In this work, the aromatic fluctuation index (FLU) that describes the fluctuation of electronic charge between adjacent atoms in a given ring is introduced as a new aromaticity measure. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized circulation of π electrons. It is defined not only considering the amount of electron sharing between contiguous atoms, which should be substantial in aromatic molecules, but also taking into account the similarity of electron sharing between adjacent atoms. For a series of rings in 15 planar polycyclic aromatic hydrocarbons, we have found that, in general, FLU is strongly correlated with other widely used indicators of local aromaticity, such as the harmonic-oscillator model of aromaticity, the nucleus independent chemical shift, and the para-delocalization index (PDI). In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of members and it can be used to analyze both the local and global aromatic character of rings and molecules.

Aromaticity cannot be measured directly by any physical or chemical experiment because it is not a well-defined magnitude. Its quantification is done indirectly from the measure of different properties that are usually found in aromatic compounds such as bond length equalisation, energetic stabilisation, and particular magnetic behaviour associated with induced ring currents. These properties have been used to set up the myriad of structural-, energetic-, and magnetic-based indices of aromaticity known to date. The cyclic delocalisation of mobile electrons in two or three dimensions is probably one of the key aspects that characterise aromatic compounds. However, it has not been until the last decade that electron delocalisation measures have been widely employed to quantify aromaticity. Some of these new indicators of aromaticity such as the PDI, FLU, I_NG, and I_NB were defined in our group. In this paper, we review the different existing descriptors of aromaticity that are based on electron delocalisation properties, we compare their performance with indices based on other properties, and we summarise a number of applications of electronic-based indices for the analysis of aromaticity in interesting chemical problems.

Electron sharing indexes (ESI) have been applied to numerous bonding situations to provide an insight into the nature of the molecular electronic structures. Some of the most popular ESI given in the literature, namely, the delocalization index (DI), defined in the context of the quantum theory of atoms in molecules (QTAIM), and the Fuzzy-Atom bond order (FBO), are here calculated at a correlated level for a wide set of molecules. Both approaches are based on the same quantity, the exchange–correlation density, to recover the electron sharing extent, and their differences lie in the definition of an atom in a molecule. In addition, while FBO atomic regions enable accurate and fast integrations, QTAIM definition of an atom leads to atomic domains that occasionally make the integration over these ones rather cumbersome. Besides, when working with a many-body wavefunction one can decide whether to calculate the ESI from first-order density matrices, or from second-order ones. The former way is usually preferred, since it avoids the calculation of the second-order density matrix, which is difficult to handle. Results from both definitions are discussed. Although these indexes are quite similar in their definition and give similar descriptions, when analyzed in greater detail, they reproduce different features of the bonding. In this manuscript DI is shown to explain certain bonding situations that FBO fails to cope with. Finally, these indexes are applied to the description of the aromaticity, through the aromatic fluctuation (FLU) and the para-DI (PDI) indexes. FLU and PDI indexes have been successfully applied using the DI measures, but other ESI based on other partitions such as Fuzzy-Atom can be used. The results provided in this manuscript for carbon skeleton molecules encourage the use of FBO for FLU and PDI indexes even at the correlated level.

We introduce a new electronic aromaticity index, AV1245, consisting of an average of the 4-center indices along the ring that keep a positional relationship of 1, 2, 4, 5.