Real-Time Propagation of the Reduced One-Electron Density Matrix in Atom-Centered Orbitals: Application to Electron Injection Dynamics in Dye-Sensitized TiO2 Clusters

The ultrafast electron-transfer (ET) processes in three dye-sensitized TiO2 systems (pycooh-, catechol-, and alizarin-) are studied by using the real-time time-dependent density functional theory (RT-TDDFT). TiO2 cluster models are used to substitute TiO2 nanocrystals in order to check the quantum size effect on ET. The initial-state geometrical optimization for the individual constituents and coupled systems and the subsequent calculations for IR spectra and the density of states (DOS) are performed at the B3LYP/Lanl2dz theory level. The calculated IR spectra, the DOS, and the low-lying excited states reveal that the couplings between three dyes and TiO2 clusters are very strong so that an ultrafast electron injection from the excited dyes to TiO2 clusters is favored. By following the electronic motion of coupled systems after the photoexcitation of adsorbates in real time without allowing the nuclei to move, we predict an electronic injection time of a few femtoseconds for the present finite systems, which is slightly longer than the experimental measurements and other theoretical predications for the ET time on the same dye-sensitized bulk TiO2 systems due to the small clusters used in our simulation. We find that the ET time is appreciably dependent on the cluster size when the cluster is quite small. However, the size effects on ET time reduce dramatically as the cluster size reaches to a moderate middle size, for example, (TiO2)(14). The electron-nuclear coupled movement does not play a significant role in the initial ET process in these three systems. The effects of different initial excited states on electronic dynamics are also discussed.