Softness quantitative definition

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. 

Although the qualitative concepts such as electronegativity and hardness have been found to be useful in understanding various chemical reactions, they were not taken very seriously until recently because they did not have legitimate theoretical genesis. Rigorous quantitative definitions and methods for calculations [36-38] of electronegativity, hardness, and related quantities such as chemical potential, local hardness, softness, Fukui function, etc., have been provided within density functional... 

Some advocates of DFT believe that DFT will displace the Hartree-Fock method and Hartree-Fock based correlation methods (MP, CC, Cl) and become the dominant way of doing quantum-chemistry calculations and the main way of theoretically interpreting chemical concepts. [DFT has been used to provide quantitative definitions of such chemical concepts as electronegativity, hardness and softness, and reactivity see Parr and Yang, Chapters 5 and 10 and W. Kohn, A. D. Becke, and R. G. Parr, / Phys. Chem., 100,12974 (1 ).]... 

In the same spirit, considering the transfer of an electron from an atom X to another identical atom X, the associated energy quantity is the energy difference, (7x - Ax), which should be a measure of the ease or difficulty of charge fluctuation between two identical atoms. This quantity, therefore, is interpreted as the measure of hardness/softness of an atomic species. The quantitative definition of the chemical hardness parameter q has thus been made fl = (7 - A)/2, which is interpreted " to represent (again, within a finite difference approximation) the second derivative of the energy quantity with respect to the electron number N, viz., q = (l/2)(3 W3N ). 

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... 

To go into this idea quantitatively, we need definitions of hardness and softness, and a rank order for acids and bases on a scale of hardness. This has been done in two ways one based on molecular orbital theory, and the other on density functional theory. 

In the work of Zachmann et al. new approaches to the quantification of surface flexibility have been suggested. The basis data for these approaches are supplied by molecular dynamics (MD) simulations. The methods have been applied to two proteins (PTI and ubiquitin). The calculation and visualization of the local flexibility of molecular surfaces is based on the notion of the solvent accessible surface (SAS), which was introduced by Connolly. For every point on this surface a probability distribution p(r) is calculated in the direction of the surface normal, i.e., the rigid surface is replaced by a soft surface. These probability distributions are well suited for the interactive treatment of molecular entities because the former can be visualized as color coded on the molecular surface although they cannot be directly used for quantitative shape comparisons. In Section IV we show that the p values can form the basis for a fuzzy definition of vaguely defined surfaces and their quantitative comparison. 

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. 

Eq. 5.30 is a general relationship for the interactions of electrophiles and nucleophiles, and is not restricted to definitions and discussions of hard and soft acids and bases. It tells us that the relative nucleophilicity of several Lewis bases will depend upon which electrophile is used, because the c s and yS values will change for each different electrophile. Similarly, the relative electrophilicities of several Lewis acids will depend upon what nucleophile is used. We will see exactly such results when we explore quantitative scales for various nucleophiles and electrophiles, where the scales are highly dependent upon the particular reaction that is chosen to analyze relative reactivities (see Chapter 8). Eq. 5.30 nicely explains the reactivity trends for soft acids and bases. It predicts that the Eoveriap will be best for Lewis acids and bases that have electrophilic and nuclephilic orbitals of roughly the same energy, which is the cases for the soft acids and bases of Table 5.8. 

---