Resonance mechanical analogy

As already pointed out, terms such as wave function, electron orbit, resonance, etc., with which we describe the formulations and results of wave mechanics, are borrowed from classical mechanics of matter in which concepts occur which, in certain respects at least, show a correspondence to the wave mechanical concepts in question. The same is the case with the electron spin. In Bohr s quantum theory, Uhlenbeck and Goudsmit s hypothesis meant the introduction of a fourth quantum number j, which can only take on the values +1/2 and —1/2- In wave mechanics it means that the total wave function, besides the orbital function, contains another factor, the spin function. This spin function can be represented by a or (3, whereby, for example, a describes the state j = +1/2 and P that with s = —1/2. The correspondence with the mechanical analogy, the top, from which the name spin has been borrowed, is appropriate in so far that the laevo and dextro rotatory character, or the pointing of the top in the + or — direction, can be connected with it. A magnetic moment and a... 

Cl, O, S, N) or Si—M—X (M C) groups, it was demonstrated that a number of anomalous physicochemical properties exist as compared to carbon analogs (a-effect). This is due to the fact that the interaction of Si and X atoms follows not only the inductive and resonance mechanisms but can also occur through space 614,617,619) jjj jjjg jjg silicon atom can interact either directly with X... 

That pyridine species with decreased electron densities at positions adjacent to the nitrogen atom make significant contributions to the resonance hybrid even in the ground state has been shown by dipole measurements (12, 14). Interaction with a nucleophilic agent is consequently expected to follow a mechanism analogous to that involving o-chloronitrobenzene (Equation 4). 

In summary, the plasmon can be taken as a quantum-mechanical analog of the classical resonance of sufficiently high electron density. Such a description of excitations can be appropriate for energy-loss spectroscopy and related methods. For dipole interaction with the electromagnetic field it seems that the existence conditions for plasmons cannot be fulfilled at all because the Brillouin theorem does not account for electron-electron... 

Clearly, the nex.t step will be to investigate the physicochemical effects, such as charge distribution and inductive and resonance effects, at the reaction center to obtain a deeper insight into the mechanisms of these biochemical reactions and the finer details of similar reactions. Here, it should be emphasized that biochemical reactions arc ruled and driven basically by the same effects as organic reactions. Figure 10.3-22 compares the Claisen condensation of acetic esters to acctoacctic esters with the analogous biochemical reaction in the human body. 

This type of process is analogous to the nucleophilic allylic rearrangements discussed in Chapter 10 (p. 420). There are two principal pathways. The first of these is analogous to the SeI mechanism in that the leaving group is first removed, giving a resonance-stabilized allylic carbanion, and then the electrophile attacks. 

Strong additional support for the assignment of the metapara-cyclophane structure 129 was obtained from dynamic NMR studies The temperature dependence of the proton resonance of this compound is analogous to that of the parent [2.2]metaparacyclophane 3>. The multiplets observed for the protons of the p-phenyl nucleus gradually broaden with increasing temperature, disappear completely at 150 °C, and reappear at 180 °C as a midway peak. The isomer of 129, the 13-methoxy[2]paracyclo[2](l,4)naphthalenophane (132), formation of which by the mechanism outlined above seems equally feasible, does not appear to occur. 

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