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<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">Dear Dr. Novak,</font></font></p>
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">Thank you very much for your last replying.</font></font></p>
<div class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font face="times new roman,serif" size="2">In your first email, you wrote:</font></div>
<div class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"><font face="times new roman,serif" size="2">Orbital field brings in Hamiltonian term linear in orbital momentum: B_orb.L, without spin-orbit coupling such term is incompatible with the space inversion symmetry.
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<div class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"></span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"><font face="times new roman,serif" size="2">
We know</font></span></div>
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P|l,m>=(-1) ^ l |l,m></font></span></div>
<div class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"></span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"><font size="2"><font face="times new roman,serif">
where P=Parity.</font></font></span></div>
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">So that we can write:</font></font></p>
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">P Vorb = P SUM_m SUM_m' Cmm' |l,m><l,m'| = (-1) ^ l Vorb =Vorb P <span style="FONT-FAMILY: Wingdings; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Wingdings">
<span style="mso-char-type: symbol; mso-symbol-font-family: Wingdings">à</span></span> [P,Vorb]=0</font></font></p>
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">Because this, I can not understand why is Vorb incompatible with space inversion symmetry, and how dose the real version of LAPW1 eliminate some term of Vorb (B_orb.L) automatically?
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<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">Best regards</font></font></p>
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt" align="left"><font size="2"><font face="times new roman,serif">Vahid Ghanbarian</font></font></p>
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