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Identifying and characterizing translationally modulated molecular crystal structures.

Carolyn Pratt Brock1, Robin Taylor2

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Summary

A new program identifies pseudotranslations in crystal structures, which are approximate translational relationships between molecules. This tool aids in understanding complex modulated structures, especially those with multiple independent molecules.

Keywords:
Z′approximate translationsmodulationspseudosymmetry

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • Displacive modulations in crystal structures create independent molecules from translationally related ones.
  • These independent molecules retain approximate translational relationships, termed pseudotranslations.
  • Identifying pseudotranslations manually is challenging due to their complexity and interaction with lattice translations.

Purpose of the Study:

  • To develop and validate a computational program for identifying pseudotranslations in crystal structures.
  • To characterize the components (translational, orientational, conformational) of identified pseudotranslations.
  • To analyze the frequency and occurrence of pseudotranslations in crystalline materials.

Main Methods:

  • A program was developed to detect and characterize pseudotranslations.
  • The program calculates fractional translational, orientational, and conformational components.
  • It assesses pseudotranslations using quality indicators and adjustable tolerances.
  • The program was applied to organic and metallo-organic structures from the Cambridge Structural Database (R ≤ 0.075).

Main Results:

  • The program successfully identified pseudotranslations, aiding in the analysis of modulated structures.
  • Pseudotranslation frequency increases with the number of independent molecules per asymmetric unit (Z').
  • Approximately 50% of structures with Z' > 4 exhibited pseudotranslations.
  • Certain structures were identified where pseudotranslations did not directly correspond to modulations, indicating complex structural relationships.

Conclusions:

  • The developed program is effective for identifying and characterizing pseudotranslations in crystal structures.
  • Pseudotranslations are common in complex modulated structures, particularly with higher Z' values.
  • The findings highlight the utility of computational tools in deciphering intricate crystallographic phenomena and understanding structural relationships beyond simple modulations.