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I want to know how bonding electrons behave when they have to cover for both atoms. Electrons can spin around only one atom right? If so, then what happens when a covalent bond forms?

Let's say we have two covalent bonds between two atoms (for example: $\ce{C=O}$), so they have two pairs of shared electrons.

Since the double bond clearly exists, how do the electrons form the clouds that cover both atoms?

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    $\begingroup$ "They can spin around only one atom right?" No. $\endgroup$
    – Mithoron
    Apr 17 at 21:56
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    $\begingroup$ "Spin around" is a wrong picture. $\endgroup$ Apr 17 at 21:56
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    $\begingroup$ If you like images, you may imagine that the electronic cloud looks like an ellipse, with the two nucleus inside. . $\endgroup$
    – Maurice
    Apr 18 at 8:38
  • $\begingroup$ I upvoted the comment of @Maurice as for it might serve to OP. However, what is linking the atoms together (bond) is in between them rather than a cloud enveloping both. It is just the spinning around figure that (again, certain useful in several occasions) is wrong. So my comment to OP is "imagine them between the atoms, so that each is under the influence of both nuclei". $\endgroup$
    – Alchimista
    Apr 18 at 8:49