Interficial Electron Transfer from a PbSe Quqantum Dot into the TiO$_{2}$ Surface*

We reporte an \textit{ab initio} nonadibatic molecular dynamics (NAMD) simulation of ultrafast photoinduced electron transfer (ET) from a PbSe quantum dot (QD) into the rutile TiO$_{2}$(110) surface. The simulation supports the obervation that the ET successfully competes with energy losses due to electron-phonon relaxation. The ET proceeds by the adibatic mechanism due to strong donor-acceptor coupling. High frequency polar vibrations of both QD and TiO$_{2}$ promotes the ET, since these modes can rapidly influence the donor-acceptor state energies and coupling. Low frequency vibrations generate a distribution of initial conditions for ET, which shows a broad variety of scenarios at the single-molecule level. The system exhibits diverse scenarios for individual electron injection events, involving a complex interplay of ET mechanims, time scales, and phonon dynamics.