# Density of states¶

Take a look at the dos.py program and try to 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 Electron spin and magnetic structure exercise (on the x-axis you have the energy relative to the Fermilevel).

• 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 the non-magnetic phase - is it magnetic at all?! Calculate the magnetization like this:

```from ase.io import write
from gpaw import GPAW
calc = GPAW('anti.gpw')
atoms = calc.get_atoms()
up = calc.get_pseudo_density(0)
down = calc.get_pseudo_density(1)
zeta = (up - down) / (up + down)
write('magnetization.cube', atoms, data=zeta)
```

and look at it.

• 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) ~ E1/2. 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 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 pdos.py. Use it to plot the s, p, and d-states on one of the Fe atoms.