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Before I start of this question, Ι want to make it clear that I know that hybridization, like pretty much all of chemical bonding, are just made up to qualitatively rationalize observations. I know that theres no actual orbital overlapping, resonance, excitation.... and what not, and the only real things governing "bonding" are electrodynamics and quantum mechanics

When I first came across hybridization, I learnt that it is just used to obtain the correct electron density distribution from atomic orbitals as the experimentally observe corresponding to least repulsion/energy. The go-to way to determine hybridization would then be to use VSEPR to find the most stable electron domain geometry. However, I've come across several molecules such as H2S, PH3 and Halogen molecules where there is no hybridization. How does VBT /hybridization theory rationalize this? And is there any way that I could predict it? (I obviously can't know the experimental observations for all possible molecules before hand)

Secondly, is rationalizing geometry the only reason for invoking hybridization? I have come across these 2 other reasons in several reliable textbooks:

  1. Hybridization occurs as hybrid orbitals are able to overlap more effectively and the bond strength is proportional to the extent of overlap. While this seems somewhat logical, I can't think of a single molecule where better overlap needs to be the reason for a specific hybridization
  2. Hybridization occurs inorder to make all orbitals degenerate before overlapping as this corresponds to the lowest energy "quantum mechanically". This one seems way too handwavy but is mentioned on wikipedia https://en.wikipedia.org/wiki/Orbital_hybridisation

Bonus question: I have another small question that I dont want to start another thread about given the multitude of questions on hybridization already present on the site but feel free to ignore this.

Why exactly do sp,sp2 & sp3 hybrid orbitals have the same exact geometries as the ones observed in electron domains? Is it just a coincidence or are they forcefully combined in such a way to match them>

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    $\begingroup$ Hybridisation is a purely mathematical way to describe the electron density. $\endgroup$ Feb 10 at 22:37
  • $\begingroup$ I know. That's why I clearly mentioned that right at the start of the question. $\endgroup$ Feb 10 at 22:38
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    $\begingroup$ I hit enter by accident. Hybridisation has no physical meaning and is just a toy to play around. As such it is a point of view, a descriptive model. Therefore hybridisation does not occur. Both those quotes (? - please add citations and sources) are therefore wrong from the start. As a strict consequence: Hybridisation always follows molecular structure, never the other way around. Why VSEPR is still quite well at predicting general shapes is a different question, which I believe has been answered here before. $\endgroup$ Feb 10 at 22:43
  • $\begingroup$ en.wikipedia.org/wiki/Orbital_hybridisation The second quote can be found under the sp3 subheading $\endgroup$ Feb 10 at 22:45
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    $\begingroup$ No, there is no such limit, it is just a convenient way to intro the subject. Any proportion is allowed provided that they are properly normalized to reflect the electron density in the product orbital. Any (positive) combination of fractions is in principle ok. The same principle works when we solve for molecular orbitals generally. Solutions (molecular orbitals) are usually constructed as combinations of linear combinations of atom-centered orbitals (eg H-like functions). $\endgroup$
    – Buck Thorn
    Feb 11 at 8:35

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