Question about phases in PROCAR

[tomic]

Dear All

I have searched the forum but was unable to locate any posts precisely defining the phases written in PROCAR file in addition to weights, when LORBIT is set to 12.

My assumption is following:

When we project Bloch states | k > onto spherical harmonics Y_lm within sphere of radius specified by RWIGS around an atom site s, we obtain coefficients

C = < Y_lm | k >

Weights are given as

|C|^2

and phases as

exp( i arg(C))

Is this correct interpretation?

Thanks

Edit: correction of the Y_lm projection


<span class='smallblacktext'>[ Edited ]</span>

[bmalone]

Hi tomic,

I'm very much interested in the same thing. I don't know what the correct answer is, but I don't think it's the one you've given. In the VASP manual it's stated that for LORBIT=1,2 that you get projections onto spherical harmonics, so I think that should be < Y_{lm}| phi_i > where phi_i is the wavefunction (whether this is the "full" wavefunction or the auxiliary wavefunction I do not know).

For LORBIT=12, looking into the source code suggests that the projection is on the PAW projectors, so probably < p_i |phi_i >. AFAIK, the projector is a radial function times a spherical harmonic, so it probably doesn't give much of a difference in terms of the qualitative picture in comparison to LORBIT <=2.

As for the phase information, I have no idea. I would have thought that the phase factor would be a factor of the form e^{i*theta}, where theta is the phase. However, this definition would have a norm of 1. Looking at some data I have generated with LORBIT=12 gives a norm which is certainly not equal to 1 (nor is it equal to the projection itself, which might be the case if the numbers in the phase factor block stood for the real and imaginary part of A*e^{i*theta}, with A being the magnitude of the projection).

If another VASP users or developer could clarify these points I would be greatly appreciative!



<span class='smallblacktext'>[ Edited Mon Aug 26 2013, 03:51AM ]</span>

[tomic]

[quote="bmalone"]Hi tomic,
so I think that should be < Y_{lm}| phi_i > where phi_i is the wavefunction (whether this is the "full" wavefunction or the auxiliary wavefunction I do not know).
[/quote]

You're completely right! I don't know what I was thinking when I wrote <k| Y |k>.

[bmalone]

In your calculations does it seem as though your phase factors make sense?

In the code sphpro.f90 there contains the comment:

! the phase factor is only qualitative, we just sum over up and down
! for the non collinear case

I'm not sure if this means that the phase factor is quantitatively incorrect in general (and in addition notes that for the non-collinear case it is calculated by summing over the up and down spin channels), or if it's quantitatively incorrect only for the non-collinear case. It's still surprising to me that the phase factor does not have unit norm. I could of course normalize it, but obviously worried that I misunderstand what is printed in the file.

It seems that this issue has bothered quite a few users previously without a definitive reply, most similarly with a post by georg in 2005 here.

Anyone aware of some post-processing scripts which use the phase data? If something like that were available it might be easy to see how the phase information is read in and used, thus elucidating its precise meaning.

[tomic]

[quote="bmalone"]It seems that this issue has bothered quite a few users previously without a definitive reply, most similarly with a post by georg in 2005 here. [/quote]</span>

[bmalone]

[quote="https://en.wikipedia.org/wiki/Phase_factor"]Wikipedia[/url]).

If what Hugo says in the earlier link is correct, it could be that the phase factor isn't really a phase factor but instead is the real and imaginary part of the projection of the wavefunction onto the PAW projectors. The reason that the mod of this number doesn't equal the numbers in the table preceding the phase information could be related to the Q_ee term he mentions. I'll try to look into the source to figure this out, although it may take a bit of time to orient myself to what the variables mean and the code logic.

[xiaoming_wang]

Hi bmalone,

Have you figured out whether the phase part is the PS KS orbitals projected onto the spherical harmonics or the projector functions?

Best,
Xiaoming