ch 41.2.2-kadosh - Chemistry

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2 The first step in the complex ET dynamics of the Graetzel cell is the ultrafast ET to the semiconductor from the attached molecular donor. The rate and mechanism of this ultrafast ET are currently under active experimental 5,16–29 and theoretical 30–36 investigation. Recently, ET on a record femtosecond timescale has been reported. A femtosecond laser study of alizarin-sensitized TiO 2 revealed ET with a 6-fs injection time, 18 and a resonant photoemission study of bi-isonicotinic acidsensitized TiO 2-determined ET with an injection time of less than 3 fs. 25 Coherent oscillations in both the ET coordinate and the vibrational wave-packet motion of the ET product were seen under ultra-high vacuum (UHV). 6,28,29 No redistribution of the vibrational excitation energy can be expected at such ultrafast timescales, 6,28 making it difficult to invoke the traditional Marcus– Levich–Jortner–Gerischer 37–40 ET mechanism, as well as the modern analytical and computational reaction rate theories. 30,41–49 Two competing mechanisms, which can be differentiated as shown in Fig. 1, and which require different conditions for optimum performance, have been proposed to explain the observed ultrafast ET between the dye and the semiconductor. 13,15 When the coupling is sufficient to induce a large splitting between the donor and acceptor state, so that the electron remains in the same adiabatic state as the system passes through the transition region, the mechanism is adiabatic. In this case the ET occurs via redistribution of the electron density of the adiabatic state due to ionic motion, and the rate may be estimated using transition state theory. 50,51 If the coupling is sufficently small and the Fig. 1. Adiabatic and nonadiabatic pathways of electron transfer. In adiabatic ET (solid bold line) the electron remains in the same adiabatic state throughout the reaction, proceeding from the reactant state to the product state through the transition state. In nonadiabatic ET, the electron proceeds from the reactant state to the product state via a direct transition (bold dotted and dashed lines). Israel Journal of Chemistry 42 2002 system passes through the transition region remaining in the same diabatic state and changing its adiabatic state, the ET is nonadiabatic (NA). NA ET occurs through a direct transition from the dye state to a manifold of acceptor states, and the rate could be calculated using standard Landau–Zener theory. 52 In experimental work the mechanism must be deduced from observables such as the reaction rate. For example, in cases where the Marcus theory of ET is applicable, the distinction between NA or adiabatic ET may be inferred from the rate equation (1) in which the transmission factor κ should be approximately unity for adiabatic reactions and much less than one for NA reactions. 50 Which mechanism is at work is a practical concern because of design implications. NA transfer relies on a high density of states in the conduction band. Since the density of states increases with energy, 53 an increase of the chromophore excited state energy relative to the edge of the conduction band will accelerate the transfer. At the same time, the photoexcitation energy and voltage will be lost due to the relaxation of the injected electron to the bottom of the conduction band. In the event of NA ET, it is also important to minimize chromophore intramolecular vibrational relaxation, 54,55 which lowers the chromophore energy and thereby the accessible density of conduction band states. NA ET is a purely quantum mechanical process with many tunneling features. In particular, the rate of NA ET will decrease exponentially with increasing distance between the donor and acceptor species. Efficient NA ET requires short donor–acceptor bridges. Conversely, the adiabatic ET rate will be much more weakly dependent on the density of acceptor states and will not exponentially decay with longer bridges. Since adiabatic transfer requires an energy fluctuation that can bring the system to the transition state, a fast exchange of energy between vibrational modes of the chromophore will increase the likelihood of adiabatic ET. Our first simulation of the ET was carried out at low temperature 34 to reflect UHV experimental conditions. 6,28,29 The simulation revealed that the earliest ET was dominated by the NA mechanism, with significant contributions from the adiabatic mechanism at the later stages. It was found that the ET was localized to the first 3 layers of the surface, with a single Ti atom closest to the chromophore contributing over 20%. The simulation predicted a complex non-single-exponential time dependence of the ET process. In the current study, the
ET is investigated in the high temperature regime typical of the majority of experimental studies. 7–9,12–15,20–22 2. THEORY The chromophore–semiconductor system and simulation protocol adopted for NA MD are similar to those of our previous work, 34 apart from the following changes. The molecular electron donor anchored to the semiconductor acceptor is modified to provide a better description of the systems studied experimentally 7–9,12–17,22–24 (Fig. 2a). A transition metal with a ligand (Fig. 2c) is added to the model chromophore of our previous work (Fig. 2b). The ground electronic states of both the experimental chromophore and the modified model are characterized by a donor–acceptor interaction between the undivided n-electron pairs of ligands and d-orbitals of the transition metal, and the photoexcitation is now appropriately described by electron promotion from d-orbitals of the transition metal to the antibonding π*-orbital of the conjugated ring. The modified model is more appropriate for the ground state of the chromophore, but does not change the excited state, whose properties govern the ET between the molecule and the semiconductor. All three chromophores in Fig. 2 have similar π* first excited states and, therefore, should show similar ET behavior. The difference between the Fig. 2. Chromophore molecules: (a) Chromophore used in experiments. 15 (b) Chromophore used in previous study. 34 (c) Chromophore used in this study. The chromophore of the previous study was chosen as an essential part of the experimental chromophore. The current modification of the model chromophore by addition of a d-electron metal and another ligand makes the ground electronic state of the n-electron donor d-orbital acceptor type similar to the experimental chromophore. The photoexcited state is of the π*-type in all three molecules. model chromophore in Fig. 2 and those typically used is less than the difference between the two chromophores for which ultrafast ET has been observed on this timescale. 18,25 Experiments for a variety of systems 15,18,28,56–62 have been carried out at temperatures ranging from UHV to ambient temperatures and above, with the majority of data available for room temperature. The low temperature UHV case was considered previously. 34 The high temperature case is investigated in this work. The temperature of the microcanonical simulation reported here averages around 350 K, with a 10-K fluctuation around the average. It has been found in the high temperature simulation that the ET dynamics are dominated by random thermal fluctuations of ions, which are similar in both the ground and excited electronic states. A directional electronic force is generally expected to act on ions once the equilibrated ground state is photoexcited. The force appears when the minima in the potential energy surfaces of the ground and excited electronic states are displaced in ionic coordinates. Ions initially located in the minimum of the ground electronic state find themselves on a slope of the excited electronic state surface. It has been found that the amplitude of thermal motion of ions at 350 K exceeds the displacement between the ground and excited state minima. The change due to photoexcitation in the electronic force acting on ions is small. Its contribution to ion dynamics can be neglected relative to thermal motions. This observation greatly simplifies the calculation. Under the assumption that the ground and excited state dynamics are similar, an ensemble of independent NA MD trajectories is not required, as it is in the traditional approaches. 63–82 The input to NA MD can be obtained from a ground state trajectory as described below. The simulation cell consists of a chromophore molecule bonded to a semiconductor surface. The surface is composed of a slab of rutile five layers thick, terminated on both sides with hydrogen and hydroxyl groups as would be expected if the surface were exposed to ambient humidity. The bottom two layers of the slab are frozen in the bulk configuration. A sufficiently large vacuum layer is added to the simulation cell to insure that the top of one slab does not interact with the bottom of the next slab within the infinite array of slabs. The chromophore molecule consists of an isonicotinic acid molecule with a silver ion bonded to the lone pair of the nitrogen, and a cyanide ion bonded to the opposite side of the silver. The chromophore is attached to the surface by a dehydrogenation reaction. The electronic structure of the combined chromophore–semiconductor system is obtained by density- Stier and Prezhdo / Thermal Effects in Photoinduced Electron Transfer 3
Page 1: Thermal Effects in the Ultrafast Ph
Page 5 and 6: Au: Is the fuzziness in (a) part of
Page 7 and 8: (a) (b) (c) (d) Fig. 4. (a) Time ev
Page 9 and 10: (a) (b) (c) ET reaction coordinate
Page 11 and 12: Au: What is PRF? connected to the s

ch 41.2.2-kadosh - Chemistry

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