# ABINIT, lesson PAW2:

## Projector augmented-wave technique : the generation of atomic data files

This lesson aims at showing how to compute atomic data files for the projector-augmented-wave method.

You will learn how to generate the atomic data and
what the main
variables are to govern their softness and transferability.

It is supposed you already know how to use ABINIT
in the
PAW case

This lesson should take about 1h30.

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**Contents of lesson
PAW2 :**

- 1. The PAW atomic dataset - introduction
- 2. Use of the generation code
- 3. First (and basic) PAW dataset for Nickel
- 4. Checking the sensitivity of results to some parameters
- 5. Adjusting partial waves and projectors
- 6. Having a look at the logarithmic derivatives
- 7. Testing efficiency of PAW dataset
- 8. Having a look at physical quantities
- 9. The Real Space Optimization (RSO) - experienced users

**1. The PAW atomic dataset - introduction
**

The PAW method is based on the definition of
atomic spheres (augmentation regions) of radius r_{PAW}around the atoms of the system in which a base of atomic partial waves φ

_{i}, of "pseudized" partial waves~φ

_{i}, and of projectors~p

_{i}(dual to~φ

_{i}) have to be defined. This set of partial-waves and projectors functions plus some additional atomic data are stored in a so-called

*PAW dataset*. A PAW dataset has to be generated for each atomic species in order to reproduce atomic behavior as accurate as possible while requiring minimal CPU and memory resources in executing ABINIT for the crystal simulations. These two constraints are conflicting.

The PAW dataset generation is the purpose of this tutorial.

It is done according the following procedure (all parameters that define a PAW dataset are in bold):

Choose and define the concerned chemical species (name and atomic number).

Solve the atomic all-electrons problem in a given atomic configuration. The atomic problem is solved within the DFT formalism, using an exchange-correlation functional and either a Schrödinger (default) or scalar-relativistic approximation. It is a spherical problem and it is solved on a radial grid. The atomic problem is solved for a given electronic configuration that can be an ionized/excited one.

Choose a set of electrons that will be considered as frozen around the nucleus (core electrons). The others electrons are valence ones and will be used in the PAW basis. The core density is then deduced from the core electrons wave functions. A smooth core density equal to the core density outside a given r

_{core}matching radius is computed.Choose the size of the PAW basis (number of partial-waves and projectors). Then choose the partial-waves included in the basis. The later can be atomic eigen-functions related to valence electrons (bound states) and/or additional atomic functions, solution of the wave equation for a given l quantum number at arbitrary reference energies (unbound states).

Generate pseudo partial-waves (smooth partial-waves build with a pseudization scheme and equal to partial-waves outside a given r

_{c}matching radius) and associated projector functions. Pseudo partial-waves are solutions of the PAW Hamiltonian deduced from the atomic Hamiltonian by pseudizing the effective potential (a local pseudopotential is built and equal to effective potential outside a r_{vloc}matching radius). Projectors and partial-waves are then orthogonalized with a chosen orthogonalization scheme.Build a compensation charge density used later in order to retrieve the total charge of the atom. This compensation charge density is located inside the PAW spheres and based on an analytical shape function (which analytic form and localization radius r

_{shape}can be chosen).

The first one is the PAW generator ATOMPAW (originally by N. Holzwarth) and the second one is the Ultra-Soft (US) generator (originally written by D. Vanderbilt). In this tutorial, we concentrate only on ATOMPAW.

It is highly recommended to refer to the following papers to well understand the generation of PAW atomic datasets:

[2] "A projector Augmented Wave (PAW) code for electronic structure calculations, Part I : atompaw for generating atom-centered functions", N. Holzwarth et al., Computer Physics Communications 135, 329 (2001)

[3] "From ultrasoft pseudopotentials to the projector augmented-wave method", G. Kresse, D. Joubert, Phys. Rev. B

[4] "Electronic structure packages: two implementations of the Projector Augmented-Wave (PAW) formalism", M. Torrent et al., Computer Physics Communications 181, 1862 (2010)

[5] "Notes for revised form of atompaw code", by N. Holzwarth

**2. Use of the generation code
**

*Before continuing, you might
consider to work in a different
subdirectory as for the other lessons. Why not "Work_paw2" ?
*

Provided that ABINIT has been compiled with the "--with-dft-flavor="...+atompaw"" option,
the ATOMPAW code is
directly available from command line.

First, just try to type: atompaw

if "atompaw vx.y.z" message appears,
everything is fine.

Otherwise, you can try "~abinit_compilation_directory/plugins/atompaw/atompaw"

In any case, in the following, we name atompaw the ATOMPAW executable.

How to use Atompaw ?

- Edit an input file in a text editor (content of input explained here)

- Run: atompaw < inputfile

_{i}, PS partial waves~φ

_{i}and projectors~p

_{i}are given in wfn.i files.

Logarithmic derivatives from atomic Hamiltonian and PAW Hamiltonian resolutions are given in logderiv.l files.

A summary of the atomic all-electrons computation and PAW dataset properties can be found in the Atom_name file (Atom_name is the first parameter of the input file).

Resulting PAW dataset is contained in:

Atom_name.atomicdata file (specific format for PWPAW code)

**3. First (and basic) PAW dataset for Nickel
**

Our test case
will be NICKEL
(1s^{2}
2s^{2} 2p^{6}
3s^{2} 3p^{6} 3d^{8} 4s^{2}
4p^{0}).

This file has been built in the following way:

1-All-electrons calculation:

- First line: define the material in the first line

- Second line: choose the exchange-correlation functional (LDA-PW or GGA-PBE) and select a scalar-relativistic wave equation (nonrelativistic or scalarrelativistic) and a (2000 points) logarithmic grid.

- Next lines: define the electronic configuration:

Besides the fully and partially occupied states, it is recommended to add all states that could be reached by electrons in the solid. Here, for Nickel, the 4p state is concerned. So we decide to add it in the computation.

- A line with the maximum n quantum number for each electronic shell; here "4 4 3" means 4s, 4p, 3d.

- Definition of occupation numbers:We choose here the 3d

^{8}4s

^{2}4p

^{0}configuration. Only 3d and 4p shells are partially occupied ("3 2 8" " and "4 1 0" lines). A "0 0 0" ends the occupation chapter.

Core shells are designated by a "c" and valence shells by a "v". All s states first, then p states and finally d states.

Here:

c

c

v

c

c

v

v

2s core

3s core

4s valence

2p core

3p core

4p valence

3d valence

Partial-waves basis generation:

- A line with l
_{max}the maximum l for the partial waves basis. Here l_{max}=2. - A
line with the r
_{PAW}radius. Select it to be slightly less than half the inter-atomic distance in the solid (as a first choice). Here r_{PAW}=2.3 a.u. If only one radius is input, all others pseudization radii will be equal to r_{PAW}(r_{c}, r_{core}, r_{Vloc}and r_{shape}). - Next
lines: add
additional partial-waves φ
_{i }if needed: choose to have 2 partial-waves per angular momentum in the basis (this choice is not necessarily optimal but this is the most common one; if r_{PAW}is small enough, 1 partial-wave per l may suffice). As a first guess, put all reference energies for additional partial-waves to 0 Rydberg.

For each angular momentum, first add "y" to add an additional partial wave. Then, next line, put the value in Rydberg units. Repeat this for each new partial wave and finally put "n"

In the present file,

0.5

n

_{ref}=0.5 Ry as been added.

0.

n

_{ref}=0. Ry has been added.

0.

n

_{ref}=0. Ry as been added.

Finally, partial waves basis contains two s-, two p- and two d- partial waves.

- Next line: definition of
the generation scheme
for pseudo partial waves~φ
_{i}, and of projectors~p_{i}. We begin here with a simple scheme (i.e. "Bloechl" scheme, proposed by P. Blöchl in ref. [1]). This will probably be changed later to make the PAW dataset more efficient. - Next line: generation scheme for local pseudopotential V
_{loc}. In order to get PS partial waves, the atomic potential has to be "pseudized" using an arbitrary pseudization scheme. We choose here a "Troullier-Martins" using a wave equation at l_{loc}=3 and E_{loc}=0. Ry. As a first draft, it is always recommended to put l_{loc}=1+l_{max}(l_{max}defined above). - Next two lines: a "2" (two) tells ATOMPAW to generate PAW dataset for ABINIT; the next line contains options for this ABINIT file. "default" set all parameters to their default value.
- A 0 (zero) to end the file.

At this stage, run atompaw !

For this purpose, simply enter: atompaw <Ni.atompaw.input1

Lot of files are produced. We will have a look at some of them.

A summary of the PAW dataset generation process has been written in a file named Ni (name extracted from first line of input file). Open it. It should look like:

Perdew - Burke - Ernzerhof GGA Log grid -- n,r0,rmax = 2000 2.2810899E-04 8.0000000E+01

Scalar relativistic calculation -- point nucleus

all-electron results

core states (zcore) = 18.0000000000000

1 1 0 2.0000000E+00 -6.0358607E+02

2 2 0 2.0000000E+00 -7.2163318E+01

3 3 0 2.0000000E+00 -8.1627107E+00

5 2 1 6.0000000E+00 -6.2083048E+01

6 3 1 6.0000000E+00 -5.2469208E+00

valence states (zvale) = 10.0000000000000

4 4 0 2.0000000E+00 -4.1475541E-01

7 4 1 0.0000000E+00 -9.0035738E-02

8 3 2 8.0000000E+00 -6.5223644E-01

evale = -185.182300204924

selfenergy contribution = 8.13253645212050

paw parameters:

lmax = 2

rc = 2.30969849741149

irc = 1445

Vloc: Norm-conserving Troullier-Martins form; l= 3;e= 0.0000E+00

Projector method: Bloechl

Sinc^2 compensation charge shape zeroed at rc

Number of basis functions 6

No. n l Energy Cp coeff Occ

1 4 0 -4.1475541E-01 -9.5091493E+00 2.0000000E+00

2 999 0 5.0000000E-01 3.2926940E+00 0.0000000E+00

3 4 1 -9.0035738E-02 -8.9594194E+00 0.0000000E+00

4 999 1 0.0000000E+00 1.0836820E+01 0.0000000E+00

5 3 2 -6.5223644E-01 9.1576176E+00 8.0000000E+00

6 999 2 0.0000000E+00 1.3369075E+01 0.0000000E+00

evale from matrix elements -1.85182309373359203E+02

The generated PAW
dataset (contained in Ni.atomicdata, Ni.GGA-PBE-paw.abinit
or Ni.GGA-PBE.xml
file) is a
first draft.

Several parameters have
to be adjusted, in order to get accurate results and efficient DFT
calculations.

Note that only Ni.GGA-PBE-paw.abinit file is directly usuable by ABINIT.

### 4. Checking the sensitivity of results to some parameters

The radial grid:

Try to select 700 points in the
logarithmic
grid and check if any
noticeable difference in the results appears.

You just have to
replace 2000 by 700 in the second line of Ni.atompaw.input1
file. Then
run atompaw
<Ni.atompaw.input1 again
and look at Ni
file:

evale = -185.182300567432

evale from matrix
elements
-1.85182301887091256E+02

You could decrease the size of the grid; by setting 400 points you should obtain:

Small grids give PAW dataset with small size (in kB) and run faster in ABINIT, but accuracy can be affected.

- Note that the final r_{PAW} value ("rc =
..." in Ni
file) change with the
grid; just because r_{PAW} is adjusted in
order to exactly
belong to the radial grid. By looking in ATOMPAW user's
guide, you
can choose to keep it constant.

- Also note that, if the results are difficult to get converged (some error produced by ATOMPAW), you should try a linear grid…

The relativistic approximation of the wave equation:

Scalar-relativistic option should give better results than non-relativistic one, but it sometimes produces difficulties for the convergence of the atomic problem (either at the all-electrons resolution step or at the PAW Hamiltonian solution step). If convergence cannot be reached, try a non-relativistic calculation (not recommended for high Z materials)

For the following, note that you always should have a look at Ni file, especially the values of valence energy ("evale"). You can find the valence energy computed for the exact atomic problem and the valence energy computed with the PAW parameters ("evale from matrix elements"). Both have to be closed !

### 5. Adjusting partial waves and projectors

Have a
look at the partial-waves, PS partial-waves and projectors.

Plot
the
wfni
(i=1 to
6=number of partial waves) files in a graphical tool of your choice.
You should get 3
curves per
file: partial wave φ_{i}, PS partial wave~φ_{i},
and projector~p_{i}.

Example here with the first s- partial wave /projector:

The φ

_{i}should meet the~φ_{i }near or after the last maximum (or minimum). If not, it is preferable to change the value of the matching (pseudization) radius.The ~φ

_{i }and ~p_{i}should have the same order of magnitude (some units). If not, you can try to get this in three ways:- Change the matching radius for this partial-wave; but this is not always possible (spheres cannot have a large overlap in the solid)...

- Change the pseudopotential scheme (see later).

- If there are two (or more) partial waves for the considered l angular momentum, decreasing the magnitude of projector is possible by displacing the references energies. Moving the energies away from each other generally reduce the magnitude of projectors, but a too big difference between energies can lead to wrong logarithmic derivatives (see following chapter).

Example: plot the wfn6 file, concerning the second d- partial wave:

This
partial wave has been
generated at E_{ref}=0 Ry and
orthogonalized with the first d-
partial wave which has an eigenenergy equal to -0.65Ry (see Ni file).
These two energies are too close and orthogonalization process produces
"high" partial waves.

Try
to
replace the reference energy for
the additional d-
partial wave. For example, put E_{ref}=1. instead of E_{ref}=0.
(line 24 of Ni.atompaw.input1
file). Run ATOMPAW again and
plot wfn6 file:

Now PS partial wave and projector have the same order of magnitude !

Note
again that you always should have a look
at the evale
values in Ni
file and keep them as
close at
possible.

If not, choices for projectors and/or partial waves
certainly are not judicious.

### 6. Having a look at the logarithmic derivatives

Have
a
look at the logarithmic
derivatives, i.e. derivatives of a l-state d(log(Ψ_{l}(E))/dE computed
for exact atomic problem and with th PAW dataset.

They are
printed
in the logderiv.l
files. Each logderiv.l
file
correspond to l
quantum
number and contains the logarithmic
derivatives of the l-state.
Here, l=0,
1
or 2.

They should have the following properties:

The 2 curves should be superimposed as much as possible. By construction, they are superimposed at the two energies corresponding to the two l partial-waves. If the superimposition is not good enough, the reference energy for the second l partial-wave should be changed.

Generally a discontinuity in the logarithmic derivative curve appears at 0<=E

_{0}<=4 Rydberg. A reasonable choice is to choose the 2 reference energies so that E_{0}is in between.Too close reference energies produce “hard” projector functions (as previously seen in 5. chapter). But moving reference energies away from each other can damage accuracy of logarithmic derivatives

As you can see, except for l=2, exact and PAW logarithmic derivatives do not match !

According to the previous remarks, try other values for the references energies of the s- and p- additional partial waves.

First, edit again the Ni.atompaw.input1 file and put E

_{ref}=3Ry for the additional s- state (line 18); run ATOMPAW again. Plot the logderiv.0 file. You should get:

Then put E

_{ref}=4Ry for the second p- state (line 21); run ATOMPAW again. Plot again the logderiv.1 file. You should get:

Note: enlarging energy range of logarithmic derivatives plots

It is possible to change the interval of energies used to plot logarithmic derivatives (default is [-5;5]) and also to compute them at more points (default is 200). Just add the following keywords at the end of the SECOND LINE of the input file:

logderivrange -10 10 500

In the above example ATOMPAW plots logarithmic derivatives for energies in [-10;10] at 500 points.

Additional information concerning logarithmic derivatives:

Another possible problem could be the presence of a discontinuity in the PAW logarithmic derivative curve at an energy where the exact logarithmic derivative is continuous.

This generally shows the presence of a “ghost state”.

- First, try to change to value of reference energies; this sometimes can make the ghost state disappear.
- If not, it can be useful to:

A second solution is to select an "ultrasoft" pseudopotential, freeing the norm conservation constraint (simply replace "troulliermartins" by "ultrasoft" in input file)

A third solution is to select a simple “bessel” pseudopotential (replace "troulliermartins" by "bessel" in input file). But, in that case, one has to noticeably decrease the matching radius r

_{Vloc}if one wants to keep reasonable physical results. Selecting a value of r

_{Vloc}between 0.6*r

_{PAW}and 0.8*r

_{PAW}is a good choice; but the best way to adjust r

_{Vloc}value is to have a look at the two values of evale in Ni file which are sensitive to the choice of r

_{Vloc}. To change the value of r

_{Vloc}, one has to detail the line containing all radii (r

_{PAW}, r

_{shape}, r

_{Vloc}and r

_{core}); see user's guide.

_{c}for one (or both) l partial-wave(s). In some cases, changing r

_{c}can remove ghost states.

- In most cases (changing pseudopotential or matching radius), one has to restart the procedure from step 5.

Look at the l=1 logarithmic derivatives (logderiv.1 file). They look like:

Edit again the file and replace 'ultrasoft" by "bessel"; then change the 17th line ("2.0 2.0 2.0 2.0") by "2.0 2.0 1.8 2.0". This has the effect of decreasing the r

_{Vloc}radius. Run ATOMPAW: the ghost state disappears !

Start from the original state of Ni.ghost.atompaw.input file and put 1.8 for the matching radius of p- states (put 1.8 on lines 31 and 32). Run ATOMPAW: the ghost state disappears !

### 7. Testing efficiency of PAW dataset

Let's use again our Ni.atompaw.input1 file for Nickel (with all our modifications).You get a file Ni.GGA-PBE-paw.abinit containing the PAW dataset designated for ABINIT.

Now, one has to test the efficiency of the generated PAW dataset. We finally will use ABINIT !

You are about to run a DFT computation and determine the size of the plane wave basis needed to get a given accuracy. If the cut-off energy defining the plane waves basis is too high (higher than 20 Hartree, if r

_{PAW}has a reasonable value), some changes have to be made in the input file.

Copy ~abinit/tests/tutorial/Input/tpaw2_x.files and ~abinit/tests/tutorial/Input/tpaw2_1.in in your working directory. Run ABINIT with them.

ABINIT computes the total energy of ferromagnetic FCC Nickel for several values of ecut.

At the end of output file, you get this:

ecut1 8.00000000E+00 Hartree

ecut2 1.00000000E+01 Hartree

ecut3 1.20000000E+01 Hartree

ecut4 1.40000000E+01 Hartree

ecut5 1.60000000E+01 Hartree

ecut6 1.80000000E+01 Hartree

ecut7 2.00000000E+01 Hartree

ecut8 2.20000000E+01 Hartree

etotal1 -3.9300291581E+01

etotal2 -3.9503638785E+01

etotal3 -3.9583278145E+01

etotal4 -3.9613946329E+01

etotal5 -3.9623543087E+01

etotal6 -3.9626889070E+01

etotal7 -3.9628094989E+01

etotal8 -3.9628458879E+01

etotal convergence (at 1 mHartree) is achieve for 18<=ecut<=20 Hartree

etotal convergence (at 0,1 mHartree) is achieve for ecut>22 Hartree

This is not a good result for a PAW dataset; let's try to optimize it.

- First possibility: use Vanderbilt projectors instead of Bloechl ones.

Keyword "bloechl" has to be replaced by "vanderbilt" in the ATOMPAW input file and r

_{c}values have to be added at the end of the file (one for each PS partial wave).

You can have a look at the ATOMPAW input file : ~abinit/doc/tutorial/lesson_paw2/Ni.atompaw.input.vanderbilt

But we will not test this case here as it produces particular results (see below).

- 2nd possibility: use RRKJ pseudization scheme for projectors.

As you can see (by editing the file) “bloechl” has been changed by ”custom rrkj” and 6 r

_{c}values have been added at the end of the file; each one correspond to the matching radius of one PS partial wave.

Repeat the entire procedure (ATOMPAW + ABINIT)... and get a new ABINIT output file.

Note: you have to look again at log derivatives in order to verify that they still are correct...

ecut2 1.00000000E+01 Hartree

ecut3 1.20000000E+01 Hartree

ecut4 1.40000000E+01 Hartree

ecut5 1.60000000E+01 Hartree

ecut6 1.80000000E+01 Hartree

ecut7 2.00000000E+01 Hartree

ecut8 2.20000000E+01 Hartree

etotal1 -3.9600401638E+01

etotal2 -3.9627563690E+01

etotal3 -3.9627901781E+01

etotal4 -3.9628482371E+01

etotal5 -3.9628946655E+01

etotal6 -3.9629072497E+01

etotal7 -3.9629079826E+01

etotal8 -3.9629097793E+01

etotal convergence (at 0,1 mHartree) is achieve for 16<=ecut<=18 Hartree

This is a reasonnable result for a PAW dataset !

- 3rd possibility: use enhanced polynomial pseudization scheme for projectors.

Optional exercice: let's go back to Vanderbilt projectors

As you can see ABINIT convergence cannot be achieved !

You can try whatever you want with radii and/or references energies in the ATOMPAW input file: ABINIT always diverges !

The solution here is to change the pseudization scheme for the local pseudopotential.

Try to replace the "troulliermartins" keyword by "ultrasoft". Repeat the procedure (ATOMPAW + ABINIT).

ABINIT can now reach convergence !

Results are below:

ecut2 1.00000000E+01 Hartree

ecut3 1.20000000E+01 Hartree

ecut4 1.40000000E+01 Hartree

ecut5 1.60000000E+01 Hartree

ecut6 1.80000000E+01 Hartree

ecut7 2.00000000E+01 Hartree

ecut8 2.20000000E+01 Hartree

etotal1 -3.9609714395E+01

etotal2 -3.9615187859E+01

etotal3 -3.9618367959E+01

etotal4 -3.9622476129E+01

etotal5 -3.9624707476E+01

etotal6 -3.9625234480E+01

etotal7 -3.9625282524E+01

etotal8 -3.9625330757E+01

etotal convergence (at 0,1 mHartree) is achieve for 20<=ecut<=22 Hartree

Note: You could have tried the "bessel" keyword instead of "ultrasoft"...

Summary of convergency results:

Final remarks:

The localization of projectors in reciprocal space can (generally) be predicted by a look at tprod.i files. Such a file contains the curve of as a function of q (reciprocal space variable). q is given in Bohr

^{-1}units; it can be connected to ABINIT plane waves cut-off energy (in Hartree units) by: ecut=q_{cut}^{2}/4. These quantities are only calculated for the bound states, since the Fourier transform of an extended function is not well-defined.Generating projectors with Blöchl’s scheme often gives the guaranty to have stable calculations. atompaw ends without any convergence problem and DFT calculations run without any divergence (but they need high plane wave cut-off). Vanderbilt projectors (and even more “custom” projectors) sometimes produce instabilities during the PAW dataset generation process and/or the DFT calculations…

In most cases, after having changed the projector generation scheme, one has to restart the procedure from step 5.

### 8. Having a look at physical quantities

Finally,
the last step is to have a careful
look at physical quantities obtained with the PAW
dataset.

Copy ~abinit/tests/tutorial/Input/tpaw2_2.in
in your working directory.

Use the
~abinit/doc/tutorial/lesson_paw2/Ni.GGA-PBE-paw.abinit.rrkj
psp file (it
has been obtained from Ni.atompaw.input2
file).

Modify
tpaw2_x.files
file according to these new files.

Run ABINIT (this may take a
while...).

ABINIT computes the converged ground state of ferromagnetic FCC Nickel for several volumes around equilibrium.

Plot the etotal vs acell curve:From this graph and output file, you can extract some physical quantities:

_{0}= 3.523 angstrom

Bulk modulus: B = 190 GPa

Magnetic moment at equilibrium: μ = 0.60

Compare these results with published results:

- GGA-FLAPW (all-electrons - ref [3]):

_{0}= 3.52 angstrom

B = 200 GPa

μ = 0.60

- GGA-PAW (VASP - ref [3]):

_{0}= 3.52 angstrom

B = 194 GPa

μ = 0.61

- Experimental results

from Dewaele, Torrent, Loubeyre, Mezouar. Phys. Rev. B 78, 104102 (2008):

_{0}= 3.52 angstrom

B = 183 GPa

You should always compare results with all-eletrons ones (or other PAW computations), not with experimental ones...

Additional remark:

It can be useful to test the sensitivity of results to some ATOMPAW input parameters (see user's guide for details on keywords):

- The
analytical form and the cut-off radius r
_{shape}of the shape function used in compensation charge density definition. By default a “sinc” function is used but “gaussian” shapes can have an influence on results. “Bessel” shapes are efficient and generally need a smaller cut-off radius (r_{shape}=~0.8*r_{PAW}). - The
matching radius r
_{core}used to get pseudo core density from atomic core density. - The integration of additional (“semi-core”) states in the set of valence electrons.
- The
pseudization scheme used to get pseudopotential V
_{loc}(r).

All these parameters have to be meticulously checked, especially if the PAW dataset is used for non-standard solid structures or thermo dynamical domains.

Optional exercice: let's add 3s and 3p semi-core states in PAW dataset !

The run is a bit longer as more electrons have to be treated by ABINIT.

Look at a

_{0}, B or μ variation.

_{PAW}radius (because semi-core states are localized).

_{0}= 3.519 angstrom

B = 194 GPa

μ = 0.60

### 8. The Real Space Optimization (RSO) - experienced users

In this chapter, an additional optimization of the atomic data is proposed which can contribute, in some cases, to an acceleration of the convergence on ecut. This optimization is not essential to produce efficient PAW datasets but it can be useful. We advise experienced users to try it. The idea is
quite simple: when expressing the different atomic radial functions
(φ_{i},~φ_{i}, ~p_{i})
on the plane
waves basis, the number of plane waves depends on the
"locallity" of these radial functions in reciprocal space.

In the
following reference (we suggest to read it): R.D. King-Smith,
M.C. Payne, J.S. Lin, Phys. Rev. B 44,
13063 (1991)

_{i }is presented:

_{i}(g) expressed in reciprocal space are modified according to the following scheme:

_{max},~p

_{i}(g) is unchanged

- If g > γ,~p

_{i}(g) is set to zero

- If g

_{max}< g < γ,~p

_{i}(g) is modified so that the contribution of~p

_{i}(r) is conserved with an error W (as small as possible).

_{i}(g) is only possible if~p

_{i}(r) is defined outside the augmentation sphere up to a radius R

_{0}(with R

_{0}>r

_{c}).

- Adjust g

_{max}according to Ecut (g

_{max}<= Ecut)

- Choose γ so that 2*g

_{max}< γ < 3*g

_{max}

_{i}and deduce R

_{0}radius.

You can test it now.

In your working directory, re-use the dataset with Bloechl projectors ( ~abinit/doc/tutorial/lesson_paw2/Ni.atompaw.input3).

Replace the last line but one ("default") by "rsoptim 8. 2 0.0001" (8., 2 and 0.0001 are the values for g

_{max}, γ/g

_{max}and W).

Run ATOMPAW.

You get a new psp file for ABINIT.

Run ABINIT with it using the ~abinit/tests/tutorial/Input/tpaw2_1.in file.

Compare the results with those obtained in chapter 7.

You
can try several values for g_{max}
(keeping γ/g_{max}
and
W constant) and compare the
efficiency of the atomic data; do not forget to test
physical properties again.

How to choose the RSO parameters ?

_{max}=2 and 0.0001 < W < 0.001 is a good choice.

g

_{max}has to be adjusted. The lower g

_{max}the faster the convergence is ; but too low g

_{max}can produce unphysical results.

Goto :

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Help files :

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**Optic**