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This link helped me a lot when learning about hybrid orbitals: https://chem.libretexts.org/Bookshelves ... _Chemistry)/Fundamentals/Hybrid_Orbitals
By definition, hybrid orbitals are the result of a model that combines atomic orbitals on a single atom in ways that lead to a new set of orbitals that have geometries appropriate to form bonds in the directions predicted by the VSEPR model.
I believe hybrid orbitals are the result of orbitals that are created when the valence electrons of two atoms/molecules bond or are attracted to each other. They are the average of the orbitals of the valence electrons.
My understanding of hybrid orbitals is that they are a result of the sharing of electrons between two atoms. Due to this sharing, these electrons kind of "blend" properties of the orbitals of their parent atoms. Thus, we are left with an average of the various kinds of orbitals that the parent atoms originally had prior to covalent bonding.
You can use hybrid orbitals to determine the amount of bonding that occurs between central atoms and some surrounding atoms. It's kind of a confirmation of the electron arrangement of the molecule and helps you see clearly if there are any pi or sigma bonds involved. You basically find the electron arrangement of the molecule using a Lewis structure, then match to the hybridization configuration, and then add the outer valence electrons into each shell.
What I do is just count the regions of electron density, and correlate it to the hybrid orbitals that have that many things. For example, sp^3 has four regions of electron density (1 s, 3 p) are has a tetrahedral electron arrangement. That being said it might be best to review the lecture or the textbook to really understand what these orbitals represent.
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