Identifying and characterizing translationally modulated molecular crystal structures

Abstract

Most structural (i.e. displacive) modulations make molecules independent that had been related by translation in a phase having a smaller or centered unit cell. In the modulated structure the independent molecules are differentiated by small translations, rotations, and/or conformational changes but an approximate translational relationship is normally retained. A program has been written to identify such pseudotranslations because they can be difficult to find by eye and because they combine with each other and with lattice translations in ways that can be confusing. To characterize the pseudotranslations the program calculates their fractional translational, orientational, and conformational components as well as several quality indicators. While many pseudotranslations are obvious, others are borderline; setting tolerances for identifying a pseudotranslation proved difficult. Defaults were chosen to reproduce experience-based judgment but they can be varied in the program input. The program was run for organic and for metallo-organic structures with R ≤ 0.075 in the 2019 release of the Cambridge Structural Database. The frequency of pseudotranslations increases with Z′ and is approximately 50% for Z′ > 4. Some structures were found in which an identified pseudotranslation cannot correspond to a modulation. These include structures in which some but not all of the molecules are related by pseudotranslations and structures in which pseudotranslations in different parts of the unit cell have different directions.

Toward Understanding High-Z′ Organic Molecular Crystals through the Superspace Method: The Example of Glycyl-l-valine

“…An overview of high- Z ′ crystal structures, where Z ′ > 1 is the result of a modulation of the molecular geometry, has been given by Brock and Taylor . Furthermore, a Z ′ = 8 modulated structure has been discovered for 2-chloro-4-nitroaniline, however, without information on a possible low- Z ′ phase.…”

“…The so-called high- Z ′ ( Z ′ > 4) structures of molecular compounds are rare, and there have been several studies in recent years discussing the origins of such structures. − Often a simple translational pseudosymmetry is featured in these crystal structures . This raises a question as to why the particular compound has crystallized as a high- Z ′ rather than as an ordinary Z ′ = 1 structure with a smaller unit cell.…”

cis-Bis(L-DOPA-κ2 N,O)copper(II) monohydrate: synthesis, crystal structure, and approaches to the analysis of pseudosymmetry

“…A number of excellent approaches to the observation and examination of molecular similarity and pseudosymmetry in crystal structures have been developed. These include the molecule-overlay options in MATCH (Collins et al, 2006), XP (Sheldrick, 2008), and Mercury (Macrae et al, 2020), the atomic-pair mid-point analysis (Baggio, 2019(Baggio, , 2020, and the identification and characterization of translationally modulated structures (Brock & Taylor, 2020). We became interested in Z 0 > 1 structures as we attempted to explore the hypothesis that there is often a direct relationship between the matrix relating pairs of independent molecules in twinned crystals having Z 0 > 1 and the twin law (Foxman & Young, 2018;Young & Foxman, 2020).…”

Preparation of polyethylene oxide single crystals via liquid gating technology and morphology design strategy

“…They have been widely used in aerospace, solar cells, transistors, drug coatings and other fields. The thermodynamics, kinetics and nanomechanics of polymer crystals have become leading topics in the polymer field (Liu et al, 2005;Laird et al, 2012;Dou et al, 2014;Gao et al, 2020;Bosi, 2019;Brock & Taylor, 2020). Therefore, the growth process and morphology of polymer crystals are highly relevant to studies of the properties of polymer materials (Drozdzal et al, 2021).…”