The Delocalization Index as an Electronic Aromaticity Criterion: Application to a Series of Planar Polycyclic Aromatic Hydrocarbons

Abstract

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.

The aromatic fluctuation index (FLU): A new aromaticity index based on electron delocalization

“…23 Due to its definition, this index can only be applied to analyze the local aromaticity of 6-MRs. Figure 5 displays the correlation between PDI and FLU for all 6-MRs appearing along the M1-M15 series. In general, there is a moderately good agreement (rϭϪ0.840) on the orderings yielded by these two criteria, the main exception being the 6-MR of benzocyclobutadiene, to which PDI attributes a high aromatic character, while HOMA ͑0.497͒ and NICS͑0͒ ͓not only NICS͑0͒ but also NICS zz (0), NICS͑1͒, and NICS zz (1) values show that the 6-MR of benzocyclobutadiene has a low or moderate aromatic character͔ ͑Ϫ4.0͒ indicators attributed it to a low or moderate aromaticity.…”

“…Lately, our group have employed electron delocalization measures derived from the second-order density 21,22 as a new descriptor of local aromaticity. In particular, we have used the para-delocalization index ͑PDI͒, 23 which is an average of all delocalization indices ͑DIs͒ of para-related carbon atoms in a given six-membered ring ͑6-MR͒. The DI value between atoms A and B, ␦(A,B), is obtained by the double integration of the exchange-correlation density over the basins of atoms A and B in the framework of the atoms in the molecules ͑AIM͒ theory of Bader ͑vide infra͒.…”

“…The DI value between atoms A and B, ␦(A,B), is obtained by the double integration of the exchange-correlation density over the basins of atoms A and B in the framework of the atoms in the molecules ͑AIM͒ theory of Bader ͑vide infra͒. 24 Previous works 23,25 have shown that for a series of planar and curved polycyclic aromatic hydrocarbons ͑PAHs͒, there is a satisfactory correlation between NICS, HOMA, and PDI. In general, larger PDIs go with larger absolute values of NICS and larger HOMA values.…”

Communication: An approximation to Bader's topological atom

“…The agreement with the QTAIM bond orders or delocalization indices (DIs) also improves with k = 4, in particular for non-bonded atoms. The observation that in benzene the DI between carbon atoms in para position is larger than in meta position 20 is better reproduced with this TFVC model.…”

Structural and electronic properties of alumaphosphinine complexes with metal ions: A theoretical study

“…Also, the Natural Bonding Orbital (NBO) [12] is used to obtain the charge transfer values. On the other hand, the aromaticity of the alumaphosphinine ring and its complexes is measured using several well-established indices of aromaticity such as the Nucleus-Independent Chemical Shift (NICS) [15,16], the Harmonic Oscillator Model of Aromaticity (HOMA) [17,18], the Para-Delocalization Index (PDI) [19], the electron Localization-Delocalization Matrices (LDMs) [20,21], and the aromatic uctuation index (FLU) [22] Figure 2. The distances between metal cations and the coordinating sites of alumaphosphinine ring in the complexes are also shown in Figure 2.…”