# What are modern approaches to describe and/or quantify aromaticity?

I know that Schleyer described an approach for evaluating aromaticity using nucleus-independent chemical shifts (NICS, see e.g. Chem. Rev. 2005, 105 (10), 3842–3888) quite some time back. I also somehow have the feeling that there should be a more direct way to describe aromaticity than via chemical shifts.

What are modern approaches to describe/quantify aromaticity? Could anyone point out some links/references on recent developments in the field?

I'm more familiar with the Electron Localization Function approach to aromaticity commented by Quantum AMERICCINO, it's been proposed that the average value of the $\text{ELF}_{\sigma}$ and $\text{ELF}_{\pi}$ bifurcations would be used for a general scale of aromaticity of a molecule or molecular cluster. The points of bifurcation can be interpreted as a measure of the interaction among the different basins or, simply, electron delocalization. Although the ELF depends on the density (i.e. no separate information of $\pi$ or $\sigma$ bond), a topological analysis on a separated ELF formed only by the $\pi$ orbitals and other formed by the $\sigma$ orbitals can be done (also you can do a separation for the spin $\alpha$ and $\beta$ contributions to the ELF). [J. Chem. Theory Comput. 2005, 1 (1), 83–86.]
Another approach is making a relationship between the amount of the electron density (due to ring size, number of $\pi$ electrons, etc) and the non-nuclear magnetic shielding (cf. NICS). [Phys. Chem. Chem. Phys. 2010, 12 (39), 12630–12637.]