BASIS SETS II: CRYSTALS
 
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.
 
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.pdf you have a graph with the results that you
should be able to reproduce.
 
Once 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 favorite property and try to get it!!!!
