Commit 3931bcbb authored by Alberto Garcia's avatar Alberto Garcia Committed by Alberto
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New structure for documentation

parent 6fea7752
......@@ -3,18 +3,12 @@
You can adapt this file completely to your liking, but it should at least
contain the root `toctree` directive.
Welcome to ATOM's documentation!
================================
ATOM documentation
==================
.. toctree::
:maxdepth: 2
:caption: Contents:
./atom
:maxdepth: 1
Indices and tables
==================
reference/index.rst
tutorial/index.rst
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`
.. container:: center
ATOM User manual
****************
  **ATOM User Manual**
**Version 4.2.0, 20 January 2017**
| Alberto Garcı́a
| ICMAB-CSIC, Barcelona
albertog@icmab.es
:author: Alberto Garcı́a, ICMAB-CSIC, Barcelona
albertog@icmab.es
PREFACE
=======
......@@ -21,7 +16,6 @@ structural changes to the April 1990 (5.0) Minnesota version while at
Berkeley and elsewhere.
Jose Luis Martins is maintaining his own version of the code:
::
http://bohr.inesc-mn.pt/~jlm/pseudo.html
......@@ -41,10 +35,8 @@ The program’s basic capabilities are:
A PRIMER ON AB-INITIO PSEUDOPOTENTIALS
======================================
Time constraints prevent the inclusion of this section in this first
release of the ATOM manual. But, in this case more than ever, there is a
lot to be gained from reading the original literature... Here are some
basic references:
In this case more than ever, there is a lot to be gained from reading
the original literature... Here are some basic references:
- Original idea of the ab-initio pseudopotential:
......
.. _reference:
Technical reference
===================
.. toctree::
:maxdepth: 1
atom
.. _tutorial-all-electron:
All-electron calculations
=========================
This tutorial ontains some exercises to illustrate some general issues
involved in computing the electronic structure of the atom. Run the
examples by typing, for example::
ae si.ae.inp.
These exercises are not essential to follow the examples of
pseudopotential generation, but they might help to broaden your
understanding.
Guide to all-electron calculation examples:
Si:
The ground state and the Si+3 ion (unpolarized calculations).
Note the insensitivity of the core electrons to the ionization of
three valence electrons. The file si.series.ae.inp contains a series
of jobs to study several excited states of the atom.
N:
We know that Hund's rule should be obeyed for orbitals not completely
full. Use the n_hund.ae.inp file to test whether that is so. In the first
calculation the effect of the spin is neglected. The second deals with
spin polarization effects, but the occupation of the 2p level is "wrong":
there are 2 electrons "down" and one "up". The third calculation should
correspond to the true ground state, with all the 2p electrons with their
spins aligned.
Fe:
Here is another example of the importance of spin effects in
certain cases. Iron has 6 electrons in the 3d orbital. The proper
spin polarization lowers the energy.
Pb:
Lead is a heavy atom, and most of the electrons have velocities which are
a significant fraction of the speed of light. A relativistic calculation
should then be essential. The Dirac equation is solved, and spin effects
appear naturally through the j quantum number.
Ba:
Its core is quite large, and it is customary to consider the 5s and 5p
as "semicore states", putting them in the valence complex.
.. _introduction:
Tutorials
===========
This set of tutorials will guide you in the exploration of ATOM's
features
.. note::
Input files have a .inp extension, and should be run using
the ae.sh (all-electron), pg.sh (ps generation), or pt.sh (ps test)
shell scripts in directory Utils. See the manual (Docs/atom.tex)
for details.
After the run, the output information and plotting scripts will
reside in a sub-directory whose name is that of the input file
without the .inp extension.
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.
(** The aliases referred to in this section apply only
to the "live" tutorials, or to users who have set up the
aliases mentioned ----
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.
--- **)
.. toctree::
:maxdepth: 1
all-electron/index.rst
ps-generation/index.rst
.. _tutorial-ps-generation:
Pseudopotential generation
==========================
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. Please see the file Guide.txt
for more information.
* 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!.
Additional notes
----------------
Extra exercises to illustrate some important concepts.
1. Consider the hydrogen atom. It might seem perverse to use a
formalism that includes interaction between parts of the 'electronic
cloud' (and also exchange and correlation effects!) when only one
electron is concerned. And it might come as a surprise that the
calculated total energy of the atom is only around 10% off (the
eigenvalue is off by more than that, but we could claim that
'what is free comes with no guarantee'). What is going on is a near
cancellation between the the Hartree term and the exchange-correlation
term of the total energy. Perform the calculation and see for
yourself. Incidentally, in a true Hartree-Fock calculation the
cancellation is perfect.
The lesson of this extreme example is to remember that we are
approximating the complicated many-body problem by a 'simple' sort of
mean-field theory. There have been attempts to incorporate
self-interaction overcounting into the LDA formalism. See for example:
J. Perdew and A. Zunger, Phys. Rev. B. 23, 5048 (1981)
which, by the way, contains also one of the more widely used
parametrizations of the Ceperley-Alder exchange-correlation
calculations for the electron gas.
2. To generate a pseudopotential one needs to start with an
electronic configuration of the atom. Usually it is the ground state,
but it need not be so, and in some cases one needs to artificially
populate an orbital which is empty in the ground state, just so that
the corresponding angular momentum is represented in the
pseudopotential. For example, consider Si, whose ground state is
[Ne]3s2 3p2. If one uses that configuration to construct the
pseudopotential, only the s and p channels will be generated. That is
why a configuration such as [Ne]3s2 3p0.50 3d0.5 is chosen (the
appearance of fractional occupancies should not scare you -- remember
we consider the electrons only through their charge density--). The
choice is more or less arbitrary, although sometimes it helps to know
something about the environment in which the atom is going to find
itself in the solid-state calculation (i.e., we would prefer an ionic
configuration for Na to do calculations for NaCl). In any case,
whatever the starting configuration, the pseudopotential, by
definition and construction, should be basically the same, and should
give equally satisfactory results when tested in any (up to a limit
explored in the following exercise) configuration. Convince yourself
of this by choosing different electronic configurations to generate
the pseudopotential for a given element (Si, or whatever) and test
them on a series of atomic configurations (such as those exemplified
bu the ATOM/ae/si.series.ae.inp file).
3. In this exercise we look more closely at the role of the r_c 'core
radius' parameter in the generation of a pseudopotential. We know that
it is *not* (or it should not be used as) an adjustable parameter to
fit condensed-state properties. By construction, the scattering
properties of the pseudopotential and the true atomic potential are
the same in an energy region around a given eigenvalue. So when we
use the pseudopotential to calculate properties of a configuration
different that that used for its generation (atomic or solid), we
should expect good results, even if the eigenvalue changes due to
hybridization, banding, etc. That is what is called transferability.
What is found 'experimentally' is that the larger the r_c, the lower
the degree of transferability, but the softer the pseudopotential. By
'softer' we mean here that one needs fewer fourier components to
represent it in Fourier space. The price of higher transferability is
a 'harder' pseudopotential.
Test this 'empirical rule', using the plots you can generate after
each pseudopotential generation.
4. While the 'rule' explored in the previous exercise is inescapable
(if r_c diminishes we are closer and closer to the 'wiggly' core
region), there are still some opportunities to play with the way in
which the pseudo-wavefunction is constructed from the true
wavefunction. The idea is to make the pseudopotentials softer for a
given degree of transferability. Thus the different methods: HSC
(Hamann-Schluter-Chiang) KER (Kerker), TM2 (Improved
Troullier-Martins), VAN (Vanderbilt 1988), BHS
(Bachelet-Hamman-Schluter), and many others. (All of them retain the
idea of norm conservation. There is a more recent method [Vanderbilt,
1990] in which that idea is abandoned, obtaining 'ultrasoft'
pseudopotentials at the expense of some complications in the use of
the potential.)
For the purposes of this exercise it will be enough to compare HSC and
TM2 potentials. The way in which TM2 fits the pseudo-wavefunction to
the true wavefunction allows the use of larger rc's (sometimes even
larger than the position of the peak in the wavefunction).
Again, Si could serve as an example, but the true usefulness of the
TM2 approach lies in the softer potentials obtained for some 'problem'
elements. Try it for C and a transition metal.
5. To obtain the 'bare' pseudopotential one has to unscreen the total
potential a valence electron sees. In the standard pseudopotential
approximation we unscreen with only the valence charge density, so we
are neglecting the effect of the overlap of the core and valence
charge densities (we dump the 'core only' terms in the
pseudopotential). It is not too serious for the Hartree term, since it
is linear (it depends on (n_c + n_v), that is, linearly). But the
exchange-correlation term depends on the 1/3th power of the total
charge density... The problems associated with this and a way to fix
them are explained in:
S.G. Louie, S. Froyen, and M.L. Cohen, Phys. Rev. 26, 1738 (1983)
(the paper makes some emphasis on spin-polarized systems, but the
method works for all cases).
The problem is more acute the larger the overlap of the 'valence'
and 'core' densities. The quotes in the previous sentence refer to the
arbitrariness in defining the terms 'core' and 'valence'. Take iron.
It would be 'evident' to everybody that, since the 3d orbital is still
filling up, one has to consider the 3d electrons as 'valence'. Now
consider Zinc. The 3d orbital is full, and there is a strong
temptation to consider it as 'core', since it makes up a full shell.
If one takes that option (do it), one can see that there is an
enormous overlap of the core and valence charge densities {Use the
chargec macro [load chargec ; chargec] to plot it, to set a scale
favoring the valence density}; it looks as if the valence charge is
almost completely contained under the core charge. Clearly this is
going to be a 'tough' case for a standard pseudopotential.
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