1.6- Biradicals

This section is intended to provide the organic chemist with relatively simple guidelines, rational structure reactivity relationships and rules-of-thumb to predict the reactivity of biradicals and their response to changes in manageable parameters such as temperature, solvent polarity and magnetic fields. The same considerations hold, mutatis mutandis, for carbenes and nitrenes. 

3 singlet states 1 covalent singlet state 2 zwitterionic 

A distinction is made between conjugated Kekule biradicals such as 3, for which at least one Kekule structure can be drawn, and non-Kekule biradicals such as 

Another important classification of conjugated diradicals depends on whether their Hiickel NBMOs can or cannot be confined to a disjoint sets of atoms.446 As discussed in 

10 kJ mol 1 and that of 21 (triplet ground state) about + 5 kJ mol 1. Although 321 is more extended, its first absorption band lies at much shorter wavelength than that of 20. The saturated singlet carbene adamantylidene exhibits a broad, weak absorption band at 620 nm.398 

If the radical centers are close enough to each other for significant interaction (usually in the case of small molecules) there will be a splitting into singlet and triplet states, just as in the case of carbenes. The two p orbitals of the radical centers 

The photochemistry of cyclopentanone (29) is characterized in terms of disproportionation versus decarbonylation and/or cyclization versus cleavage reactions. The proposed mechanism involves electronic excitation of the ketone 29 followed by intersystem crossing (ISC) and an a-cleavage reaction in the triplet state 

A biradical mechanism is also proposed for the formation of certain biomolecules found in marine sporolides that have a chlorobenzene unit as part of their structure. In this mechanism a halide salt provides the halogen. A model reaction with the 

Radicals (often referred to as free radicals) are atoms, molecules, or ions with unpaired electrons or an open shell. 

The frontier orbital of a free radical is called the singly occupied molecular orbital. Anything that would stabilize an anion or a cation will stabilize a radical. Radicals are also stabilized by resonance and by interaction with either filled or empty orbitals. 

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Wliile the earliest TR-CIDNP work focused on radical pairs, biradicals soon became a focus of study. Biradicals are of interest because the exchange interaction between the unpaired electrons is present tliroiighoiit the biradical lifetime and, consequently, the spin physics and chemical reactivity of biradicals are markedly different from radical pairs. Work by Morozova et al [28] on polymethylene biradicals is a fiirther example of how this method can be used to separate net and multiplet effects based on time scale [28]. Figure Bl.16.11 shows how the cyclic precursor, 2,12-dihydroxy-2,12-dimethylcyclododecanone, cleaves upon 308 mn irradiation to fonn an acyl-ketyl biradical, which will be referred to as the primary biradical since it is fonned directly from the cyclic precursor. The acyl-ketyl primary biradical decarbonylates rapidly k Q > 5 x... 

Figure Bl.16.11. Biradical and product fonnation following photolysis of 2,12-dihydroxy-2,12-dimethylcyclododecanone. Reprinted from [28].

Closs G L, Miller R J and Redwine O D 1985 Time-resolved CIDNP applications to radical and biradical chemistry Acc. Chem. Res. 18 196-202... 

Closs G L and Redwine O D 1985 Direct measurements of rate differences among nuclear spin sublevels in reactions of biradicals J. Am. Chem. Soc. 107 6131-3... 

Morozova O B, Tsentalovich Y P, Yurkovskaya A V and Sagdeev R Z 1998 Consecutive biradicals during the photolysis of 2,12-dihydroxy-2,12-dimethylcyclododecanone low- and high-field chemically induced dynamic nuclear polarizations (CIDNP) study J. Rhys. Chem. A 102 3492-7... 

Closs G L and Forbes M D E 1991 EPR spectroscopy of electron spin polarized biradicals in liquid solutions. Technique, spectral simulation, scope and limitations J. Phys. Chem. 95 1924-33... 

Avdievich N I and Forbes M D E 1995 Dynamic effects in spin-correlated radical pair theory J modulation and a new look at the phenomenon of alternating line widths in the EPR spectra of flexible biradicals J. Phys. Chem. 99 9660-7... 

Forbes M D E, Avdievich N I, Schulz G R and Ball J D 1996 Chain dynamics cause the disappearance of spin-correlated radical pair polarization in flexible biradicals J. Phys. Chem. 100 13 887-91... 

Forbes M D E, Closs G L, Calle P and Gautam P 1993 The temperature dependence of the exchange coupling in polymethylene biradicals. Conclusions regarding the mechanism of the coupling J. Phys. Chem. 97 3384-9... 

One can note some interesting features from these trajectories. For example, the Mulliken population on the participating atoms in Figure 1 show that the departing deuterium canies a full electron. Also, the deuterium transferred to the NHj undergoes an initial substantial bond stretch with the up spin and down spin populations separating so that the system temporarily looks like a biradical before it settles into a normal closed-shell behavior. 

An anchor, as defined above, contains stable molecules, conformers, all pairs of radicals and biradicals formed by a simple bond fission in which no spin re-pairing took place, ionic species, and so on. Figure 1 shows some examples of species belonging to the same anchor. Thus, an anchor is a more general and convenient temi used in the discussion of spin re-pairing. 

Assuming that the cis isomer is the reactant, the bans isomer product is expected to be accompanied by others arising from secondary reactions of the biradical, as observed experimentally [58]. 

THE cvcLOBUTADENE-TETRAHEDRANE SYSTEM. A related reaction is the photoisomerization of cyclobutadiene (CBD). It was found that unsubstituted CBD does not react in an argon matrix upon irradiation, while the tri-butyl substituted derivative forms the corresponding tetrahedrane [86,87]. These results may be understood on the basis of a conical intersection enclosed by the loop shown in Figure 37. The analogy with the butadiene loop (Fig. 13) is obvious. The two CBDs and the biradical shown in the figure are the three anchors in this system. With small substituents, the two lobes containing the lone electrons can be far... 

The energies of this Cl and of the other ones calculated in this work are listed in Table III. The calculated CASSCF values of the energies of the two lowest electronically states are 9.0 eV (5i, vertical) and 10.3 eV ( 2, vertical) [99]. They are considerably higher than the expenmental ones, as noted for this method by other workers [65]. In all cases, the computed conical intersections lie at much lower energies than the excited state, and are easily accessible upon excitation to Si. In the case of the H/allyl Cl, the validity confirmation process recovered the CHDN and 1,3-CHDN anchors. An attempt to approach the third anchor [BCE(I)] resulted instead in a biradical, shown in Figure 43. The bhadical may be regarded as a resonance hybrid of two allyl-type biradicals. 

Molecules 1,4-CHDN 1,3-CHDN BCE benzene -I- H2 BCE/allyl biradical... 

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

The concept of biradicals and biradicaloids was often used in attempts to account for the mechanism of photochemical reactions [2,20,129-131]. A biradical (or diradical) may be defined as [132] an even-electron molecule that has one bond less than the number permitted by the standard rules of valence. 

The biradical model suggests a connection between the single coordinate model, emphasizing reactions on a single energy surface, and the two-coordinate model, in which the coupling between states is important. 

Scheme 1.2. Schemetical representation of a zwitterionic and a biradical pathway of a Diels-Alder reaction.

For singlet spin molecules at the equilibrium geometry, RHF and UHF wave functions are almost always identical. RHF wave functions are used for singlets because the calculation takes less CPU time. In a few rare cases, a singlet molecule has biradical resonance structures and UHF will give a better description of the molecule (i.e., ozone). 

The problem of the synthesis of highly substituted olefins from ketones according to this principle was solved by D.H.R. Barton. The ketones are first connected to azines by hydrazine and secondly treated with hydrogen sulfide to yield 1,3,4-thiadiazolidines. In this heterocycle the substituents of the prospective olefin are too far from each other to produce problems. Mild oxidation of the hydrazine nitrogens produces d -l,3,4-thiadiazolines. The decisive step of carbon-carbon bond formation is achieved in a thermal reaction a nitrogen molecule is cleaved off and the biradical formed recombines immediately since its two reactive centers are hold together by the sulfur atom. The thiirane (episulfide) can be finally desulfurized by phosphines or phosphites, and the desired olefin is formed. With very large substituents the 1,3,4-thiadiazolidines do not form with hydrazine. In such cases, however, direct thiadiazoline formation from thiones and diazo compounds is often possible, or a thermal reaction between alkylideneazinophosphoranes and thiones may be successful (D.H.R. Barton, 1972, 1974, 1975). 

Closed-shell molecules have a multiplicity of one (a singlet). Arad-ical, with one unpaired electron, has a multiplicity of two (a doublet). A molecular system with two unpaired electrons (usually a triplet) has a multiplicity of three. In some cases, however, such as a biradical, two unpaired electrons may also be a singlet. 

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