<div dir="ltr">Dear
Thomas Brumme,<div><br></div><div>Thank you for the explanation, I really appreciate it.</div><div><br></div><div>Sincerely,</div><div>Hari Paudyal</div><div>Binghamton University, SUNY</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Nov 10, 2021 at 3:59 AM Thomas Brumme <<a href="mailto:tbrumme@msx.tu-dresden.de">tbrumme@msx.tu-dresden.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<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 href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.115106" target="_blank">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>On 11/9/21 10:01 PM, Hari Paudyal via
users wrote:<br>
</div>
<blockquote type="cite">
<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>
<fieldset></fieldset>
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</blockquote>
<pre 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 href="mailto:thomas.brumme@tu-dresden.de" target="_blank">thomas.brumme@tu-dresden.de</a></pre>
</div>
</blockquote></div>