A software package for the analysis of X-ray absorption spectroscopy (XAS) data is presented. This package is based on the IFEFFIT library of numerical and XAS algorithms and is written in the Perl programming language using the Perl/Tk graphics toolkit. The programs described here are: (i) ATHENA, a program for XAS data processing, (ii) ARTEMIS, a program for EXAFS data analysis using theoretical standards from FEFF and (iii) HEPHAESTUS, a collection of beamline utilities based on tables of atomic absorption data. These programs enable high-quality data analysis that is accessible to novices while still powerful enough to meet the demands of an expert practitioner. The programs run on all major computer platforms and are freely available under the terms of a free software license.

http://cars9.uchicago.edu/xafs_school/Material/Articles/Horae%20JSR2005.pdf

ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT.

Anomalous scattering factors Δf′ and Δf″ have been calculated relativistically for Cr, Fe, Cu, Mo, and Ag Kα radiations for the atoms Li through Cf. An interpolation scheme for other wavelengths is included in a separate report. Relativistic calculations of the photoelectric cross section have been made and the integral for the principal contribution to Δf′ has been evaluated numerically without approximation to the form of the cross section‐vs‐energy curve, as has been done in previous calculations. Many of the results are significantly different from previous calculations. Where experimental values exist, agreement for Δf″ is improved. For the rare gases, except for xenon, agreement between Δf′ and experiment is improved. Because of the more rigorous evaluation of Δf′ from cross‐section information, it is presumed that the present Δf′ values are more accurate than previous calculated values. Calculated mass absorption coefficients for the elements are included as incidental information.

Relativistic Calculation of Anomalous Scattering Factors for X Rays

A technique for reduction of the Dirac equation, which initially omits the spin-orbit interaction (thus keeping spin as a good quantum number), but retains all other relativistic kinematic effects such as mass-velocity, Darwin, and higher order terms is presented. The spin-orbit interaction can be included as a perturbation once the 'relativistic' spin-polarised bands and wavefunctions have been obtained. The technique is used together with the local spin density approximation for exchange and correlation to calculate the self-consistent charge and spin density of a neutral Gd atom. The calculated magnetic form factor agrees extremely well with experiment. Comparison with a paramagnetic RAPW calculation shows the procedure should be accurate and fast for general band structure determinations.

https://iopscience.iop.org/article/10.1088/0022-3719/10/16/019/pdf

A technique for relativistic spin-polarised calculations

The computer code system PENELOPE (version 2008) performs Monte Carlo simulation of coupled
electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to
about 1 GeV. Photon transport is simulated by means of the standard, detailed simulation scheme.
Electron and positron histories are generated on the basis of a mixed procedure, which combines
detailed simulation of hard events with condensed simulation of soft interactions. A geometry package
called PENGEOM permits the generation of random electron-photon showers in material systems
consisting of homogeneous bodies limited by quadric surfaces, i.e., planes, spheres, cylinders, etc. This
report is intended not only to serve as a manual of the PENELOPE code system, but also to provide the
user with the necessary information to understand the details of the Monte Carlo algorithm.

/pdf/penelope-2006-a-code-system-for-monte-carlo-simulation-of-43nx3zmw6c.pdf

PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport

All of the x-ray emission wavelengths have recently been reevaluated and placed on a consistent \AA{}* scale. For most elements these data give a highly overdetermined set of equations for energy level differences, which have been solved by least-squares adjustment for each case. This procedure makes "best" use of all x-ray wavelength data, and also permits calculation of the probable error for each energy difference. Photoelectron measurements of absolute energy levels are more precise than x-ray absorption edge data. These have been used to establish the absolute scale for eighty-one elements and, in many cases, to provide additional energy level difference data. The x-ray absorption wavelengths were used for eight elements and ionization measurements for two; the remaining five were interpolated by a Moseley diagram involving the output values of energy levels from adjacent elements. Probable errors are listed on an absolute energy basis. In the original source of the present data, a table of energy levels in Rydberg units is given. Difference tables in volts, Rydbergs, and milli-\AA{}* wavelength units, with the respective probable errors, are also included there.

Reevaluation of x-ray atomic energy levels.

Self-Consistent-Field Dirac-Slater Wave Functions for Atoms and Ions. I. Comparison with Previous Calculations

Relativistic self‐consistent Dirac–Slater and Dirac–Fock wavefunctions have been used to evaluate the spin–orbit coupling constant and matrix elements of rn for most of the actinide ions and neutral atoms. Empirical corrections for the Dirac–Slater ζ5f constants based on experimental results are suggested which enable one to predict free‐ion values more accurately. Values of ζ5f from crystal and solution spectra show reductions from these estimates which are independent of atomic number Z, but vary roughly according to ionic charge and ligand electronegativity. It is shown that 〈r−3〉 parameters from atomic beam measurements on Sm, Eu, Pu, and Am can be accounted for fairly well with relativistic Dirac–Slater wavefunctions and intermediate coupling eigenvectors; configuration interaction, core polarization, and other contributions to hyperfine coupling are neglected. Similar calculations with hyperfine coupling constants from crystal EPR spectra are less consistently satisfactory.

Calculation of Spin–Orbit Coupling Constants and Other Radial Parameters for the Actinide Ions Using Relativistic Wavefunctions

Total energies of several configurations of the elements in the range of atomic numbers 104–132 were computed using the Liberman–Waber–Cromer program to determine the probable ground‐state configurations. These calculations provide evidence for eka‐actinium (s2d) at 121, partial filling of the 6f shell through 124 and beginning of a new superactinide series at element 125, in which the 5g shells fill progressively as the atomic number increases.

SCF Dirac–Slater Calculations of the Translawrencium Elements

Melamine, C3N6H6, or 2,4,6‐triamino‐s‐triazine, is monoclinic, space group P21/a, with a = 10.537(2), b = 7.477(1), c = 7.275(1) A, β = 112°9′(1), and Z = 4. Data were collected with an automatic diffractometer using crystal monochromated MoKα radiation. In addition to the usual spherical free atom model with anisotropic thermal parameters, least‐squares refinements were made with one‐center and two‐center generalized scattering factors. The aspherical distortions found are chemically reasonable and in most cases have the symmetry of the molecule although the symmetry is not crystallographically required. Addition of the generalized scattering factor parameters produced a significant improvement between observed and calculated intensities but made no significant change in the molecular geometry.

Don T. Cromer

Papers

Relativistic Calculation of Anomalous Scattering Factors for X Rays

Self-Consistent-Field Dirac-Slater Wave Functions for Atoms and Ions. I. Comparison with Previous Calculations

Calculation of Spin–Orbit Coupling Constants and Other Radial Parameters for the Actinide Ions Using Relativistic Wavefunctions

SCF Dirac–Slater Calculations of the Translawrencium Elements

Crystal structure refinements with generalized scattering factors. II. Melamine, 2, 4, 6‐triamino‐s‐triazine