Chemical Significance

Bohmian formalism provides a much clearer link to chemical phenomena than the conventional interpretation. The remainder of this book concentrates on this topic. 

There are two important conclusions to be drawn from this insight, namely the additive nature of many molecular properties and the existence of nonlocal intramolecular interactions. Charge distribution and conformation of molecules are determined holistically by non-local interaction. All local features are consequences of the whole. However, molecules of any complexity are rarely the product of a one-step reaction that starts from the constituent atoms, but are more likely built up from intermediate fragments that retain some of their own molecular properties on incorporation into a bigger whole. This mechanism explains the large number of additivity rules that have been discovered empirically in molecular systems [51]. Diverse addi- 

The non-local holistic interaction is a function of fragment size (i.e. the quantum potential). When a fragment loses its integrity under the influence of holistic interaction, intramolecular rearrangement occurs. The rearranged structure is an emergent property. 

All thermodynamic and electronic properties of molecules are closely linked to the quantum potential. Many of these, for instance electronegativity, only known from empirical relationships before, can now be demonstrated to be of fundamental theoretical importance. The close similarity between chemical potential of a system and the quantum potential of component molecules establishes a direct link between quantum mechanics and thermodynamics, without statistical considerations. This relationship has direct bearing on the nature, mechanism and kinetics of chemical bond formation, including sterically improbable intramolecular rearrangements. 

The stubborn believe that each molecular wave function relates to a 

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Weston R E and Flynn G W 1992 Relaxation of molecules with chemically significant amounts of vibrational energy the dawn of the quantum state resolved era Ann. Rev. Rhys. Chem. 43 559-89... 

Kuhn B, Rizzo T R, Luckhaus D, Quack M and Suhm M A 1999 A new six-dimensional analytical potential up to chemically significant energies for the electronic ground state of hydrogen peroxide J. Chem. Phys. Ill 2565-87... 

Figure C3.3.4. A schematic diagram of an apparatus described in the text for studying vibrational energy transfer to small bath molecules from donor molecules having chemically significant amounts of internal vibrational energy.

A fundamental set is also called a smallest set. Usually such a smallest set is selected that it also contains the smallest rings the smallest set of smallest rings (SSSR). This makes chemical sense in indane (Figure 2-38a), for example, where only the six- and the five-membered rings are of chemical significance whereas the enveloping nine-membered ring is not. 

There are finer details to be extracted from such Kohonen maps that directly reflect chemical information, and have chemical significance. A more extensive discussion of the chemical implications of the mapping of the entire dataset can be found in the original publication [28]. Gearly, such a map can now be used for the assignment of a reaction to a certain reaction type. Calculating the physicochemical descriptors of a reaction allows it to be input into this trained Kohonen network. If this reaction is mapped, say, in the area of Friedel-Crafts reactions, it can safely be classified as a feasible Friedel-Qafts reaction. 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

The concentration of hydroxide ion is too small in acid solution to be chemically significant... 

Metallocene (Section 14 14) A transition metal complex that bears a cyclopentadienyl ligand Metalloenzyme (Section 27 20) An enzyme in which a metal ion at the active site contributes in a chemically significant way to the catalytic activity... 

Only the positive root has any chemical significance since the negative root implies that the concentration of H3O+ is negative. Thus, the [H3O+] is 2.6 X 10 M, and the pH to two significant figures is still 1.59. 

Copper is required for all forms of aerobic and most forms of anaerobic life. In humans, the biological function of copper is related to the enzymatic action of specific essential copper proteins (66). Lack of these copper enzymes is considered a primary factor in cerebral degeneration, depigmentation, and arterial changes. Because of the abundance of copper in most human diets, chemically significant copper deficiency is extremely rare (67). 

It would be desirable to achieve a quantitative version of the Hammond postulate. For this purpose we need a measure of progress along the reaction coordinate. Several authors have used the bond order for this measure.The chemical significance of bond order is that it is the number of covalent bonds between two atoms thus the bond orders of the C—C, C==C, bonds are 1, 2, and 3,... 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

The isotope has a nuclear spin quantum number I and so is potentially useful in nmr experiments (receptivity to nmr detection 17 X 10 that of the proton). The resonance was first observed in 1951 but the low natural abundance i>i S(0.75%) and the quadrupolar broadening of many of the signals has so far restricted the amount of chemically significant work appearing on this rcsonance, However, more results are expected now that pulsed fourier-transform techniques have become generally available. 

It is often asked whether or not the constituent structures of a resonating system, such as the Kekul4 structures for the benzene molecule, are to be considered as having reality. There is one sense in which this question may be answered in the affirmative but the answer is definitely negative if the usual chemical significance is attributed to the structures. A substance showing resonance between two or more valence-bond structures does not contain molecules with the configurations and properties usually associated with these structures. The constituent structures of the resonance hybrid do not have reality in this sense. 

Interpretation of an FI spectrum involves a consideration of the chemical significance of the ions observed in the mass spectrum and then using this information to derive an unequivocal structure. For a detailed consideration of the interpretation of FI mass spectra, the text by McLafferty and Turecek [7] is recommended. 

A closer examination of the RICs presented in Figure 3.20, however, shows that, because of the difference in absolute intensity of the ions involved, a mass spectrum at the second peak maximum, after 5.10 min, will show significant contributions from the compound eluting after 4.67 min. Under these circumstances, the relationship between particular ions can be investigated in two other ways, i.e. (a) the relative intensities of the ions may be examined, and (b) the chemical significance of these ions may be considered. 

It i usually convenient to work with a set of internal displacement coordinates, 5, as they have chemical significance. In the limit of small amplitudes of atomic displacements, the two sets of coordinates are linearly related. Thus,... 

One of the most popular of the semi-empirical LCAO methods is that of Hfickel. It is applicable to planar molecules which have n -electron systems. The delocalization of these systems, as treated by this method, has particular chemical significance. The traditional application is to the benzene molecule. Historically, different structures of this molecule were suggested by K6kuI6+ and by Dewar that are described in virtually all textbooks of organic chemistry. These structures represented the first efforts to represent the delocalization of the 3r orbitals in such systems. In the present context the delocalization can be better specified with the use of the method of Hilckel. 

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