic coherence and adiabatic systems, the time resolution of the experiments have to be improved. Although the generation of few-femtosecond pulses in the UV−vis range has been demonstrated decades ago, such pulses are rarely used for studying HET. Research on the coupling of vibrational degrees of f reedom to HET and its coherence, on the other hand, will benefit from energy-resolved and ultrafast twodimensional spectroscopic techniques that allow for measuring the electronic and vibrational dynamics simultaneously. Finally, progress in both fields depends on the synthesis and preparation of reliable well-defined test systems that allow for changing the relevant HET parameters and that gives selective access to products and reactants of the HET reaction.

coupling. However, theoretical and experimental results suggest that many of the dye molecules that are anchored directly via short anchor groups, like carboxylic acid, give rise to coupling that is in the intermediate to strong regime. For example, the parametrized fully quantum mechanical model mentioned above predicts a 16 fs ET time with a transfer coupling of about 50 meV that corresponds to a Landau−Zener transition probability of around 0.4. This value is clearly less but not much less than 1, that is, the limit for nonadiabatic transfer. Such systems are positioned in-between both limiting cases. Depending on the bridge group, the transition probability turns out to be between 0.1 and 0.7 for the different perylene dyes when attached to TiO2. For the lowest probabilities; a nonadiabatic treatment is still appropriate, whereas for probabilities around 0.7, strong interaction is already apparent from the strong broadening in the ground state absorption spectra upon binding to TiO2.33 In the intermediate range of coupling strengths, ET dynamics are expected to show a mixture of properties that are characteristic for both regimes. The differences will be most apparent when the influence of highenergy vibrational modes on HET dynamics is measured. In case of nonadiabatic HET these modes strongly influence the spectrum due to Franck−Condon factors and wave packet dynamics, cf. Figure 4. In the intermediate regime Franck− Condon overlap and vibrational coherence are expected to play a much smaller role. This intermediate regime was investigated theoretically by Prezhdo et al., among others. Their TDDFT approach allows for distinguishing between adiabatic and nonadiabatic contributions to ET and shows that even in the case of strongly coupled molecules like isonicotinic acid with a measured ET time of a few femtoseconds,60 around 15% of ET proceeds via a nonadiabatic mechanism.61 These calculations only include vibrational modes with energies around kT. A review of this work has been published recently.62 Vibrational energy distribution and coherent wave packet motion can in principle be measured by probing molecular states of the system. Experimental investigations have mostly focused on vibrational excitation in the donor state so far.63 First indications of wave packet dynamics influencing HET have been observed in a perylene/TiO2 system.31 However, these measurements are complicated due to the need of very short laser pulses and are only sensitive to vibrational modes that are coherently excited and keep coherence in the course of the ET reaction. Such systems allow for studying the interplay of nuclear and electron dynamics. They offer a compelling test of our understanding of the extent of electron−nuclear coupling in ET reactions, which is neglected in the widely applied Born−Oppenheimer approximation. Studying the vibrational energy distribution in the product state and its coherence presents one way to study the transition from adiabatic to nonadiabatic HET experimentally and test recent theoretical predictions. In addition, vibrational coherence opens the way for laser pulse control of HET. The possibilities for controlling the rate and the pathway of HET has been explored theoretically, predicting among others things a dependence of the controllability of the ET rate as a function of coupling strength that agrees with the reduced influence of vibrational modes near the adiabatic limit.64 Recently, coherence effects in biological systems and the prospect of coherent control of HET has revived the interest in electronic and vibrational coherence in excited states and their influence on ET.65−69 Research on electronic coherence between donor and acceptor states is largely missing and has mostly been computational in nature.70,71 In photoinduced HET a short excitation pulse can generate a superposition of the photo excited state and the charge

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies Jesus Nieto-Pescador is a Ph.D. student at the University of Delaware studying heterogeneous electron transfer under the supervision of Prof. Lars Gundlach. Born in Durango, Mexico, he obtained a bachelor’s in engineering at Durango Insitute of Technology and a M.Sc. in physics from CINVESTAV-IPN (Mexico City). Baxter Abraham received his B.S. in Chemistry from the University of Central Florida in 2012. Currently a Ph.D. student at the University of Delaware, his research focuses on the use of third-order spectroscopy to study excited state dynamics. Professor Lars Gundlach received his Master in Physics from the Free University of Bremen, Germany, in 2000, and his Ph.D. from the Free University of Berlin, Germany, in 2005. He is currently an Assistant Professor at the University of Delaware (http://www.udel.edu/chem/ gundlach/). His research includes ultrafast studies of charge carrier dynamic in heterogeneous system and in nanoparticle.

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ACKNOWLEDGMENTS

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REFERENCES

We thank Dr. Piotr Piotrowiak for discussion and constructive comments on the manuscript.

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