Conformation with Cartesian matrices

Each point in a Dugundji space represents a chemical constitution for which there can exist a multiplicity of stereoisomers, corresponding to a set of CC-matrices associated with the BE-matrix of the constitution a). Owing to their interdependence, the constitutional and stereochemical features of chemical systems do not form a cartesian product, whereas the configurations and conformations can be represented as cartesian products. 

All possible conformers lie between these upper and lower distance bounds—the task of distance geometry is to convert or embed this usually uncertain distance information into accurate three-dimensional Cartesian coordinates. Crippen and HavePi solved the problem for the case of an exact distance matrix, where all distances are known. Much additional effort has gone into finding efficient and practical methods for solving the general problem of a distance bounds matrix, where only a subset of the distances is known exactly. This remains a very difficult problem for large molecules with more than 1000 atoms. 

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