Re: ghost states for Pb ( No.1 ) 
 Date: 2008/05/16 18:15
 Name: T.Ozaki
 Dear Dr. A. Lusakowski,
Sorry for my too late response. Anyway, I reply you as below:
Since finding eigenfunctions for pseudopotentials requires an iterative solution due to the nonlocality of potential, the iterative method can fail to convenge in some case.
In most cases like you showed us:
> 1. "warning!, could not find an appropriate matching point." > I do not know what do You mean by matching point. This communicate is always > accompanied by "warning!, could not find any bound state for L=1" or for L=0.
the message means that the iterative solution did not converge. If so, you don't need to worry about that for OpenMX calculations. It just concerns a problem of ADPACK.
> 2. If there is no the above communicate I usually get " For L=0, > a ghost state is found UNDER correct eigenstates." or ABOVE. > As I understand such informations tell us that the generated pseudopotentials > are invalid. There is no bound state for AE energy or there are ghost states.
If you observe the resonance around the energy region told by ADPACK in the logarithmic derivative of the pseudopotential, then above message should be taken seriously. Otherwise, the logarithmic derivative itself can be realible more than the message.
> That is why I am not sure if I properly understand the above communicates. May be, > producing the pseudopotentials, only the comparison of logarithmic derivatives is > important?
In my opnion, the logarithmic derivative is just one of indicators whether the pseudopotential is better or not. It would be better to judge accuracy on the pseudopotential in several aspects such as band dispersion, structural parameter, and etc.
> And the last question: Why the pseudopotentials for Pb and Te are produced for such > large number of valence electrons? May be it is impossible to produce them for a > smaller number?
Unfortunately, I haven't obtained lots of experiences for calculations of Pb and Te. Maybe, such a "light" pseudopotential for Pb and Te may work if a relatively hard PCC charge is used. But, this should be checked by yourself.
Best regards,
TO

Re: ghost states for Pb ( No.2 ) 
 Date: 2008/05/20 22:40
 Name: A. Lusakowski <lusak@ifpan.edu.pl>
 Dear Professor Ozaki,
Thank you very much for your answers and advices. During last weeks I tried to understand at least part of the ADPACK code. I met some points which I do not understand. I would be very grateful for clarifying these problems for me. 1.The first is the use Schrodinger or Dirac approach. As far as I understand the pseudopotentials are calculated using fully relativistic Dirac equation. But the logarithmic derivatives are calculated using Schrodinger equation. Is this connected with the fact that the logarithmic derivatives are calculated far from the nucleus, where the relativistic effects are less important? 2. Your program calculates pseudo atomic orbitals which are one of the main inputs to OpenMX program. As far as I am able to understand the code these pseudo atomic orbitals are calculated using Schrodinger equation. If I am right, is it possible to change the OpenMX code to take into account relativistic effects on the PAO level (it means the fully relativistic pseudo atomic orbitals to be atomic orbital basis to OpenMX)? Do you plan such changes in the future? 3. The next question is concerned with optimization of pseudo orbitals. At present this function does not work for fully relativistic calculations with spinorbit coupling. Are there serious problems with the implementation of it? This would speed very much calculations for heavy elements compounds. 4. The last question is connected with the division of electrons between different j (total angular momentum) for the same l (angular momentum). For example for d shell the division is 55 instead of 64. Do you think this does not make any difference? Let me stress that all above questions are based only on my understanding of the code and I admit that this understanding may have nothing to do with the real calculations your program does. But I am really interested in OpenMX because according to my knowledge this is the only open source program which offers fully relativistic calculations based on atomic orbitals basis. I think this is a better starting point to investigate such elements like europium or gadolinium (4f shell) comparing to plane waves basis approach. That is why I would like to understand better what I calculate. With best regards Andrzej Lusakowski

