Radicals, such as the methyl and trimethyl radicals shown above
are very reactive species because they only have one electron in their
2p orbital. Radicals lack electrons in their 2p orbitals, similar to carbocations,
so similar conclusions can be made about the stability of radicals. Like
carbocations, the more substituted the carbon radical, the more stable
it is. In this case the trimethyl radical is more stable than the methyl
radical. This is due to hyperconjugation of the 2p orbital and the carbon-hydrogen
bond of the adjacent carbon atoms.
In carbon radicals, the 2p orbital of the carbon atom lacks an electron but this does not signify that it has charge. The carbon radicals are very reactive for this reason, not because they have charge like the carbocations. The green color on the surfaces of both molecules indicate the neutrality of the molecule.
The diagrams depicting the placement of electrons are shown here. The methyl radical is on the left and the trimethyl radical is on the right. The blue area in both pictures represent the abscence of an electron in the 2p orbital of the carbon atom. However notice how the blue area in the methyl radical is more localized and therefore larger than the blue area in the trimethyl radical. The positive charge in the trimethyl radical is delocalized because the adjacent carbon-hydrogen sigma bonds contribute some of its electron density to the partially empty 2p orbital. This explains why the carbon atoms in the trimethyl radical have less electron density than the carbon atoms in the methyl radical.
Shown here is the allyl radical. The blue color in the diagram on the right does not show areas of positive and negative charge but rather, it indicates areas of unpaired electron density. Using this information, it is evident that the allyl radical is not as stablalized as the trimethyl radical, but nonetheless the allyl radical is highly stabalized. Both molecules are more stable than the methyl radical but for different reasons. The allyl radical can form resonance structures and therefore spread out the unpaired electron density over the two end carbons. Once again, Mother Nature hates localized unpaired electron denstiy, so the allyl radical is relatively more stable than the methyl radical.