HSAB definition

An HSAB analysis of singlet carbene reactivity based on B3LYP/6-31G computations has calculated the extent of charge transfer for substituted alkenes,122 and the results are summarized in Figure 10.3 The trends are as anticipated for changes in structure of both the carbene and alkene. The charge transfer interactions are consistent with HOMO-LUMO interactions between the carbene and alkene. Similarly, a correlation was found for the global electrophilicity parameter, co, and the ANmax parameters (see Topic 1.5, Part A for definition of these DFT-based parameters).123... 

This chapter is intended to provide basic understanding and application of the effect of electric field on the reactivity descriptors. Section 25.2 will focus on the definitions of reactivity descriptors used to understand the chemical reactivity, along with the local hard-soft acid-base (HSAB) semiquantitative model for calculating interaction energy. In Section 25.3, we will discuss specifically the theory behind the effects of external electric field on reactivity descriptors. Some numerical results will be presented in Section 25.4. Along with that in Section 25.5, we would like to discuss the work describing the effect of other perturbation parameters. In Section 25.6, we would present our conclusions and prospects. 

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. 

Eq. (1) with no obvious advantages for this additional complication since "strength of hardness and strength of softness would have to change in a way contrary to the accepted definition of the words. This equation doesn t correlate our quantitative data, and the HSAB concept as usually applied is not an adequate way to describe intermolecular... 

Model Definition. The HSAB model classifies Lewis acids (electrophiles) and bases (nucleophiles) as either "hard" or "soft." Hard acids and bases are relatively small, and exhibit low polarizability and a comparatively low tendency to form covalent bonds. Soft acids and bases have the opposite characteristics (24). Stated simply, the model postulates that hard acids react most readily with hard bases, and soft acids react most readily with soft bases (26). 

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],... 

Br0nsted theory, 23 Definition of Ka, 24 Lewis theory, 24 HSAB Theory, 12 Activation energy, 313-317 Chemisorption, 167 Physical adsorption, 167 Activity, 45-48, 51-53 Ionic strength, 45 Free metal-ions in solution, 45 Complex ionic species, 53 Activity coefficients, 45-48 Equations, 46 Ions in water, 21 Single-ions, 51... 

Brpnsted theory, 23 Definition of Kb, 38 Lewis theory, 24 HSAB theory, 12 Base saturation (%), 163 Basic organic compounds, 356 Bicarbonate, 30-33 Biotite, 104, 108 Boltzmann equation, 143 Bonding, 6-12 Covalent, 7 Ionic, 7 Boron, 127 Buffer capacity, 86... 

It is worthwhile to point out some obvious anomalies in HSAB theory. Some ligands do not show definite hard or soft behaviour. Consider OH- which reacts with most central atoms in M(II) and M(III) with the exceptions of Ca, Sr, Ba, Eu and Ra irrespective of the softness of the central atom. This behaviour is probably due to the consecutive deprotonation of ligated water molecules to hydroxy and then to oxo complexes which is pH dependent and due to increase in ionic potential Z/rl0n. 

Particularly relevant to the present crmtext is the fact that the olefinic double bond is considered as a soft base in Pearson s theory, while many Lewis acids used in cationic polymerisation (BF3, BCI3, AICI3, etc.) are classed as hard acids. Obviously, n-acceptors like chloranil or tetracyanoethylene are considered as soft acids. Thus, the interactions between Lewis acids and olefins must be considered as very weak in the context of the HSAB theory. This prediction is well substantiated by the tenuous character of the complexes observed in experimental studies (see Chap. IV). On the other hand, carbenium ions are usually placed at the borderline between hard and soft acids and are definitely softer than the Lewis acids mentioned above. Consequently, their interactions with olefins must be rather strong, which suggests that that propagation in cationic polymerisations promoted by Lewis acids should be faster than initiation. 

Our approach was outlined in the framework of the Hard-Soft Acid-Base theory (HSAB, Ref. 90). In a short definition, the HSAB theory states that hard nucleophiles prefer to react with hard electrophiles and soft nucleophiles prefer to react with soft electrophiles. 

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. 

Unfortunately this equation is as quantitative as HSAB gets. There was no exact definition of hardness, ry, and no operational definition which allowed it to be measured. The values in Tables 1.4 and 1.5 are useful only in ordering acids and bases. They are not transferable as numbers to any other examples. Therefore applications have always been qualitative. Even so, the HSAB concept has been extremely useful in correlating and understanding a great deal of experimental data. 

The really serious objection to the HSAB concept was that no exact definition of hardness or softness was given. There was an operational definition as given by Ahrland, Chatt and Davies, but it only put Lewis acids into one of two boxes. There was no way to rank-order within the boxes, though there were borderline cases. There was a rank-ordering of bases, given by (2), but it was only approximate and did not distinguish between all the bases with the same donor atom. Finally all that was done was to put bases into one of the two boxes labelled hard and soft. 

In spite of its limitations, the HSAB concept proved to be useful in almost all areas of chemistry, and related fields. This was more true for chemists actually working in the laboratory, trying to make definite compounds, or materials with certain properties. A good example is given by the work of Chatt and his co-workers. While probably not thinking in terms of hard and soft, they drew the same conclusions. It hardly needs to be said how successful this kind of thinking was. 

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... 

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. 

The really serious objection to the HSAB concept was that no exact definition of hardness existed. There was no defining statement based on existing theory, nor was there an operational definition linking hardness to experiment. As a result, it was not possible to give an experimental, or theoretical, value to t], for various acids and bases. The concept could not be quantified. 

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... 

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