Playing around with MP, a tool for the analysis of pseudosymmetry: recurrent appearance of local pseudo-space groups in the asymmetric unit of Z′ = 4 structures

Abstract

A systematic application of the MP procedure [Baggio (2019). Acta Cryst. C75, 837–850] to a subset of Z′ = 4 structures in the literature revealed a number of suggestive properties in many of the cases analysed, which allowed us to conclude that: (i) very few of those structures showed no pseudosymmetry (PS) whatsoever linking any of the possible moiety pairs in the asymmetric unit (AU), the vast majority disclosing, instead, at least two (and frequently more) molecules linked by these PS operations; (ii) on occasion, two pairs of molecules were related, each by the same PS element, enabling the resulting pair of dimers to be viewed locally as a Z′ = 2 rather than a Z′ = 4 case; (iii) sometimes all four moieties in the AU appeared interrelated by PS relationships, closely suggesting a distribution of symmetry operations as found in real space groups; (iv) in many cases, this resemblance was of a superior quality, leading to surprising local replicas of real space groups in the reduced realm of the AU, thus locally reducing the description to a Z′ = 1 one. Through a systematic application of the MP procedure, we analyze in this article a number of these latter cases, which proved to be surprisingly common, far beyond any original expectation, and leaving open the question about the eventual reasons for the phenomenon, which would certainly merit appropriate theoretical attention.