Topological analysis of the electron localization function applied to delocalized bonds

What is a local viewpoint of delocalized bonds? We try to provide an answer to this paradoxical question by investigating representative conjugated organic molecules (namely, allyl cation, trans-butadiene, and benzene) together with reference nonconjugated systems (ethylene and propene) by means of topological analysis of the electron localization function ELF. The valence attractors of the ELF gradient field are classified according to their synaptic order (i.e., connections with core attractors). The basin populations [Formula: see text] (i.e., the integrated density over the attractor basins) and their standard deviation, σ, have been calculated and are discussed. The basin populations and their relative fluctuations, defined as [Formula: see text] are sensitive criteria of delocalization. In the case of well-localized C—C or C=C bonds, λ ~0.4, whereas for delocalized bonds λ increases to about 0.5. Another criterion of delocalization is provided by the basin hierarchy, which is defined from the reduction of the localization domains. For most systems, delocalization occurs not only for neighboring carbon-carbon disynaptic attractor basins, but also for nearest neighbor disynaptic protonated attractor basins. Key words: electron localization function, topological analysis, delocalization, population analysis.