A recently developed method to the full quantitative analysis of the XAS spectra extending from the absorption edge to the high-energy region is presented. This method is based on the use of two independent approaches to the analysis of the EXAFS and XANES data, the well-known GNXAS and the newly developed MXAN procedures. Herein, we report the application of this technique to two iron complexes of known structure where multiple-scattering effects are prominent, the potassium hexacyanoferrat(II) and -(III) crystals and aqueous solutions. The structural parameters obtained from refinements using the two methods are equal and compare quite well with crystallographic values. Small discrepancies between the experimental and calculated XANES spectra have been observed, and their origin has been investigated in the framework of non-muffin-tin correction. The ligand dependence of the theoretical spectra has been also examined. Analysis of the whole energy range of the XAS spectra has been found to be useful in elucidating both the type of ligands and the geometry of iron sites. These results are of particular use in studying the geometrical environment of metallic sites in proteins and complexes of chemical interest.

Abstract. We present a rigorous derivation of a real space Full-Potential MultipleScattering-Theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space-partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wave function. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach, provides a straightforward extension of MST in the Muffin-Tin (MT) approximation, with only one truncation parameter given by the classical relation l max = kR b , where k is the electron wave vector (either in the excited or ground state of the system under consideration) and R b the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l max → ∞ limit. Consequently, this feature provides a firm ground to the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

These lectures give an elementary introduction to the subject of four dimensional black holes (BHs) in supergravity and the Attractor Mechanism in the extremal case. Some thermodynamical properties are discussed and some relevant formulae for the critical points of the BH effective potential are given. The case of MaxwellEinstein-axion-dilaton (super)gravity is discussed in detail.Analogies among BH entropy and multipartite entanglement of qubits in quantum information theory, as well moduli spaces of extremal BH attractors, are also discussed.