Minimum polarizability principle

Torrent-Sucarrat, M., Luis, J. M., Duran, M., and Sola, M. 2002. Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations J. Chem. Phys. 117 10561-10570. 

The breakdown of the maximum hardness and minimum polarizability principles for nontotally symmetric vibrations... 

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... 

In this chapter, we have presented an overview of our research on the breakdown of the maximum hardness and minimum polarizability principles in nontotally symmetric vibrations. Although these nuclear displacements hold the most favorable conditions for the fulfillment of these two principles, it has been shown that there are a number of aromatic, 7r-conjugated, non-rr-conjugated, or even non-rr-bonded organic and inorganic... 

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. 

Popular qualitative chemical concepts such as electronegativity [1] and hardness [2] have been widely used in understanding various aspects of chemical reactivity. A rigorous theoretical basis for these concepts has been provided by density functional theory (DFT). These reactivity indices are better appreciated in terms of the associated electronic structure principles such as electronegativity equalization principle (EEP), hard-soft acid-base principle, maximum hardness principle, minimum polarizability principle (MPP), etc. Local reactivity descriptors such as density, Fukui function, local softness, etc., have been used successfully in the studies of site selectivity in a molecule. Local variants of the structure principles have also been proposed. The importance of these structure principles in the study of different facets of medicinal chemistry has been highlighted. Because chemical reactions are actually dynamic processes, time-dependent profiles of these reactivity descriptors and the dynamic counterparts of the structure principles have been made use of in order to follow a chemical reaction from start to finish. 

A many-particle quantum system is completely characterized by N and v(7>). Whereas % and rj measure the response of the system when N changes at fixed v(T), the polarizability (a) measures the response of the system for the variation of (v(r)) at fixed N when a weak electric field is the source of v(T), in addition to that arising out of a set of nuclei. Based on the inverse relationship [185] between a and rj, a minimum polarizability principle has been proposed the natural direction of evolution of any system is toward a state of minimum polarizability [186]. 

The values in Table 4.17 and the shapes represented in Figure 4.31 turns out that the polarizability decrease along the periods, while the hardness has to increase along the periods. Such trend can sustain once more (here, at atomic level) the maximum hardness and minimum polarizability principles. 

The conceptual density functional theory has added Maximum Hardness Principle, (MHP) (Pearson 1987) and Minimum Polarizability Principle, (MPP) (Chattaraj and Sengupta 1996) to the list of the fundamental laws of nature. The CDFT has been successfully exploited in elucidating and correlating mechanistic aspects viz. regio-selectivity, catalysis, aromaticity, intramolecualr rotation, inversion and isomerization reactions (Zhou and Parr 1989 Parr and Chattaraj 1991 Chattaraj et al. 1994 Pearson and PaUce 1992 Pal et al. 1993 Chattaraj et al. 1995 Ayers and Parr 2000 Ghosh et al. 2000, 2002). 

A softer species is more polarizable" " " and more magnetizable" " . The inverse relationship" " between hardness and polarizability/ magnetizability provides two other electronic structure principles to complement the maximum hardness principle. The minimum polarizability principle" " " (MPP) states that, The natural direction of evolution of any system is towards a state of minimum polarizability and the statement of the minimum magnetizability principle" " (MMP) is, A stable config-uration/conformation of a molecule or a favorable chemical process is associated with a minimum value of the magnetizabihty . 

The relative stabilities of the [MAU]" (M = Li" ", Na" ", K+, Rb" ", Cs" ", Cu" ", Ag+, Au+) isomers have been investigated on the grounds of the minimum polarizability principle [161]. According to the minimum polarizability and maximum hardness principles, the stability of the pyramidal isomer decreases with the augmentation of the atomic number. It is no wonder that for the [AuAU]" the planar isomer is finally more stable than the pyramidal structure. The minimum polarizability and the maximum hardness principles have also been examined to describe the relative stability of various isomers of the [ c-Cu4 Na] , [ c-Cu4 Li] , [ c-Al4 Cu] , [ c-Ag4 Li] , [ c-Au4 Li] , [ c-Ag4 Na] , [ c-Au4 Na] , [ c-Al4 Ag] , and [ c-Al4 Au] using MP2 calculations [162]. The results showed that the pyramidal structures are more stable than the planar ones. 

Hohm, U. (2000). Is there a minimum polarizability principle in chemical reactions Journal of Physical Chemistry A, 104(36), 8418-8423. 

Fuentealba, P Simon-Manso, Y. Chattaraj, P. K. Molecular electronic excitations and the minimum polarizability principle. J. Phys. Chem. A 2000,104, 3185. 

Torrent-Sucarrat M, Luis JM, Duran M, 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... 

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