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<p>The lower bound of structure determinants connecting given structural units into the connected structure, referred to as implicit hierarchical depth (IHD) of the structure, is dependent on the rank of the symmetry group of the structure, the number of orbits occupied by the structural units, and on their site-symmetry groups. The equation relating the IHD of a crystal structure and crystallographic data is given herein in a general form. A crystal structure tends to, but not always, acquires the most parsimonic arrangement of the structural units in terms of IHD because of geometric limitations and contacts formed parallel to the process of crystallization and hence redundant for crystal structure formation. The code was developed and written in the GAP environment to estimate the values of IHD for 1731 Wyckoff positions of space groups. Some applications of IHD to reticular chemistry are discussed using molecular crystals, but not only them, as examples.</p>

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How many unique bonds linking structural units are needed to form a crystal structure?

  • 期刊论文

  • 发表日期：

    2025年10月25日

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  • Alexander M. Banaru,
  • Konstantin G. Seravkin,
  • Sergey M. Aksenov,
  • Andrey A. Antonov,
  • Daria A. Banaru,
  • Sergey N. Volkov,
  • Dmitry O. Charkin

摘要

The lower bound of structure determinants connecting given structural units into the connected structure, referred to as implicit hierarchical depth (IHD) of the structure, is dependent on the rank of the symmetry group of the structure, the number of orbits occupied by the structural units, and on their site-symmetry groups. The equation relating the IHD of a crystal structure and crystallographic data is given herein in a general form. A crystal structure tends to, but not always, acquires the most parsimonic arrangement of the structural units in terms of IHD because of geometric limitations and contacts formed parallel to the process of crystallization and hence redundant for crystal structure formation. The code was developed and written in the GAP environment to estimate the values of IHD for 1731 Wyckoff positions of space groups. Some applications of IHD to reticular chemistry are discussed using molecular crystals, but not only them, as examples.