PREDICTION OF MODELS FOR TETRAHEDRAL FRAMEWORKS BASED ON THE ENUMERATION OF GRAPHS. H.-J. Klein, Inst. f. Informatik u. Prakt. Mathematik, Universität Kiel, 24098 Kiel, Germany

For tetrahedral frameworks with corner sharing tetrahedra a graph-based method ist presented which allows to generate models of frameworks in a systematic way. Under reasonable assumptions concerning bond lengths the method is complete insofar as it generates all hypothetical models with a given number of non-equivalent tetrahedra.

Tetrahedral frameworks can be described by graphs with nodes representing tetrahedra and lines representing links between these tetrahedra. Because of space group symmetries, it is possible to transform the infinite graphs for ideal structures into finite directed graphs wit nodes corresponding to central atoms of tetrahedra in a fixed asymmetric unit and with lines having symmetry operations as labels. This kind of non-redundant description is well suited for generating for each space group all graphs representing frameworks with a given maximal number of translationally non-equivalent tetrahedra. Enumeration can be done in a goal-directed way by incorporating restriction conditions concerning topological properties of structures. Thus, complete enumeration of graphs becomes feasible for interesting classes of structures, e.g. zeolites or structures where all tetrahedra are topologically equivalent.

To check whether graphs can be realized geometrically as tetrahedral frameworks, nodes are placed into the centre of gravity of their immediate neighbours in the graph. Using the knowledge of bond lengths and Wyckoff positions, the cell parameters and the arrangement of atoms are refined for realizable graphs by applying simulated annealing techniques and gradiant methods.

Our approach is applicable more generally to classes of crystal structures with only one type of polyhedron and one type of link between polyhedra. Completeness and adaptability are the main features in which it differs from other approaches for the prediction of structures.