Identifying and characterizing translationally modulated molecular crystal structures

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.