Revisited relativistic Dirac–Hartree–Fock X-ray scattering factors. I. Neutral atoms with Z = 2–118

Abstract

In this first of a series of publications, the X-ray scattering factors for neutral atoms are revisited. Using the recently developed DBSR_HF program [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287–303] the fully relativistic Dirac–Hartree–Fock ground-state wavefunctions for all atoms with Z = 2–118 (He–Og) have been calculated using the extended average level scheme and including both the Breit interaction correction to the electronic motion due to magnetic and retardation effects, and the Fermi distribution function for the description of the nuclear charge density. The comparison of our wavefunctions with those obtained in several previous studies in terms of the total and orbital (spinor) electronic energies, and a number of local and integrated total and orbital properties, confirmed the quality of the generated wavefunctions. The employed dense radial grid combined with the DBSR_HF's B-spline representation of the relativistic one-electron orbitals allowed for a precise integration of the X-ray scattering factors using a newly developed Fortran program SF. Following the established procedure [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554–589], the resulting X-ray scattering factors have been interpolated in the 0 ≤ sin θ/λ ≤ 2 Å−1 and 2 ≤ sin θ/λ ≤ 6 Å−1 ranges using the recommended analytical functions with both the four- (which is a current convention) and five-term expansions. An exhaustive comparison of the newly generated X-ray scattering factors with the International Union of Crystallography recommended values and those from a number of previous studies showed an overall good agreement and allowed identification of a number of typos and inconsistencies in the recommended quantities. A detailed analysis of the results suggests that the newly derived values may represent an excellent compromise among all the previous studies. The determined conventional interpolating functions for the two sin θ/λ intervals show, on average, the same accuracy as the recommended parametrizations. However, an extension of each expansion by only a single term provides a significant improvement in the accuracy of the interpolated values for an overwhelming majority of the atoms. As such, an updated set of the fully relativistic X-ray scattering factors and the interpolating functions for neutral atoms with Z = 2–118 can be easily incorporated into the existing X-ray diffraction software with only minor modifications. The outcomes of the undertaken research should be of interest to members of the crystallographic community who push the boundaries of the accuracy and precision of X-ray diffraction studies.