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Density of states

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Take a look at the :git:`~doc/exercises/dos/` program and try to
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get a rough idea of what it can do for you.  Use it to plot the
density of states (DOS) for the three Fe configurations from the
:ref:`iron_exercise` exercise (on the *x*-axis you have the energy
relative to the Fermilevel).
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* Do the DOS plots integrate to the correct numbers? (i.e.
  number of bands).

* The DOS for the anti-ferromagnetic phase looks a bit like that for
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  the non-magnetic phase - is it magnetic at all?!  Calculate
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  the magnetization like this:

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  .. literalinclude::
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  and :ref:`look at it <iso>`.
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* Calculate the DOS for bulk Aluminum and compare it
  (qualitatively) to the DOS for the non-magnetic calculation. The DOS
  for a simple metal has this shape: *g*\ (*E*) ~ *E*\ :sup:`1/2`.  Explain
  the qualitative difference.

* Plot also the DOS for bulk Si and the CO molecule.  Identify the
  bandgap between valence and conduction bands for Si and the
  HOMO-LUMO gap for CO. Make sure that your **k**-point mesh for
  Si is dense enough to sample the band structure.

Projected Density of states (PDOS)

The projected density of states is useful for for analyzing chemical
bonding. There exist several studies where the density projected onto
the d states of a given surface atom is used. This short exercise
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demonstrates how to construct the PDOS of Fe.

We will get a feel for the local density of states by plotting the
PDOS for the ferro-magnetic Fe crystal.  Look at
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:git:`~doc/exercises/dos/`. Use it to plot the s, p,
and d-states on one of the Fe atoms.