Electronegativity equalization principle

As already mentioned, through DFT, it has been possible to explain the electronegativity equalization principle [1,7,10-13] and the hard and soft acids and bases principle [12,15-22] and, additionally, it has also been possible to introduce new ones like the maximum hardness principle [52,53] and the local hard and soft acids and bases principle [20,54—56]. 

These descriptors have been widely used for the past 25 years to study chemical reactivity, i.e., the propensity of atoms, molecules, surfaces to interact with one or more reaction partners with formation or rupture of one or more covalent bonds. Kinetic and/or thermodynamic aspects, depending on the (not always obvious and even not univoque) choice of the descriptors were hereby considered. In these studies, the reactivity descriptors were used as such or within the context of some principles of which Sanderson s electronegativity equalization principle [16], Pearson s hard and soft acids and bases (HSAB) principle [17], and the maximum hardness principle [17,18] are the three best known and popular examples. 

Nalewajski, R. F. and O. Sikora. 2000. Electron-following mapping transformations from the electronegativity equalization principle. J. Phys. Chem. A 104 5638-5646. 

The crudest one is Sanderson s electronegativity equalization principle [39, 40] according to which atoms-in-molecule make electron transfers from lower to higher electronegative parts thus achieving equilibrium in electronegativity. 

Just like Sanderson s electronegativity equalization principle, the Hard and Soft Acids and Bases principle was originally introduced without strong theoretical basis. Nevertheless, it was used widely from its formulation on. The principle states that hard acids prefer to coordinate with hard bases and soft acids with soft bases [82], In 1983, Parr and Pearson provided a definition for the chemical hardness [25]... 

The electronegativity equalization principle then demands that for the final molecule... 

This corresponds to an electronegativity equalization principle and means that the sum of the E-states in the molecule depends on only the number and type of atoms, not on their mutual interactions. 

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... 

The equalization principle for the electronic chemical potential (equivalently, the electronegativity equalization principle) may be couched in a form reminiscent of the argument from classical thermodynamics [4], However, the chemical potential equalization principle follows most directly from the variational principle and, in particular, Eq. (32). First, define the local chemical potential by... 

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. 

Fig. 12a, b. Evaluation of basicity by XPS and IR of adsorbed pyrrole correlation between the partial charge on N as derived from the Sanderson electronegativity equalization principle and the (a) N Is BE and (b) wavenumber of the NH vibration. Taken from HuzmgM.Adnot A, Kaliaguine S (1992) J Am Chem Soc 114 10005, with kind permission from the American Chemical Society... 

It is commonplace among chemists to think of a molecule as formed from its constituent atoms and accordingly to try to relate molecular properties to respective atomie properties. For example, Sanderson s electronegativity equalization principle (EEP) states that molecular electronegativity (chemical poten-... 

Quantumchemical methods have not been very successful in describing the properties rooted in the Density Functional theory. Early works typically concentrated on orbital electronegativities under the tyranny of the Sanderson electronegativity equalization principle [40-46]. An integral study resulting in electronegativity parameters for bonded atoms was made by Ponce [47]. 

According to the electronegativity equalization principle, the average electronegativity X of an n-atomic molecule can then be written as the arithmetic mean ... 

For transition metals, the participation of d orbitals must also be taken into account, and values have been tabulated for the first row series [87] At first sight it seems that equations (1), (2-4) and (6) are all what we need to compute partial charge distributions. This is not the case and the main problem lies in the evaluation of the chemical hardnesses. This can be easily understood by applying (1) and (2-4) to a simple diatomic molecule A-B where B is more electronegative than A. If we apply the electronegativity equalization principle XA = XB — 0 )> it comes with qA = —5jj = q ... 

Gdrardin, C., Henry, M., and Taulelle, F. (1993) Evaluation of Chemical Shifts in Solid-state NMR by Electronegativity Equalization Principle, in J.A. TosseU (ed.), in Nuclear Magnetic Shieldings and Molecular Structure, NATO-ASl Series C, 386, 566, Kluwer, Dordrecht. 

The linear expression in the electric charge associated with the electronegativity equalization principle (Principle EN5), allowed to Huheey to calculate the group electronegativity (-A5J, respectively the partial charges distributed to each atom in the group, by solving the system ... 

Basically, this method do not allow the separate treatment of the isomers (-CHjCFH toward—CFHCH3, for example), do not allow a simple treatment of the multiple bonds and uses the electronegativity equalization principle in its total form, FEOE (Full Equalization Orbital Electronegativity). 

We, therefore, conclude that the present effort of deriving an algorithm for the evaluation of the hardness of the carbon containing poly atomic molecules is a successful venture. The detailed study would suggest that the paradigm of the hardness equalization principle may be another law of nature like the established electronegativity equalization principle. 

Hardness Equalization Principle Analogous to the Electronegativity Equalization Principle... 

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