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[Pio Baettig <baettigp@gmx.net>]

Dear Joe, Marc, Abinit-users

thank you very much for your help. Today I ran some more test cases (fcc 
and rhombohedras Al(Joe's PAW+ Ca and Cu with the PAWs from N. 
Holzwarth's website.

--
In short what follows: I observed the same kind of discrepancys in the 
energies for a unitcell with one atom and four atoms for Al using the 
PAWs from 
http://www.wfu.edu/%7Enatalie/papers/pwpaw/periodictable/periodictable.html 
, from J. Zwanziger and the FHI-PP provided on the abinit homepage.
Cu also yields errors using the PAW(PP not yet tested)

For Ca, the difference between the energy for (4*1 atom) and 4 atoms is 
nearly zero, leading me to suspect an l-dependency of the errors forthe 
kinetic energy and the Local psp-energy (l=1 and 2) and the Hartree and 
Exchange-energy (l=2).
--

long version:

Firstly, the energy compositions for Al using N.H.'s PAW's.
The energy difference seems to stem from the kinetic energy 
component(and to a lesser degree frp, the local Psp-Energy), as can be 
seen in the energy-decomposition (14*14*14 kpts, ecut=40 Ha):

----------
Aluminium LDA, PAW from N. Holzwarth's website:
Energy comparison
                       Cubic  Rhombohedral  c-4r
Kinetic energy      30.465676    7.688697  -0.289111
Hartree energy      71.653858   17.913520  -0.000224
XC energy          -31.052499   -7.763111  -0.000055
Ewald energy      -144.973209  -36.243302  -0.000002
PspCore energy       4.368516    1.092129   0.000000
Loc. psp. energy  -238.136208  -59.532814  -0.004952
Spherical terms    -17.883466   -4.473954   0.012349
>>>>>>>>> Etotal  -325.557331  -81.318834  -0.281995

Double Counting Energies
Band energy        -76.413035  -19.036473  -0.267141
Ewald energy      -144.973209  -36.243302  -0.000002
PspCore energy       4.368516    1.092129   0.000000
Dble-C XC-energy   -61.907795  -15.477011   0.000249
Spherical terms    -46.631880  -11.654177  -0.015170
>>>> Etotal (DC)  -325.557402  -81.318834  -0.282064

Total energy in eV     -8858.865720  -2212.798059  -7.673482
Total DC energy in eV  -8858.867637  -2212.798071  -7.675351

The total energy differs by 7.7 eV for 4 atoms...
----------


----------
Aluminium LDA, PAW from J. Zwanziger

Unfortunately, the calculations using Joe's PAW for Al lead to (almost) 
the same discrepancy, here the energies:
Cubic, 14*14*14 K-Points
       10 Ha     15 Ha     20 Ha     25 Ha     30 Ha     35 Ha     40 Ha
   -8.469208 -8.469236 -8.469243 -8.469245 -8.469246 -8.469246 -8.469247
rhomb
   -2.046804 -2.046812 -2.046814 -2.046814 -2.046814 -2.046815 -2.046815
c-4r
   -0.281991 -0.281988 -0.281988 -0.281988 -0.281988 -0.281988 -0.281988

                     cubic       rhomb        c-4r
Kinetic energy    3.385753    0.929934   -0.333981
Hartree energy    0.014341    0.004014   -0.001713
XC energy        -3.202658   -0.801073    0.001633
Ewald energy    -10.783131   -2.695783    0.000000
PspCore energy    0.125193    0.031298    0.000000
Loc. psp. energy  0.337001    0.085699   -0.005794
Spherical terms   1.654234    0.399085    0.057893
>>>>>>>>> Etotal -8.469267   -2.046826   -0.281962

Band energy       1.355787    0.409184   -0.280949
Ewald energy    -10.783131   -2.695783    0.000000
PspCore energy    0.125193    0.031298    0.000000
Dble-C XC-energy  0.955553    0.238587    0.001203
Spherical terms  -0.122648   -0.030102   -0.002241
>>>> Etotal (DC) -8.469247   -2.046815   -0.281988
----------


I then wanted to check another element and ran the same calculations for 
Ca, with changed lattice constant

----------
Calcium LDA, PAW from N. Holzwarth's Website

I ran the same calculations for Ca with the PAWs from the N.H. and there 
the energy-difference converged to acceptably small values ( around 
-0.000088 for the difference cubic-4*rhombohedral) (a_cubic=5.5884Ang, 
otherwise same input files).
The same energy differences and decompositions for Ca (PAW from N.H.'s 
website) as follows:

Here the energies for Ca, 12*12*12 k-points:
Ca LDA
               10 Ha       15 Ha       20 Ha       25 Ha       30 Ha
cubic
12*12*12 -147.978283 -148.003771 -148.005966 -148.005966 -148.006164
rhomb
12*12*12  -36.994563  -37.000950  -37.001495  -37.001511  -37.001520
c-4r
12*12*12   -0.000031    0.000031    0.000012    0.000076   -0.000085

                        cubic       rhomb      c-4r
Kinetic energy      19.227278    4.807066  -0.000986
Hartree energy      32.672013    8.168202  -0.000795
XC energy          -18.336461   -4.584145   0.000117
Ewald energy       -86.830024  -21.707506   0.000001
PspCore energy       2.182091    0.545523   0.000000
Loc. psp. energ y -133.101114  -33.275600   0.001287
Spherical terms     36.180053    9.044931   0.000330
>>>>>>>>> Etotal  -148.006164  -37.001530  -0.000046

Band energy        -27.474860   -6.868556  -0.000634
Ewald energy       -86.830024  -21.707506   0.000001
PspCore energy       2.182091    0.545523   0.000000
Dble-C XC-energy   -26.999598   -6.750089   0.000757
Spherical terms     -8.883697   -2.220894  -0.000119
>>>> Etotal (DC)  -148.006087  -37.001523   0.000004

Total energy in eV     -4027.452641  -1006.862848 -0.001248
Total DC energy in eV  -4027.450554  -1006.862668  0.000117

The biggest Error (around 30meV) this time stems from the Local 
Psp-Energy term, but is nearly compensated by the other contributions, 
so that the Difference in total energy for four Atoms comes to 1 meV.
----------


In order to check, whether this behaviour is l-dependent, I did some 
calculations for Cu, same and rhombohedral unit cell a_cubic=3.6074 Ang, 
a_rhomb=3.6074/SQRT(2) Ang, 6*6*6 k-points.


----------
Copper LDA, PAW from N. Holzwarth's Website

6*6*6        Cubic        Rhomb      c-4*r
10 Ha  -789.818197  -197.392483  -0.248266
15 Ha  -789.836947  -197.397170  -0.248268
20 Ha  -789.843359  -197.398740  -0.248400
25 Ha  -789.844050  -197.398909  -0.248416
30 Ha  -789.844543  -197.399029  -0.248426
35 Ha  -789.844603  -197.399044  -0.248427
40 Ha  -789.844696  -197.399067  -0.248428

                       Cubic       Rhomb      c-4*r
Kinetic energy     24.452912    6.037244   0.303935
Hartree energy    102.418151   25.331062   1.093904
XC energy         -54.694376  -13.631902  -0.166767
Ewald energy     -485.590638 -121.397660   0.000000
PspCore energy     51.438893   12.859723   0.000000
Loc. psp. energy -265.842987  -66.110176  -1.402282
Spherical terms  -162.025042  -40.487417  -0.075373
>>>>>>>>> Etotal -789.843087 -197.399126  -0.246584

Band energy       -81.583815  -20.727952   1.327992
Ewald energy     -485.590638 -121.397660   0.000000
PspCore energy     51.438893   12.859723   0.000000
Dble-C XC-energy  -85.273190  -21.058260  -1.040150
Spherical terms  -188.835947  -47.074919  -0.536270
>>>> Etotal (DC) -789.844696 -197.399067  -0.248428

Total energy in eV       -21492.723943  -5371.503516  -6.709881
Total DC energy in eV    -21492.767723  -5371.501912  -6.760076

Here, the Hartree energy and the Local Psp energy contribute most to the 
error, yielding in the end an energy-difference of 6.7 eV for four atoms.
----------





It seems, that there might be some l-dependency of the errors, affecting 
the kinetic energy and the Local psp-energy (l=1 and 2) and the Hartree 
and Exchange-energy (l=2).

pawmix should not be the problem, as it was left untouched (default=10)

The input files were the same as provided last time (but for nbands =15 
and 60 for the rhombohedral and cubic cases respectively for Ca and Cu 
and adjusted lattice constants as mentioned above)

I hope that I did not overlook some important parameter in my analysis 
which would lead to the correct results.
I can provide the inputs and outputs upon request.

I would be very happy if someone could run my input-files for Al and 
report, whether they also observe energy-differences.
(Abinit was compiled under MacOSX 10.4.9 using ifort 9.1.039. I didn't 
change any of the options set by configure, so the fortran-flags in the 
makefile are all:
FCFLAGS =  -extend_source -vec-report0
I used the serial version for all of these test)


Thank you very much for your help.

Best regards,

Pio Baettig




P.S. I also repeated the calculations using the FHI-Al-PP downloaded 
from the Abinit-website for 6*6*6 k-points with ecut ranging from 10 to 
35 Ha and observed the same behavior.

6*6*6      Cubic      Rhomb      c-4*r
10 Ha  -8.354034  -2.020847  -0.270644
15 Ha  -8.357242  -2.021717  -0.270373
20 Ha  -8.357672  -2.021817  -0.270403
25 Ha  -8.357772  -2.021843  -0.270400
30 Ha  -8.357853  -2.021863  -0.270401
35 Ha  -8.357870  -2.021867  -0.270402
                     Cubic      Rhomb      c-4*r
Kinetic energy    3.441747   0.940965  -0.322115
Hartree energy    0.014425   0.004002  -0.001583
XC energy        -3.199332  -0.800153   0.001281
Ewald energy    -10.783131  -2.695783   0.000000
PspCore energy   -0.399455  -0.099864   0.000000
Loc. psp. energy  0.719443   0.175475   0.017543
NL   psp  energy  1.848433   0.453490   0.034472
>>>>>>>>> Etotal -8.357870  -2.021867  -0.270402

Total energy(eV)  -227.429211  -55.017800  -7.358010






Josef Zwanziger wrote:
> Hi, you might try as an alternative USpp2Abinit together with 
> Vanderbilt's code. I've attached the Al PAW data I made this way. It 
> uses two projectors in the s and p channel; for aluminum metal, run
> with occopt 3 and the default tsmear, 6x6x6 kpt mesh, it converges
> the total energy to about 1 part in 10^5 for ecut = 15 Ha. In general
> I have had better luck with USpp2Abinit than with atompaw; I don't
> know why, I think just because I have put a lot more time into
> understanding the Vanderbilt approach (though atompaw should be
> easier!) I also read your post yesterday about Bi PAW; that's
> something I'm playing with too and will post you something if and
> when I get something good. I would also encourage you to set aside
> some substantial time to get the feel for making your own pseudo's
> and paw data; the downloadable files are typically good for something
> but not necessarily for your application, and you will get much more
> satisfactory answers (and a better feel for what might be going
> wrong) if you make your own pseudo's.
>
> Good luck,
>
> Joe

Marc Torrent wrote:
> Dear Pio,
>
> 1) Concerning the convergence behaviour with respect to ecut: It
> seems that the results you get are the same as those published (for 
> pwpaw code) at 
> http://www.wfu.edu/%7Enatalie/papers/pwpaw/periodictable/atoms/Al/Al_dat,
>  provided that you use the following translation formula: 
> ecut_abinit=gcut_pwpaw**2/2 So, this atomic data file, created by
> PWPAW group seems to have a slow convergence vs ecut; it could be
> improved...
>
> 2) Concerning the energy difference: a) did you try with a
> norm-conserving pseudopotential ? is the behaviour the same in that
> case... b) did you have a look at the decomposition of energy (at the
> end of each datasry in output file) ? you could perhaps identify
> which term of energy is responsible for the non-zero value...
>
>
> Marc Torrent CEA-Bruyeres-la-Chatel France