On interpretation of well-known topological indices.

Abstract

Many topological indices lack an interpretation in terms of simple physicochemical quantities. We have reexamined the structural interpretation of well-known topological indices: the connectivity index (1)chi, the Wiener index W, and the Hosoya topological index Z. We relate the success of various indices in structure-property studies to the degree to which they differentiate contributions from more exposed terminal bonds and more buried interior bonds. When considering bond additive properties of alkanes we find better regressions when greater weights are assigned to terminal CC bonds and lesser weights to internal CC. We suggest here that topological indices be discussed in terms of their partitioning into bond contributions, which for different indices and different bonds will assume different values. With this insight we modified the Wiener index W into a new index W, in which bond contributions are determined using the reciprocal of the product of the number of atoms on each side of a bond. Similarly we modified the Hosoya index Z into Z in which the frequency of occurrence of individual CC bonds in the patterns of disjoint bonds are considered. Novel indices are compared with other indices and they show to yield better regressions for boiling points of octane isomers. This suggests a useful classification of topological indices based on the relative magnitudes of the contributions of terminal and interior bonds. To extend such considerations to other indices one needs to consider partitioning of global molecular indices into bond additive terms. A general scheme for partitioning of molecular descriptors into bond contributions is outlined for indices derived from a selection of matrices associated with molecular graphs.