Allyl radical resonance description

When considering the stability of spin-delocalized radicals the use of isodesmic reaction Eq. 1 presents one further problem, which can be illustrated using the 1-methyl allyl radical 24. The description of this radical through resonance structures 24a and 24b indicates that 24 may formally be considered to either be a methyl-substituted allyl radical or a methylvinyl-substituted methyl radical. While this discussion is rather pointless for a delocalized, resonance-stabilized radical such as 24, there are indeed two options for the localized closed shell reference compound. When selecting 1-butene (25) as the closed shell parent, C - H abstraction at the C3 position leads to 24 with a radical stabilization energy of - 91.3 kj/mol, while C - H abstraction from the Cl position of trans-2-butene (26) generates the same radical with a RSE value of - 79.5 kj/mol (Scheme 6). The difference between these two values (12 kj/mol) reflects nothing else but the stability difference of the two parents 25 and 26. 

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... 

To illustrate the technique we will consider a few examples of free radicals which have been prepared in the rotating cryostat. In particular phenyl and acetyl radicals and methyl-substituted allyl radicals are of interest as they have not been trapped previously or identified with certainty. Since electron spin resonance has been used extensively to detect and identify the free radicals, account of the results will inevitably involve some description and analysis of their spectra, but we wish to focus the main discussion on the conclusions that can be drawn about structure and reactivity of the radicals. For information about the principles of e.s.r. and the interpretation of the spectra of free radicals the reader is referred to review articles and books on the subject (Symons, 1963 Norman and Gilbert, 1967 Maki, 1967 Horsfield, 1967 Carrington and McLachlan, 1967 Ayscough, 1967 Carrington and Luckhurst, 1968). 

The overlap of the p orbitals in both directions, and the resulting participation of each electron in two bonds, is equivalent to our earlier description of the allyl radical as a resonance hybrid of two structures. These two methods of representation, the drawing of several resonance structures and the drawing of an electron cloud, are merely our crude attempts to convey by means of pictures the idea that a given pair of electrons may serve to bind together more than two nuclei. It is this... 

Equation 4.52 can be used to calculate the charge density for each position of the allyl cation, radical, and anion, and the results are shown in Table 4.1. These values are comforting, because they agree with our chemical experience with allylic systems. The resonance description of the allyl cation and radical (Figure 4.13) suggests that exactly half of the charge or unpaired electron density is associated with each of the terminal carbon atoms, and the HMO result is the same. 

An explanation of the stability of the allyl radical can be approached in two ways in terms of molecular orbital theory and in terms of resonance theory (Section 1.8). As we shall see soon, both approaches give us equivalent descriptions of the allyl radical. The molecular orbital approach is easier to visualize, so we shall begin with it. (As preparation for this section, it may help the reader to review the molecular orbital theory given in Sections 1.11 and 1.13.)... 

PROBLEM 12.20 Add electrons to both the resonance and molecular orbital descriptions in Figure 12.47 to form the allyl anion, radical, and cation. 

We first show in Sect. 13.3.1 that the space-based HL-P and energy-based HL-CI methods give comparable results in the description of the resonance of the allylic systems (cation, radical and anion), except for the radical case, where the HL-P method is more reliable as it respects symmetry. 

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