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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.</div>
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Thanks,</div>
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Miles Johnson</div>
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Institute of Technology</span><br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> users <users-bounces@lists.quantum-espresso.org> on behalf of Johnson, Miles R. <mjohnso7@caltech.edu><br>
<b>Sent:</b> Thursday, November 17, 2022 1:34 PM<br>
<b>To:</b> Paolo Giannozzi <paolo.giannozzi@uniud.it>; Quantum ESPRESSO users Forum <users@lists.quantum-espresso.org><br>
<b>Subject:</b> Re: [QE-users] Interpretting projwfc.x output</font>
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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="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" data-ogsc="" style="font-size:11pt"><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="x_PlainText elementToProof">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>
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