HSAB principle definition

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

Infrared and NMR-spectral analysis, and x-ray diffraction data, testify [42-54] that in case of complexes of the already discussed pseudohalide ions, the competitive coordination can be explained by the HSAB principle hard Pearson acids are bound with hard N-center, and soft acids with soft X- donor (S, Se) centers. This situation allows us to obtain directly the coordination compounds of pseudohalides with a definite localization mode of the coordination bond, i.e., to carry out the regioselective synthesis on the basis of the higher stability of complexes which are obtained as a result of hard-hard or soft-soft interactions [2]. 

The HSAB principle can be considered as a condensed statement of a very large amount of experimental information, but cannot be labelled a law, since a quantitative definition of the intuitive concepts of chemical hardness (T ) and softness (S) was lacking. This problem was solved when the hardness found an exact, and also an operational, definition in the framework of the Density Functional Theory (DFT) by Parr and co-workers [2], In this context, the hardness is defined as the second order derivative of energy with respect to the number of electrons and has the meaning of resistance to change in the number of electrons. The softness is the inverse of the hardness [3]. Moreover, these quantities are defined in their local version [4, 5] as response functions [6] and have found a wide application in the chemical reactivity theory [7],... 

Note that this Principle is simply a restatement of the experimental evidence which led to Table 1.2. It is a condensed statement of a very large amount of chemical information. As such it might be called a law. But this label seems pretentious in view of the lack of a quantitative definition of hardness. HSAB is not a theory, since it does not explain variations in the strength of chemical bonds. The word prefer in the HSAB Principle implies a rather modest effect. Softness is not the only factor which determines the values of A/Z° in Equation (1.1). There are many examples of very strong bonds between mismatched pairs, such as H2, formed from hard H+ and soft H. H2O, OH and 0 are all classified as hard bases, but there are great differences in their base strength, by any criterion. 

As Pearson has pointed out, "while the HSAB principle has proved useful in many ways, it has been justifiably criticized because of the lack of a precise definition of hardness and the inability to assign numbers to this property".30 The hardness parameter (13) is now defined in terms of electronegativity, as in Equation... 

The purpose of this work is to start from the basic equations of density functional theory to describe the changes in the energy associated with the transition from one ground-state to another, in terms of different sets of variables. In this process one will find the natural definitions of the hardness and softness kernels, the local hardness, the local softness, the global hardness and the global softness [23]. Then, we will proceed to establish their relation with ionization potentials and electron affinities, in order to confirm their behavior as a measure of chemical hardness or softness [14, 24]. Finally, this theoretical framework will be used to analyze the maximum hardness and the HSAB principles. 

Concepts of acidity and basicity are, in practice, defined and evaluated by their utility. Since overly formd definitions can be restrictive the concepts of acidity evolve towaids more comprehensive definitions. For example the Lewis definition includes the Broensted definition simply regarding the proton as an electron acceptor. Because the interaction of Broensted acids and bases in solutions involves a common process, protic transfer, scales of acidity can be established, for example the Hammett [1] acidity function. For Lewis acid-base interaction there is no common process to provide a unique basis for comparisons of acid strength. Experimentally, the strength of a Lewis acid depends upon the particular Lewis base. The classification of acids and bases as hard or soft in the principle of hard and soft acids and bases (HSAB principle) clarifies the interactions of Lewis acids and bases [2a]. Strong interactions occur between hard acid and hard base, or between soft acid and soft base, hi the hard-hard interaction there is a considerable electrostatic contribution to bonding and in the soft-soft interaction there is a major covalent contribution to bonding. The use of density functional analysis has clarified the concepts of hardness and softness and an empirical ranking of Lewis acids, based on local hardness is, proposed [2c]. 

Any theoretical approach to the local HSAB principle needs a mathematical definition of local hardness and local softness consistent with the principle itself. The definition of local softness seems not to be a problem. Yang and Parr defined local softness as... 

Although the proposed models have been successful in describing several weak to moderate types of molecular interactions, it is important to note the definition of ad hoc parameter K. The computation of this parameter is rather difficult hence, further study should be made on the evaluation of the parameter K. Another critical aspect is that because the descriptors of isolated reactants are anployed in the energy expression, these models are expected to be applicable only for the cases where the influence of one monomer reactant on another molecule is comparatively less. Having said the limitations of the proposed models, these models, nevertheless, can rationalize the relative influence of the hardness/softness parameters in determining the nature of different types of interactions and stabilization of the molecular complexes, thus transforming the once thought qualitative HSAB principle into a quantitative one. 

In chemistry, the American chemist Ralph G. Pearson (1963) introduced the concept of hardness. Originally, the definition referred to hard and soft acids and bases. The hard-soft acid-base (HSAB) principle states that hard Lewis acids prefer hard Lewis bases and conversely that soft Lewis acids prefer soft Lewis bases. We will not dig deeply into the chemical background here. What is important is that Pearson (-1980) later found that hardness may simply be defined as... 

In the beginning when the HSAB principle was Just introduced, the meaning of hardness was not easy to understand. Certainly, it is not the hardness that measures the resistance against deformation. Then, what is it It was not un il the last several years that the real definition of absolute hardness received a quantitative and theoretical backing. ... 

Note that this Principle is simply a restatement of the experimental evidence which led to Table 2. It is a condensed statement of a very large amount of chemical information. As such it might be called a law. But this label seems pretentious in view of the lack of a quantitative definition of hardness. HSAB is not a theory, since it does not explain variations in the strength of chemical bonds. 

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