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["D. R. Hamann" <drhamann@mat-simresearch.com>]

Dear Zhang,

This is quite an interesting case, now that I understand the structure. 
(I created a picture from the coordinates in your .in file, and am 
attaching it as a .png file so other readers can follow my discussion.) 
It is somewhere between an ionic and a molecular solid, nominally 
(NO)-(NO3)+ but according to the most recent paper on it I could find, 
M. Somayazulu et al., Phys. Rev. Lett. 87, 135504 (2001), it is actually 
much more weakly ionic than the nominal charges indicate. Therefore van 
der Waals forces play a significant role in the bonding, and as I said 
in my first reply, neither Abinit nor any other density-functional 
program is going to treat such inter-molecular bonding accurately.

Now, as to your problems with the crazy elastic-tensor results, I have 
several things to suggest. First, I ran the ground-state part of your 
.in file, guessing that you may have used certain pseudopotentials that 
pack with Abinit, and found the following:

../tests/Psps_for_tests/7n.pspnc
../tests/Psps_for_tests/8o.pspnc

cartesian forces (hartree/bohr) at end:
1 0.03660293425389 0.00000000000000 0.02053060803930
2 -0.03660293425389 0.00000000000000 -0.02053060803930
3 -0.00395472238676 0.00000000000000 0.01380113510543
4 0.00395472238676 0.00000000000000 -0.01380113510543
5 -0.03618912651856 0.00000000000000 -0.01854089769997
6 0.03618912651856 0.00000000000000 0.01854089769997
7 0.00984558061427 0.00000000000000 -0.02989238681737
8 -0.00984558061427 0.00000000000000 0.02989238681737
9 -0.00200413398381 0.00608961305921 0.00699288835468
10 0.00200413398381 -0.00608961305921 -0.00699288835468
11 0.00200413398381 0.00608961305921 -0.00699288835468
12 -0.00200413398381 -0.00608961305921 0.00699288835468

Cartesian components of stress tensor (hartree/bohr^3)
sigma(1 1)= 1.57193973E-04 sigma(3 2)= 0.00000000E+00
sigma(2 2)= 3.34301737E-05 sigma(3 1)= 1.16533739E-05
sigma(3 3)= 2.00164483E-04 sigma(2 1)= 0.00000000E+00

While the stresses aren’t too bad, the atomic forces are far from 
relaxed. This will give meaningless results for the interatomic force 
constants which play a major role in the relaxed-atom elastic tensor 
calculation. Maybe you used different psp’s, for which the forces were 
fully relaxed (I’d say <10^-6 would be needed for a difficult system 
like this) but these forces are so large that if the choice of psp made 
that much difference, something else is likely wrong.

Now, supposing you do get your atomic forces and your lattice parameters 
fully relaxed. Then there are at least two more concerns. One I already 
mentioned is the large range of eigenvalues of the dynamical (more 
precisely, the force-constant) matrix caused by the difference between 
the stiff covalent intra-molecular bonds and the soft inter-molecular 
bonds. This would make the inversion of this matrix to compute the 
relaxed-atom elastic tensor unstable and susceptible to large changes 
from small convergence errors. (It also creates difficulties with full 
structural relaxation.) The second, suggested in the PRL referenced 
above, is that at low pressures the NO and NO3 moieties may be 
rotationally disordered, which would indicate that some rotational 
phonon modes might be unstable even in a very fully converged and 
physically accurate calculation. This would make the inversion of the 
matrix and the zero-temperature elastic-tensor calculation meaningless. 
This is a physics problem, not an Abinit problem.

For the benefit of me and other Forum readers, please look at your GS 
calculation output to check the forces and stresses, and at your RF 
output to see how many negative phonon frequencies you have, and report 
back to the Forum.

Regards,
Don Hamann


waigen zhang wrote:
> Dear Dr.Hamann,
> The only connection of my post about alpha-Al2O3 is they are all 
> calculating the elastic constants.
> Here I am calculating the ionic NONO3.Since you told so,I am really 
> wondering that whether I can use abinit for this system or not? If 
> this kind of ionic material is poorly described by ABINIT,I should 
> quite it.
> (There is no much experimental data can be compared).
> Your reply is appreciated.
>
> Regards,
> W.G.Zhang
>
> On 6/11/07, *D. R. Hamann* < drhamann@mat-simresearch.com 
> <mailto:drhamann@mat-simresearch.com>> wrote:
>
>     Dear Zhang,
>
>     In general, if you have negative diagonal elements in your elastic
>     tensor, it indicates that you have an unstable structure which would
>     also be indicated by negative gamma-point phonon frequencies in your
>     RF-run output. The relatively small negative acoustic-mode eigenvalue
>     flagged in the anaddb warning shouldn't cause major problems like
>     this.
>     Getting very different results from two runs of the same data is very
>     strange, and indicates that some quantities are poorly converged,
>     with
>     the errors perhaps magnified when anaddb takes the pseudo-inverse of a
>     nearly-singular dynamical matrix to calculate the relaxed-atom elastic
>     tensor.
>
>     Beyond this, I'm not sure I understand your input data or if this
>     relates to your recent posts on Al2O3. This looks like an N4O8 unit
>     cell, in which case nband is wrong. If this is supposed to be an
>     (NO2)4
>     molecular crystal, these are notoriously hard to structurally
>     optimize
>     because you have very stiff covalent bonds and very soft van der Waals
>     bonds (which are poorly described by LDA anyway).
>
>     Don Hamann
>
>     waigen zhang wrote:
>     > Hi,
>     > Thanks for the reply for my last question.
>     > Another problem is that I am getting some results(elastic constant)
>     > case sensitive for my material.I used the same structural
>     geometry and
>     > same ecut,ngkpt,psp...,but each time the outcomes of elastic
>     constants
>     > are quite different.BTW,I did the structural optimization and the
>     > optimized structure seems no problem before any calculation.
>     > I notice that there is a warning in the output file
>     >
>     > elast9 : WARNING - :
>     > Acoustic sum rule violation met : the eigenvalues of accoustic mode
>     > are too large at Gamma point
>     > increase cutoff energy or k-points sampling.
>     > The three eigenvalues are: 2.354541E-04 3.769631E-06
>     > -9.936443E-05
>     >
>     > and the elastic tensor from two different runs with same input
>     > parameters are
>     >
>     > Elastic Tensor (relaxed ion) (unit:10^2GP):
>     > (at fixed electric field boundary condition)
>     > 0.5479039 -0.2078001 0.4736602 0.0000000 -0.4454188 0.0000000
>     > -0.2078002 -1.6226535 -0.1456602 0.0000000 -0.0503831 0.0000000
>     > 0.4736602 -0.1456602 -1.7632272 0.0000000 -0.8610705 0.0000000
>     > 0.0000000 0.0000000 0.0000000 -0.1100148 0.0000000 -0.0896016
>     > -0.4454189 -0.0503831 -0.8610705 0.0000000 0.4057265 0.0000000
>     > 0.0000000 0.0000000 0.0000000 - 0.0896016 0.0000000 -0.2808213
>     >
>     > Elastic Tensor (relaxed ion) (unit:10^2GP):
>     > (at fixed electric field boundary condition)
>     > -2.4936683 -1.4720537 -0.7323263 0.0000000 0.4624234 0.0000000
>     > -1.4720537 -3.5190605 -1.2099844 0.0000000 -0.3453437 0.0000000
>     > -0.7323263 -1.2099843 -0.5868132 0.0000000 0.0348794 0.0000000
>     > 0.0000000 0.0000000 0.0000000 -1.1759601 0.0000000 -0.3877170
>     > 0.4624235 -0.3453437 0.0348793 0.0000000 -0.7692686 0.0000000
>     > 0.0000000 0.0000000 0.0000000 -0.3877171 0.0000000 -1.5326429
>     >
>     > Attachment is the input file.Thanks for you suggestion.
>
>     --
>     D. R. Hamann
>     Mat-Sim Research LLC | Deptartment of Physics
>     P.O. Box 742 | and Astronomy
>     Murray Hill, NJ 07974 | Rutgers University
>     phone: 908-370-8079 | 732-445-4381
>
>     email: drhamann@mat-simresearch.com
>     <mailto:drhamann@mat-simresearch.com>

--
D. R. Hamann
Mat-Sim Research LLC    | Deptartment of Physics
P.O. Box 742            |  and Astronomy
Murray Hill, NJ 07974   | Rutgers University
phone: 908-370-8079     | 732-445-4381

email: drhamann@mat-simresearch.com