Graphical approach for defining natural internal coordinates

A simple, customizable connectivity scheme is rigorously defined in which pairs of atoms are classified into three categories. The tools of graph theory are used to analyze the molecular graph and to efficiently find rings and ring assemblies through a combination of pruning and homeomorphic reduction. The definition of natural internal coordinates is extended in a nonredundant fashion for the various cases of weakly interacting components and for fused ring systems. The ring system coordinates were tested and found to be superior to Z-matrix coordinates.