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When you think of a molecule as simple as methane CH4, you can see that it has four identical C-H bonds. Carbon has 6 electrons, 2 in 1s, 2 in 2s and 1 in 2px, 1 in 2py and 0 in 2pz. Interestingly, one of the electrons in 2 s goes to 2pz. How does methane form 4 identical C-H bonds with just 1 s and 3 p orbitals? The answer is that carbon uses hybridized atomic orbitals called sp3 that has 25% s-character and 75% p-character.

Molecular orbital theory can explain why we have triple bonds. For example, ethyne. The sigma bond formed by the sp-sp overlap along with the two perpendicular p-orbitals that are parallel with each other that form 2 pi bonds explains the triple bond.

I've also noticed that unpaired sp3 bonds like those in ammonia (NH3) are used to form bonds and paired sp3 are the lone pairs.

I was wondering how any of this knowledge is useful for someone wanting to find out about the physical properties of compounds? Do chemists think about these things?

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Certainly the electronic structure of compounds are of interest when predicting or interpreting the physical properties - but not necessarily the molecular orbital theory in and by itself. The symmetry of compounds (and by extension this also means;) the symmetry of the bonds in the compound are vital to many physical properties. However, MO theory is mainly used to describe bonding in more detail, not to infer "macro"-properties FROM bonding - so I guess the answer is... "no and yes". Yes, chemists think about these things, at least the ones that work close to the quantum realm. No, MO theory is not really useful in the way you are describing - with one giant exception:

When we are talking about "possible" physical properties of not-yet-synthesized compounds, the answer is resoundingly "yes". Graphene, for instance, has more theoretically predicted qualities than have been measured. Super conductance, tensile strengths, diffusion rates... there is just so much exiting being suggested all a result of computer modeling on the quantum level from MO theory and the likes.

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Yes, things like boiling points can be calculated today, but only with crude approximations because such calculations are very time consuming. Let's say chemists have been moderately successful with this as in what has been calculated so far is completely useless for anything other than academic amusement because of the massive error bars. People are working on it though.

This however has nothing to do with hybridization. Hybridization is a model concept that, at its best, describes qualitatively the geometry of very simple molecules. You are asking for properties that are the result of molecular interactions. Anyways, the idea of atomic orbitals mixing with each other and then forming bonds with each other is fundamentally wrong and not useful for anything quantitative I can think of. However, molecular orbitals are still a useful tool in the calculations mentioned earlier. Explaining this in detail goes beyond this question I fear.

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