Valence bond structure allyl radical

From bond energies (Table 4-6) we know that the weakest C—H bonds of propene are to the allylic hydrogens, H2C=CHCH2—H. Therefore, in the first step of radical-chain chlorination of propene, an allylic hydrogen is removed by a chlorine atom (Equation 14-1). The allylic C-H bonds are weaker than the alkenic C-H bonds because of the extra stabilization of the radical obtained on hydrogen abstraction (Equation 14-1). Two equivalent valence-bond structures (1a and 1b) can be written for the 2-propenyl radical the electron delocalization enhances the stability of the radical (see Section 6-5C) ... 

The valence bond structures of the doublet allyl radical are more complicated. The transformation properties under orbital permutation of the doublet, covalent Gel fand states are shown below ... 

In terms of the conventional valence-bond structures we employ, it is diflicult to visualize a single structure that is intermediate between the two structures, 1 and II. The orbital approach, on the other hand, gives us a rather clear picture of the allyl radical the density of electrons holding the central carbon to each of the others is intermediate between that of a single bond and that of a double bond. 

A curious effect, prone to appear in near degeneracy situations, is the artifactual symmetry breaking of the electronic wave function [27]. This effect happens when the electronic wave function is unable to reflect the nuclear framework symmetry of the molecule. In principle, an approximate electronic wave function will break symmetry due to the lack of some kind of non-dynamical correlation. A typical example of this case is the allyl radical, which has C2v point group symmetry. If one removes the spatial and spin constraints of its ROHF wave function, a lower energy symmetry broken (Cs) solution is obtained. However, if one performs a simple CASSCF or a SCVB [28] calculation in the valence pi space, the symmetry breaking disappears. On the other hand, from the classical VB point of view, the bonding of the allyl radical is represented as a superposition of two resonant structures. 

Radicals containing nitrogen atoms as 7c-centers are included only when, in terms of valence bond resonance structures, the unpaired electron is not located at nitrogen (e.g. 2-aza-allyl, 3-aza-cyclohexadienyl). 

An analysis of the NBMO of allyl nicely ties together the valence bond concept of resonance (see Chapter 1) with the MO concepts presented in this chapter. The NBMO only has coefficients on the end carbons, meaning that allyl radical does not have radical character on the central carbon at this level of theory. (See, however, the discussion of negative spin density in Section 17.3.2.) This is exactly what the resonance structures for allyl radical tell us. 

Although satisfactory for allyl cation. Figure 10.1 is insufficient for species with more than two tt electrons because the tt orbital in (c) can accommodate only two electrons. Molecular orbital (MO) theory, however, offers an alternative to resonance and valence-bond theory for understanding the structure and reactions of not only allylic cations, but radicals (three rr electrons) and anions (four tt electrons) as well. In a simplification known as the Hiickel, or ir-electron, approximation the tt MOs are considered as separate from... 

---