Factor 2—Resonance

The Q-e Scheme. The magnitude of and T2 can frequentiy be correlated with stmctural effects, such as polar and resonance factors. For example, in the free-radical polymerization of vinyl acetate with styrene, both styrene and vinyl acetate radicals preferentially add styrene because of the formation of the resonance stabilized polystyrene radical. 

The ortho effect may consist of several components. The normal electronic effect may receive contributions from inductive and resonance factors, just as with tneta and para substituents. There may also be a proximity or field electronic effect that operates directly between the substituent and the reaction site. In addition there may exist a true steric effect, as a result of the space-filling nature of the substituent (itself ultimately an electronic effect). Finally it is possible that non-covalent interactions, such as hydrogen bonding or charge transfer, may take place. The role of the solvent in both the initial state and the transition state may be different in the presence of ortho substitution. Many attempts have been made to separate these several effects. For example. Farthing and Nam defined an ortho substituent constant in the usual way by = log (K/K ) for the ionization of benzoic acids, postulating that includes both electronic and steric components. They assumed that the electronic portion of the ortho effect is identical to the para effect, writing CTe = o-p, and that the steric component is equal to the difference between the total effect and the electronic effect, or cts = cr — cte- They then used a multiple LFER to correlate data for orrAo-substituted reactants. 

A clear demonstration of the relative importance of steric and resonance factors in radical additions to carbon-carbon double bonds can be found by considering the effect of (non-polar) substituents on the rate of attack of (nonpolar) radicals. Substituents on the double bond strongly retard addition at the substituted carbon while leaving the rate of addition to the other end essentially unaffected (for example, Table 1.3). This is in keeping with expectation if steric factors determine the regiospeeificity of addition, but contrary to expectation if resonance factors are dominant. 

The reaction is generally believed to proceed via the formation of ionic acylam-monium intermediate compounds (Reaction 1, Scheme 2.27). The equilibrium constant of the acylammonium formation depends mostly on steric and resonance factors, while the basicity of the tertiary amine seems to play a secondary role.297 In die case of the less basic compounds, such as acidic phenols, and of strong tertiary amines, such as Uialkylamines, the reaction has been reported to proceed through a general base mechanism via the formation of hydroxy-amine H-bonded complexes (Reaction 2, Scheme 2.27).297... 

Taft (21) has suggested that the electrical effect of a substituent is composed of localized (inductive and/or field) and delocalized (resonance) factors. Thus we may write the substituent constant of the group X as... 

Percent Yields/IOO [A] and Percentage Sn(ANRORC) Mechanism/IOO [B] Obtained in the Amination oe 2-X-4-Phenylpyrimidines,Xanrorc [A x B], Nonresonance Constants F, AND Resonance Factors R oe Substituents X. 

As in the oxepin-arene oxide system, the resonance effect will also influence the position of equilibrium in the analogous organosulfur series. Compounds (46) and (53) thus appear to exist exclusively in the thiepin form. Since the resonance factor would favor the 1,2-episulfide of naphthalene over the thiepin tautomer (54) it is highly improbable that this thiepin will be detectable at ambient temperature. Both thiepins (46) and (55) have been isolated as thermolabile compounds (78JOC3379, 81MI51700). 

The ionization constants of a series of hindered polynuclear aromatic acids have been determined by Newman and Boden (1961). Two factors are held to affect the acidic strength of such acids the decrease of solvation and the inhibition of resonance due to steric effects. Solvation of an ion should be an acid-strengthening factor and if steric factors decrease the amount of anion solvation, the acid should be correspondingly weaker. The resonance factor only comes into play with aromatic (or unsaturated) acids. Here resonance would involve transfer of... 

The resonance factor, Q, can be used as a guide to compare the laboratory results of various experimenters. It is calculated as the quotient of the peak wavelength divided by the difference between the wavelengths of the two half-amplitude points for the spectrum of each chromophore. When computing the precise spectral characteristics of the chromophores of vision as found in laboratory experiments (that occurs in Chapter 16 17) the appropriate Qwas determined. 

It should be noted that the Lamb equation is appropriate for a low frequency filter rather than a resonant phenomenon such as spectral absorption by the chromophores. Its asymptotic character at short wavelengths leads to a half-amplitude value that is quite different from the similar half-amplitude value for a resonant phenomenon of arbitrary resonance factor, Q. 

The blue solution is characterized by (I) its color, which is independent of the metal involved (2) its density, which is very similar to that of pure ammonia (3) its conductivity, which is in the range of electrolytes dissolved in ammonia and (4) its paramagnetism, indicating unpaired electrons, and its electron paramagnetic resonance. -factor, which is very close to that of the free electron. This has been interpreted as indicating that in dilute solution, alkali metals dissociate to form alkali metal cations and solvated electrons ... 

Whenever an atom with an unshared electron pair is attached to a carbon atom of a double bond which is conjugated with a group such as those discussed in (1), the resonance contribution of the ionic forms becomes particularly important. This generalization follows from (2) and (3) since the resonance factors of such a combination act to reinforce each other. 

When the halogen atoms are separated by twro carbon atoms, the resonance factor cannot operate and the bulk of the halogen atom is removed from the site of reaction. Consequently, permanent polarizat ion controls the situation. 2 is facilitated and 1 is retarded. Thus 1,2-diiodocthanc undergoes 8 2 reactions more rapidly than ethyl io-... 

Where the D m and t/ji are the appropriate resonance factors given next ... 

Gilman invoked resonance factors to explain why lithiation occurs to a smaller extent at 1-position in 2-methoxynaphthalene. According to him, the electron density at 1-position would be more due to resonance interaction of the ring with the OCHj substituent. This electron density would decrease the acidity of H at that position. The H at 3-position would be relatively more acidic and lithiation would be favoured there. 

More recently Schmidt and Brauer [45] have extended the work of Hurst and Schuster. The key finding was a strong exponential correlation between experimentally determined fcqi values and the solvents highest energy fundamental frequency for a comprehensive range of solvent ta values. By calculating off-resonance energy differences, Esm, the use of Eqs. (25) and (26) for exothermic and endothermic transfer respectively allowed estimation of the off-resonance factor, Rsm, where a is assumed to be a solvent-independent quantity. 

In Chapter 4, we developed the notion that individual resonant filters can be used to model each vibrational mode of a system excited by an impulse. Thus, modal synthesis is a form of subtractive synthesis. For modeling the gross peaks in a spectrum, which could correspond to resonances (although these resonances are weaker than the sinusoidal modes we talked about in Chapter 4), we can exploit the resonance-factored form of a filter to perform our subtractive synthesis. The benefits of this are that we can control the resonances (and thus, spectral shape) independently. The filter can be implemented in series or cascade (chain of convolutions) as shown in Figure 8.4. The filter can also be implemented in parallel (separate subband sections of the spectrum added together), as shown in Figure 8.5. 

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