Understanding LORBIT=11

[chengcheng_xiao1]

---------------
QUESTION:
---------------

LORBIT=11 is probably the community "default" for generating projected band structures or projected density of states.
However, no dedicated section about what's actually being computed can be found.
One can only infer from pages like PROOUT(wiki/index.php/PROOUT), RPOCAR(wiki/index.php/PROCAR), LOCPROJ(wiki/index.php/LOCPROJ), LORBIT(wiki/index.php/LORBIT) that, for LORBIT=11, PAW projectors are used so that the projection is strictly within the PAW sphere (hence no need to set RWIGS).

However, after some digging, I find that in subroutine SPHPRO_FAST in sphpro.F, the actual projection coefficient has a prefactor PP%QTOT:

CSUM(NB,NK,II)=W%CPROJ(LMIND,NB,NK,ISP)*PP%QTOT(LP,L)*GCONJG(W%CPROJ(LMIND_,NB,NK,ISP))

this prefactor is calculated in `RAD_CHECK_QPAW` in radial.F during initialization and apparently is the radial distribution of the AE radial wavefunction (dot r and squared, read from POTCAR) integrated up to the PAW cutoff radius.

From my understanding, W%CPROJ it self is the projection coefficient and one only need to square it to obtain a real number and I'm quite puzzled by the appearance of PP%QTOT.

---------------
BEHAVIOR:
---------------

For elements with very spread valence orbitals, this perfector effectively quench the projection coefficients.
For example, using Na_sv, an isolated atom calculation yields a projection coefficient of 0.024 for the 3s orbital while the projection coefficient is 0.99 for 2s.

Deleting this pp%QTOT from mentioned prompts the projection coefficient for the 3s orbital to 0.99, as one would expect from an isolated atom calculation.

P.S. this behavior seems to persist in LOCPROJ with the PAW projectors as the SPLINE fit in locproj.F includes OPTPROJ which is obtained from QTOT in SET_OPT_PROJ in paw.F.

Any help would be much appreciated!

[chengcheng_xiao1]

The same behavior is also observed in Quantum Espresso's projwfc.x.

According to their documentation (https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html), the value should be interpreted as:
the weight factors thus approximate the real charge within the augmentation sphere of each atom.

A quick look at their source code (https://github.com/QEF/q-e/blob/152ffa9 ... .f90#L1082 and https://github.com/QEF/q-e/blob/152ffa9 ... .f90#L1044) suggests that they also weight the projection coefficients (squared) with the corresponding AE charge inside the PAW sphere.

Although this should not be specified as a bug, the behavior of this implementation can, in some cases, cause misinterpretation of the orbital features of the bands. Hence, a clearer documentation of what these values correspond is needed.

[andreas.singraber]

Hello!

I am not knowledgeable in this topic but I had a discussion yesterday with our expert Martijn Marsman. He completely agrees with your analysis and actually congratulates you to your thorough understanding !

Indeed, when running an isolated Na atom with POTCAR Na_sv one can observe a low projection coefficient for the 3s orbital. As you pointed out this is due to the QTOT prefactor that is summed up only within the PAW sphere. However, Martijn mentioned that a version without this factor may not be unambiguously defined and therefore the current implementation will remain as it is now. Of course this comes with the trouble of potential misinterpretation as you mentioned. You are right that this should be stated more clearly in the documentation and we will update the corresponding Wiki pages soon!

Thanks a lot for your valuable contribution!

All the best,
Andreas Singraber

[alpinnovianus]

I was about to post a question on LORBIT too, and found this recent post.

So I write below on what I would love to see more documentations about in the LORBIT wiki.

I would like to know more details between the two different approaches, LORBIT < 10 that require RWIGS to be specified, and LORBIT >= 10 (especially 11, since that's what we use typically) which doesn't use RWIGS.

(since LORBIT=11 and others in the latter category don't use RWIGS, how do they work? are they inferior/superior/on equal footing compared to the RWIGS-requiring categories to describe PDOS, at least qualitatively? When should it not be used? (known failure cases), etc.)

[chengcheng_xiao1]

Hi alpinnovianus,

As a short summary:

The main difference between LORBIT < 10 and >10 is the radial part of the projection functions:

- LORBIT > 10 uses the PAW projector (see wiki/index.php/Projector-augmented-wave_formalism) for the radial part of the projector. Since the PAW projector is strictly contained within the PAW sphere, one doesn't need to set a cutoff radius.

- For LORBIT < 10, the radial part of the projector is constructed using the solutions to an "electron in an infinite spherical potential well" problem, which are spherical Bessel functions. The principle quantum number n (or the nodes in the spherical Bessel functions) is set to 1,2,3 (because most pseudo-wavefunctions only have up to 3 nodes) and the L quantum number for the Bessel functions of the first kind is set to whichever angular momentum quantum number you are using.

---

For LORBIT > 10, the output reflects the number of electrons inside the PAW sphere. So, if you have a very dispersive orbital, the number will be very small. However, for backward compatibility reason and to assign a physical meaning to the number, this behavior won't be changed in the upcoming versions.

For LORBIT < 10, the results, to me, is more arbitrary as the radial part is Bessel functions, and Bessel functions don't have exponential decaying tails unto the "hard wall". Nonetheless, one can interpenetrate it, again, as the number of electrons inside the hard wall cut off(RWIGS). And that's why the wiki asks you to set the RWIGS so that the spheres cover the volume of the whole unit cell and one can approximately recover the total electron count.

---

As for the up and down sides of both methods:
- LORBIT > 10 retains the "real" atomic feature, but can have large deviation if you are probing very dispersive orbitals (s-orbitals for example)
- LORBIT < 10 can be used to describe very dispersive orbitals but doesn't have a "real" atomic feature in the radial part of the projector

---

A better way to do projection would be to use LOCPROJ with PAW pseudo partial waves, but as of VASP 6.3.1 it cannot be used in combination with line-mode in KPOINTS, so no projected band structure can be calculated this way without some modification to the source code.

I hope this answers your question.

[alpinnovianus]

Hi chengcheng_xiao1 and/or VASP admins,

I want to know the radius of the PAW sphere for integrating magnetic moment at copper sites when using LORBIT = 11.
I have question about where to find this radius from the POTCAR headers?
Which line should I be looking at? Is it the RWIGS tag?

(but isn't RWIGS ignored for LORBIT >= 10?)

Also, if there's already a documentation for how magnetization is computed, similar to the first few posts in this thread, I want to know.

TITEL = PAW_PBE Cu 22Jun2005
LULTRA = F use ultrasoft PP ?
IUNSCR = 1 unscreen: 0-lin 1-nonlin 2-no
RPACOR = 2.000 partial core radius
POMASS = 63.546; ZVAL = 11.000 mass and valenz
RCORE = 2.300 outmost cutoff radius
RWIGS = 2.200; RWIGS = 1.164 wigner-seitz radius (au A)
ENMAX = 295.446; ENMIN = 221.585 eV
ICORE = 3 local potential
LCOR = T correct aug charges
LPAW = T paw PP
EAUG = 586.980
DEXC = 0.000
RMAX = 2.344 core radius for proj-oper
RAUG = 1.300 factor for augmentation sphere
RDEP = 2.302 radius for radial grids
RDEPT = 1.771 core radius for aug-charge