The Breakdown of the Minimum Polarizability Principle in Vibrational Motions as an Indicator of the Most Aromatic Center

In previous works, we have shown that bond length alternation vibrational modes in -conjugated organic molecules may break the minimum polarizability principle (MPP). To arrive at this conclusion, we have developed a method that diagonalizes the polarizability Hessian matrix with respect to the vibrational nontotally symmetric normal coordinates. The vibrational motions that disobey the MPP in -conjugated molecules are distortions of the equilibrium geometry that produce a reduction of the polarizability due to the localization of -electrons. For aromatic species, this electronic localization is responsible for the subsequent reduction of the aromaticity of the system. In the present work, we apply our methodology 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 use as an indicator of local aromaticity ​
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