<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><font face="Times New Roman">Dear Dr. Novak,</font></p>
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<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><font face="Times New Roman">Thank you very much for your attention. There are three questions.</font></p><pre style="MARGIN-LEFT: 42pt; TEXT-INDENT: -24pt; TEXT-ALIGN: justify; mso-list: l0 level1 lfo1; tab-stops: list 42.0pt left 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt">
<span style="mso-fareast-font-family: 'Courier New'"><span style="mso-list: Ignore"><font size="2">1.</font><span style="FONT: 7pt 'Times New Roman'"> </span></span></span><span dir="ltr"><font size="2">For the extra averaging of the LDA+U potential for system without the centre of inversion, when LAPW1 must be complex, dose the WIEN2k put Vmm, V-m-m ->(Vmm+V-m-m)/2 automatically or we must do this work by hand? If by hand, how?
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<i><span style="mso-fareast-font-family: 'Courier New'"><span style="mso-list: Ignore"><font size="2">2.</font><span style="FONT: 7pt 'Times New Roman'"> </span></span></span></i><span dir="ltr"><font size="2">Is the orbital field equal to zero when Vmm=V-m-m? If no, why do we put Vmm, V-m-m ->(Vmm+V-m-m)/2?
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<i><span style="mso-fareast-font-family: 'Courier New'"><span style="mso-list: Ignore"><font size="2">3.</font><span style="FONT: 7pt 'Times New Roman'"> </span></span></span></i><span dir="ltr"><font size="2">When is the orbital field important?
<i></i></font></span></pre><pre style="TEXT-ALIGN: justify"><i><font size="2"> </font></i></pre><pre style="TEXT-ALIGN: justify"><font size="2">Thanks</font></pre><pre style="TEXT-ALIGN: justify"><font size="2">Vahid Ghanbarian
</font></pre><pre style="TEXT-ALIGN: justify"><font size="2"> </font></pre><pre><font size="2">>Dear Vahid Ghanbarian,</font></pre><pre><font size="2"> </font></pre><pre><font size="2">>On Mon, 5 Dec 2005, vahid ghanbarian wrote:
</font></pre><pre><font size="2"> </font></pre><pre><font size="2">>><i> Dear WIEN2k users</i></font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">
>><i></i></font></pre><pre><font size="2">>><i> In the ORB section of user's guide, the below statements were written:</i></font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>>
<i> If LDA+U is used in an unrestricted, general way, it introduces an orbital</i></font></pre><pre><font size="2">>><i> field in the calculation. If the LDA+U orbital polarization is not needed,</i></font></pre><pre>
<font size="2">>><i> it is sufficient to run real version of LAPW1, which then automatically puts</i></font></pre><pre><font size="2">>><i> the orbital field equal to zero. For systems without the center of inversion
</i></font></pre><pre><font size="2">>><i> when LAPW1 must be complex, an extra averaging of LDA+U potential is</i></font></pre><pre><font size="2">>><i> necessary.</i></font></pre><pre><font size="2">>>
<i></i></font></pre><pre><font size="2">>><i> I have some questions.</i></font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i> 1. Is this statement true? When we have a system with the centre of
</i></font></pre><pre><font size="2">>><i> inversion, all of the component of orbital dependent potential will be real.</i></font></pre><pre><font size="2">>Orbital potential is a hermitean matrix, while the diagonal elements >are
</font></pre><pre><font size="2">>real, nondiagonal are in general complex.</font></pre><pre><font size="2"> </font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i> 2. Dose the real version of LAPW1 put the orbital field equal to zero in a
</i></font></pre><pre><font size="2">>><i> system with the centre of inversion that has only real component of orbital</i></font></pre><pre><font size="2">>><i> dependent potential?</i></font></pre><pre><font size="2">
>Yes, orbital field brings in Hamiltonian term linear in orbital momentum:</font></pre><pre><font size="2">>B_orb.L, without spin-orbit coupling such term is incompatible with the</font></pre><pre><font size="2">>space inversion symmetry.
</font></pre><pre><font size="2"> </font></pre><pre><font size="2">><i></i></font></pre><pre><font size="2">>><i> 3. How can we do the extra averaging of the LDA+U potential for system</i></font></pre><pre><font size="2">
>><i> without the centre of inversion, when LAPW1 must be complex?</i></font></pre><pre><font size="2">>Orbital potential is a matrix in space of sherical harmonics Ylm.</font></pre><pre><font size="2">>To average orbital potential you put Vmm, V-m-m -> (Vmm + V-m-m)/2.
</font></pre><pre><font size="2"> </font></pre><pre><font size="2">>Regards</font></pre><pre><font size="2">>Pavel Novak</font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i></i>
</font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i> Best regards</i></font></pre><pre><font size="2">>><i></i></font></pre><pre><font size="2">>><i> Vahid Ghanbarian.</i>
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