Finite difference method calculations of long - range X - ray absorption fine structure for copper over k 20 Å 1

X-ray Absorption Fine Structure (XAFS) is calculated for copper using the cluster based Finite Difference Method for Near-Edge Structure (FDMNES). This approach is conventionally used to produce high accuracy XAFS theory in the near edge region, however, we demonstrate that it can be readily extended to encompass an energy range of more than 1.5 keV (k 20 Å 1 ) from the K absorption edge. Such calculations require extensions to FDMNES to account for thermal effects, in addition to broadening effects due to inelastic processes. Extended calculations beyond the range of near-edge structure also require consideration of technical constraints such as cluster sizes and densities. We find that with our approach, we are able to produce accurate theory ranging from the absorption edge to the smooth atom-like region at high energies, with a single consistent model that is free from any fitting parameters. & 2009 Elsevier B.V. All rights reserved. X-ray Absorption Fine Structure (XAFS) refers to the complex series of oscillations seen in the photoelectric absorption curve just beyond an absorption edge. These oscillations convey important structural information about the absorbing material, including the relative positions of atoms in the crystal lattice. They are produced by the interference of the wavefunctions of photoelectrons ejected from the absorbing atoms with those returning due to backscattering from surrounding atoms. As a result, XAFS oscillations at high energies are dominated by a Fourier transform of the radial electron density from an absorber [1,2]. At energies close to the absorption edge, however, multiple scattering, many body and polarization effects have a significant impact on the spectrum. Historically, attempts to theoretically model XAFS have required assumptions regarding atomic and crystal potentials that greatly simplify calculations in order to make the problem manageable. Simplifications such as the muffin-tin approximation common to multiple scattering approaches [3], and models using infinite crystalline lattices [4] can be sufficient for qualitatively accurate results [5]. The speed of such calculations is also of significant benefit in many applications. High accuracy experimental XAFS data, however, shows that these approaches have shortcomings, particularly in the near-edge region (sometimes called the XANES region) [6]. This problem is particularly exacerbated for complex molecular structures such as are common in medical and biological applications. Since one of the most commonly cited ll rights reserved. (C.T. Chantler). benefits of structural determination via XAFS is its suitability for probing such structures, it is clear that we need an alternative approach. We therefore employ the Finite Difference Method (FDM), as implemented for XAFS calculations via the package Finite Difference Method for Near-Edge Structure (FDMNES) [7]. This approach has already been demonstrated to give improved results in the near-edge region for complex materials [8]. The principal drawback of FDMNES is its reputed unreliability beyond the nearedge region, where it becomes computationally intensive and is prone to grossly exaggerating the magnitude of absorption peaks. Our previous investigations showed that the latter problem can be overcome by extending FDMNES to account for thermal effects and inelastic processes [9], which enabled us to produce theoretical copper XAFS up to 300eV from the absorption edge. Our current work deals additionally with the efficiency problem, and enables us to extend our theory to 1.5 keV beyond the absorption edge, thus probing not only all of the XAFS spectrum, but joining the smooth atom-like absorption region beyond. This unlocks the possibility of producing accurate theory for complicated materials across any energy range, with a single consistent approach that requires no fitting parameters or limiting approximations. FDMNES performs calculations on spherical clusters of atoms in order to produce the photoelectric absorption cross-section [7]. This is given by