Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

In a recent paper [J. Am. Chem. Soc. 123, 7951 (2001)] we have shown for the first time the existence of molecules with nontotally symmetric vibrational modes that break the maximum hardness (MHP) and minimum polarizability (MPP) principles. We present here an extension of this previous work by devising a mathematical procedure that helps to determine the nontotally symmetric molecular distortions of a given molecule that do not follow the MPP or the MHP. This methodology is based on the diagonalization of the Hessian matrix of the polarizability or the hardness with respect to the vibrational normal coordinates. For a relatively large series of molecules, we have carried out diagonalizations of the Hessian matrix of the polarizability to determine the molecular distortions with a more marked MPP or anti-MPP character. From the results obtained, we have derived a set of simple rules that allow to predict a priori without calculations the existence of vibrational modes that break the MPP. With respect to the MHP, the results strongly depend on the method of calculation, but the same rules are useful to predict the existence of vibrational modes that disobey the MHP when the Koopmans' approximation is used to calculate the hardness. (C) 2002 American Institute of Physics.