Chemical hardness Pearson

Equation 16.12 expresses a relation between q and B.This is not a universal relation, but it does apply to the sp-bonded elements of the first four columns of the Periodic Table. Using chemical hardness values given by Parr and Yang (1989), and atomic volumes from Kittel (1996), it has been shown that the bulk moduli of the Group I, II, III, and IV elements are proportional to the chemical hardness density (CH/atomic volume) (Gilman, 1997). The correlation lines pass nearly through the coordinate origins with correlation coefficients, r = 0.999. Thus physical hardness is proportional to chemical hardness (Pearson, 2004). 

This expression was derived through considering also the chemical softness index as the inverse of the global chemical hardness (Pearson, 1997), quantifying the degree of electronic cloud polarizability (propensity to deformation), in competition with the chemical hardness, under the normalized form ... 

An antecedent of the bond modulus is the chemical hardness of Pearson (1997) which measures the stabilities of molecules. Also, bond moduli are proportional to the physical hardnesses of Yang, Parr, and Uytterhoeven (1987) which they proposed for minerals. 

Chemical hardness is an energy parameter that measures the stabilities of molecules—atoms (Pearson, 1997).This is fine for measuring molecular stability, but energy alone is inadequate for solids because they have two types of stability size and shape. The elastic bulk modulus measures the size stability, while the elastic shear modulus measures the shape stability. The less symmetric solids require the full set of elastic tensor coefficients to describe their stabilities. Therefore, solid structures of high symmetry require at least two parameters to describe their stability. 

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. 

R. G. Pearson, Chemical Hardness, Wiley-VCH, Weinheim, Germany (1997). 

Pearson, R. G. (1997). Chemical Hardness. Wiley-VCH, New York. This book is devoted to applications of the concept of hardness to many areas of chemistry. 

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]... 

For examples see Pearson, R.G. Chemical Hardness, John Wiley-VCH, Weinheim, 1997. 

J. Maruani, A. Khondir and M. Tronc, Progr. Theor. Chem. Phys. B3 (2000) 123. R. G. Pearson, Chemical Hardness (Wiley, New York, 1997). 

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... 

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]... 

Pearson, R. G. Chemical hardness - Applications from molecules to solids VCH-Wiley Weinheim, 1997. 

Pearson RG. Chemical Hardness. Weinheim, Germany Wiley-VCH, 1997. Kaneko K. Carbon 26(6) 903-905, 1988. 

Sen, K. D. and Jprgensen, C. K. (Eds.), Electronegativity, Structure and Bonding 66, Springer, Berlin (1987) Sen, K. D. (Ed.), Chemical Hardness, Structure and Bonding 80, Springer, Berlin (1993) Pearson, R. G., Chemical Hardness Applications from Molecules to Solids, Wiley-VCH, Weinheim (1997). 

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