The "density of delocalized electrons" is a concept that is intuitively used to explain the electronic structure of conjugated systems. Unfortunately, however, there is no rigorous way to separate the total electron density in a density of localized and delocalized electrons. Like aromaticity, bond order, point charge, and other important concepts of chemistry, a definition for the density of delocalized electrons has to be derived from more fundamental quantum theoretical parameters.
As observables, magnetic properties are a suitable starting point for a general description of of delocalization and conjugation. In analogy to the anisotropy of the magnetic susceptibility, which is a powerful measure of aromaticity, we investigate the anisotropy of the current (induced) density (ACID). Similar to the square of the wavefunction which defines the total electron density, the ACID scalar field defines the density of delocalized electrons.
The ACID method proved to be an extremely versatile and descriptive tool to analyze delocalization in ground-state molecules, excited states, transition states, organometallics, hyperconjugation and other through-bond and through-space interactions.
Delocalization of Electrons in Molecules
D. Geuenich, R. Herges, J. Phys. Chem. A 2001, 105, 3214-3220.
Anisotropy of the Induced Current Density (ACID), a General Method To Quantify and Visualize Electronic Delocalization
D. Geuenich, K. Hess, F. Koehler, R. Herges, Chem. Rev. 2005, 105, 3758-3772.
ACID is implemented in Gaussian® 09 since Revision D.01. To obtain the ACID software package, feel free to contact us by e-mail (rherges [at] oc.uni-kiel.de).