The breakdown of the minimum polarizability principle in vibrational motions as an indicator of the most aromatic center

The vibrational motions that disobey the minimum polarizability principle (MPP) in pi-conjugated molecules are distortions of the equilibrium geometry that produce a reduction in the polarizability due to the localization of pi electrons. For aromatic species, this electronic localization is responsible for the subsequent reduction in the aromaticity of the system. In the present work, we diagonalize the Hessian matrix of the polarizability with respect to the vibrational nontotally symmetric normal coordinates, to calculate the nontotally symmetric distortions that produce the maximum breakdown of the MPP in a series of twenty polycyclic aromatic hydrocarbons. It is shown that the nuclear displacements that break the MPP have larger components in those rings that possess the highest local aromaticity. Thus, these vibrational motions can be used as an indicator of local aromaticity.