I've moved this from the long old thread (http://van.physics.illinois.edu/qa/listing.php?id=1295
) since it's really starting a new topic.
To the extent that an electron is shared between two atoms, its wave function is spread out over both atoms. Actually, quantum mechanics explains why that would promote bonding. A more spread-out wavefunction can be made of longer-wavelength, lower-energy waves. Thus spreading out between atoms can lower the energy. (In the actual lowest energy state, there's some further rearrangements which raise that kinetic energy term and lower the potential energy term, to obey the virial theorem, but the bonding is essentially driven by the term we described.)
In molecules made of different types of atoms, the spread-out wavefunction isn't symmetrical between the atoms, so more of it is lumped up near one than another. That gives the bonds some ionic character.
So the standard language ("sharing and stealing") actually fits the wavefunction picture pretty well.
(published on 11/23/2010)