Parr and Pearson

The low stability of the complex 3.6 is consistent with the hard and soft acids and bases principle of Pearson (1963, 1968 Parr and Pearson, 1983 theoretical aspects Pearson, 1989 Chatteraj et al., 1991 monograph Ho, 1977). According to that principle hard acids will tend to complex with hard bases and soft acids with soft bases. Water is a hard base, whereas the nitrosyl ion is classified by Pearson as a borderline acid with a tendency to be soft. 

The next step is the identification of the concept of chemical hardness, 17, with the second derivative of the energy with respect to the number of electrons, formulated by Parr and Pearson [14]... 

Chemical hardness and softness are much newer ideas than electronegativity, and they were quantified only fairly recently. Parr and Pearson (1983) proposed to identify the curvature (i.e. the second derivative) of the E versus N graph (e.g. Fig. 7.10) with hardness, rj [151]. This accords with the qualitative idea of hardness as resistance to deformation, which itself accommodates the concept of a hard molecule as resisting polarization - not being readily deformed in an electric field if we choose to define hardness as the curvature of the E versus N graph, then... 

Parr and Pearson 1301 defined a parameter 17, which they called "absolute hardness" (17 V4[IP-EA]), and calculated 17 for a variety of neutral and ionic Lewis acids and bases possessing from one to four atoms. These authors showed that the qualitative predictions of the HSAB model regarding the relative reactivities of these species toward one another may be obtained using the results from simple calculations of stabilization energies using 17 and electronegativity values. 

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]... 

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. 

Parr and Pearson introduced the concept [10-13] of the absolute hardness ( y) of a species defined as half the negative rate at which its electronegativity change with a change in its electron population at constant potential ... 

It has been realized by Parr and Pearson [52] that electronegativity alone cannot properly account for all facets of a chemical process and another parameter, hardness, is necessary. Whereas electronegativity is the tangent to E vs. N curve, the corresponding curvature has been identified as hardness. 

The qualitative concepts of hardness and softness were first introduced by Pearson [30-32,34], which later culminated in enunciation of the famous hard-soft acid-base principle. Quantification of these concepts had been in order and was accomplished within density functional theory by Parr and Pearson [52]. The energy stabilization due to soft-soft interaction can be expressed by rearranging Eq. (61) as [52] ... 

The Keefer-Roller nitrosation is not such as case, however, if one includes the mechanistic role of the catalyst, as shown in the sequence given in (4-9, R = H for formaldehyde). The aldehyde reacts first with the amine, forming an iminium ion. The Hard and Soft Acid and Base principle of Pearson (1963, 1968 Parr and Pearson, 1983 see also Zollinger, 1994, Sect. 3.2) predicts that the reaction of one of the O-atoms of the nitrite ion with the aldehyde C-atom of the iminium ion is the most likely reaction. In the last step, this addition product rearranges through an NN bonded four-membered ring transition state or intermediate into the nitrosoamine and the aldehyde. This mechanism is consistent with Casado s kinetic results. 

The necessity for a quantitative definition for chemical hardness was addressed by Parr and Pearson [6], who defined the hardness as... 

Hard acids prefer to coordinate with hard bases and soft acids prefer to coordinate with soft bases for both their thermodynamic and kinetic properties [2] . The first attempt at a proof of this principle was provided by Parr and Pearson [6]. They took the amount of charge transfer during the formation of a diatomic molecule AB from its constituent atoms A and B as... 

The breakthrough made by Parr and Pearson in 1983 [4] by unifying electronegativity and hardness within the DF (Density Functional) theory, brought the old problem of scale into the light is it possible and useful to define a uniform scale of hardness Experimentally observable properties of atoms and molecules which can be related to hardness, provide a clue. 

Parr and Pearson considered the simplest case of two noninteracting atoms exchanging electrons until their electronegativities are equal [4]. Then the charge transfer AN is ... 

Compared to a chosen set of reasonable , quantumchemical charge transfer values in diatomic molecules, it is surprising how well arc they reproduced by the Pauling electronegativities (column I). The Parr and Pearson equation... 

Molecule/bond Pauling (x a " X b)/ b Parr and Pearson F.q. n Komorowski Eq. 14 Quantum-chemical PNDO) Ref 29... 

Molecule Pauling (x a - X b) Charge Transfer Affinity in electron volts Parr and Pearson Komorowski Eq. 17 (R = TIa + nJ ) in Eq. 20 Pauling A (experiment)... 

It seems intuitively reasonable that charge capacity should be related to polarizability [25], and this has indeed been quantitatively confirmed [7]. From Eq. (3) and the definition of hardness proposed by Parr and Pearson [26], it also follows that r] = 1/2k [7] ti is the hardness, introduced by Pearson as a means of rationalizing a great deal of chemical behavior [27,28]. 

One of the first general rules of chemistry established theoretically within a qualitative CSA has been the HSAB principle [16, 17], which can be summarized in a short general rule among A—B reactants Hard (H) likes hard and soft (S) likes soft . The first CS rationalization of Parr and Pearson [18], based upon the Ecr expression (61), have explained the S-S part of this rule, stressing the decisive role of the covalent part of the bond (large Ncr) in interactions... 

As a last illustration we recur to the experimental results of Komorowski [59] the hardness of the C-atom was found to depend on the coordination number, the highest one corresponding to the hardest carbon (t)c = 28.6 eV for -C-, He = 26.2 eV for =C< and Hc = 25.8 eV for -). This is reasonable because a high coordination number means a soft environment (see also Sect. 3.2) and thus a hard central atom (these values must not be confused with the isolated-atom hardnesses given by Parr and Pearson [11]). 

Parr and Pearson showed in 1983-1989 that (Parr Pearson, 1983 Pearson, 1986, 1987, 1988a-6, 1989) ... 

Furthermore, we have performed a vahdity test of the suggested formula for evaluating molecular hardness by the application of the global hardness data of the carbon containing poly atomic molecules in the real field of hard-soft acid-base reactions. We have noticed that the hardness data of this calculation can draw the exact picture of the model of the chemical reaction surfaces. However, the hardness data evaluated through the ansatz and operational and approximate formula of Parr and Pearson poorly correlate the same reaction surfaces. 

Although, Perdew (1988), and Yang et al. (2000) have tried to formulate the E vs. N curve and justify the approximate formula of Parr and Pearson (1983), the incoherency between the definition and measurement of hardness is apparent (Reed 1997 Ghosh and Islam 2009). 

In Table 13.2, we have studied, invoking the Eq. 13.29, the reaction surfaces of 8 well known chemical reactions in terms of the hardness data computed by us. Also we have evaluated the same reaction surface in terms of the hardness data of such chemical species in terms of the ansatz and operational and approximate formula of Parr and Pearson [9], Eq. 13.6. Such result is also presented in Table 13.2. We have chosen such carbon containing poly atomic molecules only whose enthalpy data are available. 

Table 13.2 Verification of hard soft acid base rule entailing the maxim of the maximum hardness principle using the sets of hardness data of the present work and those computed through the ansatz and operational and approximate formula of Parr and Pearson...

Here R is the reactant P is the product Present work ab initio or Parr and Pearson Hardness data taken from (Pearson 1988)... 

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