Minimum polarizability principle validity

Torrent-Sucarrat, M., Luis, J. M., Duran, M., and Sola, M. 2001. On the validity of the maximum hardness and minimum polarizability principles for nontotally symmetric vibrations. J. Am. Chem. Soc. 123 7951-7952. 

In this chapter, we review our latest results on the validity of the maximum hardness and minimum polarizability principles in nontotally symmetric vibrations. These nuclear displacements are particularly interesting because they keep the chemical and external potentials approximately constant, thus closely following the two conditions of Parr and Chattaraj required for the strict compliance with the maximum hardness principle. We show that, although these principles are obeyed by most nontotally symmetric vibrations, there are some nontotally symmetric displacements that refuse to comply with them. The underlying physical reasons for the failure of these two principles in these particular nuclear motions are analyzed. Finally, the application of this breakdown to detect the most aromatic center in polycyclic aromatic hydrocarbons is discussed. 

Associated with these properties, important chemical reactivity principles have been rationalized within the framework of conceptual DFT the hard and soft acids and bases principle (F1SAB) [9], the Sanderson electronegativity equalization principle (EEP) [11], the maximum hardness principle (MF1P) [9,12,13], and the minimum polarizability principle (MPP) [14], The aim of this chapter is to revise the validity of the last two principles in nontotally symmetric vibrations. We start with a short section on the fundamental aspects of the MF1P and MPP (section 2). Section 3 focuses on the breakdown of these principles for nontotally symmetric vibrations, while section 4 analyses the relationship between the failure of the MF1P and the pseudo-Jahn-Teller (PJT) effect. A mathematical procedure that helps to determine the nontotally symmetric distortions of a given molecule that produce the maximum failures of the MPP or the... 

In February 2000, after a seminar given by Jaque in our institute entitled On the validity of the minimum polarizability principle in molecular vibrations and internal rotations, some of us started a discussion about the validity of the MPP in bond length... 

The linear response function [3], R(r, r ) = (hp(r)/hv(r ))N, is used to study the effect of varying v(r) at constant N. If the system is acted upon by a weak electric field, polarizability (a) may be used as a measure of the corresponding response. A minimum polarizability principle [17] may be stated as, the natural direction of evolution of any system is towards a state of minimum polarizability. Another important principle is that of maximum entropy [18] which states that, the most probable distribution is associated with the maximum value of the Shannon entropy of the information theory. Attempts have been made to provide formal proofs of these principles [19-21], The application of these concepts and related principles vis-a-vis their validity has been studied in the contexts of molecular vibrations and internal rotations [22], chemical reactions [23], hydrogen bonded complexes [24], electronic excitations [25], ion-atom collision [26], atom-field interaction [27], chaotic ionization [28], conservation of orbital symmetry [29], atomic shell structure [30], solvent effects [31], confined systems [32], electric field effects [33], and toxicity [34], In the present chapter, will restrict ourselves to mostly the work done by us. For an elegant review which showcases the contributions from active researchers in the field, see [4], Atomic units are used throughout this chapter unless otherwise specified. 

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