The electron localization function (ELF) has been separated in its sigma and pi components. The topological analysis of the new ELFsigma and ELFpi functions has been used to quantify the concept of resonance. The highest bifurcation values of these functions describe in a correct way the aromaticity of classical ring molecules and some new aromatic compounds as B6CO6, Al4(2-), and N5-. In the case of Al4(2-), an important sigma delocalization contribution has been found, which is in agreement with previous interpretation.

Aromaticity of borazine, which has been subject of controversial discussions, is addressed. Beside a short review on aromaticity of borazine we report a detailed analysis of two molecular fields, the induced magnetic field (B ind ) and the electron localization function (ELF). The induced magnetic field of borazine shows a long-range shielding cone perpendicular to the molecular plane, as in benzene, but lower in magnitude. Contrary to benzene, borazine shows two weakly paratropic regions, one of them inside the ring, and the second one enveloping the boron atoms. It is necessary to separate r and p contributions to identify whether borazine exhibits p-aromatic character comparable to benzene. Nucleus-independent chemical shift (NICS) isolines show that the r electrons are much stronger localized than p electrons, their local paramagnetic contributions generate a short-range response and a paratropic (deshielding) region in the ring center (similar to an anti-aromatic response). Three regions can be identified as chemically meaningful domains exhibiting an internally strong electron delocalization (ELF = 0.823). Borazine may be described as a p aromatic compound, but it is not a globally aromatic species, as the electronic system is not as delocalized as in benzene.

In this work, the average bifurcation value of the electron localization function (ELF) of both σ (ELFσ) and π (ELFπ) contributions was used to construct an aromaticity scale for chemical compounds. We have validated the scale with a series of well-known molecules and then used it to evaluate global aromaticity on aluminum based clusters, which present σ aromaticity and π antiaromaticity. The proposed scaled predicts an overall antiaromatic character for the Al4(4)(-) moiety.