Re: External pseudopotentials and large structures ( No.1 ) 
 Date: 2017/04/20 17:02
 Name: T. Ozaki
 Hi,
I checked your PAO (nb.pao) and VPS(nb.vps), found that nb.pao looks okay. However, it turns out that the local potential is extremely deep at the origin. I think that the large variation of the potential in the vicinity of the origin is enough to cause the numerical problem. The local potential is used to construct the neutral atom potential, which leads to a quite deep neutral atom potential at the origin. Since you employ the projector expansion method with "scf.BufferL.VNA 6" "scf.RadialF.VNA 11", I wonder that the large variation cannot be well reproduced by such a parameter set. Also please note that the projector expansion is NOT applied to a dimer case as discussed in our paper: http://www.openmxsquare.org/tech_notes/tech15.pdf The fact might be related to the fact that your calculation for the dimer looks okay.
To check this, you may perform the calculations with the NONprojector expansion method with very high cutoff energy of several thousands Ryd. By comparing results with/without the projector expansion method, you may be able to narrow down possible sources of the problem.
Also, I noticed that your projet.energie seems to be quite large in some channel. I guess that this might be related to the large rounding off error, resulting in ghost states.
If you would like to use your PAO and VPS, you need to identify very carefully places in the code where numerical instabilities take place, while this will require considerable efforts.
Best regards,
TO

Re: External pseudopotentials and large structures ( No.2 ) 
 Date: 2017/04/20 23:05
 Name: Daniil
 Thanks.
Theoretically, I can increase the minimum R value of vps grid, in order to 'hide' singularity. This will lead to a loss of precision, but that's better than a completely wrong result. Probably, I'll try to estimate this effect.
Do you mean Nb2Cl10 by 'dimer'? If so, could you please clarify, why the projector expansion is not applied there? I briefly read the paper, but didn't found the particular statement about it.
As for cutoff, do you mean scf.energycutoff, or 1DFFT.EnergyCutoff?
Also, as I understand from Blochl projector form, it is possible to decrease project energies and vectors in a same way as it is done for MBK scheme in ADPACK, where energies are normalized to 1. What limits for energies are recommended?
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.3 ) 
 Date: 2017/05/20 05:03
 Name: Daniil
 Dear Prof. Ozaki,
I made some investigations, and found that at least one reason of my problem was the presence of ghost states. And now, as it is possible for me to use larger basis (thanks Kylin for _IO_vfprintf fix), ghost states appear even for nb2 system. I obtained cube files for wrong orbitals and it is clearly visible that in my case ghost states have shape of porbitals. However, it looks like I have enough Blochl projectors in that radial range for L=1. (I changed the projectors basis since previous message). I tried to use different projectors sets, but with no success, so that either I am missing something important, or there is a problem in processing my projectors in openmx code. I am not very experienced in separabilization yet, so, can you give me an advice, how to eliminate these states? (my data is shared at the same dropbox folder, there are also plots of my projectors basis, old files are deleted)
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.4 ) 
 Date: 2017/05/20 08:37
 Name: T. Ozaki
 Dear Daniil,
Did you compare the logarithm derivatives of your separable form with those of the all electron potential? If those of the separable form does not match well to the all electron ones and/or unexpected singularities appear at energies which are not eigenenergies, this apparently suggests that your PP is not accurate.
Regards,
TO

Re: External pseudopotentials and large structures ( No.5 ) 
 Date: 2017/05/21 03:17
 Name: Daniil
 Dear Prof. Ozaki,
Can you please explain, what are logarithmic derivatives in the current case? Neither in ADPACK manual, nor in X. Gonze et al. reference I haven't found the exact formula. I know what is a logarithmic derivative of function in general case, but I cannot understand how it is Edependent.
Btw, I tried to generate a lot of different projector sets: pseudofunctions, allelectron orbitals, local potential orbitals, even sine waves; and in all cases I got the same 3 'ghost' states. So, probably, these are not real ghost states resulting from incomplete separabilization, but instead, have a different origin.
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.6 ) 
 Date: 2017/05/24 09:21
 Name: T. Ozaki
 Dear Daniil,
At each chosen energy, the logarithmic derivative is calculated by dr(log(psi))/dr.
The calculation of logarithmic derivative is easy for wave functions of the all electron potential and semi local potentials. In our implementation, psi is expressed by u/r, and u=r^(l+1)L. Thus, we have
dr(log(psi))/dr = 1/r(l+M/L)
where M=dL/dx with x=log(r).
However, for separable pseudoptentials, the calculations of the logarithm derivative becomes much more complicated due to the nonlocality of pseudopotentials. In the case, we need to perform an iterative calculation to obtain a convergent logarithmic derivative.
The data shown in http://www.jaist.ac.jp/~tozaki/vps_pao2013/ were calculated by the scheme.
Our implementation can also be confirmed in a routine 'Log_DeriF.c' of ADPACK.
I hope this helps you.
Regards,
TO

Re: External pseudopotentials and large structures ( No.7 ) 
 Date: 2017/05/24 21:08
 Name: Daniil
 Dear Prof. Ozaki,
Thanks for your answer, but I still don't understand the "At each chosen energy" part. What energy do you mean exactly, and how can it be "chosen"?
Btw, we are trying to make a smoothed versions of our pseudopotentials. The one limited by value of 1000 in r=0 has fixed the nb2 problem, however more complex structures like nbocl3 or nb2cl10 still give wrong results, so I am now trying a 500limited one. Despite being smoothed, they are still considerably larger at r=0 than default openmx ones. I use increased 1DFFT values to fit them: 1DFFT.NumGridK 10000 1DFFT.NumGridR 10000 1DFFT.EnergyCutoff 24000 I also use scf.BufferL.VNA 6 scf.RadialF.VNA 14 Is this enough, and are there any other keywords that must be changed?
And, can you please clarify, how do you combine the Fourier transform, which results in a periodic function, with the conception of cutoff spheres?
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.8 ) 
 Date: 2017/05/25 00:21
 Name: T. Ozaki
 Dear Daniil,
> I still don't understand the "At each chosen energy" part. What energy do you mean > exactly, and how can it be "chosen"?
As you can see the database Ver. 2013 e.g. at http://www.jaist.ac.jp/~tozaki/vps_pao2013/Mg/index.html we scan the energy ranging from e.g., 2 to 2 Hartree. Though the chosen energy may not be an eigenenergy, one can numerically solve the Dirac or Schlodinger equation from the origin.
> The one limited by value of 1000 in r=0 has fixed the nb2 problem, however more > complex structures like nbocl3 or nb2cl10 still give wrong results, so I am now > trying a 500limited one.
I hope you read the last paragraph of the left column in the page 4: http://www.openmxsquare.org/tech_notes/tech15.pdf The problem in the nb2 is different from those in nbocl3 or nb2cl10. It is likely that the problem for the latter cases comes from the projector expansion.
> Is this enough, and are there any other keywords that must be changed?
I have never experienced such hard pseudopotentials. Therefore, I am not sure how the convergence can be achieved and to which extend the numerical stability of the implemented algorithm can be guaranteed. As I mentioned before, a systematic and stepbystep investigation should be performed to address the issue with the theoretical and numerical foundation.
> And, can you please clarify, how do you combine the Fourier transform, which results > in a periodic function, with the conception of cutoff spheres?
As shown in Eqs. (37) and (38) of the notes at http://www.openmxsquare.org/tech_notes/tech11_2.pdf the Fourier transform is not a discrete one. Thus, we are free from the periodicity issue.
Regards,
Taisuke Ozaki

Re: External pseudopotentials and large structures ( No.9 ) 
 Date: 2017/05/30 03:56
 Name: Daniil
 Dear Prof. Ozaki,
I made some tests, and it seems that smoothed PPs yield reasonable energy for both nb2 and larger structures, when scf.ProExpn.VNA is off, but fail when scf.ProExpn.VNA is on. So that, the only possible way for me is to disable expansion in my calculations. What should I take into account for such a scheme? You have mentioned energy cutoff, but haven't answered, if it is 1DFFT.EnergyCutoff or scf.energycutoff. (Increasing the latter one significantly increases memory usage)
Another question is about projector basis: in ADPACK it is expanded by adding v^i(f) (i = 1..n) functions (with "ortonorming" after). Is it a common technique to expand a projector basis, or a specific one, which works only for a limited set of pseudopotentials?
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.10 ) 
 Date: 2017/06/01 11:50
 Name: T. Ozaki
 Hi,
> but fail when scf.ProExpn.VNA is on
Relevant keywords for scf.ProExpn.VNA are
1DFFT.NumGridK 1DFFT.EnergyCutoff 1DFFT.NumGridR scf.BufferL.VNA scf.RadialF.VNA
I wonder that the last two keywords may largely change the results.
> Another question is about projector basis: in ADPACK it is expanded by adding > v^i(f) (i = 1..n) functions (with "ortonorming" after). Is it a common technique > to expand a projector basis, or a specific one, which works only for a limited set > of pseudopotentials?
This is just one of ways, and there must be many other ways. During many trials, I found that the scheme works well for our pseudopotentials.
BTW, if you want to obtain allelectron wave functions with proper cusp, I wonder that a projector method:
H. Kageshima and K. Shiraishi, Phys. Rev. B 56, 14985 (1997)
might be an easier way.
Regards,
TO

Re: External pseudopotentials and large structures ( No.11 ) 
 Date: 2017/06/01 19:14
 Name: Daniil
 Dear Prof. Ozaki,
I continued testing with 'scf.ProExpn.VNA off' and both total and orbital energies are good even in structures like Nb16O40 cluster or Nb2O5 periodic crystal with rather large basis sets (s9p8d5f3 for Nb and s6p5d3f1 for O). However, in some cases there is a difference of about 0.05 between up and down electron, while the system should be closedshell.
As for scf.RadialF.VNA, I thought that in cannot be more than PAO.Mul in PAO file. Is it right, or it can be increased above this limit?
> This is just one of ways, and there must be many other ways. > During many trials, I found that the scheme works well for our pseudopotentials.
What do you think about using the eigenfunctions of the local potential as additional projectors? As a ghost state is the function, which is not enough affected by Blochl projectors, but lies in the local potential, it is likely to resemble to a certain extent an eigenfunction of the local potential, or a combination of eigenfunctions. Or there is something I missed?
Best regards, Daniil

Re: External pseudopotentials and large structures ( No.12 ) 
 Date: 2017/06/24 16:47
 Name: T. Ozaki
 Hi,
I am wondering why you are sticking 'scf.ProExpn.VNA on', since you got the good results with 'scf.ProExpn.VNA off'.
> As for scf.RadialF.VNA, I thought that in cannot be more than PAO.Mul in PAO file. > Is it right, or it can be increased above this limit?
scf.RadialF.VNA can be more than PAO.Mul in PAO file. The relevant part of code is around the line of 1149 to 1197 in SetPara_DFT.c.
Regards,
TO

