Determination of London Susceptibilities and Ring Current Intensities using Conjugated Circuits

Conjugated circuits have been employed to accurately reproduce the aromatic stabilization, London susceptibility, and ring current maps in polycyclic aromatic hydrocarbons, PAHs, focusing on polybenzenoids. Starting from a wave function ansatz, constructed as a superposition of Kekulé valence bond structures, the conjugated circuit resonance energy is derived using the second quantization formulation. Approximated expressions for the resonance energy, London susceptibility, and ring electron current intensity have been obtained. In these expressions, the benzene molecule is employed as a reference for the calculation in a graph theoretical fashion of properties in larger polybenzenoids. Comparison of the results obtained with conjugated circuits with those obtained using more accurate quantum chemical methods reflects the power of the conjugated circuit concept as a quantitative tool for the study of magnetic properties in PAHs. Besides the usefulness of this methodology for understanding and interpreting both the aromatic stabilization and the magnetic behavior of small and medium size PAHs, it provides a straightforward alternative way for the computation of these properties in giant PAHs for which ab initio calculations are not applicable.