Guide to the pseudopotential exercises 

INTRODUCTION

Please refer to the user manual for the ATOM program for details on
how to run the program and how to make sense of the output. For these
exercises we have created the aliases ae, pg, and pt to perform
all-electron, pseudopotential generation, and pseudopotential tests,
respectively, and the alias gp to stand for gnuplot -persist. The
alias energies, when used in the work directory, will show the
inter-configuration energy changes (it is equivalent to grep "&d"
OUT).  The aliases eigenvalues X, with X being s, p, d, will display
the appropriate eigenvalues when applied to the OUT file.

There are two directories: 

* All electron -- contains some exercises to illustrate some general
issues involved in com- puting the electronic structure of the
atom. Please see the file Example.guide and run the examples by
typing, for example ae si.ae.inp. Those exercises are not essential to
follow the examples of pseudopotential generation, but they might help
to broaden your understanding.

* PS_Generation -- holds the exercises for pseudopotential generation
and test. The material for each exercise is contained in a directory
named after the element. Typically there are several XX.YYY.inp files,
where XX is the element's symbol, and YYY is some identifier.  Input
files for tests have the word test somewhere in YYY.  

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 the program can only deal with one pseudized state
per angular momentum channel, this implies the elimination of the
"genuinely valence" 6s state from the calculation (and also the 6p,
not occupied in the atom but involved in scattering of solid-state
electrons). 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. 

*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!.
