X-ray absorption near-edge structure (XANES) spectroscopy is a powerful technique to probe the empty states in solids.

Moreover XANES gives information about the atomic arrangement around the probed atom up to the medium range order. Nevertheless the interpretation of XANES spectra is not straightforward and often requires sophisticated simulation tools. In the case of K or L1 edges, real space multiple scattering theory has been extensively used in the past twenty years. However, multiple scattering theory has traditionally suffered from a drawback, i.e., the ``muffin-tin'' approximation of the potential.

I will present a reciprocal-space ``non muffin-tin'' scheme for calculating XANES spectra. The method uses pseudopotentials and reconstructs all-electron wave functions within the Projector Augmented Wave framework. The method incorporates a recursive method to compute absorption cross section as a continued fraction, that permits the treatment of core-hole interaction through large supercells (hundreds of atoms).

Several applications of the method will be shown and comparison will be made with real-space (''muffin-tin and 'non muffin-tin'') calculations, and with recently developed Bethe-Salpeter approach.