On characterization of the conformations of nine-membered rings
Milan Randi · International Journal of Quantum Chemistry · 1995
We have undertaken the task of characterizing conformations of nine-membered rings. Each of the 16 symmetrical conformations of puckered nine-membered rings considered is characterized by distance-dependent Dk structural invariants, referred to as molecular profiles. In this way we succeeded to map a three-dimensional molecular object by a one-dimensional mathematical object, a sequence. The quantity D1 represents the average row sum of the distance matrix and is proportional to the average interatomic separations in a molecule. The corresponding Dk values give the average of the row sums for the kth power of interatomic separations normalized by the factorial k!. Hence, derived molecular profiles are independent of the orientation of a molecule or labeling of its atoms, i.e., derived molecular profiles are structural invariants. Properties of the derived profile sequences for the nine-membered rings are analyzed and discussed. Molecular profiles were used to establish which pairs of nine-membered ring conformers are the least similar and which are the most similar—a task that is difficult to do by mere inspection of the corresponding molecular models and cannot be considered using standard graph theoretical schemes that are devoid of information pertaining to the relative orientation of molecular groups in the 3-dimensional space. © 1995 John Wiley & Sons, Inc.