Understanding LORBIT=11

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chengcheng_xiao1
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Understanding LORBIT=11

#1 Post by chengcheng_xiao1 » Sun Aug 14, 2022 4:31 pm

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QUESTION:
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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.

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BEHAVIOR:
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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! :)

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Re: Understanding LORBIT=11

#2 Post by chengcheng_xiao1 » Fri Aug 19, 2022 3:47 pm

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.

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Re: Understanding LORBIT=11

#3 Post by andreas.singraber » Wed Aug 24, 2022 8:20 am

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

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Re: Understanding LORBIT=11

#4 Post by alpinnovianus » Sun Sep 04, 2022 9:47 am

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.)

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