Systems 1 Biradicals

In some well-known transformations involving inorganic ring systems, biradicals act as reaction intermediates that are sufficiently persistent to be detected by EPR spectroscopy (see Section 3.6). For example, the polymerisation of cyclo-Sg to form the helical sulfur polymer Soo (plastic sulfur) occurs via the... 

Forbes M D E 1993 The effect of n-system spacers on exchange couplings and end-to-end encounter rates in flexible biradicals J. Phys. Chem. 97 3396-400... 

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. 

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... 

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. 

Four-membered heterocycles are easily formed via [2-I-2] cycloaddition reac tions [65] These cycloaddmon reactions normally represent multistep processes with dipolar or biradical intermediates The fact that heterocumulenes, like isocyanates, react with electron-deficient C=X systems is well-known [116] Via this route, (1 lactones are formed on addition of ketene derivatives to hexafluoroacetone [117, 118] The presence of a trifluoromethyl group adjacent to the C=N bond in quinoxalines, 1,4-benzoxazin-2-ones, l,2,4-triazm-5-ones, and l,2,4-tnazin-3,5-diones accelerates [2-I-2] photocycloaddition processes with ketenes and allenes [106] to yield the corresponding azetidine derivatives Starting from olefins, fluonnaied oxetanes are formed thermally and photochemically [119, 120] The reaction of 5//-l,2-azaphospholes with fluonnated ketones leads to [2-i-2j cycloadducts [121] (equation 27)... 

An alternative approach to stabilizing the metallic state involves p-type doping. For example, partial oxidation of neutral dithiadiazolyl radicals with iodine or bromine will remove some electrons from the half-filled level. Consistently, doping of biradical systems with halogens can lead to remarkable increases in conductivity and several iodine charge transfer salts exhibiting metallic behaviour at room temperature have been reported. However, these doped materials become semiconductors or even insulators at low temperatures. 

The parameterization of MNDO/AM1/PM3 is performed by adjusting the constants involved in the different methods so that the results of HF calculations fit experimental data as closely as possible. This is in a sense wrong. We know that the HF method cannot give the correct result, even in the limit of an infinite basis set and without approximations. The HF results lack electron correlation, as will be discussed in Chapter 4, but the experimental data of course include such effects. This may be viewed as an advantage, the electron correlation effects are implicitly taken into account in the parameterization, and we need not perform complicated calculations to improve deficiencies in fhe HF procedure. However, it becomes problematic when the HF wave function cannot describe the system even qualitatively correctly, as for example with biradicals and excited states. Additional flexibility can be introduced in the trial wave function by adding more Slater determinants, for example by means of a Cl procedure (see Chapter 4 for details). But electron cori elation is then taken into account twice, once in the parameterization at the HF level, and once explicitly by the Cl calculation. 

By including electron correlation in the wave function the UHF method introduces more biradical character into the wave function than RHF. The spin contamination part is also purely biradical in nature, i.e. a UHF treatment in general will overestimate the biradical character. Most singlet states are well described by a closed-shell wave function near the equilibrium geometry, and in those cases it is not possible to generate a UHF solution which has a lower energy than the RHF. There are systems, however, for which this does not hold. An example is the ozone molecule, where two types of resonance structure can be drawn. Figure 4.8. 

The biradical resonance structure for ozone requires two singly occupied MOs, and it is clear that an RHF type wave function, which requires all orbitals to be doubly occupied, cannot describe this. A UHF type wave function, however, allows the a and /3 orbitals to be spatially different, and can to a certain extent incorporate both resonance structures. Systems with biradical character will often have a (singlet) UHF wave function different from an RHF. 

It should be noted that CASSCF methods inherently tend to give an unbalanced description, since all the electron correlation recovered is in die active space, but none in the inactive space, or between the active and inactive electrons. This is not a problem if all the valence electrons are included in the active space, but this is only possible for small systems. If only part of die valence electrons are included in the active space, the CASSCF methods tend to overestimate the importance of biradical structures. Consider for example acetylene where the hydrogens have been bent 60° away from hnearity (this may be considered a model for ort/zo-benzyne). The in-plane jt-orbital now acquires significant biradical character. The true structure may be described as a hnear combination of the three configurations shown in Figure 4.11. 

The structure on the left is biradical, while the two others are ionic, corresponding to both electrons being at the same carbon. The simplest CASSCF wave function which qualitatively can describe this system has two electrons in two orbitals, giving the three configurations shown above. The dynamical correlation between die two active electrons will tend to keep them as far apart as possible, i.e. favouring the biradical structure. Now... 

When pyrrole is irradiated, only decomposition products were obtained. Theoretical data can fit this statement (Fig. 6). In fact, the direct irradiation populates the excited singlet state, which can be converted into the Dewar pyrrole or into the corresponding triplet state. Clearly, the intersystem crossing to the triplet state allows the system to reach the lowest energy state. The excited triplet state can give the biradical intermediate, and this intermediate can give either the decomposition... 

A number of diradicals (also called biradicals) are known. When the unpaired electrons of a diradical are widely separated (e.g., as in CH2CH2CH2CH2 ), the species behaves spectrally like two doublets. When they are close enough for interaction or can interact through an unsaturated system (as in trimethylene-methane, " they... 

Scheme 30 represents the energy diagram for the photorearrangement shown in Scheme 29. Quenching of the triplet state of the sensitizer by the cis allyl phosphate, c/s-1, generates the triplet state, T , of the 1,2-biradical 2. The 1,2-biradical is trapped by the phosphorus atom to afford the triplet state, TP, of the spirophosphoranyl 1,3-biradical 3. Then, inter-system crossing generates the...

The reason for this behavior can be seen in the structure of the intermediate biradical. The rigidity of the cyclobutyl ring prevents a parallel alignment of the p orbitals with the 0 bond, which is held practically perpendicular. In order for type II cleavage to occur, an initially severely strained olefin must be formed. Hence radical recombination to yield the bicyclopentane system predominates. 

Interestingly enough, some biradical character has been observed in systems similar to (136) even when there are no bulky chlorine atoms present to inhibit delocalisation sterically. Thus with the system (138) = (139),... 

We have also examined the behavior of copolymers of o-tolyl vinyl ketone and methyl vinyl ketone (CoMT). In this case the light is absorbed exclusively at the aromatic carbonyl chromophore and the reaction proceeds from this site, while the methyl vinyl ketone moieties provide a relatively constant environment but prevent energy migration along the chain. The values of Tg and Tip in benzene have been included in Table II. These copolymers axe also soluble in some polar solvents for example, we have used a mixture of acetonitrile acetone methanol (30 30 Uo, referred to as AAM). This mixture is also a good solvent for the electron acceptor paraquat (PQ++) which has been shown to be good biradical trap in a number of other systems (9.). 

---