Hard-soft, acid-bases absolute softness

In this equation, r) the absolute hardness, is one-half the difference between /, the ionization potential, and A, the electron affinity. The softness, a, is the reciprocal of T]. Values of t) for some molecules and ions are given in Table 8.4. Note that the proton, which is involved in all Brdnsted acid-base reactions, is the hardest acid listed, with t — c (it has no ionization potential). The above equation cannot be applied to anions, because electron affinities cannot be measured for them. Instead, the assumption is made that t) for an anion X is the same as that for the radical Other methods are also needed to apply the treatment to polyatomic... 

There are two major approaches to quantitative measures of acid-base reactions. One, developed by Pearson, uses the hard-soft terminology, and defines the absolute hardness, ll, as one-half the difference between the ionization energy and the electron affinity (both in eV) ... 

For electron donors, a simple attempt at classifying hard and soft bases is illustrated Table 6.3. Such classification schemes reveal, not suipris-ingly, that hard and soft are not absolute, but gradually varying qualities. Pearson (1963) has proposed, in generalizing hardness and softness properties for Lewis acids and bases for many kinds of systems, the so-called HSAB (hard and soft acid-base) rules. 

Recently Parr and Pearson have used the b parameter to investigate the hard and soft properties of metal ions and ligands. They have termed this the absolute hardness in comparison to the Mulliken-Jaff6 a parameter which they call absolute electronegativity. They provide strong arguments for the use of the absolute hardness parameter in treating hard-soft acid-base (HSAB) interactions. 

There are more structural variables to consider in catalysis by Lewis acids than in the case of catalysis by protons. In addition to the hard-soft relationship, steric, geometric, and stereoelectronic factors can come into play. This makes the development of an absolute scale of Lewis acid strength difficult, since the complexation strength depends on the specific characteristics of the base. There are also variations in the strength of the donor-acceptor bonds. Bond strengths calculated for complexes such as H3N+-BF3" (22.0 kcal/mol) and (CH3)3N+-BH3 (41.1 kcal/mol) are substantially... 

Lewis [5] was the first to describe acids and bases in terms of their electron accepting and electron donating properties. Mulliken [6] further refined the understanding of the acid base interactions for which he was awarded the Nobel Prize for Chemistry. His quantum mechanical approach introduced the concept of two contributions, an electrostatic and a covalent, to the total acid-base interaction. Pearson [7] introduced the concept of hard and soft acids and bases, the HSAB principle, based on the relative contributions from the covalent (soft) interaction and the electrostatic (hard) interaction. In his mathematical treatment he defined the absolute hardness of any acid or base in terms of its ionisation potential and electron affinity. Pearson s is probably the most robust approach, but the approaches in most common use are those developed by Gutmann [8] and Drago [9], who separately developed equations and methods to quantify the acid or basic strength of compounds, from which their heats of interaction could be calculated. 

Based on the research of Klopman, and Parr and Pearson (Klopman 1968 Parr and Pearson 1983), Pearson described the absolute hardness (ri) quantitatively as being proportional to the difference between I (ionization potential) and A (electron affinity) of the species (Pearson 1988). Absolute softness is defined as t). The absolute electronegativity (x) and the absolute hardness (Tj) are applied quantitatively to any given acid-base reaction. Table 3.10 presents x and Tj values for some representative metal ions. 

We attempt to extend the Hard-Soft Acid-Base (HSAB) principle for the reactions in solutions to interactions in solids. First we point out the important link between the absolute hardness of acid-and-base and the average energy gap. Then we discuss the electronic band structures of various solids, e.g., metals, semimetals, semiconductors and insulators. On the basis of energy gaps, we elaborate various consequences of the acid-base interactions in solids. The applications of HSAB principle and the frontier orbital concept to the solid adhesion and surface interactions between metals and polymers will be verified by experimental results reported in the literature. The new findings reported in this paper should be beneficial to those who are carrying out research in or processing thin-film microelectronic devices or thick-film multilayer structures. 

The hard character of the BF3 affinity scale has been confirmed theoretically. The theoretical absolute hardness of BF3, p = 9.7 eV, is fairly high compared with other molecular Lewis acids (see Table 1.17). The hardness of the interaction of BF3 with NH3, NMc3 and CO has been studied [70] through the local Hard-Soft Acid-Base principle. 

R. G. Pearson, Hard and soft acids and bases—the evolution of a concept. Coord. Chem. Rev. 100, 403-425 (1990) R. G. Pearson, Absolute electronegativity and hardness. Application to inorganic chemistry. Chem. Br. 31, 444-447 (1991) R. G. Pearson, Recent advances in the HSAB concept. J. Chem. Educ. 64, 561 (1987). 

The Principle of Hard and Soft Acids and Bases states that hard acids form more stable complexes with hard bases and soft bases form more stable complexes with soft acids. In orbital terms hard molecules have a large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and soft molecules have a small HOMO-LUMO gap. In recent years it has been possible to correlate the hardness with the electronic properties of the atoms involved. Thus, if the enthalpy of ionisation (I) and the electron affinity (A) are known the so-called absolute hardness (t ) and absolute electronegativity (%) can be found from r = (I - A) / 2 and % = (I + A) / 2. For example, the first and second ionisation enthalpies of sodium are 5.14 and 47.29 eV. Thus for Na+, I = + 47.29 and A = + 5.14, so r = (47.29 - 5.14) / 2 = 21.1. Similarly for silver the first and second ionisation enthalpies are 7.58 and 21.49eV, so for Ag+ we have, n = (21.49 - 7.58) 12 = 6.9. 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

Finally, let us not forget that there is a single, simple frame of understanding which correctly, albeit qualitatively, predicts the energetic order of mercury carbodiimide and mercury cyanamide, and it is based on chemical ideas, namely Pearson s concept of hard and soft acids and bases soft prefers soft and hard prefers hard. The absolute softness of Hg + (7.7 eV, see Table 2.3) lies between those of Pb and Ag+ such that a cyanamide anion and not a carbodiimide anion will be the preferred bonding partner for Hg +, just as for Pb + and Ag+. I cannot refrain from noting that I find this quite remarkable. 

Pearson appbed the concept of hard and soft acids and bases to nucleo-philicity in the 2 reaction by using the concept of absolute hardness, rj ... 

Besides the estimation of the strength of the -OH bonding at the active site in the zeolite by ab initio calculation of the energy levels, it is possible to extract information relating to the intrinsic acidity using concepts in the framework of hard and soft acids and bases. The fundamental parameter is the absolute hardness t), defined as the second derivative of the energy with respect to the number of particles... 

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