Biradical definition

As seen in the previous section, one characteristic of the triplet state is its paramagnetism. This alone would of course not suffice as a definition of the triplet since there are many odd-electron species that also exhibit paramagnetism but do not exist as triplets. Thus we might state that a triplet is a paramagnetic even-electron species. This still does not constitute a limiting definition since compounds containing even numbers of electrons may exhibit two, three, or even five distinct electronic levels. For example, when in a biradical the radical centers are separated by several carbon atoms as below, no interaction between the electron spins occurs and the radicals appear as two doublet states ... 

Localization of an unpaired electron in the framework of a definite molecular fragment can sometimes lead to the formation of ion-radicals with spatially separated charge and radical sites. They can be considered free radicals with an appended, remote charge. These species form a particular class of distonic ion-radicals. Distonic is from the Greek word diestos and the Latin word distans, both meaning separate. Yates et al. (1984) introduced this term for ions that formally arise by the removal of an electron from a zwitterion or a biradical. 

The calculations showed an apparent preference for the inversion of configuration in the reaction, for which the PES had a very distinct local minimum corresponding to a biradical. It was suggested that an experimental observation of a preference for inversion of configuration at the migrating carbon should not be taken as definitive evidence against a biradical mechanism. The dynamics effect may make mechanistic discussion by means of product analyses less straightforward. 

These three different types of natural isomers are present in the respective percentages of 99.76%, 0.04%, and 0.2%. Despite this difference in the number of nucleons, the number of electrons (e ) rotating around the nucleus is always eight, The e rotates in five different orbitals represented as IS, 2S, and 2Pz that each contain a couple of e", and as 2PX and 2Py that each contain one e only, Since every element that has a single e (unpaired) in an orbital is defined as a free radical, O by definition is a biradical,... 

If we use the definition that an intermediate is a distinct chemical species, detectable or inferential, along the reaction profile between reactant and isolated product, then the biradical has intellectual validity as well as predictive capabilities. 

From this state, ring strain facilitated predissociation to a "biradical-like" transition state [135] or vibrational relaxation (k ) to S may occur. It is also conceivable that transition state [135] could be produced directly from S °. Alternatively, molecules in the S ° state could intersystem cross (kST) to the triplet manifold (T ). For 2-alkylidenecyclobutanones, reactivity is manifested in isomerization about the exocyclic carbon-carbon double bond, while for the saturated cyclobutanone derivatives studied, definitive evidence for solution-phase reactivity is not available. If analogy is again made to the vapor-phase photochemistry of cyclobutanone [21], reactivity could conceivably result in decarbonylated products. Indeed, preliminary evidence has been obtained from sensitization experiments employing m-xylene as triplet sensitizer that decarbonylation of a saturated cyclobutanone is enhanced by selective population of its state (35). ... 

The postulation that the "biradical-like" transition state [135] (and not a freely rotating acyl alkyl biradical intermediate) is the precursor of the oxacarbene intermediate [136] is made primarily to accomodate the fact that the ring-expansion reaction is stereoselective. Transition state [135] could also decay by S-cleavage and/or decarbonylation [both stereospecific (23), although definitive evidence concerning this point is not available in the solution phase. Finally [135] could decompose back to the starting cyclobutanone, which would explain the observed lack of efficiency in the previously described photolyses. (See Section II.E for a further discussion of this point.)... 

A second obvious problem with the ordinary definition of adiabatic reactions is the vagueness of the term product. If the product is what is actually isolated from a reaction flask at the end, few reactions are adiabatic. (Cf. Example 6.7.) If the product Is the first thermally equilibrated species that could in principle be isolated at sufficiently low temperature, many more can be considered adiabatic. A triplet Norrish II reaction is diabatic if an enol and an olefin are considered as products. It would have to be considered adiabatic, however, if the triplet 1,4-biradical, which might easily be observed, were considered the primary photochemical product. (See Section 7.3.2.)... 

Others have reported that there is a definite effect of aryl substituents and that the derivative 39 undergoes cyclization in the presence of dissolved oxygen to yield the hydroxyflavone 40. The cyclization involves the formation of a biradical 41 that cyclizes in the presence of oxygen to yield the hydroxyflavone 42. The cyclization of such chalcones has been known for many years and studied in some detail . Research showed that the derivatives 43 undergo efficient cyclization to 44 (Scheme 4) on irradiation at wavelengths >365 nm in dioxan or ethyl acetate solution . The reaction is solvent-dependent and poorer yields are obtained in benzene or chloroform solution . Further studies demonstrated, for the conversions shown in Scheme 5, that the cyclizations probably arose from a 7171 transition . ... 

Benzophenone is the most important representative of this class of compound. A benzophenone molecule is excited by an absorbed light quantum to the triplet state [Refs. 60,116, 483, 624]. In the triplet state the spins of two electrons of the carbonyl group are parallel, which is similar to a biradical [257]. In the excited triplet state the unpaired electrons, however, belong to a definite energetic state of a molecule, whereas in a biradical they are ascribed to determined atoms or fragments of a molecule [399, 408, 409]. 

These reactions proceed by initial ozone attack on the C = C bond of the olefin. An intermediate ozonide is formed, which rapidly decomposes to a carbonyl and a biradical. The biradical can be stabilized, or it can decompose. Paulson et al. (1991b) found the products methacrolein, methyl vinyl ketone, and propene, in yields of 68%, 25%, and 7%, respectively. Based on the presence of epoxides in the ozone/isoprene system, Paulson et al. concluded that 0(3P) was being formed. Calculations indicated that 0.45 0(3P) radicals were formed for every ozone/isoprene reaction. However, Atkinson et al. (1993) recently showed that the epoxides were formed directly from the reaction with ozone rather than the reaction with 0(3P). The epoxides formed were l,2-epoxy-2-methy 1-3-butene and l,2-epoxy-3-methyl-3-butene, in yields of 0.028 and 0.011, respectively. There was also definite evidence for the formation of OH radicals in the ozone system, thus causing difficulties in product analyses. Each ozone/isoprene reaction yielded 0.68 OH radicals (Paulson et al., 1991b). 

Generation of a radical pair or biradical in a definite electron spin state. This has already been expounded on in Section II.A, item 1. 

According to this interpretation, the vinyl double bonds of two styrene molecules can react /3, jS or The biradical (la) definitely does not start any... 

Ultimately, these experimental studies cannot completely rule out biradical intermediates in the Cope rearrangement, especially for the heavily substituted systems. In the end, only theory can make a definitive statement about the structure of a transition state. The interplay between theory and experiment in the Cope rearrangement and other pericyclic processes has at times been contentious. In addition, differing theoretical models have often made diametrically opposed predictions (see the Going Deeper highlight on page 900). This further fueled the debate over the true nature of pericyclic transition states. 

Research into spin dynamics is presented in numerous papers devoted to the definition of the range of values of in biradicals. This approach also allows an estimate to be made of the range of values in radical ion pairs. 

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