The ABINIT Users Mailing List ( CLOSED )

[Natalie Holzwarth <natalie@wfu.edu>]

Dear Pio,
     Thanks for performing careful tests on the PAW functions.  The Al
functions on our website are very "hard" and would need a ecut of at least
18 Ha.  They would be more appropriate for use in ionic compounds of Al
than for metallic Al perhaps, However, we do find that they do a good job
of reproducing the binding energy curve (Total energy in Ry) vs (lattice
constant in bohr) for metallic Al shown in the enclosed graphs comparing
pwpaw results with lapw results using the wien2k code.  (We have not yet
run them with abinit, but hopefully the results will be the same as for
pwpaw.)  I am not sure about your descrepancies.  What lattice constant
did you use for your calculations?     Natalie



On Thu, 26 Apr 2007, Pio Baettig
wrote:

> 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
>
>
>

N. A. W. Holzwarth                      email: natalie@wfu.edu
Department of Physics                   www: http://www.wfu.edu/~natalie
Wake Forest University                  voice: 336-758-5510
Winston-Salem, NC 27109-7507            fax: 336-758-6142
U. S. A.

Attachment: Al-lda-compare.ps
Description: lda plots

Attachment: Al-gga-compare.ps
Description: gga plots