Unraveling the e_g Orbital Splitting in TiO₂: The Role of Local Distortion in Ligand Field Multiplet Theory

This study investigates the electronic structure of titanium dioxide polymorphs (anatase and rutile) using ligand field multiplet theory calculations, supported by a combination of X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). To interpret the measured Ti XAS and RIXS spectra, we incorporate crystal field parameters (10Dq, Ds, and Dt) into our model Hamiltonian to account for local symmetry breaking of the Ti 3d orbitals. In an ideal Oh environment, these orbitals split into eg (dx2–y2, dz2) and t2g (dxy, dxz,yz) levels; under lower symmetry D4h, they further divide into four distinct a1g (dx2–y2), b1g (dz2), b2g (dxy), and eg (dxz,yz) energy levels. By analyzing the relationship between Ti L3-edge splitting and distortion parameters Ds and Dt, we demonstrate that the eg peak splitting is highly sensitive to local structural distortions. Our results reveal a strong correlation between the magnitude of local distortion parameters and the observed high-energy L3-edge spectra features, consistent with distortion within the titanium first coordination shell.