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Band theory electron counting rules for metals/insulators

  1. Nov 13, 2014 #1
    I'm a little confused by the description I commonly hear about the electron "counting rule" in band theory. The general statement I find is that a solid with an "odd number of electrons per unit cell is a metal" (because this would imply a partially filled band), while an "even number of electrons could be an insulator or a metal" (since the band could be partially occupied or full). We know that this is not always true, due to strong correlations, etc., in certain materials. Two examples, CuO and VO2, are often described as unexpected insulators for this reason, citing their respective 3d9 and 3d1 configurations. However, CuO has four formula units per unit cell, and VO2 has two (or four, depending on which structural phase it's in), so neither of these materials has an odd number of electrons per unit cell. Why would band band theory predict them to be metallic if this is the case? For some reason, they're expected to be metallic due to "counting rules", although the odd number of electrons per unit cell clearly doesn't hold.

    Note: I am aware that these are NOT metals - I'm just trying to understand why the band theory "counting argument" would suggest that they are.
     
  2. jcsd
  3. Nov 18, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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