Interpretation of Pre-Edge Fine Structures (PEFS) of K Edge of Titanium in Rutile TiO₂

Abstract
A method based on the local density approximation and on the multiple scattering wave calculation taking into account screened X-ray hole potential for the final state has been used to analyze the experimental XANES spectra of the TiO₂ rutile. The effect of cluster size on the computations has been analyzed concluding that taking into account atoms forming all neighboring octahedra lead to a reasonable agreement between theoretical and experimental spectra. In the crystal structure containing only slightly distorted regular octahedra in ground state, only two peaks corresponding to 1 s -> t_2g and e_g transitions are obtained. In contrast, due to the effect of the core hole potential calculated self consistently, the locally projected 3d density (DOS) is shifted down by about 3 eV giving rise to quadrupole transition. The 3d DOS arising from neighboring octahedra is not shifted by the core hole potential and contains non-centrosymmetric wave functions arising from solid state effect giving rise to dipole transitions. Temperature vibrations of atoms decrease the symmetry of the system thus making dipolar transitions to t_2g and e_g of absorbing octahedron allowed, this increases the intensities of the two first peaks A₁ and A₂ in the pre-edge region.