Relativistic Dirac-Hartree-Fock X-ray scattering factors. III. Chemically relevant atomic anions for Z = 1-85.

Abstract

Relativistic X-ray scattering factors are reported for a broad and systematically defined set of chemically relevant atomic anions, including mono- and multivalent species, for elements with atomic numbers Z = 1-85 [Greenwood & Earnshaw (1997). Chemistry of the Elements]. Dirac-Hartree-Fock wavefunctions were generated using the DFRATOM code [Matsuoka & Watanabe (2001). Comput. Phys. Commun. 139, 218-234], with soft radial confinement applied where necessary to stabilize diffuse anionic states. The influence of this confinement on the resulting X-ray scattering factors is explicitly and systematically analyzed to ensure that the reported data reflect physically meaningful electronic structure trends rather than artifacts of the stabilization procedure. The quality of the resulting wavefunctions was assessed using previously reported high-quality benchmark energies [Visscher & Dyall (1997). At. Data. Nucl. Tables 67, 207-224], radial metrics, and direct comparison of X-ray scattering factors with established reference data for neutral atoms and several monovalent anions [Rez et al. (1994). Acta Cryst. A50, 481-497; Su & Coppens (1997). Acta Cryst. A53, 749-762; Macchi & Coppens (2001). Acta Cryst. A57, 656-662]. To ensure physically meaningful results, an X-ray scattering based perturbation metric was introduced to quantify the impact of confinement on the calculated X-ray scattering factors, together with additional high-sin θ/λ consistency checks. The resulting X-ray scattering factors were computed and tabulated in a format consistent with that used in the International Tables for Crystallography [Maslen et al. (2006). Vol. C, Section 6.1.1, pp. 554-589], facilitating direct crystallographic use. Analysis of representative main-group, transition-metal and heavy p-block elements demonstrates that electron attachment leads to a systematic enhancement of the X-ray scattering factors at small momentum transfer, governed primarily by the expansion of the valence electron density, while the high-sin θ/λ region remains dominated by largely invariant core electron contributions. The data presented here provide the first broad, internally consistent reference set of fully relativistic X-ray scattering factors spanning a wide range of multivalent atomic anions of chemical and crystallographic interest, and represent a natural extension of the studies by Olukayode et al. [Acta Cryst. (2023), A79, 59-79; Acta Cryst. (2023), A79, 229-245].