Base Softness Parameters

Chen et al. (2000) considered the relationships among three solvent softness scales relevant to bases, namely, Marcus s n (discussed in Chapter 3), (discussed earlier) 

FIGURE 4.13 Six parameters for base softness. Three (ji, D, and AAi/(C-I)) are discussed by Chen et al. (2000). is the volume polarization, is derived from the Drago parameters Cg and and is the reciprocal of the LUMO-HOMO energy difference. Values from Mu et al. (1998). 

The separation of the two clusters may be because and R are properties of the whole molecule, whereas n, D, and S relate specifically to the coordination site. Why A Av(I-C) lies so far from both clusters (nearly orthogonally) is not clear (but ICN is a rather strange sort of acid). Apparently base softness, like basicity itself, is not a simple property. 

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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. 

They indicated that the softness parameter may reasonably be considered as a quantitative measure of the softness of metal ions and is consistent with the HSAB principle by Pearson (1963, 1968). Wood et al. (1987) have shown experimentally that the relative solubilities of the metals in H20-NaCl-C02 solutions from 200°C to 350°C are consistent with the HSAB principle in chloride-poor solutions, the soft ions Au" " and Ag+ prefer to combine with the soft bisulfide ligand the borderline ions Fe +, Zn +, Pb +, Sb + and Bi- + prefer water, hydroxyl, carbonate or bicarbonate ligands, and the extremely hard Mo + bonds only to the hard anions OH and. Tables 1.23 and 1.24 show the classification of metals and ligands according to the HSAB principle of Ahrland et al. (1958), Pearson (1963, 1968) (Table 1.23) and softness parameter of Yamada and Tanaka (1975) (Table 1.24). Compari.son of Table 1.22 with Tables 1.23 and 1.24 makes it evident that the metals associated with the gold-silver deposits have a relatively soft character, whereas those associated with the base-metal deposits have a relatively hard (or borderline) character. For example, metals that tend to form hard acids (Mn +, Ga +, In- +, Fe +, Sn " ", MoO +, WO " ", CO2) and borderline acids (Fe +, Zn +, Pb +, Sb +) are enriched in the base-metal deposits, whereas metals that tend to form soft acids... 

Ag" ", Au" ", Tl" ", Tp+) are enriched in the gold-silver deposits. Metals that have high values of the softness parameter (Ag", Hg+, Tl" ", Cd ) are associated with the gold-silver deposits, whereas those that have low values of the softness parameter (Zn +, In +, Bi +, Te, Mn +, Sn" +, Ga " ) are found with the base-metal deposits. 

These relations highlight the fact that the formalism of DFT-based chemical reactivity built by Parr and coworkers, captures the essence of the pre DFT formulation of reactivity under frontier molecular orbital theory (FMO). Berkowitz showed that similar to FMO, DFT could also explain the orientation or stereoselectivity of a reaction [12]. In addition, DFT-based reactivity parameters are augmented by more global terms expressed in the softness. 

The soft donor properties of EPD solvents have also been quantified by the softness parameter SP of Gritzner [173, 240]. This parameter is solely based on the standard molar Gibbs energies of transfer of Ag+ ions from benzonitrile as reference solvent to other soft solvents and should be used for soft/soft interactions only. 

The donor properties of soft EPD solvents have also been deseribed by the softness parameter SP of Gritzner [290, 303], This parameter is based on the standard molar Gibbs energies of transfer of soft Ag+ ions from benzonitrile as a referenee solvent to other soft solvents and should only be used for soft solute/soft solvent interaetions. Further solvent softness parameters based on the Raman IR absorption of the symmet-rieal stretehing vibration of the Hg-Br bond in HgBr2 have been developed by Persson et al. [287, 292] cf. also Seetion 3.3.2. The relationships between these solvent softness seales have reeently been reviewed [304]. 

The softness parameters are correlated with the oxidation potential and, hence, the polarizability of the acids and bases. 

Ahrland (10) reasoned that the more completely the energy for positive ion formation in the gas phase is regained by introduction of the ion in a hard solvent (e.g., H2O) the harder the ion is. He then proposed a softness parameter based on the dehydration energy and the ionization potential for the formation of M" (gas). A large difference between the two quantities indicates a soft ion. 

The concept of softness has also been introduced, and the softness parameter S has been defined as the reciprocal of hardness, viz., 5 = if = 2(7 - A). The DFT-based definition for the softness parameter is also through the concept of local softness, as given by... 

The softness parameter of Misono and Saito (Y ) (Misono and Saito 1970) is based on the use of a regression model where the log of stability constants of halogeno-complexes of metal ions (Log k) is a function of two parameters. One parameter corresponds to hardness (X) and the other to softness (Y),... 

The originally published [27] softness parameters are based on the arbitrary assignment of zero to the hydrogen ion for cations and to the hydroxide ion for anions, but a common scale for ions of both charge signs, 3, is produced when 0.3 units are subtracted from these cation values and 0.3 is added to the anion values. Positive values of the softness parameter denote soft ions and negative values denote hard ions. The values of many ions are recorded in Table 2.4. 

Sharmina R, Sundararaja U, Shah S, Griend LV, Sun YJ. Inferential sensors for estimation of polymer quality parameters industrial application of a PLS-based soft sensor for a LDPE plant. Chem Eng Sci 2006 61 6372-6384. 

Hammett equation(s) 78, 93, 148ff., 151 f., 153ff., 167f., 190, 193, 196, 297, 299, 308, 312, 375, 381, 392, see also Dual substituent parameter, and Quantitative structure-reactivity relationships Hammond postulate, in additions of nucleophiles to diazonium ions 157 Hard and soft acids/bases principle (Pearson) 49, 54, 109... 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

The most useful and important application of Fukui function and local softness resides in the interpretation and thereby, prediction of reaction mechanism, especially in the site selectivity or regioselectivity. Since long FMO theory has generally been used to probe the regioselective nature of a reaction, in particular of organic compounds, but the DFT-based local reactivity parameters have emerged as... 

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