Re: Bessel expansion of PAO/VPS ( No.1 ) 
 Date: 2017/04/20 13:05
 Name: T. Ozaki
 Hi Artem,
> (i) Do I have to choose a very fine grid to include wavefunction / PAO features > at the origin?
Since PAOs are basis functions for pseudopotentials, the variation near the origin is not so large compared to all electron cases. So, we do not need to have a very fine grid near the origin.
> (ii) If yes, why is it N log N complexity? I would rather call it N exp N provided N > is the number of points in the logarithmic grid.
The complexity comes from the FFT in Eqs. (8), (19), and (20), resulting in N log N.
> (iii) Isn't it more efficient to do the Fourier integration of Eq. 8 on the logarithmic > grid with complecity N^2 rather than having a very fine grid and effective complexity N > exp N? > (iv) Did you consider Logarithmic Fourier Transform with even smallest complexity > "N" for this problem?
If the SiegmanTalman method is used, we can keep the logarithmic grid. The case is shown in Fig. 7. From the comparison, we found that regular mesh is more efficient than the logarithmic grid for PAOs.
Regards,
TO

Re: Bessel expansion of PAO/VPS ( No.2 ) 
 Date: 2017/04/29 01:49
 Name: Artem Pulkin
 Dear Taisuke,
May I use this thread and your attention to enlighten myself in DFT basics.
As I understood, the calculations of overlap matrix and nonlocal potential matrix can be done with the same set of tools. However, the data found in VPS files has to be transformed into separable KleinmanBylander form. The latter relies on some initial spherical basis set. I found that Siesta uses eigenstates of an atomic Hamiltonian. Is it also the case in OpenMX? Can I use different spherical functions, say, those from PAO files?

Re: Bessel expansion of PAO/VPS ( No.3 ) 
 Date: 2017/05/18 10:57
 Name: T. Ozaki
 Hi Artem,
> Can I use different spherical functions, say, those from PAO files?
Data stored in the VPS files, *.vps are already in the separable form. The data structure of the VPS file can be found at http://tozaki.issp.utokyo.ac.jp/winterschool16/2PPOzaki.pdf If multiple valance states for a Lchannel are included in PP, the separable form is generated by a modified procedure of Vanderbilt, while the separable form is generated by Blochl's technique if a valence state for a Lchannel is included in PP. For the latter case, the radial functions of PAO can be utilized.
Anyway, you need to deeply touch the pseudopotential generator: ADPACK.
Regards,
TO

Re: Bessel expansion of PAO/VPS ( No.4 ) 
 Date: 2017/05/24 08:46
 Name: Artem Pulkin
 Dear Taisuke,
Do I understand it right: the nonlocal part of the pseudopotential is presented in the form Eq.(7) of Bolchl PRB (1990) where the radial part of the product 1/sqrt(c_i) v*phi_i> are columns in VPS file (units are square roots of energy)?
Otherwise where do I find the angular momentum of the corresponding spherical harmonic? What about the spin part?
For example, there are 12 nonlocal components in
http://www.jaist.ac.jp/~tozaki/vps_pao2013/H/H_CA13.vps
As far as I understood this number is factorized into 3 Blochl projectors ( Blochl.projector.num) times two shells, L=0 (1s) and L=1 (2p), times 2 spins. Am I right? What is the column order in "Pseudo.Potentials" with respect to these numbers?
Thank you in advance.
Artem

Re: Bessel expansion of PAO/VPS ( No.5 ) 
 Date: 2017/05/24 09:45
 Name: T. Ozaki
 Dear Artem,
> the nonlocal part of the pseudopotential is presented in the form Eq.(7) > of Bolchl PRB (1990)
Yes, for the both cases: Blochl and MBK we have the same form. One can see in case of hydrogen that there are 15 columns in between <Pseudo.Potentials and Pseudo.Potentials>, where the sequence is as follows:
x, log(x), Vlocal, Vs1(l+1/2), Vs1(l1/2), Vs2(l+1/2), Vs2(l1/2), Vs3(l+1/2), Vs3(l1/2), Vp1(l+1/2), Vp1(l1/2), Vp2(l+1/2), Vp2(l1/2), Vp3(l+1/2), Vp3(l1/2).
Vlocal: local potential Vs1(l+1/2): 1st nonlocal potential of schannel with l+1/2, and the other cases can be deduced from the notation.
Note that though Vs does not depend on j=l+1/2, we have two columns for l+1/2 for the format to be consistent for other Lchannels.
Regards,
Taisuke

