The Pearson Classification

At this point, there is worth, since having the geometric information characteristic to a crystalline solid structure, to give a uniform classification of the chemical compounds (inoiganic, organic, and mineral) with respect to the space group where the crystalline solid of the compound can be 

This way, the set of 230 possible space groups corresponds to the broader minimal classification that can be given to the chemical compounds. It is minimal because having only 230 such possibilities is much less than the almost infinite set of chemical compoimds (natural and S5m-thetic). Then, it is broad because this classification is very rigorous for the space group perspective, while being also able to broaden the information to the physical, mathematical and quantum properties. 

In other words, due to the aim to rigorously classify as conceptually-compact as it can be the chemical compoimds, with the indexing given by spatial groups, one may introduce also an alternative classification which may be the terminus point of any crystallographic analysis. 

TABLE 2.17 The Categories of Pearson Classification With -the Total Number of Atoms in the Unit Cell  

Crt Pearson Symbols (Protolype/Syngony/Groups) Unit cell s pattern 

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This chapter is principally concerned with ligand systems which contain a carbon atom linked to two oxygen atoms. In the vast majority of the complexes to be considered the donor atom is the relatively small, less polarizable oxygen atom, i.e. hard under the Pearson classification. As a consequence these ligands are seldom found in conjunction with low oxidation state metals. Considerable advances have been made in this area in recent years. The most notable of these has been the work of Cotton, who has made extensive use of the ability of such ligands to bring metal... 

Drobot et al. (3 ) have studied the thermal decomposition of Mol in evacuated sealed ampoules at various temperatures. X-ray diffraction and chemical analyses of the condensed decomposition products showed the existence of a homogeneity range in which the atomic ratio of I/Mo varied from 3.00 to 2.5. The crystal structure of Mol- is 0PI6 ( ) in the Pearson classification system. 

Accordingly, the Pearson classification is merely reductive than complete, as long as no parameter is specified, for example, the number of atoms per unit cell, which however varies. Overall, the Pearson indexing serves for an immediate view of the type of structure, at the same time indicating stoichiometric information for the unit cell. 

TABLE 2.19 The Diagrammatic/Projective Representation of the Space Groups and the Pearson Classification for Representative Examples of Crystals Primitives ... 

The FD chain relationships confirm that the Pearson classification is only partly fulfilled by marking in bold the cases when the actual analysis fits with Pearson one, clearly appears that in the case of acids, in each Pearson classes (soft, borderline, and hard) only one acid from the computed set is recovered for bases only those classified as soft are here recovered as such although in an enlarged set. Therefore, the percentage of actual/Pearson approaches goes to 33% for both acids and bases considered apart of some internal ordering relativity. 

The relationship 5.20 is shown in Figure 5.13. It is difficult to assess the relative importance of model and experimental errors in these correlations. However, it is clear that the Ai7(Bl2)-Av(I—CN) correlation is less family dependent than the pAlBi2- i (I I) and p7fBicN-Av(I—CN) relationships shown in Figures 5.12 and 5.10. Hence the relationships 5.19 and 5.20 may support the use of Av(I—CN) as a spectroscopic scale of soft affinity. Indeed, diiodine is the archetype of soft Lewis acids in the Pearson classification since it has a very low absolute hardness (rj = 3.4 eV). Moreover, Av(I—CN) values obey the HSAB principle (soft acids prefer soft bases) since they decrease with the absolute hardness of the donor atom (in a given column of the periodic table), as shown in Table 5.28. 

The ratio, C/E, gives a quantitative order of relative hardness or "softness for the various Lewis acids and agrees fairly well with the qualitative classification of Pearson (2). The adds which do not follow the qualitative classification are BF3 and SO2. As mentioned above, the parameters for BF3 were determined from data limited to oxygen donors. The qualitative ordering of SO 2 is incorrect, Emd as will be shown shortly when strong interactions are compared with weak ones, the procedures... 

Donors coordinating by F, O or N possess a general ability to coordinate both hard and soft acceptors, showing no special preference for soft ones. In the Pearson (2) classification such donors are termed hard. If their coordination are governed only, or at least mainly, by the electro-... 

Table 10 Classification of metal ions into A and B- type and after the Pearson concept into hard and soft acids with preferred ligands (after Stumm and Morgan 1996)...

Bismuth occurs in nature as Bi203 and as bismuth sulfide ores. This reflects the fact that Bi(ni) is an intermediate acid in the Pearson s classification of hard and soft acids-bases (see Hard Soft Acids and Bases). Interestingly, over-the-counter dmg formulations involve primarily oxygen-donor ligands snch as salicylate, citrate, and nitrate, while in vivo reactions... 

Table 1.3. Classification of Lewis Acids and Bases According to the Pearson Hardness Concept...

Similarity coefficients for binary variables are also used as —> classification parameters for two-dass problems among these, the most used is the Pearson coeffident (Table S9), which is also known as Matthews correlation index. 

The above classification is generally in agreement with Pearson s acid-base concept. Protic solvents are hard in nature, and they solvate small anions with strong hydrogen bonds, whereas dipolar aprotic solvents have a soft character, and they interact more strongly with the large, polarizable anions. 

Lanthanides, e.g. La(III), are considered as hard acids in the HSAB classification of Pearson (7), located between Sr (II) and Ti(IV). Divalent lanthanides are Lewis acids, as deduced from their chemical properties.Uranium ions (U(VI), U(IV)) are also hard acids. 

With the aid of the Pearson indexing the inverse path of the crystallographic classification is crossed, i.e., by reducing the classification of the chemical compounds to the set of 230 space groups to the number of 14 Bravais lattice, yet leaving open (like a variable) the total number of atoms present in the elementary cell, a number that varies from case to case. 

Besides the classification of acids and bases, the Pearson principle introduced the idea of binding preference, namely hard acids prefer to bind to hard bases, and soft acids prefer to bind to soft bases. 

According with Pearson, classification of acids and bases as hard and soft needs the recourse to the concept of strength although litde insight this... 

In this context, the actual hard and soft classification scheme will be in next compared and discussed against the traditional Pearson classification for a limited, however representative, series of molecular Lewis acids and bases as displayed in the Tables 3.1 and 3.2, respectively. 

The coordination is depending on the nature of the monomer and on the metal of the catalyst and follows generally the hard-soft acid-base rule of the Pearson s classification. 

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