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<p>Dear Hari Paudyal,</p>
<p>in case of SOC, the orbital quantum number is not a good quantum
number anymore and you<br>
have to use the total angular momentum. Thus, strictly speaking
there is no pz-state anymore.<br>
Yet, if you work through the details of spin-orbit coupling and
the details given in this<br>
publication which - I think - describes the implementation in QE:<br>
</p>
<p><a class="moz-txt-link-freetext" href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.115106">https://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.115106</a></p>
<p>you will understand that the pz mixes with other states and that
the SOC states with a large<br>
contribution of pz-character are those with m_j = +- 1/2 for both
j = 5/2 and j = 3/2<br>
</p>
<p>Cheerio</p>
<p>Thomas Brumme</p>
<p><br>
</p>
<p>P.S.: Signing your email with your affiliation is highly
recommended.</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 11/9/21 10:01 PM, Hari Paudyal via
users wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAFuJS7UFnGAmEkHeQnyU164VKJHO5SyRP6cjpFgAxOjswvekjw@mail.gmail.com">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<div dir="ltr">Hi experts,
<div><br>
</div>
<div>Can anyone help me to identify pz, px, py characters in the
spin-orbit coupling (SOC) band projection?</div>
<div><br>
</div>
<div>It is well explained without SOC, the order will be pz, px,
py as follows (in my calculation for Se atom)</div>
<div>......<br>
state # 12: atom 2 (Se ), wfc 2 (l=1 m= 1)<br>
state # 13: atom 2 (Se ), wfc 2 (l=1 m= 2) <br>
state # 14: atom 2 (Se ), wfc 2 (l=1 m= 3) <br>
.....</div>
<div><br>
</div>
<div>However, with SOC, it shows as follows based on j = l+s,
and j = l-s, where s = 0.5</div>
<div>....</div>
<div> state # 23: atom 2 (Se ), wfc 2 (l=1 j=1.5
m_j=-1.5)<br>
state # 24: atom 2 (Se ), wfc 2 (l=1 j=1.5 m_j=-0.5)<br>
state # 25: atom 2 (Se ), wfc 2 (l=1 j=1.5 m_j= 0.5)<br>
state # 26: atom 2 (Se ), wfc 2 (l=1 j=1.5 m_j= 1.5)<br>
state # 27: atom 2 (Se ), wfc 3 (l=1 j=0.5 m_j=-0.5)<br>
state # 28: atom 2 (Se ), wfc 3 (l=1 j=0.5 m_j= 0.5)<br>
</div>
<div><br>
</div>
<div>for l = 1 (p orbital), and s = 0.5 j = 1.5, and mj = -1.5,
-0.5, 0.5, 1.5</div>
<div>for l = 1 (p orbital), and s = -0.5 j = 0.5, and mj = -0.5,
0.5<br>
</div>
<div>This makes sense, but which one are pz, px, and py?</div>
<div><br>
</div>
<div>Sincerely,</div>
<div>Hari Paudyal</div>
<div><br>
</div>
<div><br>
</div>
</div>
<br>
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</blockquote>
<pre class="moz-signature" cols="72">--
Dr. rer. nat. Thomas Brumme
Theoretical chemistry
TU Dresden - BAR / II49
Helmholtzstr. 18
01069 Dresden
Tel: +49 (0)351 463 40844
email: <a class="moz-txt-link-abbreviated" href="mailto:thomas.brumme@tu-dresden.de">thomas.brumme@tu-dresden.de</a></pre>
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