A question about pseudopotentials and basis sets

[ziand]

ATK comes with an extensive set of pseudopotentials (PPs). Those are norm-conserving PPs as parameterized by Troullier and Martins in the nonlocal form of Kleinman and Bylander, right? Are those PPs generated taking relativistic effects into account and what about nonlinear partial-core corrections?

Now, about basis sets: ATK uses the well established SIESTA-type pseudo-atomic orbitals. They are closely related to the famous Sankey-Fireballs (but with a more soft confinement), right? ATK provides parameters for the orbitals for many basis sets (SZ, SZP, ...  for LDA, GGA) of all elements. Those parameters include conf. strength (V_0), conf. start (r_inn), conf. cutoff (r_c), split norm (r_split).

o  r_split is found impirically to be 0.15. OK.
o  V_0 is 20 Hartree. Why?
o  How is r_c determined? (For the Fireballs it is the position of the first node of the PP eigenstate at a slightly excited energy (energy shift dE ~ +0.1 eV). The same here?)
o  How is r_inn determined or optimized?

Is there a paper where those things are described?
(I know for example:
Soler et al. [J. Phys.: Condens. Matter 14 (2002) 2745–2779] where it is mentioned that that it is usually better to fix a common energy shift, rather than a common radius r_c.
Artacho et al. [phys. stat. sol. (b) 215, 809 (1999)] again enegry shift as single parameter.
Anglada et al. [PRB 66, 205101 (2002)] mention the soft confinement, discuss r_c but seem to miss any comment on r_inn.
Junquera et al. [PRB 64, 235111 (2001)] discuss an optimization precedure for V_0, r_c and r_inn.
)

I noticed that the definition of the confining potential in [PRB 66, 205101 (2002)] and [PRB 64, 235111 (2001)] (SIESTA) differs from the one in the ATK manual. Is the one in the manual indeed the one used in ATK?


Thanks for your help.

[Nordland]

Hey ziand.

I will perhaps answer you in more than one post, but let me try to give you answers on most of the questions.

Yes the pseudo-potentials are generated with nonlinear core-correction for many of the elements where it makes sense.
At the current point I dont have an exact list of which of the pseudo-potentials that are calculated with relativistic, but the heavier elements
usually are.

The V_0 is the confinement strength, or rather how fast the potential becomes infinity, so therefore it is require to have a value that gives a smooth tail, and still becomes very close to infinity as soon as you reach the r_c. The value of 20.0*Hartree is a good value, but it is not a magic value and you can often vary it without any significant results. Of course if you make it very large you would effectively move the cutoff radius to the inner radius.

The basis set shipped with 11.8 the r_c is calculated exactly as you state - just with the value of 0.05 eV

The inner radius is in our current parameters always set to be 0.8 of the r_c, as this gives a smooth decaying tail of the orbitals (when you have a value of 20 Ha for V_0) , again it is not a magic value, but don't change it without a proper cause.

I think the confining potential is identical in the Siesta and ATK version, but the formula given in the reference formula is the special case where n=1.
In ATK 11.8 and earlier it was only possible to set the confinement_power to 1 (n=1), but in 12.2 it is now possible to set the confinement power to any value.

We have started major work on optimizing all the basis sets parameters to give much better results with the same computational effort - using a scheme similar to to the approach in Junquera et al.

[ziand]

Thank you very much for the clear explanations.

There is one remaining unclearity on my side: Okay you can set the confinement power in the new version. Why not. However, the formula I found in cited literature doesn't do so.
It reads

V₀ exp[-(r_c-r_inn) / (r-r_inn)] / (r_c-r).

Why not using that one?

But okay, for the versions of ATK I used so far, the formula in the manual is the one that is actually used. That was what I wanted to be confirmed.

[Nordland]

Hey ziand.

I have looked a bit deeper into it, and the formula we are using for the confinement potential,
and this is inspired by a paper from Soler ( I will have to dig out the reference if you need it )

V = V0 exp[-(rc-rinn) / (r-rinn)] * ((rc - ri) / (rc-r))^n

So the major difference between the referenced formula is that in the ATK formula
the parameter V0 (Ha*Bohr) is independent of the choice of rc and an ri, where in the Siesta formula
have to adjust V0 (Ha) together with rc and ri.

In the earlier version of ATK you were not allow to set n, but you are now usnig the keyword
confinement_power. (The default is still 1, but I have some experience with n=2 gives a more smooth tail
for ELF calculations etc).
The special case of n=1 gives the exact same shape as the formula you have written, when it is taken into account the different
in the definition of V0 in ATK and Siesta.