Unstable resonators

FIGURE 26 Schematic of an injection-locked resonator (unstable). 

For bulk structural detemiination (see chapter B 1.9). the main teclmique used has been x-ray diffraction (XRD). Several other teclmiques are also available for more specialized applications, including electron diffraction (ED) for thin film structures and gas-phase molecules neutron diffraction (ND) and nuclear magnetic resonance (NMR) for magnetic studies (see chapter B1.12 and chapter B1.13) x-ray absorption fine structure (XAFS) for local structures in small or unstable samples and other spectroscopies to examine local structures in molecules. Electron microscopy also plays an important role, primarily tlirough unaging (see chapter B1.17). 

W, g potential functions, k 1, has been discussed in various papers (see, for example, [6, 11, 9, 16, 3]). It has been pointed out that, for step-sizes /j > e = 1/ /k, the midpoint method can become unstable due to resonances [9, 16], i.e., for specific values of k. However, generic instabilities arise if the step-size k is chosen such that is not small [3, 6, 18], For systems with a rotational symmetry this has been shown rigorously in [6j. This effect is generic for highly oscillatory Hamiltonian systems, as argued for in [3] in terms of decoupling transformations and proved for a linear time varying system without symmetry. 

Phenol condenses with phthahc anhydride in the presence of concentrated sulphuric acid or anhydrous zinc chloride to yield the colourless phenolphthalein as the main product. When dilute caustic alkah is added to an alcoholic solution of phenolphthalein, an intense red colouration is produced. The alkali opens the lactone ring in phenolphthalein and forms a salt at one phenolic group. The reaction may be represented in steps, with the formation of a h3q)othetical unstable Intermediate that changes to a coloured ion. The colour is probably due to resonance which places the negative charge on either of the two equivalent oxygen atoms. With excess of concentrated caustic alkali, the first red colour disappears this is due to the production of the carbinol and attendant salt formation, rendering resonance impossible. The various reactions may be represented as follows ... 

Even though resonance tells us that the negative charge m cycloheptatnenyl anion can be shared by all seven of its carbons this delocalization offers little m the way of sta bilization Indeed with eight rr electrons cycloheptatnenyl anion is antiaromatic and rel atively unstable... 

Because the carbon atom attached to the ring is positively polarized a carbonyl group behaves m much the same way as a trifluoromethyl group and destabilizes all the cyclo hexadienyl cation intermediates m electrophilic aromatic substitution reactions Attack at any nng position m benzaldehyde is slower than attack m benzene The intermediates for ortho and para substitution are particularly unstable because each has a resonance structure m which there is a positive charge on the carbon that bears the electron withdrawing substituent The intermediate for meta substitution avoids this unfavorable juxtaposition of positive charges is not as unstable and gives rise to most of the product... 

Electrophilic attack on ring heteroatoms ties up an electron pair (which may have been engaged in resonance in the parent species) and confers positive charge on the system, thereby inviting nucleophilic attack or elimination reactions to follow. In small systems the primary product is usually quite unstable. Nucleophilic attack on protonated or Lewis acid-coordinated species will be treated below (Section 5.2.7), because it is not always clear whether such reactions are preceded by an electrophilic step (e.g. protonation) or not. 

This resonance-stabilized intermediate can be protonated to give hydroxyethyl-TPP. This well-characterized intermediate was once thought to be so unstable that it could not be synthesized or isolated. However, its synthesis and isolation are actually routine. (In fact, a substantial amount of the thiamine pyrophosphate in living things exists as the hydroxyethyl form.)... 

Triazanaphthalene (449) is the most unstable of the pyrido-pyrimidines to ring-degradation at pH 2 or pH 7.7 The 4-oxo derivative was converted into the 4-thioxo compound via nucleophilic displacement of the acyloxy intermediate formed with phosphorus pentasulfide. The 4-carboxymethylthio-pyridopyrimidine underwent some substitution by hydroxide ion but primarily gave the ring-opening reaction, which is facilitated by resonance activation of the 2-position by the 6-aza moiety. 

Aliphatic primary amines also undergo the diazotization reaction in weakly acidic solution however the resulting aliphatic diazonium ions are generally unstable, and easily decompose into nitrogen and highly reactive carbenium ions. The arenediazonium ions are stabilized by resonance with the aromatic ring ... 

Such diazo compounds 3 however, that contain two electron-withdrawing substituents, are unstable under these reaction conditions. They further react by hydrolytic cleavage of one carbonyl substituent to give an anionic species 6, that is stabilized by resonance, and which yields the hydrazone 4 upon acidic workup ... 

Although five equivalent resonance structures can be drawn for all three species, Huckel s rule predicts that only the six-ir-electron anion should be aromatic. The four-77-electron cyciopentadienyl carbocation and the five-7r-electron cyciopentadienyl radical are predicted to be unstable and antiaromatic. 

In this book the discussion has been restricted to the structure of the normal states of molecules, with little reference to the great part of chemistry dealing with the mechanisms and rates of chemical reactions. It seems probable that the concept of resonance can be applied very effectively in this field. The activated complexes which represent intermediate stages in chemical reactions are, almost without exception, unstable molecules which resonate among several valence-bond structures. Thus, according to the theory of Lewis, Olson, and Polanyi, Walden inversion occurs in the hydrolysis of an alkyl halide by the following mechanism ... 

In the course of the further investigation of resonating valence bonds in metals the nature and significance of this previously puzzling unstable orbital have been discovered, and it has become possible to formulate a rational theory of metallic valence and of the structure of metals and intermetallic compounds. 

When primary aromatic amines are treated with nitrous acid, diazonium salts are formed. The reaction also occurs with aliphatic primary amines, but aliphatic diazonium ions are extremely unstable, even in solution (see p. 448). Aromatic diazonium ions are more stable, because of the resonance interaction between the nitrogens and the ring ... 

This short and far from complete survey shows that the previously obscure field of chemical induction is becoming more and more understood. The accelerating pace of progress has furnished from the forties onwards a great deal of interesting information about the chemistry of unstable intermediates, e.g. chromium(V), chromium(IV), arsenic(IV), tin(III), HO2, OH, SO4 radicals. These results were obtained mostly by conventional methods. Therefore, it may be expected that the more extensive application of methods suitable for detection and estimation of short-living entities (e.g. resonance methods, fast reaction techniques) will enable our somewhat qualitative knowledge (as it is today) to be put onto a quantitative basis. 

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