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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. 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, ING, and INB were defined in our group. In this paper, we review the different existent 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.2

This work introduces a new local aromaticity measure, defined as the mean of Bader's electron delocalization index (DI) of para-related carbon atoms in six-membered rings. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized distribution of pi-electrons. We have found that this DI and the harmonic oscillator model of aromaticity (HOMA) index are strongly correlated for a series of six-membered rings in eleven planar polycyclic aromatic hydrocarbons. The correlation between the DI and the nucleus-independent chemical shift (NICS) values is less remarkable, although in general six-membered rings with larger DI values also have more negative NICS indices. We have shown that this index can also be applied, with some modifications, to study of the aromaticity in five-membered rings.

In 1972 Erich Clar formulated his aromatic π-sextet rule that allows discussing qualitatively the aromatic character of benzenoid species. Now, 40 years later, Clar's aromatic π-sextet rule is still a source of inspiration for many chemists. This simple rule has been validated both experimentally and theoretically. In this review, we select some particular examples to highlight the achievement of Clar's aromatic π-sextet rule in many situations and we discuss two recent successful cases of its application.

Based on an Atoms-in-Molecules (AIM) analysis, Matta et al. recently claimed evidence for the existence of hydrogen-hydrogen bonding between ortho-hydrogen atoms, pointing towards each other from adjacent phenyl groups in planar biphenyl. This AIM result is opposed to the classical view that nonbonded steric repulsion between the ortho-hydrogen atoms is responsible for the higher energy of the planar as compared to the twisted geometry of biphenyl. In the present work, we address the question if hydrogen-hydrogen bonding in biphenyl exists, as suggested by AIM, or not. To this end, we have analyzed the potential energy surface for internal rotation of biphenyl in terms of two interacting phenyl radicals using density functional theory (DFT) at BP86/TZ2P. A detailed analysis of the bonding mechanism and a quantitative bond energy decomposition in the framework of Kohn-Sham DFT show that Pauli (or overlap) repulsion, mainly between C(ortho)--H(ortho) phenyl MOs, prevents biphenyl from being planar and forces it to adopt a twisted equilibrium geometry. Furthermore, a derivative of biphenyl in which all four ortho-hydrogen atoms have been removed does adopt a planar equilibrium geometry. Thus, our results confirm the classical view of steric repulsion between ortho-hydrogen atoms in biphenyl and they falsify the hypothesis of hydrogen-hydrogen bonding.

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.

Aromaticity is a central chemical concept widely used in modern chemistry for the interpretation of molecular structure, stability, reactivity, and magnetic properties of many compounds. As such, its reliable prediction is an important task of computational chemistry. In recent years, many methods to quantify aromaticity based on different physicochemical properties of molecules have been proposed. However, the nonobservable nature of aromaticity makes difficult to assess the performance of the numerous existing indices. In the present work, we introduce a series of fifteen aromaticity tests that can be used to analyze the advantages and drawbacks of a group of aromaticity descriptors. On the basis of the results obtained for a set of ten indicators of aromaticity, we conclude that indices based on the study of electron delocalization in aromatic species are the most accurate among those examined in this work.

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