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I want to ask a question about the varying sizes in the LUMO of acrolein during a 1,2- or 1,4-addition.

Today in our introductory lesson to Organic Synthesis with 1,2- and 1,4-addition we were listening to the reason why some nucleophiles may attack one functional group compared to another.

The following picture was discussed:

enter image description here

Now, as shown here, the far orbital on the alkene is far larger than the orbital on the $\ce{C}$ of the $\ce{C=O} $ bond. This implies that for a larger orbital, a nucleophile finds it is easier to attack the alkene than the carbonyl.

This makes sense.

However, when finding an explanation for these varying sizes in orbitals, I couldn't find anything to explain this.

This question was the closest which explained the effects of varying orbital sizes but did not differentiate between $\ce{C1}$ of the alkene and $\ce{C3}$ of the carbonyl.

Why are there two different orbital sizes?

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    $\begingroup$ Don't take the picture too literally. I believe the apparent size in fact represents the coefficient with which every AO contributes to the MO. $\endgroup$ – Ivan Neretin Oct 13 at 15:27
  • $\begingroup$ The coefficients of the LUMO on each atom are determined via mathematical methods. E.g. Applying a perturbation to the orbitals derived from Huckel theory. I believe there is no chemically intuitive way of deriving these coefficients on your own. $\endgroup$ – Tan Yong Boon Oct 14 at 1:23

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