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

