Exercise 2


Here we will focus on a crystalline material, FCC Al. 

In bulk systems the electronic states can be characterized 
by a continuous quantum number, the so-called Bloch 
vector or crystalline quasi-momentum of the electrons. 
The space of allowed Bloch vector (the Brillouin zone) is 
usually sampled using a finite grid. The most popular 
scheme to generate this integration mesh is the 
Monkhors- Pack algorithm. This is also used in SIESTA. 
The integration grid in the Brillouin zone is specified 
using the block kgrid_Monkhorst_Pack

For metals there are electronic bands that are not 
completely filled and therefore for an accurate description 
of the total energy, forces and all properties of the 
materials it is necessary to use a better sampling in 
reciprocal space (Bloch vectors) than for insulators. In the 
input file Al_bulk.fdf a 4x4x4 grid is used. This might be 
insufficient for a good description of aluminium.

You should explore the convergence of total energy, 
the lattice parameter, and density of states respect to 
the fineness of the  k-sampling. 

To plot the DOS you have to use the utility program 
eig2dos.x. This program reads the information contain in 
the file Al.EIG which contains all the eigenvalues for 
each k-point.
In order to run the program eig2dos.f you have to add 
some extra information to the first line of this file, 
namely, a broadening for each states in eV (a value of the 
order of 0.1 eV is usually reasonable), the number of 
energy points where the DOS will be calculated and the 
Emin and Emax of the energy window where the DOS 
will be calculated.
(Read the comments in the header of file eig2dos.f for 
more details)
Once you have add this info to the file Al.EIG you just 
need to execute 

eig2dos.x < Al.EIG > dos 

and plot dos using gnuplot.

The file Al_bulk.fdf will also produce a file Al.bands 
containing the band structure along the several lines in 
the Brillouin zone as specified using the block 
BandLines. To plot the band structure you need to use 
the utility program gnubands.x 

gnubands.x < Al.bands > out.bands

and you can plot out.bands using gnuplot
A SZ basis set is specified in the file Al_bulk.fdf, 
however, it might be quite interesting to see how the band 
structure changes when more complete basis sets are used 
(DZ,DZP).

