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So my question is in the title : Why can s and p orbitals of one atom form hybrid orbitals but the overlapping of one s orbital and one p orbital (perpendicular to the bond axis) of two different atoms don't form a molecular orbital (MO)?

I'm confused because I see both resulting orbitals (hybrid and non-existent MO) as a linear combination of atomic orbitals (LCAO) and that in the case of Molecular orbital theory (MOT), I learned that atomic orbitals of different atoms can interact to form molecular orbital only if they have the same symmetry (and are close in energy) so that their overall overlapping is positive or negative (=non zero).

If someone could explain where I'm wrong or what I see incorrectly, it would be very helpful. Thanks

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  • $\begingroup$ This actually isn't a trivial question. Hybridisation is just mathematical tool and shouldn't be used within the MOT context. MO are by design delocalised. With this in mind, of course s and "perpendicular" p orbitals will overlap and my form a MO. This, however, might not be the most stable state, or might not lead to a lower lying state. The reason for this is basically the cancellation of two effects. $\endgroup$ Nov 2, 2023 at 13:14

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$s$ and $p$ atomic orbitals can make hybrids if and only if their energies are identical or nearly identical. It can happen in a given atom. It cannot happen between different atoms.

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  • $\begingroup$ Thanks but do you have an explanation of why the symmetry of the atomic orbitals don't matter to fhe hybridization but do for bonding ? $\endgroup$
    – dispatchh
    Oct 16, 2023 at 17:05
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    $\begingroup$ The symmetry has nothing to do in this problem. It is only a question of energy. The energy of the two orbitals to be hybridized must be equal, or nearly equal, as they are both solutions of the Schrödinger equation. $\endgroup$
    – Maurice
    Oct 17, 2023 at 9:09
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    $\begingroup$ This is really not a good answer, if any at all, for this question. First and foremost there is the issue, that hybridisation is a mathematical concept that is completely independent of the energy. Then that there are no hybrid orbitals in MOT. It does not even consider the part about the the overlap of orbitals between atoms, which I think is key. $\endgroup$ Nov 2, 2023 at 12:14
  • $\begingroup$ @Martin Yes, Hybridization is a mathematical concept, that is independent of the energy. But hybridization can only occur in combining wave function which has the same energy as solution of the Schrödinger equation. Orbitals 2s and 2p can hybridize, because they produce the same or nearly the same value of energy in their solutions of Schrödinger equation. Orbitals 2s and 3p can never make hybrids because their energies are rather different $\endgroup$
    – Maurice
    Nov 2, 2023 at 20:05
  • $\begingroup$ The way you describe this is very fuzzy. Hybridisation is a concept from Valence Bond Theory, so using this in the same context of MO Theory is an approximation at best. If we stay in the framework of MOT, then Molecular Orbitals will/ay form. You can later use localisation models to approximate contributions and infer hybridisation from this. But that is not the same as starting with it from scratch like in VBT. And it is certainly not the reason for anything. When we stay within VBT then yes, we could only describe meaningfully sp^x hybrids from A= similar in energy. $\endgroup$ Nov 3, 2023 at 12:47

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