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To describe molecules quantum mechanically we can take the atomic orbitals from the atoms and recombine them to form molecular orbitals and that works well for diatomic we can take s and P orbitals and overlap them and form molecular orbitals the s and P orbitals have the appropriate arrangement and symmetry for a diatomic molecule but what if we get more complicated even if you go to a very simple diatomic or if you go to something with strict number two how do we accommodate strict number two how do we have a carbon bond to something on this side and something on this side if I use my p orbital over here to make a molecular orbital with this I don't have a p orbital available to make a molecular orbital with this I can't reuse my orbitals to make more bonds, so I have to have bonds and orbitals that have the right orientation the atomic orbitals forming bond angle 180 can't quite do that so forming acetylene isn't really possible, and it gets a little more complicated when I go to strict number three so if I have a bond angle of 120 degrees there aren't even atomic orbitals that have a hundred and twenty degree orientation to each other so what atomic orbital can make that accommodation to form something like graphite for instance where all the bond angles are 120 degrees or tetrahedral arrangements where the strict number is 4 I have to have 109 degree bond angles in things like polyethylene and diamond those bond angles need to be accommodated so what I need are a set of atomic orbitals where I can combine them and get the various angles for the various strict numbers and that's what we'll look at next
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