How do electron localization functions describe p-electron delocalization?

Scalar fields provide an intuitive picture of chemical bonding. In particular, the electron localization function (ELF) has proven to be highly valuable in interpreting a broad range of bonding patterns. The discrimination between enhanced or reduced electron (de) localization within cyclic pi-conjugated systems remains, however, challenging for ELF. In order to clearly distinguish between the local properties of ten highly and weakly pi-(de) localized prototype systems, we compare the ELFs of both the canonical wave functions and electron-localized states (diabatic) with those of two closely related scalar fields: the electron localizability indicator (ELI-D) and the localized orbital locator (LOL). The simplest LOL function distinguishes enhanced from weak p-(de) localization in an insightful and reliable manner. LOL offers the finest contrast between annulenes with 4n/4n + 2 pi electrons and their inorganic analogues as well as between hyperconjugated cyclopentadiene derivatives. LOL pi also gives an appealing and intuitive picture of the pi-bond. In contrast, the most popular ELF fails to capture subtle contrasting local electronic properties and suffers from the arbitrariness of the sigma/pi dissection. The orbital separation of the most recent ELI-D is clear-cut but the interpretations sometime less straightforward in the present context.