Absolute Hardness Parameters

Compare the results of Problems 17 and 18 with the absolute hardness parameters of Appendix B-5 for BF3, NH3, and pyridine (C5H5N). What value of t would you predict for B(CH3)3 (Compare NH3 and N(CH3)3 as a guide.)... 

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. 

Later on, Pearson tried to establish a quantitative scale of absolute hardness and softness.Absolute hardness is characterized by the value 17 and absolute electronegativity by the value %. The absolute hardness (rj) (is given by the expression r/ = (/ - A)/2, and the absolute softness (cr) by the expression (7 = 1/r/. Table 2.7.5. contains a selection of Pearson s absolute hardness parameters. 

Parr RG, Pearson RG (1983) Absolute hardness companion parameter to absolute electronegativity. J Am Chem Soc 105(26) 7512-7516... 

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. 

We define two parameters the absolute electronegativity, which is approximately the same as electronegativity as Mulliken originally defined it for atoms, namely the average of the ionisation potential I and the electron affinity A (Equation 3.1). The other is called the absolute hardness, rj, which is identified with the difference in energy between the ionisation potential I and the electron affinity A (Equation 3.2). 

The second approach to defining the absolute hardness rj has a companion parameter taken from density functional theory, called the electronic chemical potential p. The value of /i is essentially the same as the negative of X, as defined in Equation 3.1, and the value of 77 is essentially the same as in the more approximate definition in Equation 3.2. Tables 3.1-3.5 record some useful values for radicals, molecules and ions based on this definition. 

Note again that the quantitative values associated with hardness and softness in this article are based wholly on experimentally determined log stability constant differences determined in aqueous solutions at room temperature. The values are not absolute addition of more metal ions might extend the scales in either direction. Small differences between metal ions should not be overinterpreted. The relative difference scales are linear in log stability constant, stretching from very hard at one end to very soft at the other. As hardness decreases, softness correspondingly increases, and vice versa. These practical scales are difficult to relate to that of Pearson, where absolute hardness values are derived from gas-phase parameters, and softness is the reciprocal of hardness. ... 

A Antisymmetrizing operator A Vector potential P First hyperpolarizability P Resonance parameter in semi-empirical theory B Magnetic field (magnetic induction) X, /r, A, cr Basis functions (atomic orbitals), ab initio or semi-empirical methods rraiipp inrliiflinp basis fiinrHon 7] An infinitesimal scalar rj Absolute hardness h Planck s constant H hjl K h Core or other effective one-electron operator hap Matrix element of a one-electron operator in AO basis Matrix element of a one-electron operator in semi-empirical theory... 

Parr, R.G. and Pearson, R.G. (1983). Absolute Hardness Companion Parameter to Absolute Electronegativity. J.Am.Chem.Soc., 105,7512-7516. 

Abraham-Klamt descriptors Linear Solvation Energy Relationships Abraham s general equation —> Linear Solvation Energy Relationships absolute hardness quantum-chemical descriptors ( hardness indices) absorption parameter property filters ( drug-like indices)... 

The curvature of E vs. N curve has been equated with hardness [36], another important parameter for understanding structure and reactivity. The absolute hardness is given as ... 

Parr and I had originally called t] the absolute hardness. The reason was that it was a companion parameter to Xu (or —p), called the absolute electronegativity, because it had a sound basis in fundamental theory. While this made sense for ju, it seemed unnecessary for rj. The other scientific use of the term hardness would be for physical or mechanical hardness. Thus the name chemical hardness seems more appropriate for rj. 

The concept of topological resonance energy was introduced to provide a relative measure of aromaticity <77JA1692>. In a newer approach, the absolute hardness, or HOMO-LUMO gap, as the measure of aromaticity is defined to be in the ionization potential of the species minus its electron affinity. The parameters of the absolute hardness and a related relative hardness for (152) are consistent with the high reactivity of this compound <89JA737l>. 

Originally the term absolute hardness was used, to indicate that q was a companion parameter to %, the absolute electronegativity [12]. The latter term seems appropriate, since there are many other scales of electronegativity. But only X has a firm origin in fundamental theory. However the use of absolute in connection with hardness seems unnecessary. The only other important scale of hardness is that measuring resistance to mechanical deformation. Hence the name chemical hardness seems to be more descriptive. 

Eq. 11) is hardly an acceptable source of the charge transfer. The novel formula, Eq. 14, produces very reasonable charge values. The set of absolute electronegativity and hardness parameters was identical in all calculations, and was quite arbitrary, given the discussion on hardness parameters in Sect. 1. Equation 14 may be reliably used for charge estimation purposes, it seems. 

Table 7. Charge Transfer AlTmity calculated by various approaches for selected pairs of atoms in diatomic molecules. Absolute electronegativity and hardness parameters as in Ref. [4]...

R, the sum of atomic radii plays important role in this formalism. As demonstrated in Sect 1.5, equivalence between the absolute atomic hardness and atomic radius is best for van der Waals or ionic radii. Thus, the R distance may be much larger than the normal bond in the AB molecule. For the purpose of this analysis, however, R/2 = Rab as a working approximation might be used, which is strictly valid for van der Waals radii and homonuclear diatomic molecules. Another choice is to follow the ehemieal approximation and use some available hardness parameters to estimate R as R = (rA + Tb) = (r A )-... 

The potential to describe the chemical reaction path is emerging from the DF theory. Pearson [69] and Parr et al. [70] have proposed a principle of maximum hardness stable molecules arrange themselves as to be as hard as possible. Zhou and Parr introduced the activation hardness parameter for the electrophilic aromatic substitution [71], The same authors have shown a correlation between the absolute hardness of a molecule and aromacity [72]. Nalewajski et al. studied the protonation reaction and described the relation between the interaction energy and charge sensitivities hardness, softness, Fukui function [28, 38]. 

Parr and al. gave in 1988 atheoretical support to the absolute hardness. In the density functional theory two basic parameters were introduced. Any chemical system can be characterized by its chemical potential, p, and its absolute hardness, T]. The chemical potential measures the escaping tendency of an electronic cloud, while absolute hardness determines the resistance of the species to lose electrons. The exact definitions of these quantities are ... 

Of course the absolute softness is the reciprocal of the absolute hardness. The apparent success of the density-functional theory is to provide two parameters from which we ean calculate the number of electrons transferred, resulting mainly from the eharge transfer between two molecules, i.e., from electrons flow until chemical potential reaehes an equilibrium. As a first approximation, the number of electron transferred is given by ... 

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