[QE-users] Interpretting projwfc.x output

[Johnson, Miles R.]

I'd like to add that the order described in the documentation does not apply to the total angular momentum, only spherical harmonics. It is not clear from the documentation what the order will be for noncolinear computations with spin orbit.

Thanks,
Miles Johnson
Applied Physics Phd Candidate
California Institute of Technology


________________________________
From: users <users-bounces at lists.quantum-espresso.org> on behalf of Johnson, Miles R. <mjohnso7 at caltech.edu>
Sent: Thursday, November 17, 2022 1:34 PM
To: Paolo Giannozzi <paolo.giannozzi at uniud.it>; Quantum ESPRESSO users Forum <users at lists.quantum-espresso.org>
Subject: Re: [QE-users] Interpretting projwfc.x output

Thank you for the response, but I was asking for clarification on the documentation. In other words, I read the documentation and I think I'm interpreting it correctly but I'm looking for confirmation.

Thanks,
Miles


________________________________
From: Paolo Giannozzi <paolo.giannozzi at uniud.it>
Sent: Thursday, November 17, 2022 1:17 PM
To: Quantum ESPRESSO users Forum <users at lists.quantum-espresso.org>; Johnson, Miles R. <mjohnso7 at caltech.edu>
Subject: Re: [QE-users] Interpretting projwfc.x output

The ordering of spherical harmonics is given in the code documentation,
notably here:
   https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html#idm100
Paolo

On 17/11/2022 21:23, Johnson, Miles R. wrote:
> Hi all,
>
> I'm trying to interpret the m labels in the output files.
>
> For collinear, spin-unpolarized, the projected dos is written PDOS_m. I
> would like to confirm that the m here labels real spherical harmonics
> https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics <https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTable_of_spherical_harmonics%23Real_spherical_harmonics&data=05%7C01%7Cpaolo.giannozzi%40uniud.it%7C70289b9d398645de783308dac8d9b5ec%7C6e6ade15296c4224ac581c8ec2fd53a8%7C0%7C0%7C638043135035130093%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=S4nfO65rh7uURPyLUtSviHWJOoIQQifPmWvPdQYPz%2Bk%3D&reserved=0>
>
> In other words, the ordering is linear combinations of the complex
> spherical harmonics
> https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Complex_Spherical_harmonics <https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTable_of_spherical_harmonics%23Complex_Spherical_harmonics&data=05%7C01%7Cpaolo.giannozzi%40uniud.it%7C70289b9d398645de783308dac8d9b5ec%7C6e6ade15296c4224ac581c8ec2fd53a8%7C0%7C0%7C638043135035130093%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=s50tNxbQTPhKzpmzuhRfL21dey5c1gxxyUFvm%2B4PM3c%3D&reserved=0> such that the ordering of the phi dependence is 1,cos(phi), sin(phi),cos(2phi),sin(2phi)...
>
> This interpretation remains true including spin-orbit coupling, except
> that m refers to m_j and the wavefunctions are eigenstates of
> J_z=L_z+S_z and J^2 as per standard addition of angular momentum.
>
> It's taken a little while for me to settle on this interpretation so
> just trying to confirm that I'm correct. Please let me know!
>
> Thanks,
> Miles Johnson
> Applied Physics Phd Candidate
> California Institute of Technology
>
>
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--
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine Italy, +39-0432-558216
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