Ab initio calculation of curved-wave EXAFS amplitude and phase functions

Abstract

The last five years have seen significant advances in the calculation of theoretical EXAFS. Most important was the development of a full curved wave formalism that was computationally rapid [ 11. The full curve-wave formalism takes into account the curvature of the outgoing and scattered photoelectron. This is most important when one wishes to examine the low-energy part of a spectrum and especially for higher Z elements. Previously it was thought that multiple scattering contributions were significant up to energies of 50 eV above the edge. Recent studies [2] have indicated that, in many cases, the multiple scattering contributions are not as significant as once believed and that the single scattering EXAFS theory is valid to much lower energies. We have previously shown a simple way to use the full curved wave formalism of EXAFS within the traditional plane-wave formalism [3,4]. Simply stated, the back-scattering amplitude and phase functions are replaced by effective backscattering amplitude and phase functions which depend on R, the interatomic separation. These functions, once calculated, can then be used in much the same way as the plane wave functions as calculated and tabulated by Teo and Lee [5] are used. We have calculated and tabulated the backscattering amplitude and phase for every element from boron to americium[3] and the tabulations are available from the authors on a single standard IBM or Macintosh disk. Until recently the most widely available set of theoretically determined amplitude and phase functions for EXAFS was that of Teo and Lee [5]. For high accuracy analysis, however, especially for the heavier elements, it still remained necessary to extract the functions from measurements of model compounds because their calculations were made using a plane wave approximation for the scattering of the outgoing photoelectron by the neighboring atom. Our use of the full-curved wave formalism makes our calculations valid for lower energies and for higher Z elements. The major advantage of tabulations such as ours is that the theoretical work can be widely and easily disseminated. Once file format standards have been established, improvements in the theoretical calculations can be transparently added to existing software without modification of actual code. They also provide a useful and standard building block on which experimentalists can build.