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2. Conceptual description

This section describes the various modules and outlines the use of the code.

2.1 Scattering potential and phase shift code, POTPH

The potentials of each atomic type are calculated as if the atoms were isolated in space using a relativistic Dirac-Fock-Slater Desclaux atom code with the von Barth-Hedin ground state LDA exchange-correlation potential. The scattering potentials are calculated by overlapping the free atom densities within the muffin tin approximation (Mattheiss prescription), and including the Hedin-Lundqvist/Quinn self energy for excited states. Muffin-tin radii are determined automatically from calculated Norman radii and scattering phase shifts are determined by matching at the muffin tin radius. XAFS spectra are referenced to the threshold Fermi level, which is estimated by electron gas theory at the mean interstitial density. Atomic configurations and core-hole lifetimes are built in, and mean free paths are determined from the imaginary part of the average interstitial potential. Dipole matrix elements are calculated using atomic core and normalized continuum wavefunctions. An absolute energy scale is obtained by a Desclaux-atom calculation of the total energy of the system with and without the core-hole. Polarization dependence is optionally incorporated in the dipole-operator.

The free atomic potentials need as input only the atomic number of the atoms, and, for the absorbing atom, the type of the core hole being considered. To do the overlapping for the unique potentials, the neighboring atoms must be identified, either by position (from a list of the cartesian coordinates of each atom) or by explicit overlapping instructions.

To save time the code calculates the overlapped atom potential for each unique potential only once, using as a sample geometry the first atom in the atom list with a given unique potential index. Thus it is essential that the neighborhood of that sample atom be appropriate.

2.2 Path enumeration, PATHS

The code uses a constructive algorithm with several path importance filters to explore all significant multiple-scattering paths in order of increasing path length, based on a list of atomic coordinates. An efficient degeneracy checker is used to identify equivalent paths (based on similar geometry, path reversal symmetry, and space inversion symmetry).

The criteria used in filtering are based on increasingly accurate estimates of each path's amplitude. The earliest filters, the pathfinder heap and keep filters, are applied as the paths are being created. A plane wave filter based on the plane wave approximation (plus a curved wave correction for multiple-scattering paths) and accurate to about 30% is applied after the paths have been enumerated and sorted. Finally, and accurate curved wave filter is applied to all remaining paths.

2.3 Scattering amplitude and other XAFS parameter calculation, GENFMT

For each path the code calculates the effective scattering amplitude (|F_eff| from which FEFF gets its name), total scattering phase shift and other XAFS parameters using the scattering matrix algorithm of Rehr and Albers. Once the scattering phase shifts and the paths are determined, no other input is necessary for this calculation.

2.4 XAFS spectrum calculation, FF2CHI

The code ff2chi constructs the XAFS spectrum chi(k) using the XAFS parameters from one or more paths. Single and multiple scattering Debye-Waller factors are calculated using a correlated Debye model. Output from this module is the total XAFS spectrum and optionally, the contribution to the XAFS from each path individually.

2.5 Calculation Strategy

The scattering phase shifts for each unique potential are necessary for both PATHS and GENFMT. They are used for the importance filters in PATHS and are the basis of the XAFS parameters calculation in GENFMT. This part of the calculation can be slow, so it is usually best to run it only once and use the results while studying the paths and XAFS.

To study the necessary paths, the pathfinder module PATHS will need the atomic positions of any atoms from which scattering is expected. If the structure is completely unknown, single-scattering paths can be created explicitly. Because the number of possible paths increases exponentially with total path length, start with a short total path length, study the few paths (representing scattering from the nearest neighbors), and gradually increase the total path length, possibly studying the path importance coefficients and using the filters to limit the number of paths. This process is not automated, and if done carelessly can yield so many paths that no analysis will be possible.

Finally, use GENFMT to calculate the XAFS parameters, and FF2CHI to assemble the results into a chi curve. Here, the slow part is GENFMT and FF2CHI is very fast. Therefore, to explore parameters such as Debye-Waller factors, mean free path and energy zero shifts, various combinations of paths and coordination numbers, run only module FF2CHI using the results saved from GENFMT.

If your model changes significantly, the phase shifts (which are based in part on the structure of the material) will have to be recalculated. Any time the phase shifts change, the XAFS parameters will have to be re-calculated. If the path filters have been used, the path list will also have to be recomputed.

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