[QE-users] Interpretting projwfc.x output

[Paolo Giannozzi]

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