The electronic structure and strain-dependent hybridization mechanisms in Cu- and Ag-doped anatase TiO 2 were investigated using density functional theory combined with maximally localized Wannier function (MLWF) analysis. In comparison with pristine TiO 2 (band gap ≈ 3 . 2 eV ), doping leads to a reduction of the band gap to ≈ 3 . 1 eV for Ag and ≈ 3 . 0 eV for Cu, accompanied by the appearance of dopant-related d -states near the band edges. The Wannier analysis shows that Cu doping results in a larger normalized spread ( Ω / N ≈ 2 . 56 Å 2 /WF) than Ag doping ( Ω / N ≈ 2 . 36 Å 2 /WF), indicating a stronger perturbation of the electronic states. Under 1% compressive strain, the spreads decrease to ≈ 1 . 87 Å 2 /WF (Cu) and ≈ 1 . 29 Å 2 /WF (Ag), while the gauge-invariant component remains dominant in both cases. The relative contribution of the off-diagonal term ( Ω OD / Ω ≈ 0 . 33 for Cu and ≈ 0 . 21 for Ag) indicates that strain enhances dopant–host hybridization without inducing strong localization. The calculated transport parameters show a clear dopant-dependent trend. Ag-doped TiO 2 exhibits lower electron effective masses (down to ∼ 0 . 83 × 1 0 − 32 kg at − 5 % strain) and higher electron mobility (up to ∼ 750 cm 2 V −1 s −1 ) compared to the Cu-doped system, where stronger localization of Cu 3 d states leads to higher effective masses and reduced mobility. The effective mass ratio suggests reduced recombination probability in the Ag-doped system. These results ithe interplay between band dispersion and dopant-induced hybridization governs the electronic properties of doped TiO 2 hybridization. The combined effect of Ag doping and compressive strain provides improved charge transport characteristics, which may be relevant for photocatalytic applications.
Azamjonov et al. (Wed,) studied this question.