Two-photon photoemission spectra related to an ultrafast heterogeneous electron transfer from perylene toTiO2

Abstract

Two-photon photoemission (2PPE) spectra related to sub-$100\text{\ensuremath{-}}\mathrm{fs}$ heterogeneous electron transfer from perylene to $\mathrm{Ti}{\mathrm{O}}_{2}$ are calculated. The approach accounts for the dominant intramolecular vibration of perylene as well as for the band structure of $\mathrm{Ti}{\mathrm{O}}_{2}$ described in a tight-binding model. The focus is on the influence of the pump and probe laser pulse duration, with the pump laser originating charge injection and the probe laser causing the photoemission process. The latter may proceed directly from the photoexcited molecule or, after charge injection, from the $\mathrm{Ti}{\mathrm{O}}_{2}$ conduction band. The time-dependent Schr\odinger equation which describes charge injection and accounts for the pump pulse is solved exactly within a time interval of about $250\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$. The action of the probe pulse is considered in linear response theory. While the vibrational structure in the 2PPE spectra broadens with decreasing pump pulse length, it is found that this structure is largely preserved when varying the probe pulse duration. In order to estimate dephasing caused by intramolecular vibrational energy redistribution in perylene and electron phonon coupling in $\mathrm{Ti}{\mathrm{O}}_{2}$, a density matrix scheme is also introduced describing heterogeneous electron transfer and the photoelectron emission processes. A finite escape depth for electrons at the $\mathrm{Ti}{\mathrm{O}}_{2}$ surface is finally taken into account to evaluate its influence on the spectra.