Stability Factors: Carbanions & Free Radicals

1. Stability of Free Radicals

A free radical is a neutral species containing an atom with an unpaired electron. Carbon radicals, like carbocations, do not have a complete octet of electrons, making them electron-deficient and reactive. Because of this electron deficiency, factors that donate electron density will stabilize a free radical.

1.1 Inductive Effect and Hyperconjugation

Similar to carbocations, the stability of alkyl radicals increases with the number of alkyl substituents on the radical carbon.

Stability Order: Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl

This trend is explained by two familiar effects:

1. Inductive Effect: Alkyl groups are weakly electron-donating and "push" electron density through the sigma bonds toward the electron-deficient radical center, dispersing its need for electrons.
2. Hyperconjugation: This is the more significant effect. It involves the overlap of adjacent, filled C-H $\sigma$-bond orbitals with the singly-occupied p-orbital of the radical.

From a molecular orbital perspective, this interaction is slightly different from the carbocation case. Here, a filled $\sigma$ orbital (HOMO) mixes with a singly-occupied p-orbital (SOMO - Singly Occupied Molecular Orbital). This creates a new, lower-energy bonding MO and a higher-energy antibonding MO. The three electrons involved (two from the $\sigma$-bond, one from the radical) populate these new orbitals. Two electrons go into the stabilized bonding MO, and one goes into the destabilized antibonding MO. The net result is a stabilization because the energy drop of the two bonding electrons is greater than the energy rise of the single antibonding electron.

1.2 Resonance Delocalization

Just as with carbocations, resonance is a powerful stabilizing effect for free radicals. If the radical's p-orbital is adjacent to a $\pi$-system, the unpaired electron can be delocalized over multiple atoms. This delocalization drastically lowers the energy of the species.

For this reason, allylic and benzylic radicals are significantly more stable than even tertiary alkyl radicals.

To understand this from a deeper, MO perspective, let's consider the allyl system. The three parallel p-orbitals combine to form three $\pi$-molecular orbitals: one bonding (${\psi }_1$), one non-bonding (${\psi }_2$), and one antibonding (${\psi }_3$). The allyl radical has three $\pi$ electrons. Two fill the bonding MO, and the lone unpaired electron resides in the non-bonding molecular orbital (NBMO), which serves as the SOMO.

The key insight is that the distribution of the unpaired electron (the "spin density") is determined by the shape of the SOMO. For the allyl radical, the SOMO is the NBMO, which has coefficients only on the terminal carbons. Thus, the radical character is entirely on C1 and C3, perfectly matching our resonance picture.

1.3 Hybridization and s-Character

The effect of hybridization on radical stability is counterintuitive and highlights a key difference from other species. The unpaired electron of a radical resides in a specific orbital.

• Alkyl radical: The carbon is nearly sp² hybridized, so the unpaired electron is in a p-orbital (~0% s-character).
• Vinylic/Phenyl radical: The carbon is sp² hybridized, and the unpaired electron is in an sp² orbital (~33% s-character).
• Alkynyl radical: The carbon is sp hybridized, and the unpaired electron is in an sp orbital (~50% s-character).

Increasing the s-character of an orbital brings it closer to the positively charged nucleus. For an orbital containing an electron pair (like in a carbanion), this is stabilizing. However, for a singly-occupied orbital, pulling it closer to the nucleus increases its electronegativity or electron affinity, making it more reactive and thus less stable.

Therefore, radical stability decreases with increasing s-character of the orbital holding the unpaired electron.

Stability Order: Alkyl (p) > Vinylic (sp²) > Alkynyl (sp)

2. Stability of Carbanions

A carbanion is a species containing a carbon atom with a lone pair of electrons and a formal negative charge. It is trigonal pyramidal and sp³ hybridized (though it can re-hybridize if it allows for stabilization). As an electron-rich species, its stability is governed by factors that can withdraw or delocalize this excess electron density.

2.1 Inductive Effect

The influence of the inductive effect is reversed for carbanions compared to carbocations.

• Electron-donating groups (like alkyl groups) push more electron density onto the already electron-rich carbon, intensifying the negative charge and destabilizing the carbanion.
• Electron-withdrawing groups (like halogens, -NO₂, -CN) pull electron density away from the carbon center, dispersing the negative charge and stabilizing the carbanion.

This leads to the opposite stability trend for simple alkyl carbanions:

Stability Order: Methyl > Primary (1°) > Secondary (2°) > Tertiary (3°)

2.2 Resonance Delocalization

Resonance is a paramount stabilizing factor for carbanions. Delocalizing the negative charge of the lone pair over several atoms is highly effective at reducing electron-electron repulsion and lowering the overall energy.

Just as with radicals, allylic and benzylic carbanions are vastly more stable than their localized alkyl counterparts. The delocalization can be represented by resonance structures and is explained at a deeper level by molecular orbital theory, as you read in the text on the allyl system.

2.3 Hybridization and s-Character

This is arguably the most important factor determining the stability of localized carbanions. The lone pair of the carbanion resides in a hybrid orbital.

• An orbital with higher s-character is held closer to the positively charged nucleus.
• Placing the negative charge (the lone pair) into an orbital closer to the nucleus is a very stabilizing electrostatic interaction.

Therefore, carbanion stability increases dramatically with the s-character of the orbital containing the lone pair.

Stability Order: sp (50% s) > sp² (33% s) > sp³ (25% s)

This trend has profound chemical consequences. It explains why the hydrogen on a terminal alkyne is acidic enough (pKa ≈ 25) to be removed by a strong base, forming a relatively stable acetylide (sp) anion. In contrast, forming a simple alkyl (sp³) carbanion requires an extremely strong base (pKa of alkanes is ~50).

Conclusion

You have now completed your survey of the fundamental factors governing the stability of the three major carbon-based reactive intermediates. By analyzing the electronic nature of each species—whether it is electron-deficient or electron-rich—you can logically predict how it will respond to its structural environment.

Key Takeaways:

Preview of the Next Lesson:
Now that we have a firm grasp on the relative stabilities of carbocations, we are ready to see this knowledge in action. In our next lesson, we will analyze carbocation rearrangements, including 1,2-hydride/alkyl shifts and ring expansions. You will see how less stable carbocations spontaneously rearrange into more stable ones, a process that dictates the products of many important organic reactions.