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Back in high school I was taught a definition of metals:

Metals are a lattice of positive nuclei embedded within a sea of delocalised electrons

Metals are conductive because the electrons aren't bound to any particular atom, and hence can flow freely throughout the entire metal.

However, I was recently taught about electron orbitals, and I'm not sure how to reconcile the two pictures. If the metal atoms were sharing pi or sigma bonds, I'm not sure how any of the electrons could be truly delocalised, and how conductivity arises. In terms of the atomic orbital theory, how does conductivity arise in metals?

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    $\begingroup$ AO theory explains atoms and ions. sigma and pi bonds are MO theory. That is a model for covalent bonds, molecules. Both are not very useful for metals. $\endgroup$ – Karl Mar 31 '16 at 2:03
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    $\begingroup$ @Karl Actually the bonding in solids can be discussed in a way that shows very strong links to MO theory for molecules and pretty much uses the same concepts. This has been done in a masterfully comprehensible way by Roald Hoffmann. $\endgroup$ – Philipp Mar 31 '16 at 13:08
  • $\begingroup$ @Philipp So? All those models are based on the same concepts. $\endgroup$ – Karl Mar 31 '16 at 22:31
  • $\begingroup$ @Karl Your first comment seemed to me to be implicating that there is little similarity between the bonding (and the concepts used to describe that) in molecules and solids. There I disagree, because you can find things like $\sigma$ and $\pi$ bonds (with slight differences compared to molecules) in solids and the LCAO-MO method to analyse the electronic structure of a molecule can be used (again with only slight alterations) for solids as well. To some extent you really can think of a solid as just a very big molecule... $\endgroup$ – Philipp Apr 1 '16 at 13:28
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    $\begingroup$ ... The problem is just that the vocabulary for the description of the electronic structur of molecules and solids differs due to being developped by different communities: for example a Bloch function is essentially just a symmetry-adapted linear-combination of atomic orbitals, i.e. an MO of the solid; a density of states is not much different from a MO diagram; the valence band edge is very much like the "HOMO" of a solid etc. Of course, one has to be aware that there are some differences and that additional effects come into play for solids but the basics can be understood with the... $\endgroup$ – Philipp Apr 1 '16 at 13:34
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It's not that the electrons are completely unbound from the atoms - they still attract each other and form the bonds with other atoms. But the attraction between the atom and its electron is pretty weak so it's easy to detach the electron from the atom.

The properties of the metals are better to be described via ionization energy - the energy needed to remove an electron from an atom. Elements to the right of the periodic table have high ionization energy - they are not willing to lose electrons. Therefore these elements are bad conductors (and are not metals).

Metals have lower ionization energy - their valence shell just started to be filling and the strength of the proton is not enough to keep them tight. Therefore these electrons are free to flow with minimum efforts applied - which would form electrical current.

The intention of the "sea" model is to describe (in simplified manner) the fact that electrons are floating around from one atom to another. And while they participate in bonding, this is a dynamic structure that breaks and forms all the time.

Here is a nice video from Khan Academy on the metallic nature.

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