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[Artem Oganov <a.oganov@ucl.ac.uk>]

Title: Message

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
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
phone: +44 (0)20-7679-3424
**************************

 

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