issue contents

ISSN: 2053-2733

May 2023 issue

Highlighted illustration

Cover illustration: The electron density (ED) of a chemical system is one of its most fundamental properties, and can in principle be reconstructed by Fourier inversion of the structure factors. However, if this procedure is terminated too early, series truncation artefacts such as spurious local ED maxima and minima can occur, which adversely affect chemical interpretation. In a pilot study in this issue, Bergner et al. [Acta Cryst. (2023), A79, 246–272] reconstruct the static ED for the challenging case of CaB6, exploring different mathematical weighting functions for theoretical structure factors. The image shows the results of a synthesis without employing such weighting functions. Prominent non-nuclear maxima are indicated by red arrows.


research papers

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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.

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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.

crystal lattices

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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.

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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.

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

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