Interpretation of pre-edge fine structures (PEFS) of K edge of titanium in rutile TiO2

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 1s --> 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 A(1) and A(2) in the pre-edge region.