The periodicity of the potential in crystal stuctures allows us to approximate the many body schrodinger equation as a one electon schrodinger equation with an effective potential, U(r) that is periodic. One extreme was treating the electons to be bounded by a weakly periodic potential so they are nearly free and the other extreme was to treat them to be tightly bounded to the atom. Group I,II,II and IV is best described by weakly bounded valence electrons whereas transition metals are better described by tight binding model. Which model works best is depends on how strongly bounded the valence electrons are? In reality, would the electrons be somewhere in between this two extremes but I believe that there are other models as well. Paul just posted on the Huckel model which is just the term chemist use for tight binding model (which physicist use for crystals) for molecules.
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I find it interesting how we only need to consider the valence electrons.
ReplyDeleteWe have two models: weak or tight potential binding them to atom.
It would make sense that actual electron binding tightness would be somehwere between the two extremes?
I suppose we would want to consider why we are interested in choosing either model (weak or tight potential).
I suppose there would be a purpose to want to decribe their binding (can't think of a reason at the moment) but depending on conditions, would we consider whichever model was easier?
I suppose this is a general comment in that wouldn't we want the easiest model?
Okay, after a little more reading.
ReplyDeleteWe have the Bloch model, of which we considered two extreme cases: weak potential and tight-binding.
The Group I, II, III, IV metals are best described by the weak potential, meaning that the valence electrons are under a small potential.
From Ashcroft and Mermin (p152), the weak potential was due to
(1) the distance between the electron and ion and
(2) effects from other electrons.
Hence, I would interpret that there would be varying magnitudes of these effects in different atoms.
Thus in reality, we should expect something between the ideal cases of the weak potential and tight binding.