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[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

Dear Doug and Artem,

I have been following your exchange of mail. Sorry not to have
taken the time to answer until now ... Actually, Doug has
correctly summarized the expected behaviour of such computation :
- slight breaking of the translational invariance by the XC term
 only.
- should be better with non-zero intxc, but the latter has not
 been implemented for response-function
And Artem has observed the same behaviour as some other persons
(but this was before the forum mailing list) :
- the deviation is larger for GGA than LDA
- the k points seem to have an effect
Also, the effect on Gamma phonon frequencies can be very large
when Hydrogen is present, because (likely) of the small
mass of H (frequencies of 100-150 cm-1 have been observed sometimes !).
(seen by Dennis Klug, Gian-Marco Rignanese, Xavier Rocquefelte,
and maybe others).

That's the situation now :
- this might be normal, and improvable by implementing intxc 1
 in Response-Function
- this might be a small bug ?!

I simply do not know yet

In practice, people impose the acoustic sum rule in IFC,
which forces the phonon frequencies to be zero at Gamma,
and the other frequencies can be modified accordingly as well.

Good continuation,
Xavier

Allan, Douglas C Dr wrote:
> Dear Artem,
>
> This is interesting.  I see the effect you describe in your output
> files.  Let me offer a quick comment and hope I can think more
> carefully about this later (after other obligations).  My comment:
> when thinking about the failure of translational invariance, I don't
> think it matters whether the actual calculation closely resembles a
> physical system (with sensible pseudopotentials, etc.).  I think what
> matters is the source of breaking translational invariance.  Without
> xc, I think I can prove that there are no terms that break
> translational invariance.  I think I can even prove, without xc, that
> the k-point sampling can't break translational invariance.  I am
> working again from memory here, but this is what I recall from when I
> last saw this problem about 6 years ago.  When you have a term that
> clearly breaks translational invariance, then the magnitude of the
> problem may well depend on things like k-point sampling.  It should
> be possible to show that mathematically, once the offending term(s)
> are identified
>
> You can think of the underlying problem as this: imagine running
> exactly the same frozen system in a ground state calculation, but
> with all the input atomic positions slightly shifted uniformly in a
> way incommensurate with the fft grid.  I think it is true that only
> the terms related to xc integrations will change in value in the two
> calculations.  The other contributions should agree to machine
> precision.  If they all agreed to machine precision, you would have
> translational invariance.  If the linear response formulation does
> not introduce new approximations, then this simple picture should
> hold for that as well.  If you feel like doing this test, I suggest
> you select a uniform translation that carries you exactly halfway
> between the fft grid points in real space in each dimension.  The
> effect should be largest there.  The effect obviously must be
> periodic and goes away by the time your uniform translation hits the
> next fft grid point.  This should be an easy test to perform (two
> ground-state calculations
>
> I am going to forward this conversation also to Xavier Gonze, who I
> am sure has thought about this and will probably have additional
> information.  He is very busy so do not hold your breath waiting for
> his answer, but he might be able to offer some quick comments or even
> a reference.  Eventually this kind of information should be captured
> for the abinit documentation.
>
> I am re-attaching the pdf so Xavier can look at it too.
>
> Regards, Doug Allan
>
> -----Original Message----- From: Artem Oganov
> [mailto:a.oganov@ucl.ac.uk] Sent: Friday, December 13, 2002 7:03 AM
> To: forum Subject: RE: [abinit-forum] Phonons at Gamma
>
>
> Dear Doug,
>
> Thank you very much for your comments and suggestions. I would like
> to give you some thoughts (and hope that you will comment):
>
> 1. I do suspect that GGA's sensitivity to density variation makes it
> numerically less stable - much finer grids may be required for
> reliable calculatons. I've actually done a more stringent test than
> suggested by you (taking ixc=0) - I took ixc=1,i.e. used LDA, and
> found no problems. I suppose the problem is not in xc itself, but in
> the difference between LDA and GGA, i.e. density gradients - and
> related numerical sensitivity. I agree that even in this case larger
> ecut should remove the problem, but in the range of ecut values I
> used (up to 80 Ha; the ground-state properties converge at 40 Ha)
> this did not happen. At the moment I am testing your idea (ixc=0) -
> I'll let you know the results. 2. In my calculations I actually found
> that k-point sampling is very important in RF calculations, in
> particular in order to get close to zero acoustic frequencies at the
> gamma-point. Attached you will find some results of my tests. I
> suppose the denser the k-point mesh, the better we emulate the true
> infinite system - this could somehow be related to the issue of
> translational invariance, although I do not immediately see how.
>
> Maybe someone else has any ideas or experience with such problems?
>
> Yours,
>
> Artem
>
> ************************** Dr. Artem R. Oganov Research Fellow,
> Crystallography and Mineral Physics Dept. of Earth Sciences
> University College London Gower Street London WC1E 6BT U.K. web:
> http://slamdunk.geol.ucl.ac.uk/~artem
> <http://slamdunk.geol.ucl.ac.uk/~artem> phone: +44 (0)20-7679-3424
> **************************
>
> -----Original Message----- From: Allan, Douglas C Dr
> [mailto:AllanDC@corning.com] Sent: Wednesday, December 11, 2002 10:17
> PM To: 'forum@abinit.org' Subject: RE: [abinit-forum] Phonons at
> Gamma
>
>
> One more comment: I see on more careful reading of the help files
> that the variable we introduced for this purpose, "intxc", was
> deprecated during further development work because it was too much
> trouble to implement this method within the response function work.
> The other developments were considered higher priority.  Thus, only
> the coarser integration is available (intxc=0) for response function
> work, while the more accurate (intxc=1) integration is available for
> ground state calculations.
>
> This does not explain why lda works better than gga for response
> functions, as both use the coarse grid, unless the nonlinearity of
> the gga (in density) makes more demands on the xc integration and
> thereby makes the errors larger.  In any event adding more plane
> waves should always make this error smaller.
>
> Does anyone else have an opinion about the cause of nonzero acoustic
> modes at Gamma and their cure?  What else can break translational
> invariance?
>
> By the way you can test to see if the xc integration is the culprit
> by running a test calculation with ixc=0.  If this still works the
> way it used to, then you will turn off all exchange-correlation and
> get a result in which errors in the xc integrals are not present.
> This is not physically sensible, as the pseudopotentials still use
> xc, but for a test there is nothing wrong this trying this.  The
> question is, do you get the acoustic modes at gamma to vanish when
> you run ixc=0.  If not, then either ixc=0 is not really fully
> implemented everywhere, or else there is some other term that also
> breaks translational symmetry.
>
> -Doug
>
> -----Original Message----- From: Allan, Douglas C Dr
> [mailto:AllanDC@corning.com] Sent: Wednesday, December 11, 2002 4:49
> PM To: 'a.oganov'; forum Subject: RE: [abinit-forum] Phonons at Gamma
>
>
>
> Dear Artem,
>
> I am responding a little late, but with a thought that others might
> not have mentioned.
>
> I recall that Xavier and I experienced spurious acoustic frequencies
> at gamma in the early days of developing the codes that eventually
> became abinit.  We discovered that the exchange-correlation
> integration breaks translational symmetry - in fact it is the only
> term that does so, as I recall.  We significantly improved the xc
> integration by adding one additional grid point at the center of each
> real space "fft cube", i.e. introduced a new fft grid shifted
> relative to the original grid by (1/2,1/2,1/2).  The density in real
> space can be computed on this new grid by fourier interpolation, so
> exactly the same fourier components of density are available on this
> grid.  Then the xc evaluation is performed.  This is a nonlinear
> operation (think of density to the 1/3 power) so using the augmented
> grid does not give the same answer as using only the original grid.
> (The augmented grid makes no difference for integration of linear
> functions.)  Thus, the error in the xc integration was cut by about a
> factor of 10.
>
> By the way, you have to work with the wavefunctions on the fourier
> interpolated grid, and not the density itself, or else you can have
> negative densities.  By fourier interpolating the wavefunctions
> before squaring them we avoided that.
>
> I can't tell you if this feature has been retained in today's abinit,
> but perhaps someone else can.  It is possible that the enhanced xc
> integration is not coded for every kind of abinit calculation.  But
> it should be.  It is a very bad result if the spurious frequencies
> are worse at larger planewave cutoff.  They should improve if my
> picture of the problem is correct.  I don't think the k-mesh is so
> critical to the vanishing of acoustic frequencies.
>
> I am recalling this from my fallible memory only, so beware.
>
> Regards, Doug Allan
>
> -----Original Message----- From: Artem Oganov
> [mailto:a.oganov@ucl.ac.uk] Sent: Wednesday, November 27, 2002 10:05
> AM To: forum Subject: [abinit-forum] Phonons at Gamma
>
>
>
> Dear ABINITioners,
>
> Doing convergence tests on phonons at the Gamma-point in stishovite
> (SiO2) using the GGA (PBE), I found rather large acoustic frequencies
> of +/-50 cm^-1. Of course, at the Gamma-point they should be zero.
> These frequencies vary a lot (from real to imaginary), but always
> remain strongly non-zero when I go to very large plane-wave cutoffs
> (80 Ha) or very dense k-point meshes. At the same time, frequencies
> of the optic modes are very well-converged and similar to the
> experimental values. Are such things normal? When I do an LDA
> calculation (with the same GGA-derived pseudopotentials and the same
> geometry), I find much more tolerable acoustic frequencies.
>
> Does anyone have ideas on how serious this error is for generating
> the IFCs and (if the problem is important) how to cope with it?
>
> Thanks a lot,
>
> Artem ************************** Dr. Artem R. Oganov Research Fellow,
> Crystallography and Mineral Physics Dept. of Earth Sciences
> University College London Gower Street London WC1E 6BT U.K. web:
> http://slamdunk.geol.ucl.ac.uk/~artem
> <http://slamdunk.geol.ucl.ac.uk/~artem> phone: +44 (0)20-7679-3424
> **************************
>
>
>
>