We present a reciprocal-space pseudopotential scheme for calculating X-ray absorption near-edge structure (XANES) spectra. The scheme incorporates a recursive method to compute absorption cross section as a continued fraction. The continued fraction formulation of absorption is advantageous in that it permits the treatment of core-hole interaction through large supercells (hundreds of atoms). The method is compared with recently developed Bethe-Salpeter approach. The method is applied to the carbon K-edge in diamond and to the silicon and oxygen K-edges in α-quartz for which polarized XANES spectra were measured. Core-hole effects are investigated by varying the size of the supercell, thus leading to information similar to that obtained from cluster size analysis usually performed within multiple scattering calculations.

No abstract

We present the first successful attempt at calculating cluster full-potential x-ray absorption near-edge structure (XANES) spectra, based on the finite difference method. By fitting XANES simulations onto experimental spectra we are able to perform electron population analysis. The method is tested in the case of Ti K-edge absorption spectrum in TiO 2 , where the amount of charge transfer between Ti and O atoms and of the screening charge on the photoabsorber is obtained taking into account both dipolar and quadrupolar transitions. [S0031-9007(99)08724-4] The close interplay between experimental measurements and theoretical analysis has been and continues to be one of the most fruitful approaches to our present understanding of the electronic structure of condensed matter. This has become particularly true following the advent of synchrotron radiation experiments with their highly sophisticated detection techniques, since they provide a wealth of information impossible to exploit completely without the assistance of an adequate theoretical analysis.The study of the occupied and unoccupied electronic states of matter by x-ray emission and absorption is one such instance. Traditionally band structure calculations in periodic systems have been of great help in this interaction process, especially for the occupied part of the states or the unoccupied part very near to the Fermi energy (10-15 eV). Nowadays one can perform very sophisticated full-potential self-consistent band calculations that can be used to advantage to analyze experimental data. However there are severe limitations regarding their applicability to systems of physical interest: (a) They can be applied only to periodic crystals; (b) band programs are not geared for calculating empty states far above the Fermi level (apart from an early attempt [1] that has remained isolated); (c) the charge relaxation around the core hole is difficult to implement (supercell calculations have to be done but it is not at all easy to reach self-consistency).In this respect short range cluster calculations [2] are far more flexible and superior, since they can be applied to the vast majority of interesting cases (in material science, e.g., nanostructured materials, biology and coordination chemistry, catalysis and industrial processes, disordered systems, absorbates, etc.), and the energy range over which absorption spectra can be calculated is virtually unlimited. Incidentally even for periodic systems a long range band calculation is not necessary, for the simple physical reason that the finite lifetime of the excited photoelectron in the final state limits the size of the region sampled around the photoabsorber.Unfortunately up to now cluster calculations have been based on multiple scattering theory with optical potential restricted to the muffin-tin approximation. This is a very limiting feature, especially at low photoelectron kinetic energies [the x-ray absorption near-edge structure (XANES) part of an absorption spectrum within about 50 eV from the edge], sinc...