Sigma bond hyperconjugation

Figure 4.5 Carbocation resonance forms and the pi-type orbital overlap that those resonance forms represent. Top Resonance with a lone pair is best. Middle Resonance with a pi bond is next. Bottom sigma bond hyperconjugation is poorest the H, pi bond resonance form is minor.

Hyperconjugation (Section 8.7) A stabilizing interaction of a sigma bonding MO with an empty p orbital on an adjacent atom. 

Over the years we came up with methods to calculate bond dissociation energies, charge distribution in sigma-bonded systems, charge distribution in pi-bonded systems, the inductive effect, the resonance effect, the hyperconjugation effect and the polarisability effect. ... 

Figure 6.7 shows a stylized representation of hyperconjugation between a sigma bonding orbital and an adjacent carbocationp orbital. 

Tertiary carbocations are stabilized because sigma bonds at three adjacent carbons contribute electron density to the carbocation p orbital by hyperconjugation (Section 6.1 IB). Secondary and primary carbocations have less stabilization by hyperconjugation. A methyl carbocation has no stabilization. Formation of a relatively stable carbocation is important in an S l reaction because it means that the free energy of activation for the... 

The tertiary cation is more substituted than the secondary cation and thus is more stable by virtue of hyperconjugative overlap of a sigma bond with the empty 2p orbital (p. 292). Substitution stabilizes the positive charge on carbon in these species. 

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