Comparative Study of Electron Transfer Pathways in Isolated Indole-Based Dyes and Their (TiO<sub>2</sub>)<sub>9</sub> Complexes: A DFT/TD-DFT Perspective

Conventional theoretical studies of dye-sensitized solar cells often use isolated-molecule models, which neglect the critical influence of the TiO2 semiconductor interface. This leads to inaccurate predictions of electron transfer pathways. To address this issue, we conducted a comparative Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT) study of two indole-based D-π-A dyes featuring triphenylethylene and para-methoxybiphenyl auxiliary groups, examining them in both isolated and (TiO2)9-bound forms. Using PBE0 for geometry optimization and CAM-B3LYP with IEFPCM for ethanol solvation in excited states, we demonstrate that the isolated models incorrectly localize the Highest Occupied Molecular Orbital HOMO on the auxiliary groups. This suggests nonphysical charge transfer from these units to the acceptor. In stark contrast, the (TiO2)9 complexes reveal the correct mechanism: photoexcited electrons originate from the indole donor and are directly injected into the TiO2 conduction band. Auxiliary groups solely serve as light-harvesting antennas. The spectroscopic data corroborate this interfacial reconstruction: the computed absorption maxima for the (TiO2)9 systems (617 and 589 nm) agree with the experimental values (628 and 600 nm) within 2 %. In contrast, the isolated models deviate by 50 – 90 nm. Furthermore, the para-methoxybiphenyl dye has a 1.7-fold greater oscillator strength, which explains its enhanced photocurrent. Minimal geometric perturbation upon adsorption confirms that electronic effects, not structural distortion, drive interfacial charge separation. This work supports the utility of the (TiO2)9 cluster as a minimal model that faithfully represents dye-TiO2 interfaces. It also establishes a robust design principle: auxiliary structures should be optimized for light-harvesting cross-sections and interfacial compatibility rather than intrinsic donor strength. This provides a clear pathway for the rational development of high-efficiency organic sensitizers.