Current understanding of ultrafast electron transfer

The basic theoretical framework for describing electron transfer in bulk solid/Uquid interfaces was developed in the 1960s (Marcus, 1965 Gerischer, 1970 Levich, 1970). Fundamentally, photoinduced electron injection from the molecular excited state to a semiconductor nanoparticle can be described as electron transfer from a discrete and localised molecular state to a continuum of delocalised k states in the semiconductor. As shown in Fig. 11.5, the reactant state corresponds to the electron in the molecular excited state and the product states correspond to the oxidised molecule and the transferred electron in the semiconductor conduction band. There is a continuous manifold of product states, corresponding to the injected electron at different electronic levels in the semiconductor. 

In the non-adiabatic limit, the total ET rate can be expressed as the sum of ET rates to all possible accepting states in the semiconductor (Marcus, 1965 Gao et al, 2000 Gao and Marcus, 2000 Gosavi and Marcus, 2000). For electron injection from an adsorbate excited state with electrochemical redox potential of U°(S /S ) to a semiconductor k state at e = E- Ecb) above the band edge (with flatband potential of U°cb), the reaction can be written as 

The driving force for this reaction is AG(e) = AGo-i- e, where the free-energy change for elecfron fransfer to the band edge is AGo = - [G cb-G°(SVS )]. The total ET rate from adsorbate to semiconductor becomes 

It is informative to evaluate the trends in the ET rate using simple models of H(e) and p(e) that are likely to be qualitatively correct for many semiconductors. For metal oxides, the conduction-band states are composed primarily of empty orbitals of the metal ions, such as Ti 3d orbitals in Ti02 and Sn 5s and 5p orbitals in Sn02 (Henrich and Cox, 1996). Many adsorbates used for sensitisation are believed to bind with the metals ions via their anchoring groups such as -PO3H2 and -COOH (Vittadini et al, 2000). It is assumed that electronic interaction of adsorbate with the nanoparticle only involves the metal ions that are in direct contact with the anchoring 

Under these assumptions, the total injection rate is independent of nanoparticle size for particles that are not in the quantum-confined regime, and can be expressed as 

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