Exercise 5

This exercise is intended to illustrate the definition of
basis sets with different numbers of orbitals and localization
radii in SIESTA. It is based on the H2O molecule.

You will find three directories: SZ, DZ and DZP, 
in which you will find input files for a H2O molecule 
which will be solved with three different basis sets:
single-Z, double-Z and double-Z plus polarizarion,
respectively. The runs will consist in structural relaxations
via Conjugate gradients, to find the equilibrium structure
of the molecule for each of the bases utilized.

The bases are defined through these three lines:

PAO.BasisSize DZP
PAO.EnergyShift  500.0 meV
PAO.Splitnorm  0.15

where the first one defines the number of orbitals in the
basis set (in this case, a double-Z plus polarization, which
means two shells of s orbitals, two shells of p orbitals,
and a polarization shell of d orbitals for oxygen,
and two shells of s orbitals and one shell of polarization
p orbitals for H); the second line indicates the energy shift
parameter, that determines the cutoff radius of each of the 
orbitals; and the third one is the Split norm parameter,
which defines the radius of the second-Z orbital in the case
of double-Z bases.

You should do runs for each of the basis sets, changing
the PAO.EnergyShift parameter, and look at the results
as a function of basis size and localization radius (or energy shift).
In particular, you should look at:

- Total energy
- Bond lenghts at the relaxed structure
- Bond angles at the relaxed structure
- CPU time
- Radius of each of the orbitals
- Shape of the orbitals

You have some files with results that you should be
able to reproduce in the Out directories.

What is the best basis set that you have found? Why?
How do the results compare with experiment? 
What do you consider a reasonable basis for the
molecule, if you need an accuracy in the geometry
of about 1%??   In order to assess convergence with
respect to basis set size, should you compare the results
with the experimental ones, or with those of a converged basis
set calculation?

Tip 1.: In order to find the bond lenghts and bond angles,
it is helpful to use the Molekel program.  Load the h2o.ANI
file (which contains the coordinates of the molecule during the
relaxation), and use the 'Geometry' option (left button of the mouse)
to measure bond lengths and angles.

Tip 2.: You can see the radii of the orbitals in the
output file, just after the line reading:
printput: Basis input -----------------------------------------------

Tip 3.: You can look at the shape of the orbitals by plotting the
contents of the ORB* files generated by SIESTA.
