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Show the HOMO for the radical

Hyperconjugation is the sharing of electrons in sigma bonds with a partially filled or empty orbital on carbon. We can (carefully!) use our understanding of resonance structures and their significance to illustrate this, but a look at the HOMO in an MO treatment illustrates it nicely. The majority of the singly-occupied MO lies in a p orbital on carbon. However, there is participation from the C-H bonds on adjacent methyl groups; this participation results in partially meeting carbon's need to attain a complete octet--the price for a single electron gets shared out among the C-H bonds.

The more alkyl groups the more this occurs, and the more stable the radical (see BDE tables).

Note the distinction with conjugation in allylic and benzylic systems, which is a stronger effect arising from p-p interactions in π systems.