Bonding in Polycyclic Aromatic Hydrocarbons in Terms of the Electron Density and of Electron Delocalization

We show that the delocalization indices calculated within the framework of the quantum theory of atoms in
molecules provide an excellent basis for the definition of a bond order in polycyclic aromatic hydrocarbons.
We show that the two-electron information contained within the delocalization index can be estimated from
the electron density at the bond critical point, a mapping that has no a priori reason to exist. The mapping
between the bond order and the electron density at the bond critical point can be exploited to provide a fast
estimate of bond orders from theoretical or experimental electron densities. Bond orders in these molecules
are shown to be associated to other one-electron properties. We provide evidence to the strong coupling of
the σ and π contributions to the electron density at the bond critical point, a nonseparability by virtue of
which the electron density at the bond critical point reflects both contributions. Another remarkable finding
is that the delocalization indices between bonded carbon atoms are also strongly negatively correlated to the
electronic energy density at the bond critical point, the latter being another example of a two electron property.
In this manner, bond order is associated to a stabilizing effect quantified by the electronic energy density at
the bond critical point. Because aromaticity is rooted in electron delocalization within a ring system, the
delocalization index is used to define an aromaticity index that measures alternation in the delocalization of
electrons within a ring of a polycyclic aromatic hydrocarbon. The proposed aromaticity index represents a
“local aromaticity measure”. We have analyzed in detail the effects of ring annealation on bond orders and
on the aromatic character of a ring and explored its correlation with independent measures of aromaticity
such as NICS and HOMA.