Molecular engineering of microporous crystals: (II) A new method to describe the structures of zeolites and related open-framework crystalline materials

A new method to describe the structures of zeolites and related open-framework crystalline solids was developed on the basis of the atom–atom distance matrix (DM). It has been mathematically proved that each such distance matrix corresponds to no more than two different (racemic) structures. For a given structure, the distance matrices for different atom-labeling schemes within a unit cell can be transformed to each other through a matrix transformation, and all these equivalent matrices correspond to the same (or the mirror) structure. A procedure was developed to standardize such representing matrices for each structure, which can be represented as a heat map, the 2-dimensional (2D) barcode or finger print of a structure. With this method, information on the connectivity of the framework atoms in the structure of zeolites or related open-framework crystalline solids was included in the heat map. The structural features of rings, channels, and cages of zeolites and related open-framework crystalline materials can also be recognized in the heat map. The inherent correlation between the structures and their heat maps is discussed. With this new method, the structure of zeolites or related open-framework crystalline solids can be studied by the well developed matrix theory, graph theory, or other mathematic tools.