Interaction diagrams radical stabilization

The ethane molecule can be constructed by union of two pyramidal methyl radical fragments. The interaction diagram is shown in Fig. 16 and the key stabilizing orbital interactions are depicted below. 

The most common and also most effective mechanism of radical stabilization involves the resonant delocalization of the unpaired spin into an adjacent 7r system, the allyl radical being the prototype case. A minimal orbital interaction diagram describing this type of stabilization mechanism involves the unpaired electron located in a 7r-type orbital at the formal radical center and the 7r- and tt -orbitals of the n system (Scheme 1). 

Structures. The methyl radical is planar and has D symmetry. Probably all other carbon-centerd free radicals with alkyl or heteroatom substituents are best described as shallow pyramids, driven by the necessity to stabilize the SOMO by hybridization or to align the SOMO for more efficient pi-type overlap with adjacent bonds. The planarity of the methyl radical has been attributed to steric repulsion between the H atoms [138]. The C center may be treated as planar for the purpose of constructing orbital interaction diagrams. 

Fig. 1. HOMO - LUMO interaction diagram for MR3 radicals. (A) Interaction of a singly occupied p orbital (HOMO) with the a (LUMO) of planar MR3 that results in stabilization of the HOMO on pyramidalization. (B) Superposition of the HOMO and LUMO from (A). Arrows show the distortion that results in a stabilizing interaction.

In cyclopropenylidene m=n=0) the highest occupied polyene radical (S) has the correct symmetry for interaction with the px orbital (S). Mixing of these orbitals leads to two new orbitals of different energy px is destabilized, and a is stabilized by bending, which reinforces the splitting of the a and the delocalized p level. This is shown in the interaction diagram for cyclopropenylidene (7). 

Essentially Flat Structure Bond Dissociation Energies Radical Stabilities Conjugation Stabilizes Best, Substitution Stabilizes Slightly Interaction Diagrams for Radical Species (Supplementary)... 

Similarly, orbital interaction diagrams can also explain the stabilization of a radical center by a pi donor (Fig. 11.3fc). The pi donor has an accessible full orbital, HOMO, close in energy to the orbital bearing the single electron, SOMO. The interaction of the SOMO with a full HOMO destabilizes one electron and stabilizes two for a net stabilization of one electron overall. We have created a pi bond with one electron in the antibonding orbital the pi bond order is thus half (our resonance structures were unable to indicate this partial pi bond with lines and dots). 

PROBLEM 6.3 Draw an interaction diagram to show the stabilization when two methyl radicals combine. How great is that stabilization For an example of an interaction diagram see Rgure 1.39, p. 33. 

Figure 4 Orbital interaction diagrams showing the stabilizing interaction between an unpaired electron and (a) a n acceptor substituent, and (b) a lone-pair donor substituent. From Bernard , F. Epiotis, N. D. Cherry, W., etal. J. Am. Chem. Soc. 1976, 98,469-478 Henry, D. J. Partdnson, C. J. Mayer, P. M. Radom, L. J. Phys. Chem. A 2001, 105, 6750-67564 Coote, M. L. Lin, C. Y. Zipse, H. In Carbon-Centered Free Radicals Structure, Dynamics and Reactivity, M. D. E. Forbes, Ed. Wiley, 2010 pp. 83-104 Hioe, J. Zipse, H. Org. Biomol. C/tem. 2010,8,3609-3617 Poutsma, M. L. J. Org. Chem. 2011, 76, 270-276. ...

As with all molecules, it is the energy of the electrons in the molecular orbitals of the radical that dictate its stability. Any interaction that can decrease the energy levels of the filled molecular orbitals increases the stability of the radical (in other words, decreases its reactivity). Before we use this energy level diagram of the methyl radical to explain the stability of radicals, we need to look at some experimental data that allow us to judge just how stable different radicals are. 

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