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Recently I was reading this answer to the question Why does boron add to the less substituted carbon in the hydroboration of an alkene?. See the transition state given in the above answer, and the reason given to explain it's stability.

As far as I know, hyperconjugation is a result of σ-p interaction in carbocations. If partial charges are developed(as in the case of linked answer), there is no empty p orbital in them.

So how can hyperconjugation be used to explain their stability?

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The solution is referring to the partial positive charge on the carbon opposite the developing C-B bond. It is stabilized by substituents similar to how a full carbocation is stabilized by substituents, e.g., in the tert-butyl carbocation. This doesn't need to be a completely empty p-orbital—electron density will be dynamically influenced by any imbalance in charge distribution—but if it's easier to conceptualize, you could imagine it as the pi-bond electrons being fully transferred to the C-B bond, leaving an empty p-orbital on the opposite carbon, which is stabilized by hyperconjugation.

The reality should be closer to a dynamic process at both sites, though. The pi-bond transfers electron density into the C-B bond, while the substituents stabilize the rising positive charge on the other carbon. As the C-B bond develops, the B-H bond simultaneously weakens, and begins moving its electron density toward the partial-positive carbon.

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