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.

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.

The phonon-induced relaxation dynamics of charge carriers in a PbSe quantum dot is studied for the first time by ab initio density functional theory in the time-domain. The picosecond time scale of the relaxation and the absence of the phonon bottleneck are rationalized by relatively high electron and hole state densities. While many of these states show only weak optical activity, most of them participate in the electron-vibrational relaxation. Our simulations demonstrate that the slight asymmetry in the electron and hole band structure is sufficient to allow symmetry-forbidden S-P, P-S, etc. transitions, which are seen in the experimental absorption spectra. The relaxation is nonexponential, in agreement with the strongly non-Lorentzian spectral line shapes observed in experiments. The energy exchanged during individual transitions is typically greater than the characteristic phonon energy, indicating that the transitions are multiphonon. Both electrons and holes interact better with low-frequency acoustic phonons, rather than higher frequency optical modes. Holes decay only slightly faster than electrons, rendering the hole-assisted Auger relaxation pathways inefficient. This relatively symmetric vibrational relaxation of electrons and holes proceeds on a picosecond time scale, much slower than the ultrafast highly efficient carrier multiplication that was reported recently in relation to improved solar power conversion.

No abstract

The electron and hole relaxation in the (7, 0) zigzag carbon nanotube is simulated in time domain using a surface-hopping Kohn-Sham density functional theory. Following a photoexcitation between the second van Hove singularities, the electrons and holes decay to the Fermi level on characteristic subpicosecond time scales. Surprisingly, despite a lower density of states, the electrons relax faster than the holes. The relaxation is primarily mediated by the high-frequency longitudinal optical (LO) phonons. Hole dynamics are more complex than the electron dynamics: in addition to the LO phonons, holes couple to lower frequency breathing modes and decay over multiple time scales.