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Prologue/Rant about online classes

We have been taught the electron sea model to explain metallic bonding and conduction of electricity by metals. Then out of the blue, the band theory was introduced, without even giving the definition of what a band is. So I was lost in the recorded online class with no method of asking a doubt. So in an attempt to not wait a day for asking the doubts, I took it on myself to clear my doubts. So I surfed through the web and almost reached a conclusion.. before referring to a textbook.

The actual doubt

So as far as I know, the MOs (on a large scale, like 10 raise to 23 atoms scale) having similar energies appear as bands. The outermost band of occupied MOs is called the valence band. But what I am confused about is what makes up the conduction bands. I reached a conclusion from the chemistry libre texts that conduction bands are made from the combination of the unoccupied atomic orbitals. But when I referred to my reference book, it stated that they are the anti bonding MOs of the valence band.

So what actually makes up the conduction band? Is it one of the two I mentioned above? Or is it a theoretical set of energy levels where an electron can move freely to conduct electricity?

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  • $\begingroup$ When you do H+H -> H2, you combine two partially occupied AO's to get both the bonding and antibonding MO's. The unoccupied atomic orbitals are not a part of the picture at all. Same thing here. $\endgroup$
    – Ivan Neretin
    Apr 14, 2021 at 9:00
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    $\begingroup$ Ok, but.. how does it answer my question tho? $\endgroup$
    – Humble_Snowman
    Apr 14, 2021 at 9:10
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    $\begingroup$ In essence in a molecule all the molecular orbitals can be expressed as linear combinations of the atomic orbitals, and you occupy the lowest energy ones with the appropriate number of electrons. Note you don't refer back to the original occupations at all, except to get the total number of electrons. A solid is just a very, very big molecule. The valence band is the highest energy occupied linear combinations, and the conductions band is the lowest energy unoccupied linear combinations. [yes, basis set completeness, translational symmetry, etc. let's keep it simple] $\endgroup$
    – Ian Bush
    Apr 14, 2021 at 9:43
  • $\begingroup$ The point is that the bands can overlap / electrons have the energy to move within the conduction band. $\endgroup$
    – Alchimista
    Apr 14, 2021 at 9:52
  • $\begingroup$ @Alchimista Strictly electrons don't move in a conduction band any more than they move in any molecular orbital - it is a stationary state solution of the Schrödinger equation and the probability density does not change with time. The point is that in a metal an infinitesimally small electric field will mix the conduction band with the valence band due to the zero band gap (and assuming the relevant MOs overlap in some sense), and it is that leads to a nett movement of charge. $\endgroup$
    – Ian Bush
    Apr 14, 2021 at 10:56

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