Time-domain ab initio study of charge relaxation and recombination in dye-sensitized TiO2

In order to investigate the electron dynamics at the alizarin/I2-/TiO2 interface this study uses a novel state-of-the-art quantum-classical approach that combines time-dependent density functional theory with surface hopping in the Kohn-Sham basis. Representing the dye-sensitized semiconductor Gr?tzel cell with the I-/I3- mediator, the system addresses the problems of an organic/inorganic, molecule/bulk interface that are commonly encountered in molecular electronics, photovoltaics, and photoelectrochemistry. The processes studied include the relaxation of the injected electron inside the TiO2 conduction band (CB), the back electron transfer (ET) from TiO2 to alizarin, the ET from the surface to the electrolyte, and the regeneration of the neutral chromophore by ET from the electrolyte to alizarin. Developing a theoretical understanding of these processes is crucial for improving solar cell design and optimizing photovoltaic current and voltage. The simulations carried out for the entire system that contains many electronic states reproduce the experimental time scales and provide detailed insights into the ET dynamics. In particular, they demonstrate the differences between the optimized geometric and electronic structure of the system at 0 K and the experimentally relevant structure at ambient temperature. The relaxation of the injected electron inside the TiO2 CB, which affects the solar cell voltage, is shown to occur on a 100 fs time scale and occurs simultaneously with the electron delocalization into the semiconductor bulk. The transfer of the electron trapped at the surface to the ground state of alizarin proceeds on a 1 ps time scale and is facilitated by vibrational modes localized on alizarin. If the electrolyte mediator is capable of approaching the semiconductor surface, it can form a stable complex and short-circuit the cell by accepting the photoexcited electron on a subpicosecond time scale. The ET from TiO2 to both alizarin and the electrolyte diminishes the solar cell current. Finally, the simulations show that the electrolyte can efficiently regenerate the neutral chromophore. This is true even though the two species do not form a chemical bond and, therefore, the electronic coupling between them is weaker than in the TiO2-chromophore and TiO2-electrolyte donor-acceptor pairs. The chromophore-electrolyte coupling can occur both directly through space and indirectly through bonding to the semiconductor surface. The ET events involving the electrolyte are promoted primarily by the electrolyte vibrational modes.     

Nonadiabatic molecular dynamics study of electron transfer from alizarin to the hydrated Ti4+ ion

Ab initio real-time nonadiabatic (NA) molecular dynamics (MD) simulations are performed in order to investigate the photoinduced electron transfer (ET) from alizarin to the hydrated Ti4+ ion and compare it with the ET into bulk TiO2 that forms the basis of the Gr?tzel type solar cell. The experimental data and electronic structure calculations indicate that the photoexcitation spectra of alizarin attached to either bulk TiO2 or the Ti4+ ion in solution are very similar. In contrast, the NAMD simulations at ambient temperature predict marked differences between the ET dynamics that follow the photoexcitation in the two systems. The simulation of ET between alizarin and the TiO2 surface shows predominantly adiabatic transfer that occurs within 8 fs (Duncan et al. J. Am. Chem. Soc. 2005, 127, 7941), in agreement with the time-resolved experimental data. The simulation of alizarin attached to the hydrated Ti4+ ion reported presently predicts that the ET does occur, but on a slower 30 fs time scale, with a substantially reduced amplitude and by a predominantly NA mechanism. The differences are attributed to the disparity in the acceptor states of bulk TiO2 and the Ti4+ ion in solution. It is shown that the predicted alizarin-Ti4+ ET dynamics can be verified experimentally.     

Temperature independence of the photoinduced electron injection in dye-sensitized TiO2 rationalized by ab initio time-domain density functional theory

Time-domain density functional theory simulations resolve the apparent conflict between the central role that thermal fluctuations play in the photoinduced chromophore-TiO 2 electron transfer (ET) in dye-sensitized semiconductor solar cells [J. Am. Chem. Soc. 2005, 127, 18234; Isr. J. Chem. 2003, 42, 213] and the temperature independence of the ET rate [e.g., Annu. Rev. Phys. Chem. 2005, 56, 119]. The study, performed on the alizarin-TiO 2 interface at a range of temperatures, demonstrates that the ET dynamics, both adiabatic and nonadiabatic (NA), are dependent on the temperature, but only slightly. The adiabatic rate increases with temperature because a fluctuation toward a transition state (TS) becomes more likely. A classical TS theory analysis of the adiabatic ET gives a Gibbs energy of activation that is equal to k B T at approximately 50 K, and a prefactor that corresponds to multiple ET pathways. The NA rate increases as a result of changes in the distribution of photoexcited-state energies and, hence, in the density of accessible TiO 2 levels, as expressed in the Fermi Golden Rule. In the system under investigation, the photoexcited state lies close to the bottom of the TiO 2 conduction band (CB), and the chromophore-semiconductor coupling is strong, resulting in primarily adiabatic ET. By extrapolating the simulation results to chromophores with excited states deeper inside the CB and weaker donor-acceptor coupling, we conclude that the interfacial ET is essentially independent of temperature, even though thermal ionic motions create a widespread of initial conditions, determine the distribution of injected electron energy, and drive both adiabatic and NA ET.     

Non-adiabatic molecular dynamics simulation of ultrafast solar cell electron transfer

A non-adiabatic (NA) molecular dynamics (MD) simulation of the photoinduced electron transfer (ET) from a molecular electron donor to the TiO₂ acceptor is carried out. The system under study is typical of the dye sensitized semiconductor nanomaterials used in solar cells, photocatalysis and photoelectrolysis. The electronic structure of the dye-semiconductor system and the adiabatic dynamics are simulated by ab initio density functional theory MD, while the NA effects are incorporated by the quantum-classical mean-field approach. A novel procedure separating the NA and adiabatic ET pathways is developed. The simulation provides a detailed picture of the ET process. For the specific system under study, ET occurs on a 30 fs time scale, in agreement with the ultrafast experimental data. Both adiabatic and NA pathways for the ET are observed. The NA transfer entirely dominates at short times and can occur due to strong localized avoided crossing as well as extended regions of weaker NA coupling. Although the adiabatic ET contribution accumulates more slowly, it approaches that of the NA ET pathway asymptotically. The electron acceptor states are formed by the d-orbital of Ti atoms of the semiconductor and are localized within the first 3–4 layers of the surface. About 20% of the acceptor state density is localized on a single Ti atom of the first surface layer. The simulation predicts a complex non-single-exponential time dependence of the ET process.     

Observation of pH-dependent back-electron-transfer dynamics in alizarin/TiO2 adsorbates: importance of trap states

The dependence of the interfacial electron transfer in alizarin-sensitized TiO2 nanoparticles on the sample pH has been examined via transient absorbance spectroscopy in the visible spectral region (443-763 nm). Excitation of the alizarin/TiO2 system with visible pump pulses (lambdaexc = 500 nm) leads to a very fast electron injection (tauinj < 100 fs) over a wide pH range. Back electron transfer shows complicated multiphasic kinetics and strongly depends on the acidity of the solution. The strong dependence of back-electron-transfer dynamics on the ambient pH value is explained by a Nernstian-type change in the semiconductor band energy. Indeed, a variation of pH values over 7 units leads to a approximately 0.42 eV change of the conduction band edge position (i.e., the nominal free energy of the electron in the electrode). Assuming a pH-independent redox potential of the dye, this change was sufficient to push the system to a condition where direct photoinitiated electron injection to intraband gap surface states could be investigated. The existence of an electron-transfer pathway via surface trap states is supported by the similarity of the observed back-electron-transfer kinetics of alizarin/TiO2 at pH 9 and alizarin/ZrO2 reported in earlier work (J. Phys. Chem. B 2000, 104, 8995), where the conduction band edge is approximately 1 eV above the excited state of the dye. The influence of surface trap states on interfacial electron transfer has been studied, and a detailed analysis of their population, depopulation, and relaxation kinetics is performed. Therefore, alizarin adsorbed on the surface of TiO2 nanoparticles is an ideally suited system, where pH-dependent investigations allow a detailed study of the electron dynamics in trap states of TiO2 nanoparticles.     

Model study of coherent quantum dynamics of hole states in functionalized semiconductor nanostructures

Functionalization of semiconductor nanocrystals can be achieved by anchoring organic ligands to the surface dangling bonds. The resulting surface complexes often introduce electronic states in the semiconductor band gap. These interband states sensitize the host material for photoabsorption at frequencies characteristic of the molecular adsorbates, leading to the well-known process of photoexcitation and subsequent femtosecond interfacial electron transfer. This paper investigates the relaxation dynamics of hole states, energetically localized deep in the semiconductor band gap, after the ultrafast electron-hole pair separation due to interfacial electron transfer. Mixed quantum-classical methods, based on mean-field nuclear dynamics approximated by ab initio density functional theory molecular dynamics simulations, reveal superexchange hole tunneling between adjacent adsorbate molecules in a model study of functionalized TiO2-anatase nanostructures. It is shown that electronic coherences can persist for hundreds of picoseconds under cryogenic and vacuum conditions, despite the partial intrinsic decoherence induced by thermal ionic motion, providing results of broad theoretical and experimental interest.     

Influence of thermal fluctuations on interfacial electron transfer in functionalized TiO2 semiconductors

The influence of thermal fluctuations on the dynamics of interfacial electron transfer in sensitized TiO2-anatase semiconductors is investigated by combining ab initio DFT molecular dynamics simulations and quantum dynamics propagation of transient electronic excitations. It is shown that thermal nuclear fluctuations speed up the underlying interfacial electron transfer dynamics by introducing nonadiabatic transitions between electron acceptor states, localized in the vicinity of the photoexcited adsorbate, and delocalized states extended throughout the semiconductor material, creating additional relaxation pathways for carrier diffusion. Furthermore, it is shown that room-temperature thermal fluctuations reduce the anisotropic character of charge diffusion along different directions in the anatase crystal and make similar the rates for electron injection from adsorbate states of different character. The reported results are particularly relevant to the understanding of temperature effects on surface charge separation mechanisms in molecular-based photo-optic devices.     

pH-dependent electron transfer from re-bipyridyl complexes to metal oxide nanocrystalline thin films

Photoinduced interfacial electron transfer (ET) from molecular adsorbates to semiconductor nanoparticles has been a subject of intense recent interest. Unlike intramolecular ET, the existence of a quasicontinuum of electronic states in the solid leads to a dependence of ET rate on the density of accepting states in the semiconductor, which varies with the position of the adsorbate excited-state oxidation potential relative to the conduction band edge. For metal oxide semiconductors, their conduction band edge position varies with the pH of the solution, leading to pH-dependent interfacial ET rates in these materials. In this work we examine this dependence in Re(L(P))(CO)3Cl (or ReC1P) [L(P) = 2,2'-bipyridine-4,4'-bis-CH2PO(OH)2] and Re(L(A))(CO)3Cl (or ReC1A) [L(A) = 2,2'-bipyridine-4,4'-bis-CH2COOH] sensitized TiO2 and ReC1P sensitized SnO2 nanocrystalline thin films using femtosecond transient IR spectroscopy. ET rates are measured as a function of pH by monitoring the CO stretching modes of the adsorbates and mid-IR absorption of the injected electrons. The injection rate to TiO2 was found to decrease by 1000-fold from pH 0-9, while it reduced by only a factor of a few to SnO2 over a similar pH range. Comparison with the theoretical predictions based on Marcus' theory of nonadiabatic interfacial ET suggests that the observed pH-dependent ET rate can be qualitatively accounted for by considering the change of density of electron-accepting states caused by the pH-dependent conduction band edge position.     

The Interplay Between Lead Vacancy and Water Rationalizes the Puzzle of Charge Carrier Lifetimes in CH3NH3PbI3: Time-Domain Ab Initio Analysis

The perovskite CH₃NH₃PbI₃ excited-state lifetimes exhibit conflicting experimental results under humid environments. Using ab initio nonadiabatic (NA) molecular dynamics, we demonstrate that the interplay between lead vacancy and water can rationalize the puzzle. The lead vacancy reduces NA coupling by localizing holes, slowing electron–hole recombination. By creating a deep electron trap state, the coexistence of a neutral lead vacancy and water molecules enhances NA coupling, accelerating charge recombination by a factor of over 3. By eliminating the mid-gap state by accepting two photoexcited electrons, the negatively charged lead vacancy interacting with water molecules increases the carrier lifetime over 2 times longer than in the pristine system. The simulations rationalize the positive and negative effects of water on the solar cell performance exposure to humidity.     

Ultrafast electron transfer in photosynthesis: reduced pheophytin and quinone interaction mediated by conical intersections

The mechanism of electron transfer (ET) from reduced pheophytin (Pheo(-)) to the primary stable photosynthetic acceptor, a quinone (Q) molecule, is addressed by using high-level ab initio computations and realistic molecular models. The results reveal that the ET process involving the (Pheo(-) + Q) and (Pheo + Q(-)) oxidation states can be essentially seen as an ultrafast radiationless transition between the two hypersurfaces taking place via conical intersections (CIs). According to the present findings, an efficient ultrafast ET implies that the Pheo- and Q move toward each other in a given preferential parallel orientation, reaching the most effective arrangement for ET at intermolecular distances (R) around 5-3 Angstrom, where the lowest CIs are predicted. Favored donor/acceptor interactions are related to orientations with some overlap between the lowest occupied molecular orbitals (LUMO) of the two systems, and they lead to state-crossings at an earlier stage of the movement (larger R). Furthermore, when the topology of the interacting moieties does not make possible the LUMOs overlap, the corresponding diabatic potential energy curves do not intersect. Thus, it is anticipated that large scale motions, which are difficult to monitor experimentally, are actually occurring in the photosynthetic reaction centers of bacteria, algae, and higher plants, to fulfill the observed ultrafast ET processes.     

The Interplay Between Lead Vacancy and Water Rationalizes the Puzzle of Charge Carrier Lifetimes in CH3NH3PbI3: Time‐Domain Ab Initio Analysis

The perovskite CH₃NH₃PbI₃ excited‐state lifetimes exhibit conflicting experimental results under humid environments. Using ab initio nonadiabatic (NA) molecular dynamics, we demonstrate that the interplay between lead vacancy and water can rationalize the puzzle. The lead vacancy reduces NA coupling by localizing holes, slowing electron–hole recombination. By creating a deep electron trap state, the coexistence of a neutral lead vacancy and water molecules enhances NA coupling, accelerating charge recombination by a factor of over 3. By eliminating the mid‐gap state by accepting two photoexcited electrons, the negatively charged lead vacancy interacting with water molecules increases the carrier lifetime over 2 times longer than in the pristine system. The simulations rationalize the positive and negative effects of water on the solar cell performance exposure to humidity.     

Role of molecular anchor groups in molecule-to-semiconductor electron transfer

The dynamics of heterogeneous electron transfer (ET) from the polycyclic aromatic chromophore perylene to nanostructured TiO2 anatase was investigated for two different anchor groups with transient absorption spectroscopy in an ultrahigh vacuum. Data from ultraviolet photoelectron spectroscopy and from linear absorption spectroscopy showed that the donor state of the chromophore was located around 900 meV above the lower edge of the conduction band. With the wide band limit fulfilled the rate of the heterogeneous ET reaction was only controlled by the strength of the electronic coupling and not reduced by Franck-Condon factors. Two different time constants for the electron transfer, i.e., 13 and 28 fs, were measured with carboxylic acid and phosphonic acid as the respective anchor groups. The difference in the ET time constants was explained with the different extension of the donor orbital onto the respective anchor group to reach the empty electronic states of the semiconductor. The time constants were extracted by means of a simple rate equation model. The validity of applying this model on this ultrafast time scale was verified by comparing the rate equation model with an optical Bloch equation model.     

Distance dependence analysis of the electron transfer reactivity for the metastable FeOH2/FeOH2 system: an ab initio investigation

A novel theoretical scheme and ab initio application in discussing the electron transfer (ET) reactivity are presented in this paper, and are also calibrated in terms of the mono-hydrated iron ion system, Fe²⁺–OH₂/Fe³⁺–OH₂. The detailed geometry optimizations have been made at UMP2(full)/6-311+G^* level, and the activation geometrical configuration and the energy have been obtained at this level of theory using the activation model and the ab initio potential energy surface fitted from MP2(full)/6-311+G^* single point energies. The corresponding energy quantities (such as the activation energy, and dissociation energy) have also been obtained at different levels of theory (HF, MP2, MP3, MP4, QCISD and PUHF, PMP2 and PMP3 with the spin-projection) and a same basis set (6-311+G^*). The electron correlation calculations include the all electron correlation and the valence electron correlation. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is calculated using two different schemes. Taking the pair distribution function and the local ET rate into account, a statistically averaged overall observed ET rate scheme and a spherically averaged local ET rate scheme are proposed. The relevant kinetic parameters are obtained in terms of these new schemes at different ab initio calculational levels. The contact distance dependence of these parameters and the applicability of the presented models and ab initio calculational method are also discussed.     

Comparison of electron injection dynamics from re-bipyridyl complexes to TiO2 nanocrystalline thin films in different solvent environments

Factors that control photoinduced interfacial electron transfer (ET) between molecular adsorbates and semiconductor nanoparticles have been intensely investigated in recent years. In this work, the solvent dependence of interfacial ET was studied by comparing ET rates in dye sensitized TiO2 nanocrystalline films in different solvent environments. Photoinduced ET rates from Re(LA)(CO)3Cl [LA=dcbpy=4,4'-dicarboxy-2,2'-bipyridine] (ReC1A) to TiO2 nanocrystalline thin films in air, pH buffer, MeOH, EtOH, and DMF were measured by femtosecond transient IR spectroscopy. The ET rates in these solvent environments were noticeably different. However, differences between the rates in pH buffer and nonaqueous solvents (MeOH, EtOH, and DMF) were much smaller than the values expected from much more negative TiO2 conduction band-edge positions in the latter solvents under anhydrous conditions. It was suggested that the presence of adsorbed water, which was evident in FTIR spectra, lowered the band edge of TiO2 in these solvents and reduced the rate differences. The important effect of adsorbed water was verified by comparing two samples of Re(LP)(CO)3Cl [LP=2,2'-bipyridine-4,4'-bis-CH2PO(OH)2] sensitized TiO2 in DMF, in which the presence of a trace amount of water was found to significantly increase the injection rate.     

Theoretical study of ultrafast heterogeneous electron transfer reactions at dye-semiconductor interfaces: coumarin 343 at titanium oxide

A theoretical study of photoinduced heterogeneous electron transfer in the dye-semiconductor system coumarin 343-TiO(2) is presented. The study is based on a generic model for heterogeneous electron transfer reactions, which takes into account the coupling of the electronic states to the nuclear degrees of freedom of coumarin 343 as well as to the surrounding solvent. The quantum dynamics of the electron injection process is simulated employing the recently proposed multilayer formulation of the multiconfiguration time-dependent Hartree method. The results reveal an ultrafast injection dynamics of the electron from the photoexcited donor state into the conduction band of the semiconductor. Furthermore, the mutual influence of electronic injection dynamics and nuclear motion is analyzed in some detail. The analysis shows that--depending on the time scale of nuclear motion--electronic vibrational coupling can result in electron transfer driven by coherent vibrational motion or vibrational motion induced by ultrafast electron transfer.     

Photoinduced electron injection from Ru(dcbpy)2(NCS)2 to SnO2 and TiO2 nanocrystalline films

Photoinduced electron injection from the sensitizer Ru(dcbpy)2(NCS)2 (RuN3) into SnO2 and TiO2 nanocrystalline films occurs by two distinct channels on the femto- and picosecond time scales. The faster electron injection into the conduction band of the different semiconductors originates from the initially excited singlet state of RuN3, and occurs in competition with intersystem crossing. The rate of singlet electron injection is faster to TiO2 (1/55 fs-1) than to SnO2 (1/145 fs-1), in agreement with higher density of conduction band acceptor states in the former semiconductor. As a result of competition between the ultrafast processes, for TiO2 singlet, whereas for SnO2 triplet electron injection is dominant. Electron injection from the triplet state is nonexponential and can be fitted with time constants ranging from approximately 1 ps (2.5 ps for SnO2) to approximately 50 ps for both semiconductors. The major part of triplet injection is independent of the semiconductor and is most likely controlled by intramolecular dynamics in RuN3. The overall time scale and the yield of electron injection to the two semiconductors are very similar, suggesting that processes other than electron injection are responsible for the difference in efficiencies of solar cells made of these materials.     

Probing inhomogeneous vibrational reorganization energy barriers of interfacial electron transfer

An atomic force microscopy (AFM) and confocal Raman microscopy study of the interfacial electron transfer of a dye-sensitization system, i.e., alizarin adsorbed upon TiO(2) nanoparticles, has revealed the distribution of the mode-specific vibrational reorganization energies encompassing different local sites ( approximately 250-nm spatial resolution). Our experimental results suggest inhomogeneous vibrational reorganization energy barriers and different Franck-Condon coupling factors of the interfacial electron transfer. The total vibrational reorganization energy was inhomogeneous from site to site; specifically, mode-specific analyses indicated that energy distributions were inhomogeneous for bridging normal modes and less inhomogeneous or homogeneous for nonbridging normal modes, especially for modes far away from the alizarin-TiO(2) coupling hydroxyl modes. The results demonstrate a significant step forward in characterizing site-specific inhomogeneous interfacial charge-transfer dynamics.     

Electronic structure and spectra of catechol and alizarin in the gas phase and attached to titanium

Ab initio electronic structure calculations elucidate the dramatic differences observed in the electronic spectra of the catechol and alizarin molecules upon binding to titanium. Catechol and alizarin are similar chromophores with analogous electronic spectra in the free state. Binding alizarin to titanium red-shifts the spectrum. The binding of catechol to titanium produces a new optically active transition, at the same time preserving the features of the free catechol spectrum. By examining the details of the calculations, we can rationalize the spectral differences in the catechol and alizarin systems by the positioning of the catechol and alizarin pi molecular orbitals relative to the conduction band of TiO(2).     

Ultrafast Electron Transfer from Photoexcited CdSe Quantum Dots to Methylviologen

The ultrafast charge separation at the quantum dot (QD)/molecular acceptor interface was investigated in terms of acceptor concentration and the size of the QD. Time‐resolved experiments revealed that the electron transfer (ET) from the photoexcited QD to the molecular acceptor methylviologen (MV²⁺) occurs on the fs time scale for large acceptor concentrations and that the ET rate is strongly reduced for low concentrations. The increase in the acceptor concentration is accompanied with a growth in the overlap of donor and acceptor wavefunctions, resulting in a faster reaction until the MV²⁺ concentration reaches a saturation limit of 0.3–0.4 MV²⁺ nm^?2. Moreover, we found significant QD size dependence of the ET reaction, which is explained by a change of the free energy (ΔG).