Radical reaction equations

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. 

By examining the expression for Q ( equation (B1.16.4)). it should now be clear that the nuclear spin state influences the difference in precessional frequencies and, ultimately, the likelihood of intersystem crossing, tlnough the hyperfme tenn. It is this influence of nuclear spin states on electronic intersystem crossing which will eventually lead to non-equilibrium distributions of nuclear spin states, i.e. spin polarization, in the products of radical reactions, as we shall see below. 

With the introduction of Gear s algorithm (25) for integration of stiff differential equations, the complete set of continuity equations describing the evolution of radical and molecular species can be solved even with a personal computer. Many models incorporating radical reactions have been pubHshed. 

Stannanes also add across double bonds offiuonnated olefins in a free radical reaction Trimethylstannane undergoes stereospecific addition to hexafluorocyclo-butene to afford trans 1,2,3,3,4,4 hexafluoro 1 (trimethylstannyl)cyclobutane [5] (equation 1)... 

The course of each of the free radical reactions shown in equations 19-21, where fluorine substitution alters the normal trans stereochemistry of addition, is ascnbed to endo fluonne stenc effects... 

The free-radical reaction may be equally initiated by photoactivated sulfur dioxide (3S02)442 (equation 79). On the other hand, polysulfones are obtained by radical copolymerization of appropriate olefins with sulfur dioxide443-449, and similarly, uptake of sulfur dioxide by a radical-pair formed by nitrogen extrusion from an azo compound yields the corresponding sulfone450 (equation 80). Correspondingly, alkylbenzenes, dibenzoyl peroxide, and sulfur dioxide yield sulfones under thermal conditions451... 

Beside these free radical reactions of sulfur dioxide, its electrophilic reactions generating sulfinates with organometallic compounds453,454 or sulfinic acids with arenes under Friedel-Crafts conditions455 are well known. To complete these three-component syntheses, the sulfinates prepared first are transformed to sulfones by reactions with appropriate electrophiles, discussed earlier in this chapter, i.e. equation 82. 

Se-phenyl areneselenosulfonates (24) undergo facile free-radical addition to alkenes to produce / -phenylseleno sulfones (25) in excellent yield86,87 (see Scheme 7). The addition occurs regiospecifically and affords anti-Markovnikov products contrary to the analogous boron trifluoride catalyzed reaction which produces exclusively Markovnikov and highly stereospecific products86 (equation 37). Reaction 36 has been shown to have the radical... 

Our treatment of chain reactions has been confined to relatively simple situations where the number of participating species and their possible reactions have been sharply bounded. Most free-radical reactions of industrial importance involve many more species. The set of possible reactions is unbounded in polymerizations, and it is perhaps bounded but very large in processes such as naptha cracking and combustion. Perhaps the elementary reactions can be postulated, but the rate constants are generally unknown. The quasi-steady hypothesis provides a functional form for the rate equations that can be used to fit experimental data. 

In its original form the Hammett equation was appropriate for use with para and meta substituted compounds where the reaction site is separated from the aromatic group by a nonconjugating side chain. Although there have been several extensions and modifications that permit the use of the Hammett equation beyond these limitations, it is not appropriate for use with ortho substituted compounds, since steric effects are likely to be significant with such species. The results obtained using free radical reactions are often poor, and the correlation is more appropriate for use with ionic reactions. For a detailed discussion of the Hammett equation and its extensions, consult the texts by Hammett (37), Amis and Hinton (12), and Johnson (47). 

In a direct comparison of the reactivity of 1-alkyl- and 2-alkylbenzotriazoles, compound 393 was lithiated in the presence of benzophenone with 1 equiv of LDA to give a mixture of alcohol 394 and dimer 395 (Equation 12) <1996LA745>. No reaction was detected at the carbon adjacent to the benzotriazol-l-yl moiety. When benzaldehyde was used instead of benzophenone, only dimer 395 was obtained. This suggests that a-benzotriazol-2-yl carbon radical reactions are much faster than those of a-benzotriazol-l-yl) carbanions. 

Opeida proposed the following empirical equation for the rate constant of the peroxyl radical reaction with C—H bonds of alkylaromatic hydrocarbons [34] ... 

Opeida [46] compared the values of the rate constants of peroxyl radical reactions with hydrocarbons with the BDE of the oxidized hydrocarbon, electron affinity of peroxyl radical, EA(R02 ) ionization potential of hydrocarbon (/Rn), and steric hindrance of a-substituent R(Fr). They had drawn out the following empirical equation ... 

Several empirical correlations are known for rate constants and activation energies of bimo-lecular radical reactions [1 4], Evans and Polyany [5] were the first to derive the linear correlation between the activation energy and the enthalpy of reaction of R,X with Na. Later Semenov [1] generalized this empirical equation for different free radical reactions in the following form ... 

Rate Constants and Activation Energies of Ethylmethylperoxyl Radical Reactions with C—H Bonds of Organic Compounds (See Equations (6.7), (6.8), (6.12), and Parameters in Table 6.1 and Table 6.2)... 

Geometrical Parameters of Transition State of Peroxyl Radical Reactions with Ethers (Equations [6.35]—[6.38])... 

The Values of AH, E, AEH, and Geometric Parameters of Secondary Alkylperoxyl Radicals Reactions with Phenols, Calculated by IPM Method (Equations (15.3)-(15.6))... 

According to these parameters, the activation energy of the peroxyl radical reaction with aromatic amine can be calculated using the reaction enthalpy by the equation [54]... 

The empirical correlation equation for re as a function of the bond dissociation energy Z>xy. difference in electronegativity AEAxy f°r the radical reaction abstraction of the type... 

The corresponding reaction with PlnSnM proceeds with complete inversion regardless of addition mode (equation 21). In this case, radical reactions appear unimportant. Displacement of the tosylate by a trimethyltin cuprate was also found to take place by inversion. 

Optically active iV-unprotected-2-pyrrolidinones 194 were obtained from selenocarboxylate or allylamine via radical cyclization and subsequent one-step cleavage of the C-O and C-N bond of the inseparable mixture of the two bicyclic oxyoxazolidinones 192 and 193 with -Bu4NF. The initial radical reaction is highly stereoselective. Products were obtained with ee up to 90%. The mandelic acid 195, which served as the chiral auxiliary in this method, was recovered with no loss of optical activity (Equation 33) <2003T6291>. 

Oxidative radical cyclization of fi-keto esters. Radical cyclizations of unsaturated 0-keto esters initiated by Mn(III) acetate (1) can be terminated by oxidative 0-hydride elimination by Cu(OAc)2 (equation I). This radical reaction can... 

A further conclusion, useful in the case of free radical reactions arises from the fact that in equation (38) is analytically zero, and that consequently, to second order. 

The properties of the minors of the secular determinant of an alternant hydrocarbon may again be used to show that the integrals for which the index is even in (44) and odd in (45) and (46) are zero. It follows that the finite change Aq is an odd function, of Sa, while AFg and Apgt are even. Any inequalities between values of any index for two different positions u), as defined in equations (31) to (34) which arise as first terms of the corresponding infinite series in (44) to (46), persist term-by-term in the expression for the exact finite changes (Baba, 1957). In consequence, the broad agreement with experiment found earlier in the description of ionic and radical reactions by the approximate method carries over to the exact form. 

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