Delocalized triplet diradicals

Of the known triplet states, the cross-conjugated non-Kekule diradicals are classified as delocalized triplet diradicals (e.g., 14). In contrast, the radical centers in localized triplet diradicals (e.g., 5-7) are not joined through a n system. For the localized 1,3-diphenyl-substitutcd cyclopentane-1,3-diyl triplet diradicals 6b and c, a planar five-membered ring with coplanar arrangement of the aryl groups is expected to allow the maximum contribution of the benzylic resonance stabilization, which is worth about 50-54 kJ mol 1 [28], For such aryl-substituted triplet diradicals (e.g., 9-12), the magnetic dipole interaction of the two uncoupled spins is given by Eq. (6). 

Hiickel s rule has been abundantly verified [17] notwithstanding the fact that the SHM, when applied without regard to considerations like the Jahn-Teller effect (see above) incorrectly predicts An species like cyclobutadiene to be triplet diradicals. The Hiickel rule also applies to ions for example, the cyclopropenyl system two n electrons, the cyclopropenyl cation, corresponds to n 0. and is strongly aromatic. Other aromatic species are the cyclopentadienyl anion (six n electrons, n = 1 Hiickel predicted the enhanced acidity of cyclopentadiene) and the cyclohep-tatrienyl cation. Only reasonably planar species can be expected to provide the AO overlap need for cyclic electron delocalization and aromaticity, and care is needed in applying the rule. Electron delocalization and aromaticity within the SHM have recently been revisited [43]. 

The theoretical spin densities, calculated by the semiempirical PM 3 method for the heteroaryl-substituted monoradicals 16, confirm the above trend (Fig. 19, D/hc x 100 = 15.4 pApB + 0.9, r2 = 0.928). Consequently, these experimental results demonstrate that electronic substituent effects of heteroaryl groups on radicals are reliably reproduced by the D values in terms of spin delocalization and provide a quantitative measure of heteroaryl conjugation. To compare their propensity to delocalize spin with the phenyl group as reference point, the ADAr parameter [Eq. (21)] is defined for convenience as the difference between the D values of the phenyl (DPh) and the heteroaryl group (DAr) in the triplet diradicals 12. 

The D values in Table 4 display some interesting and remarkable trends in the spin-delocalizing ability of the heteroaryl substituents. The three regio-isomeric pyridyl-substituted triplet diradicals 12g ( — 0.01), 12i ( — 0.05), and 12k (—0.06) delocalize spin worse than the phenyl reference system in the order para > ortho > meta phenyl. Especially in the ortho and para isomers delocalization is definitely less effective than for phenyl. Thus, the pyridyl derivatives act as spin donors by enhancing the spin density at the radical site, although the effects are relatively small. The small effects are mainly due to destabilizing aminyl-type radical structures with unfavorable spin accumulation at the nitrogen atom (Fig. 20) [61]. 

The comparison of the ADAr parameters of the unfunctionalized, pyridyl-substituted triplet diradicals 12g ( — 0.01), 12i ( — 0.04), and 12k ( — 0.06) with the fury] derivatives 12c ( + 0.49) and 12m ( — 0.33) and the thienyl ones 12b ( + 0.61) and 121 ( — 0.12), makes it evident that the five-membered ring heteroaryl substituents interact much more strongly with the radical center. In view of the lower aromatic character of the five- versus the six-membered ring aryl substituents [63], the 6w-electron system of the former is more easily perturbed by spin delocalizing effects. Also the calculated spin densities (px) at the radical sites for the furyl and thienyl derivatives (Table 4) bear out this trend since the changes in px are more pronounced in the five- versus six-membered ring heteraryl substituents. 

As to the electronic effect of the nitrogen atoms adjacent to the benzylic center in the diaza derivative 7d, semiempirical calculations show that only 2% of the a. spin density is delocalized onto the nitrogens of the urazole moiety. Therefore, the urazole-bridged derivatives 7 are localized triplet diradicals and their lower D values (Table 5) derive from the slightly lower spin densities and the somewhat higher interradical distance dAB. The latter is a consequence of angle widening due to the shorter N—N versus C—C distance ( 144 vs. 154 pm [67]). 

The present results clearly establish the D parameter of localized triplet diradicals as a reliable spectral tool to probe for electronic factors that control spin delocalization and radical stabilization in the benzyl-type radicals 14. Equation (8) offers us the opportunity to interpret the experimental results through semiempirical MO calculations in terms of the theoretically accessible a-spin-density variations. The spectroscopic AD scale does not suffer from the limitations (polar vs. radical contributions) inherent in the kinetic chemical scales and provides us with over 40 aryl substituents, which is the most comprehensive collection of electronic effects on radicals. Its extension to heteroaryl-substituted diradicals (12) provides for the first time a quantitative experimental measure of delocalization in aromatic n systems. The salient features of this novel method are... 

Fig. 5a-c Through-bond interactions in the triplet state of 1,3-diradical, a Mechanism of electron delocalization and polarization of a-spin electrons, b Cyclic orbital interaction, c Orbital phase continuity... 

SOMO and SOMO, too. The delocalized spin on the donor site and the localized spin on the radical site in these cation diradicals are oriented in a parallel manner. As will be seen in Chapter 7 (Section 7.4), such a spin orientation results in ferromagnetic coupling (triplet interaction) between the spins. In contrast, an antiparallel type of mutual orientation of the spins results in antiferromagnetic coupling. The parallel type is crucial in the design of organic materials with magnetic properties. 

Aryl cations are highly reactive intermediates with two possible electronic configurations, the singlet and triplet states. The former is a localized cation with a vacant a orbital at the dicoordinated carbon atom, whereas the latter has a diradical character with single occupancy of the g orbital and the charge being delocalized in the... 

Biradical (Synonymous with diradical) An even-electron molecular entity with two (possibly delocalized) radical centres which act nearly independently of each other. Species in which the two radical centres interact significantly are often referred to as biradicaloids. If the two radical centres are located on the same atom, they always interact strongly, and such species are called carbenes, nitrenes, etc. The low-est-energy triplet state of a biradical lies below or at most only a little above its lowest singlet state (usually judged relative to kT, the product of the Boltzmann constant k and the absolute temperature T). The states of those biradicals whose radical centres interact particularly weakly are most easily understood in terms of a pair of local doublets. Theoretical descriptions of low-energy states of a biradical display the presence of two unsaturated valences (biradicals contain one fewer... 

The rate constant of the triplet carbene with a typical quencher such as O2 and 1,4-cyclohexadiene can be employed as a more quantitative measure of the reactivity. However, neither ko nor chd appreciably correlated with the D value (Table 2). Presumably, simple linear correlations with spin delocalization factors may not be expected for the reaction of triplet carbenes (diradicals) to form the corresponding monoradicals since the extents of the delocalization of unpaired electrons should be different between the two states. An additional... 

To a first approximation the energies of these states are the same and it can be shown that the total energy (4j3) is the same as that of two isolated double bonds. In other words, the delocalization energy is zero. Using Hund s rules, it would now appear that the diradical triplet state (IXd)... 

The triplet reaction proceeds through the formation of a cyclopropyl diradical intermediate. The less stabilized diradical center utilizes its odd electron density to open the cyclopropane ring and forms a more stabilized 1,3-diradical intermediate. The new 1,3-diradical intermediate gives the cyclopropane derivative as major product of the reaction. Thus, in a 1,4-diene system, a terminus substituted with aryl groups will cyclize in preference to an unsubstituted or alkyl-substituted terminus because of the greater stability of the diradical intermediate by delocalization with aryl groups. The following example of 43 demonstrated the mechanism of the triplet reaction [40]. 

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