# 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 1 hour to be done.

##### Copyright (C) 2005-2006 ABINIT group (FJ,MT,FB)
This file is distributed under the terms of the GNU General Public License, see ~abinit/COPYING or http://www.gnu.org/copyleft/gpl.txt .
For the initials of contributors, see ~abinit/doc/developers/contributors .

Goto : ABINIT home Page | Suggested acknowledgments | List of input variables | Bibliography

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### Contents of lesson PAW2 :

- 1. The PAW atomic data
- 2. Installation of the generation code
- 3. Calculation of the all-electron data
- 4. Calculation of the pseudized data
- 5. Test of the physical properties

- rc
- lloc
- rcloc
- rpcor
- Optimal parameters

- 6. The Real Space Optimisation
- 7. Description of the PAW atomic data file

### 1. The PAW atomic data

Norm-concerving plane wave calculations in ABINIT are done in the frame of the pseudopotential approach: only valence electrons are explicitely taken into account, the interactions between ionic core and valence electrons being treated through a pseudopotential. This is why, for each element, there is one pseudopotential file to be used in the calculation. The PAW method is based on the definition of atomic spheres of radius rc, around the atoms of the system in which a base of atomic wavefunctions φi, of "pseudized" wavefunctions of φi, tφi, and of projectors pi , dual to tφi have to be defined. All these data , and some other ones that will be precised hereunder, are called PAW atomic data. As for pseudopotentials, a PAW atomic data file must be generated for each element. This generation is the purpose of this tutorial.

For the moment, it has been decided not to write a specific PAW atomic data generator from scratch for ABINIT, but to interface two already existing generators. The first one is the PAW generator Atompaw, promoted by N. Holzwarth and the second one is the Ultra-Soft (US) generator USPP promoted by D. Vanderbilt. You can find how to use these two packages on the ABINIT web site.
In this tutorial, we concentrate only on USPP.

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

[1] "Soft self-consistent pseudopotentials in a generalized eigenvalue formalism", by D. Vanderbilt, Phys. Rev. B 41, 7892 (1990)
[2] "Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials", K. Laasonen et al., Phys. Rev. B 47, 10142 (1993)
[3] "A projector Augmented Wave (PAW) code for electronic structure calculations, PartI : atompaw for generating atom-centered functions", by N. Holzwarth et al., Computer Physics Communications 135, 329 (2001)
[4] "From ultrasoft pseudopotentials to the projector augmented-wave method", G. Kresse, D. Joubert, Phys. Rev. B 59,1758 (1999)

### 2. Installation of the generation code

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

You will find the USPP + USPP2ABINIT interface here. You have first to unzip and untar the file.
Go into /Uspp2Abinit directory and edit Makefile file; modify it according to your machine specifications.

Into /Uspp2Abinit directory:
Type: make
It compiles a patched version of USPP (with Abinit’s PAW add-ons) and creates runatom.x in /uspp-xy z/USpp2Abinit directory
Type : make install
It installs "patched" runatom.x into /uspp-xyz/Bin directory

At this stage you get a patched version of USPP package; you can use it like original USPP.

### 3. Calculation of the all-electron data

We are going to generate atomic data for Titanium. Go into /Work/022-Ti/022-Ti-ca-sp-vgrp directory.
There are six files:

- README: some informations about the PAW atomic data for the element (physical properties, convergency, transferability ...)
- ti_ae_s2d1.adat: input file for all electron calculation in the s2d1 configuration.
- ti_ae_s2d2.adat: input file for all electron calculation in the s2d2 configuration.
- ti_ps.adat: input file for the pseudization.
- ti_test_s2d2.adat: input file for test calculation in the s2d2 configuration.
- Makefile: management of the calculation.

The first thing to do is to choose a ionic configuration for Titanium to generate the atomic data.
The neutral configuration is s2d2. However, in order to produce transferable data, the generation is sometimes performed on ionic configuration, s2d1 for instance.
We shall start here from a s2d1 configuration. This means that for the all electron calculation, the file ti_ae_s2d1.adat will be used.
Go into the Makefile. At the beginning of the file you will find the following lines:

#################################################################
# This is the only section that usually needs to be modified
#
# Set parameters:
# ATOM = chemical symbol of atom
# CFG = atomic or ionic configuration used for generation
# CFT = atomic or ionic configuration used for testing
ATOM= ti
CFG= s2d1
CFT= s2d2
#################################################################

You could put CFG=s2d2 to start from a neutral configuration.

The Makefile is built so that when typing make, an all electron calculation will be made with the input file ti_ae_s2d1.adat, followed by a pseudization calculation with the input file ti_ps.adat.
You are now ready to start the generation.
Open the input file ti_ae_s2d1.adat. Open also the file /DOC/INPUT_AE. This is the documentation for the all electron file. Read it carefully in order to understand the signification of all the input variables. Remember that the units of the code are Rydberg for energies and Bohr for the distances. Remember also that USPP is written in Fortran 77 and that you have to respect formats (number of spaces and digits) when modifying the input data.
For PAW, you have only to take care of the input variable exfact, that governs the exchange-correlation functionnal:
exfact=0 is to be taken for a LDA PZ Ceperley Adler functionnal
exfact=-1 is to be taken for a LDA Wigner functionnal
exfact=-2 is to be taken for a LDA Hedin-Lundquist functionnal
exfact=5 is to be taken for a GGA PBE functionnal.
The other choices are not compatible with ABINIT.
In the present tutorial we propose to generate a GGA atomic dataset for ABINIT.
In the ti_ae_s2d1.adat file, modify the value of the exfact parameter (put 5. in place of 0. value).
Repeat the same operation in the ti_ae_s2d2.adat file file (useful for tests; see below).

### 4. Calculation of the pseudized data

4.a Description of the input file and relevant parameters for the generation of PAW atomic data

Open the input file ti_ps.adat. Open also the file /DOC/INPUT_GEN. This is the documentation for the pseudization file. Read it carefully in order to understand the signification of all the input variables. Remember that the units of the code are Rydberg for energies and Bohr for the distances. Remember also that USPP is written in Fortran 77 and that you have to respect formats (number of spaces and digits) when modifying the input data.
The more sensistive variables in ti_ps.adat are:

- rc: defines the PAW sphere radius (at rc the φi/tφi becomes equal). It plays a role in the softness of the pseudization (greater rc is softer the pseudized functions are). A compromise has however to be found because a too large rc value leads to an unphysical overlap between neighbouring spheres.

- nbeta: defines the total number of atomic basis functions. Experience shows that two functions per l angular momentum is a good compromise.

- lll,keyee,eeread: define the reference energies associated with each atomic basis function. In the frame of this tutorial we shall not change these values; however in general case they are to be adjusted to obtain good physical results.

- lloc: defines the channel chosen as local along the pseudization generation process (0 for s, 1 for p, 2 for d and 3 for f). Projectors are indeed computed as solution of an equation including a "local" potential.

- rcloc: defines the radius used to pseudize the potential (at rcloc the pseudized and the all-electron local potentials are equal).

- rpcor: defines the pseudization radius used for the electronic core density (at rpcor core density becomes equal to pseudized core density).

As an example, in the ti_ps.adat file, modify the value of the rc parameter (put 2. in place of 1.8 value):

2.0 2.0 2.0 rc (4f10.5)

4.b Generation of the PAW atomic data file

In order to generate PAW atomic data (in a format readable by ABINIT) with the 'patched" USPP, you just have to type:

make clean&&make

in the /Work/022-Ti/022-Ti-ca-sp-vgrp directory.
You should obtain the following error message:
all electron calculation completed
../../../Bin/runatom.x ti_ps.adat ti_ps.out ti_ae_s2d1.ae ti_ps.atwf ti_ps.logd ti_ps.uspp
beginning execution pseudopotential program version 7.3.5
make: *** [ti_ps.uspp] Error 1
Look at the end of the ti_ps.out file:
***error in subroutine readin
need ifqopt=3 for gga, exfact= 5.00000000000000
As suggested by the error message, modify the value of the ifqopt parameter in the ti_ps.adat file (put 3 in place of the 2 default value).
You also need to modify the value of nqf and npf parameters to be compatible with ifqopt=3 value (put 8 in place of the 5 default value).
The modification of the ifqpot/nqf/npf parameters has influence on the pseudization of core density.
Type again:

make clean&&make

At the end of the ti_ps.out file, you can read:
vhxc: negative density at 439 r-values
As suggested in the /DOC/TUTORIAL file, you have to decrease the value of rinner parameter in the ti_ps.adat file (put 0.6 in place of the 1. value).
The modification of the rinner parameter is needed in the context of ultrasoft pseudopotential generation; it has no influence on the generation of PAW atomic data. But we had to change it to reach the end of USPP execution without error.
Now you can type again:

make clean&&make

The code now runs without error.
Among the several files created you may be interested in the following:

- ti_ae_s2d1.out: output information of the all-electron calculation.
- ti_ps.out: output information of the pseudization process.
- ti_ps.uspp: "standard" Vanderbilt ultra-soft pseudopotential (binary format).
- ti_ps.abinit.paw: PAW atomic data for ABINIT.

Have a look at the ti_ps.abinit.paw file; it looks like described here.
The aim of the present tutorial is to obtain a transferable and efficient ti_ps.abinit.paw file.

4.c Test of the transferability of the atomic data

As in the norm-conserving case, we have to check various features of the atomic data. In particular, its capabability to reproduce (in some range) the all-electron eigenvalues and the all-electron logarithmic derivatives. The matching between the pseudo and all-electron features indicates the confidence degree we can have in our atomic data; which is the so-called transferabilility.
These two features are reproduced in the output file coming from the pseudopotential generation process.
Open the ti_ps.out file.
» Search the "chart: log derivatives" text. In this figure are displayed the logarithmic derivatives with the numbers 1 for the all-electron s wave function, 2 for the all-electron p wave function, 3 for the all-electron d wave function, 4 for the pseudized s wave function, 5 for the pseudized p wave function and 6 for the pseudized d wave function. The numbers 1 with 4, 2 with 5 and 3 with 6 are almost superimposed, so the matching between the all-electron and pseudo logarithmic derivatives is excellent.
» The second text to be searched is "comparison of all-electron and pseudo eigenvalues". You can read:

nlm all-elec pseudo diff
300 -5.555248 -5.555246 -0.000002
310 -3.789191 -3.789190 -0.000001
400 -0.877223 -0.877222 -0.000001
320 -1.166236 -1.166236 0.000001
The differences between the all-electron and pseudopotential eigenvalues are almost equal to zero.
According to these results we could have confidence in our atomic data.
However, what should we do in a case of a bad transferability?
Among various quantities, two play a crucial role on the transferability.
» The first one is the number of atomic functions (φi) considered in the spherical basis set.
In the ti_ps.adat file, this number is governed by the variable nbeta. By default, we use two basis functions φi by angular momentum: 2 for s, 2 for p and 2 for d. So nbeta=6.
Replace the nbeta value in ti_ps.adat by 5 and remove the line corresponding to the second d function (do not forget to save a backup copy of ti_ps.adat):
2 0 0.3 2 lll,keyee,eeread,iptype (2i5,f10.5,i5)
Type make clean&&make and check again the "log derivatives" and "eigenvalues" in the ti_ps.out file.
If the differences between the all-electron and pseudo eigenvalues are close to zero, the logarithmic derivatives of the d channel do not match any more.
From an empirical point of view, two basis functions by angular momentum are needed to obtain a good transferability.
» The second one is the all-electron electronic configuration used in the generation process. In the Makefile file, we have seen that the all-electron file used is the ti_ae_s2d1.adat one (the CFG keyword). So the all-electron electronic configuration is 3s23p64s23d1, corresponding to an ionized Titanium atom Ti+. This permits us to better reproduce some Titanium oxidization states obtained in ionic compounds (rutile, perovskites, ...) without debasing the quality of the atomic data in the 3s23p64s23d2 neutral configuration.
For this purpose, revert to the saved ti_ps.adat file, and type make clean&&make in order to regenerate the "right" atomic data.
Then type make test in order to test the atomic data on the 3s23p64s23d2 neutral configuration (the CFT keyword in the Makefile file indicates that the ti_ae_s2d2.adat file is then used). Open the ti_test_s2d2.out file and check again the logarithmic derivatives and the eigenvalues differences.
Small variations are obtained for the first one whereas 1 mRy differences are listed for the eigenvalues:

nlm all-elec pseudo diff
300 -4.603371 -4.602221 -0.001151
310 -2.856239 -2.854948 -0.001290
400 -0.328313 -0.328313 0.000000
320 -0.313034 -0.313463 0.000430
Now, we are going to generate and test the opposite electronic configurations. In the Makefile file, invert the CFG and CFT keywords in order to take the 3s23p64s23d2 neutral configuration as the generation one and the 3s23p64s23d1 ionic configuration as the test one.
Create a ti_test_s2d1.adat file from ti_test_s2d2.adat (just copy and rename it).
Type make clean&&make&&make test and open the ti_ps.out file.
As previously, the all-electron and pseudo eigenvalues as well as logarithmic derivatives match very well.

However, in the test file ti_test_s2d1.out file, we obtain that the atomic data generated by using a neutral electronic configuration is not able to reproduce some oxidized states (it is not transferable). The logarithmic derivatives are no more superimposed and the eigenvalues differences are too large:

nlm all-elec pseudo diff
300 -5.555248 -2.260718 -3.294530
310 -3.789191 -1.483931 -2.305260
400 -0.877223 -2.260718 1.383495
320 -1.166236 -0.579318 -0.586918

### 5. Tests on the physical properties

Various input values can play a significant role on the cutoff energy convergence and on the physical properties. In the following, we detail the influence of four of them (rc, lloc, rcloc and rpcor), wich are the most relevant in the pseudopotential generation process. We perform in this section a systematic study and generate 16 atomic data, with values in the range of:

- rc=1.8; 2.0; 2.2
- lloc=0;1;2;3
- rcloc=1.8; 2.0; 2.2; 2.4
- rpcor=0.7; 0.9; 1.1; 1.3; 1.5

The reader is supposed here to test only the influence of rc parameter.
Then, in the following, the results for lloc, rcloc, rpcor studies are given.
The test process is a long but straightforward job. It is strongly suggested to adopt a rigorous method, for example by creating script files calling ABINIT several times.
The atomic data can be renamed ti_ps.abinit.paw.lloc0 or ti_ps.abinit.paw.rpcor07 (for instance). For each one a convergence with respect to the cutoff energy and the lattice parameter has to be performed. As a consequence, this corresponds in all to 32 ABINIT runs. Two ABINIT input files are needed (tpaw2_1.in and tpaw_2.in).
Concerning physical properties, we have to compare with all-electron calculations to validate the atomic data.
For titanium you can refer to: M. Korling, J. Haglund, Phys. Rev. B 45, 13293 (1992)
In this reference, structural parameters for FCC titanium in the GGA approximation are:
a0 = 7.98 a.u.
B0 = 108 GPa

In the following we detail the results corresponding to each variable independently:

» rc
This quantity defines the PAW sphere radius (at rc the φi/tφi become equal) .
An increasing of the PAW sphere radius improves the convergence with respect to the cutoff energy (both the tφi and pi pseudized functions become softer). But overlap augmentation spheres can produce erroneous results (however a little overlap can be allowed in ABINIT by setting pawovlp input variable to 1).
Using the ti_ae_s2d1.adat and ti_ps.adat files obtained at chapter 4.b, generate three PAW atomic data files:

- ti_ps.abinit.paw.rc18 with rc=1.8 in ti_ps.adat file
- ti_ps.abinit.paw.rc20 with rc=2.0 in ti_ps.adat file
- ti_ps.abinit.paw.rc22 with rc=2.2 in ti_ps.adat file

¤ Note that, in ti_ps.adat file, the value of rlogd parameter always has to be greater than the value of rc.
You might now create a subdirectory of the ~abinit/tests/tutorial/Input directory, and use it in this part of the tutorial. In what follows, the name of files are mentioned as if you were in this subdirectory.
Copy the three ti_ps.abinit.paw.rc?? files in the working directory. Copy the two ../tpaw2_1.in and ../tpaw2_2.in files in that directory also.
Create a "files" file calling the tpaw2_1.in and using the ti_ps.abinit.paw.rc20 psp file (or use ../tpaw2_x.files). Run ABINIT.
Repeat the previous operation two times using ti_ps.abinit.paw.rc18 and ti_ps.abinit.paw.rc22 psp files.
Create a text file with the results of the three previous ABINIT runs (only etotal results are needed here); it should look like the following:
#ecut etotal(rc=1.8) etotal(rc=2.0) etotal(rc=2.2)
4. -54.702532616197 -55.710863969983 -57.800171866404
8. -58.348646858819 -58.414320137319 -58.438738840950
12. -58.449804130981 -58.456112238439 -58.450166214856
16. -58.450428483630 -58.456992098107 -58.451567157579
20. -58.450793003544 -58.457287569160 -58.451635622379
24. -58.451015923712 -58.457349722341 -58.451658007096
28. -58.451184667996 -58.457374066182 -58.451705857156
32. -58.451219375226 -58.457380473063 -58.451727845194
36. -58.451240087944 -58.457398273827 -58.451747515816
40. -58.451264954410 -58.457407724961 -58.451772233280
For a better visualization, it is better to substract the last line (ecut=40. Hartree) from all the others. You get a file like this.

Note: to create the previous text files you can use a little shell script given here.

Use a graphical tools (for the pictures here we used xmgrace) and plot the three curves (deltae vs ecut). Choose a logarithmic scale for a better legibility.
At this stage we have performed a convergence on cutoff energy study. Now we have to test the physical parameters.
You can use now the ../tpaw2_2.in file and run ABINIT three times using successively the three atomic data files (ti_ps.abinit.paw.rc18, ti_ps.abinit.paw.rc20 and ti_ps.abinit.paw.rc22). The results you should obtain are here.
With the three "Etotal vs volume" curves, it is possible to adjust some fit (Birch-Murnaghan for instance) and deduce the values of the equilibirum lattice parameter and bulk modulus.
With the three previous curves we find the following:

| rc=1.8 a.u. | rc=2.0 a.u. | rc=2.2 a.u.
a0 (a.u.) | 7.789 | 7.792 | 7.832
B0 (GPa) | 104.0 | 104.5 | 100.2

Finally we have to choose an optimal value for rc radius.
As you can see above, the value rc=1.8 a.u. gives poor convergence results for Ecut>10 Hartree.
On the other hand, the lattice parameter is increasing and the bulk modulus is decreasing when rc increases.
A reasonnable choice seems to be rc=2.0 a.u..
You just have to read the rest of this chapter, without running ABINIT. It seemed useful for a clear understanding to mention the complete optimization process (lloc, rcloc,rpcor, ...). But, within the framework of the present tutorial, it would be too long to detail.
» lloc
The lloc parameter defines the channel chosen as local along the pseudization generation process (0 for s, 1 for p, 2 for d and 3 for f). More details are given in Ref. [1].
However we have to emphasize the following point: the lloc variable does not modify the potential Vloc(r) of the ti_ps.abinit.paw atomic data file, as expected if we use the local part coming from the Kleinman-Bylander separation. In our formulation, this one is rather computed by starting from the all-electron and pseudized core densities, so is lloc independent. On the other hand, the lloc variable acts on the pseudized projectors pi, as it is highlighted by the equation (3) of Ref. [1].
Here again, for a complete study, we have to generate 4 atomic data files (with lloc=0, 1, 2 or 3). Then, using ../tpaw2_1.in and ../tpaw2_2.in files, we can produce curves and exploit them. The results are shown below:

| lloc= 0 | lloc= 1 | lloc= 2 | lloc= 3
a0 (a.u.) | 7.792 | 7.793 | 7.790 | 7.800
B0 (GPa) | 104.6 | 104.6 | 104.9 | 104.0

Whatever the lloc values we obtain the same physical properties. On the other hand, for the variation of the total energy with respect to the cutoff energy is concerned, we obtain various behaviours. The best convergence is obtained for lloc=3 which is often (always?) the channel used as local in the generation of d elements atomic data (or norm-conserving pseudopotentials).
A good choice is lloc=3.
» rcloc
rcloc defines the radius used to pseudize the potential (at rcloc the pseudized and the all-electron local potentials are equal). Even if it is not evident in this case, an increasing of rcloc generally yields softer pseudized projectors pi, and consequently improve the convergence with respect to the cutoff energy.
Results of convergence and physical properties studies are shown below:

| rcloc= 1.8 a.u. | rcloc= 2.0 a.u. | rcloc= 2.2 a.u. | rcloc= 2.4 a.u.
a0 (a.u.) | 7.792 | 7.800 | 7.833 | 7.869
B0 (GPa) | 104.5 | 104.0 | 102.2 | 99.9

We obtain an increasing of the lattice parameter and a decreasing of the bulk modulus as rcloc increases. As in the norm-conserving case, the strength of the bond is weaked as rcloc increases.
We adopt a compromise solution between the cutoff energy and the physical properties.
The optimal value seems to be rcloc=2.0 a.u..
» rpcore
This quantity defines the pseudization radius used for the electronic core density (at rpcor core density becomes equal to pseudized core density). When rpcor increases the pseudized core density becomes softer and consequently the convergence on cut-off energy is improved.
In the ti_ps.adat file, ifpcor flag controls the rpcor parameter:
- If ifpcor=1, the code use the value of rpcor put in the ti_ps.adat file.
- If ifpcor=0, an "automatic" and optimal value of rpcor is computed.
Below are shown the results for rpcor=0.7; 0.9; 1.1; 1.3; 1.5; automatic value (1.67):

| rpcore= 0.7 a.u. | rpcore= 0.9 a.u. | rpcore= 1.1 a.u. | rpcore= 1.3 a.u. | rpcore= 1.5 a.u. | rpcore= 1.67 a.u. (auto)
a0 (a.u.) | 7.786 | 7.796 | 7.799 | 7.800 | 7.800 | 7.800
B0 (GPa) | 104.6 | 104.1 | 104.1 | 104.0 | 104.0 | 104.0

The physical properties are only slightly modified along the variation of rpcor.
The rpcor=1.5 a.u. value seems to be optimal. (we also could choose the "automatic" value).
» Optimal parameters
In our case we have chosen:
rc = 2.0 a.u.
rcloc = 2.0 a.u.
rpcor = 1.5 a.u.
lloc = 3

- With the produced atomic data (here is the file), a cut-off energy Ecut = 12 Ha is needed to achieve a convergence lower than 1 mHa on the total energy. This is sufficient to compute well-converged structural properties in the FCC phase (a0 and B0 around 7.798 a.u. and 104 Gpa, respectively; which is around 2% far from the all-electron values).
- The sphere radius is not too large (rc=2.0 a.u.) and avoid spurious overlap between spheres. The valence states 4s23d2 as well as the semi-core states s23p6 are included in the valence.
- For the sake of comparison, the norm-conserving pseudopotential is converged for ecut = 53 Ha. (with the same criterion).

### 6. The Real Space Optimization (RSO)

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 atomic data but it can be useful. We advise experienced users to try it.

The idea is quite simple: when expressing the different atomic radial functions (φi, tφi, pi) on the plane waves basis eigr, 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)

a method to enforce the locallity (in reciprocal space) of projectors pi is presented.
Projectors pi(g) expressed in reciprocal space are modified according to the following scheme:
The reciprocal space is divided in 3 regions:
- If g < gmax, pi(g) is unchanged
- If g > γ, pi(g) is set to zero
- If gmax< g < γ, pi(g) is modified so that the contribution of pi(r) is conserved with an error W (as small as possible).
The above transformation of pi(g) is only possible if pi(r) is defined outside the augmentation sphere up to a radius R0 (with R0>rc).
In practice we have to:
- Impose an error W (W is the max. error admitted on total energy)
- Adjust gmax according to Ecut (gmax<= Ecut)
- Choose γ so that 2*gmax < γ < 3*gmax
and the USPP2Abinit code apply the transformation to pi and deduce R0 radius.
You can test it now.
Go back to uspp-xyz/Work/022-Ti/022-Ti-ca-sp-vgrp directory.
Create a text file named uspp2abinit.dat (this name is compulsory) and fill it with:
ECUT_RSO= 12.
GAMMAFACT_RSO= 2.
WERROR_RSO= 0.001
- ECUT_RSO is the value of gmax
- GAMMAFACT_RSO is the value of γ/gmax
- WERROR_RSO is the value of W

Launch USPP (by typing make clean&&make). The new ti_ps.abinit.paw file contains optimized pi(r) projectors (with 0 < r <R0) according to gmax, γ and W.

You can try several values for ECUT_RSO parameter and compare the efficiency of the atomic data (convergence vs Ecut); do not forget to test physical properties again.

How to choose the RSO parameters ?

γ/gmax=2 and 0.0001 < W < 0.001 is a good choice.
gmax (ECUT_RSO) has to be adjusted
The lower gmax the faster the convergence is ; but too low gmax can produce unphysical results.

### 7. Description of the PAW atomic data file

Standard ABINIT's pseudopotential header Paw atomic data extracted from US-psp (D.Vanderbilt): titanium 22.000 12.000 20050809 : zatom,zion,pspdat 7 2 2 0 573 0. : pspcod,pspxc,lmax,lloc,mmax,r2well
Information about the format of PAW atomic data paw3 2 : pspfmt,creatorID
Atomic basis data (basis size, angular momenta) 6 18 : basis_size,lmn_size 0 0 1 1 2 2 : orbitals
Definition of radial meshes 3 : number_of_meshes 1 2 573 0.1126705535E-03 0.1694915254E-01 : mesh 1, type,size,rad_step[,log_step] 2 2 578 0.1126705535E-03 0.1694915254E-01 : mesh 2, type,size,rad_step[,log_step] 3 2 673 0.1126705535E-03 0.1694915254E-01 : mesh 3, type,size,rad_step[,log_step]
Radius of augmentation spheres (Bohr) 1.8290765154 : r_cut(SPH)
Shape function definition (g(r) in Ref. [3], k(r) in Ref. [4]) 2 0. : shape_type(SIN),rshape
Atomic wave functions (φi) and pseudized wave functions (tφi) ===== PHI 1 ===== #phi(r), for phi(r)/r*Ylm) 1 : radial mesh index 0.000000000000000 -0.6667615969374328E-04 -0.1344906497696365E-03 [...] ===== TPHI 1 ===== #tphi(r), for tphi(r)/r*Ylm) 1 : radial mesh index 0.000000000000000 -0.5021771489799263E-05 -0.1012938315469165E-04 [...]
Projectors (pi) 1 : radial mesh index 0.000000000000000 0.1954439730141254E-05 0.3955013763944399E-05 [...]
Atomic core density and pseudized core density ===== CORE_DENSITY ===== 2 : radial mesh index 8203.917140628238 8203.748730155929 8203.577440941630 [...] ===== TCORE_DENSITY ===== 2 : radial mesh index 0.2433791231654809E-02 0.2433791231615136E-02 0.2433791231574785E-02 [...]
Frozen part of the "pseudopotential strength" Dij ===== Dij0 ===== 0.6464638641949085 -0.2927052680497827 0.1099009759446245 [...]
Initial values of the augmentation occupancies (ρij) ===== Rhoij0 ===== 2.000000000000000 0.000000000000000 2.000000000000000 [...]
Local potential (VHartree(ntildZC)) ===== VHntZC (Vloc(r)) ===== 3 : radial mesh index -15.99117369823717 -15.99117369816541 -15.99117369809242 [...]

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