Theory of ultrafast photoinduced heterogeneous electron transfer

Abstract

Ultrafast heterogeneous electron transfer (HET) between a molecule attached to a semiconductor surface and the conduction band of the semiconductor is discussed theoretically with emphasis on the perylene–TiO₂ system. The used description accounts for the specialty of the molecule, i.e. its particular electronic level scheme together with its vibrational degrees of freedom. The band continuum of the semiconductor is included and the approach is ready to describe different optical excitation and detection processes. Using a diabatic-state like separation of the whole system into molecular and semiconductor states, femtosecond photoinduced dynamics are studied. Since the HET is ultrafast standard rate theories cannot be applied. Instead, the respective time-dependent Schrödinger equation governing the electron–vibrational wave function is solved. Based on this approach and using a time-dependent formulation, the steady state linear absorption is calculated. Parameters of perylene attached to nano-structured TiO₂ via different bridge–anchor groups are adjusted by a comparison with measured spectra. A direct charge transfer excitation into the conduction band continuum is included into the description. This time-dependent formulation of the absorbance is confronted with a direct formulation in the frequency domain using the molecular Green's function. Then, it is explained how to observe the energetic distribution of the injected electron which carries signatures of the molecular vibrations in a two-photon photon emission spectrum. Some speculations on a laser pulse control of ultrafast HET are finally given.

Keywords:

• Ultrafast heterogeneous electron transfer
• Perylene on TiO₂
• Steady state linear absorption
• Molecular Green's function
• Two-photon photon emission spectrum
• Laser pulse control

Acknowledgements

The financial support by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 450 is gratefully acknowledged.