Temperature independence of the photoinduced electron injection in dye-sensitized TiO2 rationalized by ab initio time-domain density functional theory

Time-domain density functional theory simulations resolve the apparent conflict between the central role that thermal fluctuations play in the photoinduced chromophore-TiO2 electron transfer (ET) in dye-sensitized semiconductor solar cells [J. Am. Chem. Soc. 2005, 127, 18234; Isr. J. Chem. 2003, 42, 213] and the temperature independence of the ET rate [e.g., Annu. Rev. Phys. Chem. 2005, 56, 119]. The study, performed on the alizarin-Ti02 interface at a range of temperatures, demonstrates that the ET dynamics, both adiabatic and nonadiabatic (NA), are dependent on the temperature, but only slightly. The adiabatic rate increases with temperature because a fluctuation toward a transition state (TS) becomes more likely. A classical TS theory analysis of the adiabatic ET gives a Gibbs energy of activation that is equal to k(B)T at approximately 50 K, and a prefactor that corresponds to multiple ET pathways. The NA rate increases as a result of changes in the distribution of photoexcited-state energies and, hence, in the density of accessible TiO2 levels, as expressed in the Fermi Golden Rule. In the system under investigation, the photoexcited state lies close to the bottom of the TiO2 conduction band (CB), and the chromophore-semiconductor coupling is strong, resulting in primarily adiabatic ET. By extrapolating the simulation results to chromophores with excited states deeper inside the CB and weaker donor-acceptor coupling, we conclude that the interfacial ET is essentially independent of temperature, even though thermal ionic motions create a widespread of initial conditions, determine the distribution of injected electron energy, and drive both adiabatic and NA ET.