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["Allan, Douglas C Dr" <AllanDC@corning.com>]

Title: Message

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

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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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