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Minus sign in Fourier transform of projectors #855
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@azadoks maybe you also paste here the table containing investigations on the QE subroutines? Thanks a lot! |
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Yes, of course, https://en.wikipedia.org/wiki/Spherical_harmonics#Parity so the formula at https://docs.dftk.org/dev/developer/useful_formulas/ can (and should) be rewritten as (-i)^l. I think we haphazardly coded the formula in the very beginning of DFTK, and then later did the docs properly, but didn't see there was an error in the code, since it doesn't affect the physical properties... Thanks a lot for finding this! You can just fix it in your wannier (or a separate) PR if that's convenient, otherwise I'll just fix it later. |
I went ahead and did it: #856 |
Thanks a lot for the clarification, this is great! |
Thanks for flagging this @qiaojunfeng ! |
While I was rewriting the Wannier interface (#854), I need to project Bloch states onto localized orbitals, so I need sth similar to
build_form_factors
here,DFTK.jl/src/terms/nonlocal.jl
Lines 219 to 225 in ff7f662
However, when I check the equations, I think it should be
(-im)^l
instead of the currentim^l
. I wrote down some formulas herehttps://wannierjl.org/theory/initial_projection/
and some numerical tests here
https://wannierjl.org/theory/pluto_fourier
I uses
(-im)^l
in the #854, in principle this is just a phase factor of wavefunctions. But for instance, if we were to construct a linear combination ofs
andpx
orbitals, then this minus sign will give us different results,s+px
ors-px
, so maybe we should also update thebuild_form_factors
?The text was updated successfully, but these errors were encountered: