Softness parameter

The van der Waals distance, Rq, and softness parameters, depend on both atom types. These parameters are in all force fields written in terms of parameters for the individual atom types. There are several ways of combining atomic parameters to diatomic parameters, some of them being quite complicated. A commonly used method is to take the van der Waals minimum distance as the sum of two van der Waals radii, and the interaction parameter as the geometrical mean of atomic softness constants. 

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... 

Metal ions Softness parameter Metal ions Softness parameter... 

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. 

The gas-phase basicity order of alkylamines can be reproduced in terms of softness of the alkyl groups (using the Fukui function and local softness parameter ), this being far more important than group electronegativity58. 

E = electron donor constant of L y = a constant, characteristic of the metal and related to a softness parameter... 

Table 1. Ionic Radii, hydration numbers, softness parameters a, surface charge densities, polarizabilities, free energies AG° enthalpies AH° and entropies A S° of hydration of metal cations from groups Za o,nd II ...

Table 3. Softness parameters according to Ahrland and to Klopman, the sum of the z first ionization energies of the gaseous atom, and the enthalpies and free energies of hydration of M+z according to Rosseinsky, and finally the heats of atomization of the elements, all in the unit 1 eV (= 23.05 kcal/mole)...

The softness parameter large number of acceptors of varying charge and character. Within each charge group, its variation rather faithfully reflects the order of softness arrived at from the chemical behaviour, as embodied in the introductory criteria. Thus, for monovalent ions, high values of noble metal ions. 

Table 12. Comparison of the softness parameters a-p, Ok ond a a for ion acceptors of various charge...

The values of orbital energy, while Klopman has it the other way round. The present procedure has been adopted primarily in order to facilitate a comparison between the softness scales obtained by the Klopman parameter and by the new parameter [Pg.145]

In the crystal, the descriptor structure has a static conotation, and crystal structure analyses provide precise information on individual three-dimensional architectures. As described in Part I A, Chap. 2.3, hydrogen-bond lengths and angles are soft parameters and in any one crystal structure, a particular bond may be compressed or expanded by up to 20% of its equilibrium bond length (Part IA, Chap. 4.3). 

With this we would have two parameters per atom, the covalent radius r° and a softness parameter d. Building on this, we could demonstrate, that it is not necessary to introduce such an extra softness parameter for each atom, rather it suffices to write... 

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]. 

As mentioned earlier, in the limit of 1/2 0 (2 —> oo), a soft particle becomes a hard particle, we call 1/2 the softness parameter. Debye and Bueche [53], on the... 

The value of 1/2, which is the reciprocal of the friction parameter 2, decreases as the drag exerted by the hydrogel layer on the liquid flow increases. In the limit of 1/2—> 0, Eq. (21.55) tends to the well-known Smoluchowski s mobility formula for hard particles. In other words, as 1/2 increases, the hydrogel layer on the particle becomes softer. That is, the parameter 1/2 can be considered to characterize the softness of the hydrogel layer on the particle. The observed reduction of the softness parameter 1/2 (1.2 nm at 30°C to 0.9 nm at 35°C) implies that the hydrogel layer becomes harder, which is in accordance with the observed shrinkage of the hydrogel. 

Drag coefficient of the ith ionic species softness parameter electrophoretic mobility... 

The effect of anions on the selectivity of alkali metal ion extraction by crown ethers has been investigated by Olsher et al. [15]. They have shown that the overall extraction efficiency decreases in the order C1O4 >I, SCN >NO3 >Br . It was also shown that this efficiency is dependent upon the solvation energy of the anion in both phases, but not upon the anion softness parameter. On the other hand, the extraction selectivity (for K /Rb by cis, syn, cw-dicyclohexano-18-crown-6) decreased in the order NOj" >SCN >C1O4 > 1 > Br . They concluded that higher selectivity was observed with nonspherical counterions. 

The tendency of particular site to be involved in frontier-controlled [33] interactions, where frontier orbital densities play important roles, is given by a local softness parameter. Local softness (T) is defined as [64] ... 

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