Absolute hardness/softness

In this equation, r) the absolute hardness, is one-half the difference between /, the ionization potential, and A, the electron affinity. The softness, a, is the reciprocal of T]. Values of t) for some molecules and ions are given in Table 8.4. Note that the proton, which is involved in all Brdnsted acid-base reactions, is the hardest acid listed, with t — c (it has no ionization potential). The above equation cannot be applied to anions, because electron affinities cannot be measured for them. Instead, the assumption is made that t) for an anion X is the same as that for the radical Other methods are also needed to apply the treatment to polyatomic... 

Pearson35,36 and Parr and co-workers366 c developed the principle of maximum hardness, which states that reacting molecules will arrange their electrons so as to be as hard as possible. Chemical equilibrium, then, is the state of maximum hardness. Soft donors prefer soft acceptors because both partners can increase their hardness by reacting with one another—the shared electrons flow to become less polarizable. To implement this theory quantitatively, Pearson et al. introduced scales of absolute hardness rj and its reciprocal, softness a ... 

The Principle of Hard and Soft Acids and Bases states that hard acids form more stable complexes with hard bases and soft bases form more stable complexes with soft acids. In orbital terms hard molecules have a large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and soft molecules have a small HOMO-LUMO gap. In recent years it has been possible to correlate the hardness with the electronic properties of the atoms involved. Thus, if the enthalpy of ionisation (I) and the electron affinity (A) are known the so-called absolute hardness (t ) and absolute electronegativity (%) can be found from r = (I - A) / 2 and % = (I + A) / 2. For example, the first and second ionisation enthalpies of sodium are 5.14 and 47.29 eV. Thus for Na+, I = + 47.29 and A = + 5.14, so r = (47.29 - 5.14) / 2 = 21.1. Similarly for silver the first and second ionisation enthalpies are 7.58 and 21.49eV, so for Ag+ we have, n = (21.49 - 7.58) 12 = 6.9. 

The equations 7, 8 and 9 fail to operate when the HOMO - LUMO energy gap becomes too small and do not consider the influence on chemical properties of other orbitals, besides the HOMO and LUMO s. Moreover, it is not possible to study the site selectivity of a chemical species considering only absolute hardness other than space-dependent (local) versions of hardness/softness concepts [5]. Thus in addition to the global definition of r) and S, the local hardness [4] and local softness [5] have been introduced as follows ... 

While the electronegativity and the absolute hardness are global properties of the system, the reaction between two molecules depends on the properties of the involved orbitals. In order to measure the chemical reactivity of a particular orbital in a molecule, different local variables, such as orbital softness (sq) and Fukui (fpolarization functions (no), can be computed through equations 24, 34, 36. 

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. ... 

There are two major approaches to quantitative measures of acid-base reactions. One, developed by Pearson, uses the hard-soft terminology, and defines the absolute hardness, ll, as one-half the difference between the ionization energy and the electron affinity (both in eV) ... 

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. 

In conclusion, the present study demonstrates that the cytotoxic activity of coumarin derivatives show a strong linear relationship with the absolute hardness, rj. Hardness and softness, apart from the electron accepting and donating properties of the molecule, are important factors for estimation of their cytotoxic activity. From the rj value, the CC50 value of the novel coumarin compounds can be estimated. CONFLEX is useful for calculating the hardness and softness of the molecule using the PM3 method. 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

There are more structural variables to consider in catalysis by Lewis acids than in the case of catalysis by protons. In addition to the hard-soft relationship, steric, geometric, and stereoelectronic factors can come into play. This makes the development of an absolute scale of Lewis acid strength difficult, since the complexation strength depends on the specific characteristics of the base. There are also variations in the strength of the donor-acceptor bonds. Bond strengths calculated for complexes such as H3N+-BF3" (22.0 kcal/mol) and (CH3)3N+-BH3 (41.1 kcal/mol) are substantially... 

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]. 

The absolute local softness s, [16] of an atom a is obtained by dividing the Fukui function by the global hardness s, = 4/fi. Global softness S is just the inverse of global hardness S = l/f [16]. The local and global softnesses can as such be directly calculated. 

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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