# Valence and Conduction Bands

1. Feb 5, 2016

### UMath1

I am not sure I quite understand the distinction between the valence and conduction bands in metals. The simple model we learned in Intro to Chemistry explained that electrons in the metals were delocalized and were shared between all the metal atoms in the metallic crystal.

I am not sure if I correctly understand the band model, so correct me if I say something incorrect. According to the band model, the electrons are confined to specific molecular orbitals in between to atoms when in the valence band. If energy is provided then the electrons can occupy higher energy level molecular orbitals in the conduction band. Usually these are the anti-bonding orbitals.

So my questions are the following:
• Aren't the higher energy level molecular orbitals still between just two atoms? How then can the electrons be shared between all the metal atoms?
• Conductivity is supposed to decrease with increasing temperature. Doesn't this contradict with the idea that adding energy will allow the electrons to escape to higher energy levels?
• What exactly does it mean when we say the electrons are delocalized in the conduction bands? Are they still confined to the atoms of the solid? They cannot just escape into a vacuum correct?

2. Feb 5, 2016

### CrazyNinja

1) I am not really sure. I will look it up once again.
2) The reason for the decrease in conductivity is not because the electrons do not escape into higher energy orbitals. It is because the kernels themselves start oscillating, increasing the resistance to the motion of the electrons.
3) You are correct here.

My teacher has advised me not to use band theory except to explain the properties of semi-conductors. This was because there are other aspects which one might neglect while making assumptions using the band theory ( like your 2nd question). Just telling you.

3. Feb 5, 2016

### DrDu

Even in simple molecules, the molecular orbitals (to be precise the so called "canonical" MO's) are not between just two atoms but extend over the whole molecule. These are the orbitals we also talk about in band theory. It is sometimes possible to introduce an alternative set of orbitals which are localized on the bonds between two atoms. In band theory, these orbitals are called Wannier functions. Now in band theory the condition for the possibility to introduce Wannier orbitals is precisely that the band is either completely full or empty. So if the band is not full, like in metals, the electrons cannot be localized in bonds but are more free to move between the atoms.

4. Feb 5, 2016

### CrazyNinja

Thanks DrDu...! You are the best...!