Basicity softness parameters

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. 

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. 

A general principle is governing the relation between physical parameters and underlying distribution functions. Its paramount importance in the field of soft condensed matter originates from the importance of polydispersity in this field. Let us recall the principle by resorting to a very basic example molecular mass distributions of polymers and the related characteristic parameters. 

Evaluation of the only appropriate Fukui function is required for investigating an intramolecular reaction, as local softness is merely scaling of Fukui function (as shown in Equation 12.7), and does not alter the intramolecular reactivity trend. For this type, one needs to evaluate the proper Fukui functions (/+ or / ) for the different potential sites of the substrate. For example, the Fukui function values for the C and O atoms of H2CO, shown above, predicts that O atom should be the preferred site for an electrophilic attack, whereas C atom will be open to a nucleophilic attack. Atomic Fukui function for electrophilic attack (fc ) for the ring carbon atoms has been used to study the directing ability of substituents in electrophilic substitution reaction of monosubstituted benzene [23]. In some cases, it was shown that relative electrophilicity (f+/f ) or nucleophilicity (/ /f+) indices provide better intramolecular reactivity trend [23]. For example, basicity of substituted anilines could be explained successfully using relative nucleophilicity index ( / /f 1) [23]. Note however that these parameters are not able to differentiate the preferred site of protonation in benzene derivatives, determined from the absolute proton affinities [24],... 

This chapter is intended to provide basic understanding and application of the effect of electric field on the reactivity descriptors. Section 25.2 will focus on the definitions of reactivity descriptors used to understand the chemical reactivity, along with the local hard-soft acid-base (HSAB) semiquantitative model for calculating interaction energy. In Section 25.3, we will discuss specifically the theory behind the effects of external electric field on reactivity descriptors. Some numerical results will be presented in Section 25.4. Along with that in Section 25.5, we would like to discuss the work describing the effect of other perturbation parameters. In Section 25.6, we would present our conclusions and prospects. 

A basic concept in the reconstruction theory of solid surfaces is the soft phonon approach of displacive structural transitions. An essential property of these structural phase transitions is the existence of an order parameter which... 

To summarize, the HSAB principle is a very good first approximation but is usually inadequate for detailed analysis of reaction mechanisms. This is not really surprising. After all, this principle is nothing else than a two parameters relationship each reactant is characterized by its acidic or basic strength and by its hardness (softness). And obviously, we cannot expect to describe the complexity of chemistry with only two parameters. On the other hand, one should not underestimate its utility. Simple Hiickel calculations are also a two parameters treatment where the initial choice of the coulombic and resonance integrals a and )3 is critical. There is no doubt however that, handled with care, these calculations may give valuable insights. The same may be said for the HSAB principle. 

More complex integrated PK/PD models are necessary to link and account for a possible temporal dissociation between the plasma concentration and the observed effect. Four basic attributes may be used to characterize PK/PD models First, the link between measured concentration and the pharmacological response mechanism that mediates the observed effect (direct versus indirect link) second, the response mechanism that mediates the observed effect (direct versus indirect response) third, the information used to establish the link between measured concentration and observed effect (hard versus soft link) and, fourth, the time dependency of the involved PD parameters (time variant versus time invariant) (Danhof et al., 1993 Steimer et al., 1993 Aarons, 1999 Lees et al., 2004). The expanded and early use of PK/PD modeling in drug discovery and development is highly beneficial for increasing the success rate of drug discovery and development and will most likely improve the current state of applied therapeutics. 

They are relatively large for aromatic solvents i.e. soft EPD solvents) compared to other empirical Lewis basicity parameters that have been determined by employing rather hard Lewis acid probes, e.g. SbCb-derived DN values [cf. Eq. (7-10)], CH3OD-derived B values [cf. Eq. (7-34)], and 4-nitrophenol-derived ji values [cf. Eq. (7-51)]. The... 

Some quantitative, instrumental methods exist for assessing fabric softness, but they are not sensitive enough to assess differences between softeners. The evaluation is usually carried out by sensory perception. The feeling of a textile is very subjective as, besides the basic physical properties of the fabrics on which it depends, it is also influenced by many evaluator-linked unquantifiable parameters such as mood and tactile sensitivity [52],... 

The efficiency and selectivity of this process has been explained on the basis of several critical structural parameters that are synergistically operating in this system. The coordination of an isonitrile to the soft metal center is proposed to lead to a facile deprotonation of the enolate precursor by the pendant basic alkylamino sidechain. The formation of a contact ion-pair between enolate and ammonium groups should lead to a preferred orientation of the metal-bound... 

Although information about the overall reaction can be obtained from knowledge of global parameters such as electronegativity and hardness, the reactivity of a particular site of a molecular species can be explained by local quantities such as electron density (p(rj), Fukui function (/(F)) [75], local softness [64], or local hardness [76,77], The dependence of these local quantities on reaction coordinate reflects the usefulness of these quantities in predicting the site selectivity of a chemical reaction. The most important local descriptor is the density p(F) itself, the basic variable of DFT [78], given as ... 

In the last years, it has been found that the intuitive concepts of electronegativity, hardness, and softness are closely related to basic variables of density functional theory [5]. Thus, through the use of this theory it has been possible to establish expressions that allow one to quantify these concepts, and it has also been possible to demonstrate the principles associated with them. The purpose of the present section is to review some fundamental aspects of density functional theory, and to establish the expressions for several reactivity parameters. 

The beauty of the Density Functional theory and a source of its remarkable successes relies on the electron density function p(r), as a basic variable of the theory. Electron density is of necessity a local value that does not distinguish between parts of a molecule, and decomposition of p(r) into contributions from individual atoms has not been pursued. Instead, properties of the molecule are inspected through the local parameter of hardness, q(r) and softness s(r), introduced by Parr and Berkowitz [35, 36, 37], as opposed to the global quantities resulting in integration over the volume of the molecule. They turned their attention to the fact, that determining all properties of the system, i.e. both the dependence on the number of electrons N and the local field K(r) is possible by even more subtle parameters hardness (or softness) kernels q(r, r ). Nalewajski explored this device in analysis of the protonation reaction path [28, 38]. 

There may exist a mechanical instmment for measuring the softness of the apple material or you may simply use a taste panel to score each apple on a scale from 1 to 10. What the multivariate regression software program then will do for you is basically to produce a model that you can use to calculate the softness of each apple (Y-variable) from the measured impedance data (X-variables) or from any data derived from the measured data, such as Cole parameters. 

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