Topological Relationship Between One-Dimensional Box Model and Randić Indices in Linear Simple Conjugated Polyenes

The alternative double bonds and conjugation in the polyene compounds are one of the main properties in these compounds. Each carbon-carbon bonds in a polyene compound along the chain has appreciable double-bond character. The p-electrons are therefore not localized but are relatively free to move throughout the entire carbon skeleton as an one-dimensional box. The skeleton be considered as a roughly uniform region of low potential bounded at the ends of the polyene by regions of infinitely high potential. Graph theory provides the useful natural mathematical frameworks for the quantitative codification of classical chemical bonding ideas. One of the useful indices for examination of structure-property relationship is Randić index. Some of properties here considered are associated with the molecular orbital method include and λmax, the difference energy level of the HOMO and LUMO orbitals (ΔE) and the length of the electron moving in carbon skeleton as one-dimensional box in polyene compounds (1-D box model). In this study, the difference of the length of carbon skeleton of polyenes and the length of the electron moving in the carbon skeleton will be discussed. For calculation the λmax of the compounds could use the Fieser-Kuhn rule. The interesting results of concerning among λmax, ΔE, the electron moving in carbon skeleton of simple linear polyenes by the use of 1-D box model and the above indices are presented.