Aromaticity Measures from Fuzzy-Atom Bond Orders (FBO). The Aromatic Fluctuation (FLU) and the para-Delocalization (PDI) Indexes

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Abstract
In the past few years, there has been a growing interest for aromaticity measures based on electron density descriptors, the para-delocalization (PDI) and the aromatic fluctuation (FLU) indexes being two recent examples. These aromaticity indexes have been applied successfully to describe the aromaticity of carbon skeleton molecules. Although the results obtained are encouraging, because they follow the trends of other existing aromaticity measures, their calculation is rather expensive because they are based on electron delocalization indexes (DI) that involve cumbersome atomic integrations. However, cheaper electron-sharing indexes (ESIs), which in principle could play the same role as the DI in such aromaticity calculations, can be found in the literature. In this letter we show that PDI and FLU can be calculated using fuzzy-atom bond order (FBO) measures instead of DIs with an important saving of computing time. In addition, a basis-set-dependence study is performed to assess the reliability of these measures. FLU and PDI based on FBO are shown to be both good aromaticity indexes and almost basis-set-independent measures. This result opens up a wide range of possibilities for PDI and FLU to also be calculated on large organic systems. As an example, the DI and FBO-based FLU and PDI indexes have also been calculated and compared for the C60 molecule.