Is it basically wrong? It just seems like hand-waving...
What do you mean?
afaik, orbital hybridisation is pretty much how it works. You got a space of probability where you can find an electron or set of electrons. The electron(s) in question is/are essentially everywhere in that cloud at once. It's like a probability cloud.
All that stuff about neat, circular orbitals is what's wrong.
I'm talking about an s orbital and 3 p orbitals nicely combining to make nice convenient orbitals which happen to point outwards tetrahedrally. I don't see how that works.
I haven't done orbital hybridisation in ages, but my guess is the orbitals are based on pure statistical math. Just because it doesn't make sense visually on first glance, doesn't mean it's wrong. Besides, most research likely supports the theory.
That being said, just looking at an s and 3 p orbitals, I can see how the resultant hybrid orbitals exist as they do.
Can anyone else chime in here?
No it's not wrong. Besides that, what precisely is your question?
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