The mean-field treatment of electron-nuclear interaction results in many qualitative breakdowns in the time-dependent Kohn-Sham (TDKS) density functional theory. Examples include current-induced heating in nanoelectronics, charge dynamics in quantum dots and carbon nanotubes, and relaxation of biological chromophores. The problem is resolved by the trajectory surface-hopping TDKS approach, which is illustrated by the photoinduced electron injection from a molecular chromophore into TiO2, and the excited-state relaxation of the green fluorescent protein chromophore.

This review describes recent research into the properties of the chromophore-TiO2 interface that forms the basis for photoinduced charge separation in dye-sensitized semiconductor solar cells. It focuses particularly on an atomistic picture of the electron-injection dynamics. The interface offers an excellent case study, pertinent as well to a variety of other photovoltaic systems, photo- and electrochemistry, molecular electronics, analytical detection, photography, and quantum confinement devices. The differences between chemists' and physicists' models for describing molecules and bulk materials, respectively, create challenges for the characterization of interfaces that include both of these components. We give an overall picture of the interface by starting with a description of the properties of the chromophores and semiconductor separately, and then by discussing the coupled system, including the chromophore-semiconductor binding, electronic structure, and electron-injection dynamics. Explicit time-dependent modeling is particularly valuable for an understanding of the ultrafast electron injection because it shows a variety of individual injection events with well-defined dynamical features that cannot be made apparent by an average reaction-rate description.

The observed 6-fs photoinduced electron transfer (ET) from the alizarin chromophore into the TiO2 surface is investigated by ab initio nonadiabatic (NA) molecular dynamics in real time and at the atomistic level of detail. The system derives from the dye-sensitized semiconductor Grätzel cell and addresses the problems of an organic/inorganic interface that are commonly encountered in photovoltaics, photochemistry, and molecular electronics. In contrast to the typical Grätzel cell systems, where molecular donors are in resonance with a high density of semiconductor acceptor states, TiO2 sensitized with alizarin presents a novel case in which the molecular photoexcited state is at the edge of the conduction band (CB). The high level ab initio analysis of the optical absorption spectrum supports this observation. Thermal fluctuations of atomic coordinates are particularly important both in generating a nonuniform distribution of photoexcited states and in driving the ET process. The NA simulation resolves the controversy regarding the origin of the ultrafast ET by showing that although ultrafast transfer is possible with the NA mechanism, it proceeds mostly adiabatically in the alizarin-TiO2 system. The simulation indicates that the electron is injected into a localized surface state within 8 fs and spreads into the bulk on a 100-fs or longer time scale. The molecular architecture seen in the alizarin-TiO2 system permits efficient electron injection into the edge of the CB by an adiabatic mechanism without the energy loss associated with injection high into the CB by a NA process.

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 Grätzel 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.

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).