<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
</head>
<body>
<p><font size="+1">Dear Elie,</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">The short answer is: You can't!</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">Spin-orbit interaction couples the orbital
angular momentum with the spin momentum and thus neither l or s
are good quantum number anymore. You now have to use the total
angular momentum J. Sure, a lot of people still use the
nomenclature from the non-SOC calculations, such as speaking in
the case of 2D TMDCs of dz˛ states at the K point, but strictly
speaking this is not correct. If you really want to understand
the relation between J and L in detail, I can recommend the
paper by Andrea Dal Corso and Adriano Mosca Conte, Phys. Rev. B
71, 115106 (2005)
(<a class="moz-txt-link-freetext" href="https://link.aps.org/doi/10.1103/PhysRevB.71.115106">https://link.aps.org/doi/10.1103/PhysRevB.71.115106</a>) which
nicely shows which spherical harmonics are included in which
spin-angle functions for which total angular momentum j. If I
remember this correctly (some time ago that I did this and I
can't find the table anymore) the states with higher mj (+-3/2
and +- 5/2) have more in-plane character</font><font size="+1"><font
size="+1"> for both j=3/5 and j=5/2</font> (i.e., the contain
terms with spherical harmonics which are usually combined such
that the result is in the xy-plane) while the states with
mj=+-1/2 have more out-of-plane character (z direction). But I
could be wrong here since I don't have the details anymore.</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">The only option for you - if you don't want to
check the paper or if this is too much and if nobody else
comments here - is to do a non-SOC calculation and then hope
that SOC is not mixing states too much and you can still call
the result, e.g., dz˛ like. OR you plot the corresponding wave
function in real space and decide by "looking" at the form of
|psi|˛.</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">Regards</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">Thomas</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1"><br>
</font></p>
<p><font size="+1">P.S.: another detail concerning, e.g., the states
at K in a WS2 monolayer - is this your system? :)</font></p>
<p><font size="+1">The states are not simple split into spin up and
spin down even if a lot of people use this nomenclature. For the
valence band the two SOC-split bands are to nearly 100% spin up
or down but not for the conduction band where you won't have
states which are 100% up or down, even if there is no in-plane
contribution... Some details can also be found here:
<a class="moz-txt-link-freetext" href="https://link.aps.org/doi/10.1103/PhysRevB.101.235408">https://link.aps.org/doi/10.1103/PhysRevB.101.235408</a><br>
</font></p>
<p><br>
</p>
<div class="moz-cite-prefix">On 7/4/21 6:52 AM, Elio Physics wrote:<br>
</div>
<blockquote type="cite"
cite="mid:DM5PR2001MB093980C0456EC9B86CB9E285EA1D9@DM5PR2001MB0939.namprd20.prod.outlook.com">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<style type="text/css" style="display:none;">P {margin-top:0;margin-bottom:0;}</style>
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
<span
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Dear
all,</span>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">I
am studying the contribution of the orbitals to the bands of a
structure, in the presence of spin orbit coupling. At the
beginning of the projwfc.x output file, I got:</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
state # 1: atom 1 (S ), wfc 1 (l=0 j=0.5 m_j=-0.5)
<div> state # 2: atom 1 (S ), wfc 1 (l=0 j=0.5 m_j=
0.5)</div>
<div> state # 3: atom 1 (S ), wfc 2 (l=1 j=0.5
m_j=-0.5)</div>
<div> state # 4: atom 1 (S ), wfc 2 (l=1 j=0.5 m_j=
0.5)</div>
<div> state # 5: atom 1 (S ), wfc 3 (l=1 j=1.5
m_j=-1.5)</div>
<div> state # 6: atom 1 (S ), wfc 3 (l=1 j=1.5
m_j=-0.5)</div>
<div> state # 7: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j=
0.5)</div>
<span> state # 8: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j=
1.5)</span></div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span>.</span></div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span>.</span></div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span>.</span></div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span>
state # 39: atom 5 (W ), wfc 3 (l=2 j=1.5 m_j=-1.5)
<div> state # 40: atom 5 (W), wfc 3 (l=2 j=1.5
m_j=-0.5)</div>
<div> state # 41: atom 5 (W), wfc 3 (l=2 j=1.5 m_j=
0.5)</div>
<div> state # 42: atom 5 (W), wfc 3 (l=2 j=1.5 m_j=
1.5)</div>
<div> state # 43: atom 5 (W ), wfc 4 (l=2 j=2.5
m_j=-2.5)</div>
<div> state # 44: atom 5 (W ), wfc 4 (l=2 j=2.5
m_j=-1.5)</div>
<div> state # 45: atom 5 (W), wfc 4 (l=2 j=2.5
m_j=-0.5)</div>
<div> state # 46: atom 5 (W), wfc 4 (l=2 j=2.5 m_j=
0.5)</div>
<span> state # 47: atom 5 (W), wfc 4 (l=2 j=2.5 m_j=
1.5)</span></span></div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span><span></span></span><br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">The
l=1 wavefunctions are the p contributions. But How can we
specifically identify which one is px, py and pz?
<br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Similary,
how to identify which ones of the 10 d orbitals are the dz^2
for example</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">regards<br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><br>
</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Elie</div>
<div
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Federal
Universiy of Rondonia<br>
</div>
<span
style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Brazil</span><br>
</div>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
Quantum ESPRESSO is supported by MaX (<a class="moz-txt-link-abbreviated" href="http://www.max-centre.eu">www.max-centre.eu</a>)
users mailing list <a class="moz-txt-link-abbreviated" href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>
<a class="moz-txt-link-freetext" href="https://lists.quantum-espresso.org/mailman/listinfo/users">https://lists.quantum-espresso.org/mailman/listinfo/users</a></pre>
</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>
</body>
</html>