<table cellspacing="0" cellpadding="0" border="0" ><tr><td valign="top" style="font: inherit;">Dr. Mostofi,<br><br>Thank you for your kind comments. Is there any way to find this rotation matrix U_mn? I see .anm and .mmn files from W90 output, but not .umn<br><br>Seunghwan Lee<br>University of North Carolina<br><br>--- On <b>Sat, 5/8/10, Arash Mostofi <i><a.mostofi@imperial.ac.uk></i></b> wrote:<br><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"><br>From: Arash Mostofi <a.mostofi@imperial.ac.uk><br>Subject: Re: [Wannier] plotting Wannier orbitals<br>To: "wannier@quantum-espresso.org" <wannier@quantum-espresso.org><br>Date: Saturday, May 8, 2010, 1:22 PM<br><br><div id="yiv1905094582">
<font face="Calibri">Dear Seunghwan,<br>
<br>
In general, the MLWFs correspond to a transformation of a <i>set</i>
of energy bands (determined by the energy windows that one defines).
Unless a particular band is isolated from the rest of the bands in the
Brillouin zone, which can happen, for example, when you have a very
localised defect level, no single particular MLWF will correspond
directly to a single particular band. <br>
<br>
Let us for a moment assume, for simplicity, </font><font face="Calibri">Gamma-point
only sampling of the BZ and that we don't need to do any
disentanglement procedure.</font><font face="Calibri"> One may want to
know how much "character" of a particular energy eigenstate $\psi_{n}$
is present in a particular MLWF $w_{m}$ (or vice versa). Then one
should look at the quantity $|< \psi_{n} | w_{m} >|^2$. If you
work it out, this is just $|U_{nm}|^2$ where U is the matrix in Eq.
(10) of Marzari & Vanderbilt, <i>Phys Rev B</i> <b>56</b>, 12847
(1997) [or, alternatively, Eq. (1) of <i>Comput Phys Commun</i> <b>178</b>,
685 (2008)]. Mathematically, this is just the square of the projection
of the eigenstate on the MLWF, and gives a measure of the amount of
overlap between them.<br>
<br>
Hope that helps.<br>
<br>
Arash<br>
<br>
</font>
<pre class="moz-signature">--<br>Dr Arash A Mostofi<br>Lecturer and RCUK Fellow<br>Depts of Materials & Physics<br>Imperial College London <br>London SW7 2AZ, United Kingdom<br><br>T +44 (0)207 594 8154<br>F +44 (0)207 594 6757<br>E <a rel="nofollow" class="moz-txt-link-abbreviated" ymailto="mailto:a.mostofi@imperial.ac.uk" target="_blank" href="/mc/compose?to=a.mostofi@imperial.ac.uk">a.mostofi@imperial.ac.uk</a><br>W <a rel="nofollow" class="moz-txt-link-freetext" target="_blank" href="http://www.cmth.ph.ic.ac.uk/people/a.mostofi">http://www.cmth.ph.ic.ac.uk/people/a.mostofi</a><br></pre>
<br>
<br>
seunghwan lee wrote:
<blockquote type="cite">
<pre>Hi All,<br><br>I have a question about plotting Wannier orbitals. The question may<br>not make any sense, but is there any way to relate a particular<br>wannier orbital and an energy band? For example, if I want to plot<br>the HOMO and LUMO of a semi-conducting system, is it possible to find<br>these orbitals from the set of MLWO calculated with W90?<br>Thank you for your help.<br><br>Seunghwan Lee<br>University of North Carolina<br><br><br> <br>_______________________________________________<br>Wannier mailing list<br><a rel="nofollow" class="moz-txt-link-abbreviated" ymailto="mailto:Wannier@quantum-espresso.org" target="_blank" href="/mc/compose?to=Wannier@quantum-espresso.org">Wannier@quantum-espresso.org</a><br><a rel="nofollow" class="moz-txt-link-freetext" target="_blank" href="http://www.democritos.it/mailman/listinfo/wannier">http://www.democritos.it/mailman/listinfo/wannier</a><br> </pre>
</blockquote>
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