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
_______________________________________________
The Quantum ESPRESSO community stands by the Ukrainian
people and expresses its concerns about the devastating
effects that the Russian military offensive has on their
country and on the free and peaceful scientific, cultural,
and economic cooperation amongst peoples
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
users mailing list [email protected]
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