Qualitative concept

Defining order in an amorphous solid is problematic at best. There are several qualitative concepts that can be used to describe disorder [7]. In figure Al.3.28 a perfect crystal is illustrated. A simple fonn of disorder involves crystals containing more than one type of atom. Suppose one considers an alloy consisting of two different atoms (A and B). In an ordered crystal one might consider each A surrounded by B and vice versa. 

The theory is initially presented in the context of small deformations in Section 5.2. A set of internal state variables are introduced as primitive quantities, collectively represented by the symbol k. Qualitative concepts of inelastic deformation are rendered into precise mathematical statements regarding an elastic range bounded by an elastic limit surface, a stress-strain relation, and an evolution equation for the internal state variables. While these qualitative ideas lead in a natural way to the formulation of an elastic limit surface in strain space, an elastic limit surface in stress space arises as a consequence. An assumption that the external work done in small closed cycles of deformation should be nonnegative leads to the existence of an elastic potential and a normality condition. 

The movement from the deterministic design criteria as described by equation 4.1 to the probability based one described by equation 4.2 has far reaching effects on design (Haugen, 1980). The particular change which marks the development of modern engineering reliability is the insight that probability, a mathematical theory, can be utilized to quantify the qualitative concept of reliability (Ben-Haim, 1994). 

The subunits which can be defined can include atoms or collections of atoms corresponding to functional groups. The subunits can be represented as regions of space defined by electon density. These representations correspond well with the qualitative concepts that arise from valence bond stmctures. The mathematical evaluation can assign shape and charge density to atoms. Table 1.17 gives the C and H charge densities in some... 

The lesson in these figures is that the qualitative concepts of chemical structures can be given a pictorial representation based on the quantitative application of the principles of quantum chemistry. Various, indeed all, molecular properties can, in principle, be calculated from the electronic distribution these pictures represent. 

DFT turns out to be well suited to quantitative expression of some of the qualitative concepts introduced in Section 1.2, such as electronegativity, hardness, and softness. The pnnciple of maximum hardness (p. 22) can be denved as a consequence of DFT, as can the concepts of hardness and softness. ... 

The steric constant Es and related quantities do not constitute the only approach to the study of steric effects on reactivity. Steric strain energy calculations and topological indices are more recent approaches. Qualitative concepts have been... 

The central role of the concept of polarity in chemistry arises from the electrical nature of matter. In the context of solution chemistry, solvent polarity is the ability of a solvent to stabilize (by solvation) charges or dipoles. " We have already seen that the physical quantities e (dielectric constant) and p (dipole moment) are quantitative measures of properties that must be related to the qualitative concept of... 

Accuracy and trueness have been defined above and it was mentioned that these terms base on qualitative concepts (ISO 3534-1 [1993]). If it is necessary to have quantitative information, the bias, which is a measure of inaccuracy, should not be used to quantify accuracy and trueness, respectively. Instead of this, the following measures might be applied... 

The isolation of cyclopropenones and their undoubtedly increased stability compared to the less-strained saturated cyclopropanones might well be attributed to the validity of the above symbolism of aromatic cyclopropenium contribution to the ground state of 7. It should nevertheless be clear, that the information available on the electronic structure of cyclopropenones demands certain refinements of this very useful qualitative concept. 

These two qualitative concepts are not opposed to each other. For example, criticizing the first approach one could mention that the electrons in any molecule are socialized, while it is impossible to establish the exact sites of localization of the charge and unpaired electron. It is not necessary to suppose that a certain trigger mechanism except accumulation of a certain amount of energy in a certain chemical bond is required to start fragmentation. Anyway both theories are qualitative and their joint usage allows successful interpretation of the spectra of various organic compounds. 

Before investigating the qualitative concepts of the VSEPR model it is worth noting that the details of the interactions between the electron pairs have been ascribed to a size-Pauli exclusion principle result . But objects do not repel each other simply because of their sizes (i.e. interpenetrations) only if the constituents of the objects interact is any interaction possible10). If we are to use the idea of orbital size at all we must avoid the danger of contrasting a phenomenon (electron repulsion) with one of its manifestations (steric effects). The only quantitative tests which we can apply to the VSEPR model are ones based on the terms in the molecular Hamiltonian specifically, electron repulsion. 

Secondly, we might mention that there are two possible attitudes to a theory of valence based on the AO expansion method. The chemist uses the electron-pair model essentially as one of his axioms or, at least, as a good working hypothesis. This model is extremely familiar and useful any theory of such a model of valence should be capable of providing at least some foundation for and extension of his qualitative concepts. To the physicist, however, the simplest molecules are quite complex many-particle systems and he would perhaps find it surprising if we are able to obtain any useful results from our coarse-grained minimal basis model in view of the complexity of the interactions involved. We must try to balance these views in any evalution we make. 

Is it so Does a rose consist only of molecules and their interactions We can answer yes, but it is also fair to say that this would represent only a first, gross approximation. First of all, notice that the term consists of does not necessarily imply that life can be explained and understood in terms of molecules and their interactions. Here comes the age-old question of the discrimination between structure and properties, and whereas the structure per se can be seen as consisting of small parts, usually properties and behavior are not - or at least additional qualitative concepts are needed. In turn, this does not necessarily mean that life holds something intrinsically unexplainable or beyond the reach of science. This is an important and subtle point, and I hope to be able to offer some clarifying ideas about that in the chapter dealing with autopoiesis and cognition. 

The most efficient method of obtaining approximate eigenfunctions of the electronic Hamiltonian (10) depends on the strength of the interaction between the atoms. This is a qualitative concept but emphasizes the fact that the best method of calculating intermolecular forces, which are generally considered as weak interactions, may be quite different to the best method of calculating valence forces which are strong interactions. 

Each enzyme in the pathway can be examined in this way, and the effects of any of several outside factors on flux through the pathway can be separately determined. Thus, in principle, we can predict how the flux of substrate through a series of enzymatic steps will change when there is a change in one or more controlling factors external to the pathway. Box 15-3 shows how these qualitative concepts are treated quantitatively. 

When this kind of interaction occurs between vibrational states instead of electronic states it is called Fermi resonance we shall discuss this later (Sect. 10.8). In fact, the whole qualitative concept of resonance stabilization as used in the valence bond theory is just the same principle in still another guise. 

For a very long time, since Faraday if not before, a qualitative conception has been established that the surface of a flame separates the region with oxygen and no fuel (the oxidation region) from the region without oxygen but with fuel (the recovery region). 

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