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<div>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.</div>
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<div>Thanks,</div>
<div>Miles</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size: 11pt;" color="#000000" data-ogsc=""><b>From:</b> Paolo Giannozzi <paolo.giannozzi@uniud.it><br>
<b>Sent:</b> Thursday, November 17, 2022 1:17 PM<br>
<b>To:</b> Quantum ESPRESSO users Forum <users@lists.quantum-espresso.org>; Johnson, Miles R. <mjohnso7@caltech.edu><br>
<b>Subject:</b> Re: [QE-users] Interpretting projwfc.x output</font>
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<div class="PlainText">The ordering of spherical harmonics is given in the code documentation,
<br>
notably here:<br>
<a href="https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html#idm100" data-auth="NotApplicable" data-ogsc="" style="">
https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html#idm100</a><br>
Paolo<br>
<br>
On 17/11/2022 21:23, Johnson, Miles R. wrote:<br>
> Hi all,<br>
> <br>
> I'm trying to interpret the m labels in the output files.<br>
> <br>
> For collinear, spin-unpolarized, the projected dos is written PDOS_m. I <br>
> would like to confirm that the m here labels real spherical harmonics <br>
> <a href="https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics" data-auth="NotApplicable" data-ogsc="" style="">
https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics</a> <<a href="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" data-auth="NotApplicable" data-ogsc="" style="">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</a>><br>
> <br>
> In other words, the ordering is linear combinations of the complex <br>
> spherical harmonics <br>
> <a href="https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Complex_Spherical_harmonics" data-auth="NotApplicable" data-ogsc="" style="">
https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Complex_Spherical_harmonics</a> <<a href="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" data-auth="NotApplicable" data-ogsc="" style="">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</a>> such
that the ordering of the phi dependence is 1,cos(phi), sin(phi),cos(2phi),sin(2phi)...<br>
> <br>
> This interpretation remains true including spin-orbit coupling, except <br>
> that m refers to m_j and the wavefunctions are eigenstates of <br>
> J_z=L_z+S_z and J^2 as per standard addition of angular momentum.<br>
> <br>
> It's taken a little while for me to settle on this interpretation so <br>
> just trying to confirm that I'm correct. Please let me know!<br>
> <br>
> Thanks,<br>
> Miles Johnson<br>
> Applied Physics Phd Candidate<br>
> California Institute of Technology<br>
> <br>
> <br>
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<br>
-- <br>
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,<br>
Univ. Udine, via delle Scienze 206, 33100 Udine Italy, +39-0432-558216<br>
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