Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. II. Chemically relevant cations and selected monovalent anions for atoms with Z = 3-112.

Abstract

The previously described approach for determination of the relativistic atomic X-ray scattering factors (XRSFs) at the Dirac-Hartree-Fock level [Olukayode et al. (2023). Acta Cryst. A79, 59-79] has been used to evaluate the XRSFs for a total of 318 species including all chemically relevant cations [Greenwood & Earnshaw (1997). Chemistry of the Elements], six monovalent anions (O^-, F^-, Cl^-, Br^-, I^-, At^-), the ns¹np³ excited (valence) states of carbon and silicon, and several exotic cations (Db⁵⁺, Sg⁶⁺, Bh⁷⁺, Hs⁸⁺ and Cn²⁺) for which the chemical compounds have been recently identified, thus significantly extending the coverage relative to all the earlier studies. Unlike the data currently recommended by the International Union of Crystallography (IUCr) [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], which originate from different levels of theory including the non-relativistic Hartree-Fock and correlated methods, as well as the relativistic Dirac-Slater calculations, the re-determined XRSFs come from a uniform treatment of all species within the same relativistic B-spline Dirac-Hartree-Fock approach [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] that includes the Breit interaction correction and the Fermi nuclear charge density model. While it was not possible to compare the quality of the generated wavefunctions with that from the previous studies due to a lack (to the best of our knowledge) of such data in the literature, a careful comparison of the total electronic energies and the estimated atomic ionization energies with experimental and theoretical values from other studies instils confidence in the quality of the calculations. A combination of the B-spline approach and a fine radial grid allowed for a precise determination of the XRSFs for each species in the entire 0 ≤ sin θ/λ ≤ 6 Å^-1 range, thus avoiding the necessity for extrapolation in the 2 ≤ sin θ/λ ≤ 6 Å^-1 interval which, as was shown in the first study, may lead to inconsistencies. In contrast to the Rez et al. work [Acta Cryst. (1994), A50, 481-497], no additional approximations were introduced when calculating wavefunctions for the anions. The conventional and extended expansions were employed to produce interpolating functions for each species in both the 0 ≤ sin θ/λ ≤ 2 Å^-1 and 2 ≤ sin θ/λ ≤ 6 Å^-1 intervals, with the extended expansions offering a significantly better accuracy at a minimal computational overhead. The combined results of this and the previous study may be used to update the XRSFs for neutral atoms and ions listed in Vol. C of the 2006 edition of International Tables for Crystallography.