Ground state allyl radicals

Similarly to the triphenylmethyl system, captodative-substituted 1,5-hexa-dienes, which can be cleaved thermally in solution into the corresponding substituted allyl radicals [15], dissociate more easily than dicaptor-substituted systems (Van Hoecke et al., 1986). Since ground-state and radical substituent effects cannot be separated cleanly, not only because of electronic but also because of steric effects, a conclusive answer cannot be provided. 

Stabilizing resonances also occur in other systems. Some well-known ones are the allyl radical and square cyclobutadiene. It has been shown that in these cases, the ground-state wave function is constructed from the out-of-phase combination of the two components [24,30]. In Section HI, it is shown that this is also a necessary result of Pauli s principle and the permutational symmetry of the polyelectronic wave function When the number of electron pairs exchanged in a two-state system is even, the ground state is the out-of-phase combination [28]. Three electrons may be considered as two electron pairs, one of which is half-populated. When both electron pahs are fully populated, an antiaromatic system arises ("Section HI). 

Alkyl derivatives of 1,3-butadiene usually undergo photosensitized Z-E isomerism when photosensitizers that can supply at least 60 kcal/mol are used. Two conformers of the diene, the s-Z and s-E, exist in equilibrium, so there are two nonidentical ground states from which excitation can occur. Two triplet excited states that do not readily interconvert are derived from the s-E and s-Z conformers. Theoretical calculations suggest that at their energy minimum the excited states of conjugated dienes can be described as an alkyl radical and an orthogonal allyl system called an allylmethylene diradical ... 

Photolysis of vinyldiazomethane in an organic glass at 6 K leads to vinylcarbene in its triplet ground state,14,56,57 which — as is indicated by the ESR spectra — forms a pair of the s-cis and s-trans isomer. The delocalization of one unpaired electron in the rr-system is similar to that of the allyl radical, while the other unpaired electron is localized in a sp2-orbital at the carbenic C atom (see formula T-33 ).58... 

Stabilized allyl radical will be stabilized further if substituents are introduced. This stabilization occurs to different degrees in the ground state and the transition structure for rotation. In the ground state the substituent acts on a delocalized radical. Its influence on this state should be smaller than in the transition structure, where it acts on a localized radical. In the transition state the double bond and the atom with the unpaired electron are decoupled, i.e. in the simple Hiickel molecular orbital picture, the electron is localized in an orbital perpendicular to the jt(- c bond. 

Table 1. Distortion energies (kcal/mol) of allyl radical and benzene in their ground states, and in their high spin states with all tc electrons having parallel spins. The distortion transforms a regular geometry into an alternated one, as in Fig. 1...

The values of AE , as directly computed in the ground states via the ct-ji partition of Eq. (1), confirm the previous conclusions arising from considerations of the high spin states A localizing distortion leading to an alternated geometry of Kekule type stabilizes the n bonds of benzene by 9.1-9.7 kcal/mol, and those of allyl radical by 0.9 kcal/mol. 

The spin density distribution in the 2A2 excited state requires the derivation of all the contributing determinants as done for allyl radical. A full treatment is given in Exercise 8.5, while here we provide an approximate description. Already at the outset one can recall that the coefficient of the QC determinant in the excited state s wave function is zero, and we therefore expect very different spin density distribution than in the ground state. To proceed, we first express the resonance structures as products of the bonds and the odd electron. Thus... 

As the MSADs have the largest coefficients in the ground-state wave function, one may expect that for alternant free radicals or polyradicals, the dominant positive spin density will be largest on the atoms that bear an alpha spin in the MSAD. An example that was analyzed in Chapter 7 is the allyl radical, where the MSAD predicts positive spin densities at positions 1, 3 and a negative density at position 2. Similarly, the MSAD of benzyl radical predicts positive spin densities on the benzylic carbon and on the ortho and para positions. 

Write the Heisenberg Hamiltonian of allyl radical and diagonalize it. Then write the wave functions for the ground and first neutral excited state. Show that the excited state has a positive a spin density on the central atom, as discussed in Chapter 1. 

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