From the wikipedia page for metallic bonding, I've noticed that there seem to be a few things at play:
(1) the delocalization of electrons, and
(2) the fact that there are a far larger number of delocalized energy states available to the electrons than there are electrons themselves (dubbed "electron deficiency").
However, I'm still struggling to understand how this constitutes a bond between the atoms (i.e. how these two factors holds metal atoms, and specifically their nuclei, together) and what makes this bond so strong.
One quote that really interested me is this one: "metallic bonding is an extremely delocalized communal form of covalent bonding...The delocalization is most pronounced for s- and p-electrons. For caesium it is so strong that the electrons are virtually free from the caesium atoms to form a gas constrained only by the surface of the metal. For caesium, therefore, the picture of Cs+ ions held together by a negatively charged electron gas is not too inaccurate."
By this, I assume they mean that the valence electrons are shared so freely that it is not correct to assume that the electrons are covalently "shared" only by each atoms neighbors, but shared with the whole chunk of metal.
But my issue is with how this constitutes a bond at all? Are the positively charged nuclei just nebulously attracted to the entire electron cloud, and therefor just held in place? If so, why wouldn't this happen in a similar fashion with non-metals like Nitrogen, Oxygen, or Sulfur?
Also, I get how the electron deficiency (the fact that there are far more energy states available to the free electrons then there are electrons in the "sea") helps to explain properties of metals like heat/electricity conduction, but how does that help explain what hold the atoms/nuclei together so strongly?
I'm really just confused as to the strength of the bond more than anything else. How would an extremely delocalized form of covalent bonding, in which electrons are shared with a vast sea of other nuclei, create (as is the case with many metals) such strong bonds?
(I'm lead to believe that a deeper understanding of tight-binding theory might help me understand this phenomenon a bit better, so if anyone has any good information/resources for that, besides the page linked, that would be great as well.)