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What you should already know about bonding



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σ overlap of s orbitals
on adjacent atoms

π overlap of p orbitals
on adjacent atoms
Valence bond model
Bonds result from overlap of s and p valence orbitals on adjacent atoms in
a σ fashion (end-on - bond density around bond axis)
s with s, s with p, or p with p if both p orbitals lie on the bond axis
or a π fashion (side-on - bond density above and below bond axis)
p with p if both p orbitals are perpendicular to bond axis
Bonding electrons are localized around the bonded atoms.

The model was modified to include use of hybrid orbitals (mixtures of s and p atomic orbitals) to rationalize composition and geometry of compounds of second-row elements (such as CH4 and BF3). Hybrid orbitals overlap in a σ fashion with other hybrid orbitals (or s or p orbitals) on adjacent atoms.

Molecular orbital theory
According to this more complete theory of bonding, electrons occupy molecular orbitals delocalized over the entire molecule.  Because this is more complicated, we will only consider diatomic molecules.