Stability of alkenes by hyper conjugation

I have learnt that for carbocations, electrons are delocalized from the $\ce{C-H}$ $\sigma$-bond to the empty p-orbital of carbon.


Moreover, alkenes are stabilized by the delocalization of electron from $\ce{C-H}$ $\sigma$-bond to the empty anti bonding $\pi$ molecular orbital.


But, don't electrons in anti bonding molecular orbitals lead to instability? So, how does hyper conjugation lead to stability of alkenes?


I believe this question has already been asked before, but I couldn't find any satisfactory and/or relevant answers.




You are confusing the *mixing* of orbitals with the *promotion* of electrons from one orbital to another. You're thinking of this:


$\hspace{50 mm}$[![Promotion of electron](https://i.stack.imgur.com/YdB1S.png)](https://i.stack.imgur.com/YdB1S.png)


I don't blame you, because the phrasing "delocalisation into an antibonding orbital" implies that, but that is *not* actually what happens.


In what actually happens, the two original orbitals are said to *mix*. They cease to exist. They overlap to give two new MOs, one which is even lower in energy and one which is higher in energy, like in this diagram:


$\hspace{45 mm}$[![Mixing](https://i.stack.imgur.com/xnW2y.png)](https://i.stack.imgur.com/xnW2y.png)


The "new MO 1" has characteristics of both the original $\ce{C-H}$ $\sigma$ as well as the original $\ce{C=C}$ $\pi^\*$, which is why we loosely say "donation into the $\pi^\*$ orbital". However, don't take it too literally. **The phrase means that two orbitals are mixed. It does not mean that electrons are promoted from one orbital to another.**


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