Theory of ultrafast photoinduced heterogeneous electron transfer

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

“…Since ប⌫͑⍀͒ ͓Eq. ͑7͔͒, which is responsible for the peak broadening, is somewhat smaller than the vibrational energy ͑0.094 eV versus 0.16 eV in the present case 16,17 ͒, this broadening does not remove the appearance of single peaks. The energy-time uncertainty only initially smears out these peaks.…”

“…The room temperature spectra of perylene ͑in a solvent͒, however, could be simulated rather well by a single-mode description, with the vibrational mode having a quantum energy ប vib of about 0.16 eV ͑1370 cm −1 , corresponding to an in-plane C-C stretching vibration͒. As in our foregoing studies, [15][16][17] we again use this model here. It results in the PES U a ͑Q͒ = ប vib ͑Q − Q a ͒ 2 / 4.…”

“…15,17 We will explicitly account for this primary vibrational coordinate. All remaining intramolecular vibrations, the secondary coordinates, are treated in an approximate way using methods of open system dynamics ͑see Sec.…”

“…11,17,18 After photoexcitation, W cb ͑⍀ , t͒ is formed by the transition from the excited molecular state into the conduction-band continuum. The first one has the electron vibrational energy ប e + ប eM , and the latter one the energy ប cb + ប⍀ + ប ion N ͑here, ប cb denotes the energetic position of the lower conduction-band edge and ប⍀ is the respective additional energy of the electron in the band͒.…”

“…[11][12][13][14][15][16][17][18][19] We will account for the involved electronic states and dominant vibrations of the molecule, the expansion of the electronic wave function across the TiO 2 levels after charge injection, and the photoemission of the electron into vacuum states. To elucidate the influence of the laser pulse durations on details of the 2PPE spectra, the pulse initiating molecular excitation and charge injection ͑the pump pulse͒ is considered beyond any perturbation theory, whereas the pulse responsible for photoemission ͑the probe pulse͒ is treated within linear response theory.…”