Exercise 6

This exercise is intended to illustrate the optimization
of the range of the basis set orbitals for a bulk system.
In the bulk, the convergence with respect to basis set
range is much faster than in molecules, since the basis
does not need to reproduce the exponential decay into vacuum

The system in which we will work is bulk bcc-Fe. 
This is a difficult system, for many reasons.
First, it needs core corrections for a proper description
of the magnetism. Second, LDA does not yield the right
ground state structure, and GGA is therefore necessary.
Third, since the d-orbitals are very compact, and
core corrections are present, a large meshcutoff is
necessary for proper convergence. Finally, metallic
character with a large density of states at the Fermi level
makes it necessary to use a fine k-point sampling.
The input files have been built to take into account
these stringent conditions.
In particular, the Fermi-Dirac smearing has
been used in order to improve the selfconsistency
and reduce the number of k-points (see the SIESTA user guide).
This is important in practice because it means that
you should not be looking at the E_KS energy in the
output file, but to the FreeEnergy (since the temperature
is not zero (I insist: see description of the temperature
smearing in the SIESTA user guide).

First, go to directory SZ-OptRc. Here, you have the input
file fe.fdf.  See that the basis set is defined explicitly
using the block PAO.Basis. It is a Single-Z basis
with both s and d orbitals localized to within rc=4.0 Bohr.

We want to see which is the optimal radius for each of the
orbitals in the Fe atom.  We will do it in a simple way.
First, maintaining the d orbitals to rc=4.0 Bohr, 
change the radius of the s orbitals from 4.0 up to 8.0 Bohrs
in increments of, lets say, 0.5 Bohrs.  Plot the energy as
a function of rc.  You will see that the energy converges quite
quickly with rc, and even it shows a minumum!. 

Now, pick the value of rc for the s orbital that gives the
minumum energy, and do the same procedure changing the rc
of the d orbital. Plot the result and find the optimal radius
for the d orbital.  Observe the results, and try to understand
what's going on.

In SZ-OptRc/Opt/rc.ps you have a graph with the results that
you should be able to reproduce.


Once that you have optimized the radii, lets go to the
directory Props.  Here, you have input files with different
sizes of basis: SZ, DZ and DZP. The radius of the first-Z is
chosen close to the optimal one found before.
Use these files to compute some physical properties of
Fe, and see how they change as a function of the basis set.
You can look at the equilibrium lattice constant, the
total spin, the bulk modulus, etc. Choose your favourite property
and try to get it!!!!



