Walter R. Duncan

Dynamics of the Photoexcited Electron at the Chromophore–Semiconductor Interface

Electron dynamics at molecular-bulk interfaces play a central role in a number of different fields, including molecular electronics and sensitized semiconductor solar cells. Describing electron behavior in these systems is difficult because it requires a union between disparate interface components, molecules and solid-state materials, that are studied by two different communities, chemists and physicists, respectively. This Account describes recent theoretical efforts to bridge that gap by analyzing systems that serve as good general models of the interfacial electron dynamics. The particular systems that we examine, dyes attached to TiO2, are especially important since they represent the key component of dye-sensitized semiconductor solar cells, or Gratzel cells. Gratzel cells offer a cheap, efficient alternative to traditional Si-based solar cells. The chromophore-TiO2 interface is a remarkably good target for theorists because it has already been the subject of many excellent experimental investigations. The electron dynamics in the chromophore-semiconductor systems are surprisingly rich and involve a great variety of processes as illustrated in the scheme above. The exact rates and branching ratios depend on the system details, including the semiconductor type, its bulk phase, and its exposed surface, the chromophore type, the presence or absence of a chromophore-semiconductor bridge, the alignment of the chromophore and semiconductor energy levels, the surface termination, the active vibrational modes, the solvent, the type of electrolyte, the presence of surface defects, etc. Still, the general principles governing the electron dynamics at the bulk-semiconductor interface can be understood and formulated by considering a few specific examples. The ultrafast time scale of the electronic and vibrational processes at the molecule-bulk interface make it difficult to invoke traditional theories. Instead, we perform explicit time-domain simulations with an atomistic representation of the interface. This approach most directly mimics the time-resolved experimental data and provides a detailed description of the processes as they occur in real time. The simulations described in this Account take into consideration the chemical structure of the system, determine the role of the vibrational motion and non-adiabatic coupling, uncover a vast variety of electron dynamics scenarios, and ultimately, allow us to establish the basic criteria that provide an understanding of this complicated physical process. The insights attained in the theoretical studies let us formulate a number of practical suggestions for improving the properties of the dye-sensitized semiconductor solar cell and for controlling the electron transfer across molecular-bulk interfaces.

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.

Regarding the validity of the time-dependent Kohn–Sham approach for electron-nuclear dynamics via trajectory surface hopping

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.

Ab initio nonadiabatic molecular dynamics of wet-electrons on the TiO(2) surface.

The electron transfer (ET) dynamics of wet-electrons on a TiO(2) surface is investigated using state-of-the-art ab initio nonadiabatic (NA) molecular dynamics (MD). The simulations directly mimic the time-resolved experiments [Science 2005, 308, 1154] and reveal the nature of ET in the wet-electron system. Focusing on the partially hydroxylated TiO(2) surface with 1-monolayer water coverage, and including electronic evolution, phonon motions, and electron-phonon coupling, the simulations indicate that the ET is sub-10 fs, in agreement with the experiment. Despite the large role played by low frequency vibrational modes, the ET is fast due to the strong coupling between the TiO(2) surface and water. The average ET for the system has equal contributions from the adiabatic and NA mechanisms, even though a very broad range of individual ET events is seen in the simulated ensemble. Thermal phonon motions induce a large fluctuation of the wet-electron state energy, generate frequent crossings of the donor and acceptor states, and drive the adiabatic mechanism. The rapid phonon-assisted NA tunneling from the wet-electron state to the TiO(2) surface is facilitated by the strong water-TiO(2) electronic interaction. The motions of molecular water have a greater effect on the ET dynamics than the hydroxyl vibrations. The former contribute to both the wet-electron state energy and the water-TiO(2) electronic coupling, while the latter changes only the energy and not the coupling. Delocalized over both water and TiO(2), wet-electrons are supported by a new type of state that is created at the interface due to the strong water-TiO(2) interaction and that cannot exist separately in either material. Similar states are present in a number of other systems with strong interfacial coupling, including certain dye-sensitized semiconductors and metal-liquid interfaces. The ET dynamics involving such interfacial states share many universal features, such as an ultrashort time scale and weak-dependence on temperature, surface defects, and other system details.

Ab initio molecular dynamics of ultrafast electron injection from molecular donors to the TiO2 acceptor

The photoinduced electron transfer (ET) from a molecular electron donor to the TiO2 semiconductor acceptor triggering Gratzel solar cells and other photochemical applications is investigated. The reported simulations reproduce the experimentally observed ET time-scale, establish the reaction mechanism, and provide a detailed picture of the ET process. The electronic structure of the chromophore-semiconductor system is simulated by density functional theory (DFT). Ab initio molecular dynamics (MD), including non-adiabatic (NA)transitions between electronic states, NAMD, is used to follow the ET reaction in real-time and at the molecular level. The simulation indicates that thermally driven adiabatic ET s dominant at room temperature. Vibrational motions of the chromophores induce oscillations of the photoexcited state energy that drives the photoexcited state in and out of the TiO2 conduction band. Two distinct types of ET events are observed depending on the initial conditions. At low initial energies the photoexcited state is well localized on the chromophore, and an activation is required for ET, with comparable contributions from both the adiabatic and NA mechanisms. At high initial energies the photoexcited state is already substantially delocalized into the TiO2 substrate. The remaining fraction of the ET process occurs rapidly and by the adiabatic mechanism.

Chapter 11 Ab initio simulations of photoinduced molecule-semiconductor electron transfer

Publisher Summary This chapter reviews the ab initio simulations of photoinduced molecule–semiconductor electron transfer. The electronic structure of the dye-sensitized semiconductor interface is illustrated with the catechol and alizarin molecules. The measured photoexcitation spectra of these molecules that are in the free state and are bound to titanium are simulated using ab initio electronic structure theory. Although catechol and alizarin are very similar molecules with analogous electronic spectra in the free state, they reveal stark differences upon binding to titanium. The alizarin spectrum is red-shifted upon binding, but it retains its shape. Binding catechol to titanium causes very little shifting of the spectrum, but it does produce a new low-energy band. In bound catechol, however, the lowest unoccupied molecular orbital (LUMO) is localized on the titanium, and the free catechol LUMO becomes a higher energy orbital. The new low energy band observed in the bound catechol spectrum is dominated by transitions from the dye-localized highest occupied molecular orbital (HOMO) to several titanium-localized unoccupied orbitals.

Photoexcitation Dynamics on the Nanoscale

The chapter describes real-time ab initio studies of the ultrafast photoinduced dynamics observed in quantum dots, carbon nanotubes, and molecule-semiconductor interfaces. The theoretical modeling of these nanomaterials establishes the relaxation and charge transfer mechanisms and uncovers a number of unexpected features that explain the experimental observations. In particular, the ultrafast electron injection from alizarin into TiO 2 surface occurs via strong coupling to a few surface states rather than through the commonly assumed interaction with multiple TiO 2 bulk states. The injection does not require high densities of acceptor states and, therefore, can function close to the edge of the conduction band, avoiding energy losses and maximizing voltages attainable in Gratzel solar cells. The phonon-induced electron and hole relaxation in the PbSe quantum dots is symmetric and slow. As a result, the carrier multiplication that generates multiple electron-hole pairs and increases solar cell efficiency becomes possible. In contrast to quantum dots, the relaxation of charge carriers in carbon nanotubes is mediated by the high frequency phonons and is, therefore, fast. Substantial contribution of the low frequency breathing modes to the dynamics of holes, but not electrons rationalizes why holes decay slower and over multiple timescales, even though they have been expected to decay more rapidly due to their denser state manifold. The systems considered here are representative of a wide spectrum of problems and contribute to the general framework for control and utilization of the novel nanomaterials.