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

Fully relativistic X-ray scattering factors for 305 chemically relevant cations, six monovalent anions (O⁻, F⁻, Cl⁻, Br⁻, I⁻, At⁻), the excited (valence) ns¹np³ states of carbon and silicon, and five exotic cations for atoms with Z > 104 (Db⁵⁺, Sg⁶⁺, Bh⁷⁺, Hs⁸⁺ and Cn²⁺) have been determined in the 0 ≤ sin θ/λ ≤ 6 Å⁻¹ range using one-electron wavefunctions evaluated via the B-spline Dirac–Hartree–Fock method of Zatsarinny & Froese Fischer [Comput. Phys. Comm. (2016), 202, 287–303]. The study also reports the analytical conventional and extended interpolating functions for the 0–2 and 2–6 Å⁻¹ sin θ/λ intervals and includes a thorough comparison with results from the earlier investigations.

Fourier-synthesis approach for static charge-density reconstruction from theoretical structure factors of CaB₆

A novel type of Fourier-synthesis approach is reported for determining electron-density distributions and their Laplacians from static structure factors of CaB₆. The approach relies on mathematical weighting functions to yield a data set, reproducing all characteristic chemical bonding features of the original quantum-chemically calculated distributions.

Parallelohedra, old and new

It is shown that from a skewed, skeletal (edges and vertices), truncated octahedron, skewed skeletons can be derived of the other four convex parallelohedra found by Fedorov in 1885.

On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity

The number of Wyckoff sequences of a given subdivision complexity is calculated by means of a generating polynomial approach and a dynamic programming approach. The result depends on the choice of space-group symmetry (which is obligatory) and Wyckoff sequence length (which is optional). It also takes into account specified values for the total number of combinatorial and coordinational degrees of freedom, thereby representing crystal structures of invariant subdivision complexity.

Boris Gruber's contributions to mathematical crystallography

Boris Gruber's fundamental contributions to the classification of crystal lattices are reviewed.