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-TiO 2 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-TiO 2 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 TiO 2 levels, as expressed in the Fermi Golden Rule. In the system under investigation, the photoexcited state lies close to the bottom of the TiO 2 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.