Quantification of Aromaticity Based on Interaction Coordinates: A New Proposal.

Attempts to establish degrees of aromaticity in molecules are legion. In the present study, we begin with a fictitious fragment arising from only those atoms contributing to the aromatic ring and having a force field projected from the original system. For example, in benzene, we adopt a fictitious C6 fragment with a force field projected from the full benzene force field. When one bond or angle is stretched and kept fixed, followed by a partial optimization for all other internal coordinates, structures change from their respective equilibria. These changes are the responses of all other internal coordinates for constraining the bond or angle by unit displacements and relaxing the forces on all other internal coordinates. The "interaction coordinate" derived from the redundant internal coordinate compliance constants measures how a bond (its electron density) responds for constrained optimization when another bond or angle is stretched by a specified unit (its electron density is perturbed by a finite amount). The sum of interaction coordinates (responses) of all bonded neighbors for all internal coordinates of the fictitious fragment is a measure of the strength of the σ and π electron interactions leading to aromatic stability. This sum, based on interaction coordinates, appears to be successful as an aromaticity index for a range of chemical systems. Since the concept involves analyzing a fragment rather than the whole molecule, this idea is more general and is likely to lead to new insights.