Formation Energy and Phonon Dispersion of Halogen-Doped Rutile TiO₂: First-Principles Investigation

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This study presents a first-principles investigation of the formation energy and phonon dispersion of halogen-doped rutile TiO₂. Calculations were performed using density functional theory (DFT) within the generalized gradient approximation (GGA), as implemented in the Quantum ESPRESSO package. A 2 × 2 × 2 supercell containing 48 atoms was constructed, and halogen atoms (F, Cl, Br, and I) were introduced by substituting oxygen atoms, corresponding to a doping concentration of 3.125%. The thermodynamic stability of the doped systems was evaluated through formation energy calculations, which indicate that halogen incorporation is energetically favorable, with stability decreasing in the order F > Cl > Br > I. Structural optimization reveals that lattice distortion increases with the increasing atomic size of the dopant. Phonon dispersion calculations based on density functional perturbation theory (DFPT) confirm the dynamical stability of the doped systems, as evidenced by the absence of imaginary phonon frequencies. Halogen doping also modifies the vibrational properties of TiO₂, resulting in systematic frequency shifts arising from differences in dopant mass and bonding characteristics. These findings offer valuable insights into the thermodynamic stability and lattice dynamics of halogen-doped TiO₂, highlighting its potential applications in photocatalysis and optoelectronic devices.

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