Benzenoid hydrocarbon aromaticity in terms of charge density descriptors

Hartree-Fock/6-31G** calculations on the benzenoid hydrocarbons benzene, naphthalene, phenanthrene, anthracene, pyrene, tetracene, triphenylene, chrysene, perylene, and coronene are used to investigate the link between aromaticity and the electron distribution. Topological charge density analysis is used, concentrating on the electron distribution rho (and its Hessian) at bond and ring critical points. With regard to the bond critical point data, it is shown that rho(c), del(2) rho(c), and the bond ''ellipticity'' epsilon are closely correlated with the bond lengths so, as aromaticity indicators, they have little to add over and above existing indices based on structure. However, the same properties evaluated at the ring critical points in the total density, and also at the equivalent stationary points in the pi and sigma densities, correlate closely with two different aromaticity indices (one based on structure, the other on magnetic properties), the curvature of rho perpendicular to the ring plane giving (marginally) the best results. Hence a ring critical point (RCP) index is proposed as a way of quantifying aromaticity, based directly on the electron distribution.