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State-of-the-art techniques for analysing X-ray absorption spectra are reviewed, with an eye to biological applications. Recent attempts to perform full spectral fitting of the XANES energy region and beyond for the purpose of structural analysis have met with encouraging success. The present paper analyses the theoretical motivations behind this success and indicates routes for future improvements. The theoretical background is not entirely new, although the point of view is, and some sections and appendices present material that the authors believe has never been published before. The aim of this paper is to provide a theoretical analysis that is as self-contained as possible.

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