PSEUDOPOTENTIAL EXERCISES

* Basic Example: Si 

A simple example to get the mechanics right. Generate a
pseudopotential by running pg Si.tm2.inp and analyze and plot the
results. Then test the resulting pseudopotential by running pt
Si.test.inp Si.tm2.vps.

* A hard element: C 

C is a first-row element, and the 2p state does not have nodes, as
there are no other p states below it. Thus the pseudization cannot
soften the wavefunction by a whole lot, and the pseudopotential can be
quite hard. Here we explore two schemes for pseudopotential
generation: Hammann-Schluter-Chiang (code hsc), and Troullier-Martins
(code tm2).  Note how the rc's can be significantly larger for tm2
while maintaining the transferability.  Check the "softness" or
"hardness" of the resulting pseudopotentials by looking at their
fourier transform.

* Core Corrections: Na 

There are two pseudopotential input files: One for a normal case
without core corrections, and another one with corrections. Note how
the transferability of the pseudopotential improves with the use of
non-local core corrections. 

* Core or valence?: Cu 

The d electrons in Cu (and in Ga, and others) can be treated either as
"core" or "valence"  (and actually as "core but corrected"). First
generate and test the "3d in valence" pseudopotential found here
(Cu.3dtm2.inp). (You will have to prepare an input file for the test.)
Then prepare an input file for a "3d in core"
pseudopotential. Generate the pseudo and test it. Finally, put core
corrections to the pseudopotential of the "3d in core" case.

* Semicore states: Ba 

A somewhat technical example involving semicore states. Both the 5s
and 5p states, which are normally thought of as "core states", are put
in the valence. As previous versions of the program could only use ps
generation configurations with one state per angular momentum channel,
the "genuinely valence" 6s state was eliminated from the calculation
(and also the 6p, not occupied in the atom but involved in scattering
of solid-state electrons). The atomic configuration for
pseudopotential generation was thus ionic. The input for this case is
in Ba.sc-ionic.inp.

Newer versions of the ATOM program do not have this limitation, and
the full configuration can be used for pseudopotential
generation. The input for this case is in Ba.sc-full.inp. The
resulting pseudopotential is almost indistinguisable from the one
generated with the ionic configuration, which attests to the soundness
of the pseudopotential approximation. 

In any case, the pseudopotential constructed is not expected to
reproduce perfectly the 6s and 6p states, as their eigenvalues are
more than 1 eV from those of the reference states 5s and 5p, but the
actual results are not bad at all. (Use the "gp pt.gplot" command in
the test directory. You can change the order of the configurations in
the Ba.test.inp file to look at the plots in sequence: only the last
configuration is plotted.)  Note that the 6s and 6p states have a
node, as they must be orthogonal to the 5s and 5p states,
respectively.

As explained in the lecture, SIESTA will generate extra
Kleinman-Bylander projectors associated to the 5s and 5p orbitals.

A technical point: in the "ionic" case, the valence charge density
written to the pseudopotential file is re-scaled so that the total
charge is the full valence charge (including semicore states), but its
range and shape are different from the true full valence charge. This
has implications for the construction of PAOs by SIESTA.

* Semicore states: Ti

Another example of semicore states.

*Fe 

These are GGA pseudopotentials for Fe, all with core
corrections. (Even if it were not strictly necessary, a pseudo-core
helps to iron out some numerical instabilities which appear near the
origin when the GGA is used.)  

Fe.gga-cc.in: Pseudopotential with a
3d6 4s2 configuration. The p-pseudo looks a bit ugly. Increasing rc
(p) (Fe.large-rp.inp) fixes this, but is the pseudopotential more or
less transferable?  

Fe.4s13d7.inp: Pseudopotential with a 3d7-4s1
configuration.  (Test the above pseudopotentials with Fe.test.inp)
Fe.sc.inp: Pseudopotential with the 3s and 3p electrons in the
valence.  

Fe.sc.opt.inp: Same as above, but with the rc parameters
roughly optimized for transferability while keeping the
pseudopotentials relatively soft.  

(To test the small-core pseudos we need a special test file:
Fe.test.sc.inp) The above examples used the GGA. It has been shown
that the LDA predicts the wrong ground-state for bulk Fe!.










