Real-Time TD-DFT Simulations in Dye Sensitized Solar Cells: The Electronic Absorption Spectrum of Alizarin Supported on TiO2 Nanoclusters.

The structural and electronic properties of the alizarin dye supported on TiO2 nanoclusters have been examined by means of time-dependent density-functional (TD-DFT) calculations performed in the time-domain framework. The calculated electronic absorption spectrum of free alizarin shows a first band centered at 2.67 eV that upon adsorption features a red shift by 0.31 eV, in agreement with both experimental and previous theoretical work. This red shift arises from a relative stabilization of the dye LUMO when adsorbed. To analyze the dependence of the electronic properties of the dye-support couple on the size of metal-oxide nanoparticles, different models of (TiO2)n nanoclusters have been used (with n = 1, 2, 3, 6, 9, 15, and 38). As a conclusion, the minimal model is good enough to theoretically reproduce the main feature in the spectrum (i.e., the energy shift of the main band upon binding to TiO2). However, it fails in creating intermediate states which could play a significant role under real experimental conditions (dynamics of the electronic transfer). Indeed, as the size of the nanocluster grows, the dye LUMO moves from the edge to well inside the conduction band (Ti 3d band). On the other hand, to assess the consistency of the time-domain approach in the case of such systems, conventional (frequency-domain) TD-DFT calculations have been carried out. It is found that, as far as the functional and basis set are equivalent, both approaches lead to similar results. While for small systems the standard TD-DFT is better suited, for medium to large sized systems, the real-time TD-DFT becomes competitive and more efficient.