Pearson number

Fig. 9. Structure diagram for phases with the MgCuj (AB2) structure. After Pearson. Numbers indicate the number of A-A, etc. contacts.

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

The last two decades have seen a growing interest in the mechanism of inorganic reactions in solution. Nowhere is this activity more evident than in the topic covered by this review the oxidation-reduction processes of metal complexes. This subject has been reviewed a number of times previously, notably by Taube (1959), Halpern (1961), Sutin (1966), and Sykes (1967). Other articles and books concerned, wholly or partly, with the topic include those by Stranks, Fraser , Strehlow, Reynolds and Lumry , Basolo and Pearson, and Candlin et al ° Important recent articles on the theoretical aspects are those by Marcus and Ruff. Elementary accounts of redox reactions are included in the books by Edwards , Sykes and Benson . The object of the present review is to provide a more detailed survey of the experimental work than has hitherto been available. 

Ahrland et al. (1958) classified a number of Lewis acids as of (a) or (b) type based on the relative affinities for various ions of the ligand atoms. The sequence of stability of complexes is different for classes (a) and (b). With acceptor metal ions of class (a), the affinities of the halide ions lie in the sequence F > Cl > Br > I , whereas with class (b), the sequence is F < Cl" < Br < I . Pearson (1963, 1968) classified acids and bases as hard (class (a)), soft (class (b)) and borderline (Table 1.23). Class (a) acids prefer to link with hard bases, whereas class (b) acids prefer soft bases. Yamada and Tanaka (1975) proposed a softness parameter of metal ions, on the basis of the parameters En (electron donor constant) and H (basicity constant) given by Edwards (1954) (Table 1.24). The softness parameter a is given by a/ a - - P), where a and p are constants characteristic of metal ions. 

More systematic (but not always unambiguous) is the designation by Pearson symbols their use is recommended by IUPAC (International Union of Pure and Applied Chemistry). A Pearson symbol consists of a lower case letter for the crystal system (cf. the abbreviations in Table 3.1, p. 24), an upper case letter for the kind of centering of the lattice (cf. Fig. 2.6, p. 8) and the number of atoms in the unit cell. Example sulfur-< F128 is orthorhombic, face centered and has 128 atoms per unit cell (a-sulfur). 

Another property that is related to chemical hardness is polarizability (Pearson, 1997). Polarizability, a, has the dimensions of volume polarizability (Brinck, Murray, and Politzer, 1993). It requires that an electron be excited from the valence to the conduction band (i.e., across the band gap) in order to change the symmetry of the wave function(s) from spherical to uniaxial. An approximate expression for the polarizability is a = p (N/A2) where p is a constant, N is the number of participating electrons, and A is the excitation gap (Atkins, 1983). The constant, p = (qh)/(2n 2m) with q = electron charge, m = electron mass, and h = Planck s constant. Then, if N = 1, (1/a) is proportional to A2, and elastic shear stiffness is proportional to (1/a). 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

Absolute rates for the addition of the methyl radical and the trifluoromethyl radical to dienes and a number of smaller alkenes have been collected by Tedder (Table l)3. Comparison of the rate data for the apolai4 methyl radical and the electrophilic trifluoromethyl radical clearly show the electron-rich nature of butadiene in comparison to ethylene or propene. This is also borne out by several studies, in which relative rates have been determined for the reaction of small alkyl radicals with alkenes. An extensive list of relative rates for the reaction of the trifluoromethyl radical has been measured by Pearson and Szwarc5,6. Relative rates have been obtained in these studies by competition with hydrogen... 

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]... 

This concept was introduced qualitatively in the late 1950s and early 1960s by Pearson, in the framework of his classification of Lewis acids and bases, leading to the introduction of the hard and soft acids and bases (HSAB) principle [19-21]. This principle states that hard acids prefer to bond to hard bases and soft acids to soft bases. In many contributions, the factor of 1/2 is omitted. The inverse of the hardness was introduced as the softness S=l/rj [22]. A third quantity, which can be expressed as a derivative with respect to the number of electrons is the Fukui function, was introduced by Parr and Yang [23,24] ... 

As mentioned in the Introduction, no structural information on these species was available for more than 40 years after the discovery of the first Zintl metal cluster anions, since no pure crystalline phases could be isolated and characterized structurally. Nevertheless, early efforts to rationalize the observed formulas and chemical bonding of these intermetallics and related molecules utilized the Zintl-Klemm concept [75, 76] and the Mooser-Pearson [77] extended (8 — N) rule. In this rule N refers to the number of valence electrons of the more electronegative metal (and thus anionic metal) in the intermetallic phases. 

Fig. 4. Alignment of two sequences using four different scoring functions. (A) From Altschul (1998) and (B-D) from Smith-Waterman alignments using SSEARCH (Pearson, 1996). Asterisks with numbers above the alignments correspond to the four HSPs indicated in Fig. 1.

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