<div dir="ltr"><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">Dear Experts,</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><br></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">I have a problem with an
apparent inconsistency in the signs of the Wannier orbital W.F. I observe in
the the wannier_plot routine (output in *.xsf), compared to the the (implied)
signs of the orbitals I observe in the Hamiltonian (*_hr.dat).</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">The problem detail is the
following:</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">I'm considering bcc Fe, where I
use a cubic unit cell with 2 (equivalent) atoms. Atom1 and atom2
have positions (0,0,0) and a/2*(1,1,1), respectively. I project on to s,
p, d atomic orbitals and do not perform minimization of the Wannier orbital
spread. I obtain an interpolated band structure from Wannier90 that fits
the plane wave solution well. </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">It suffices to consider the (s,
px) orbitals on atom 1 and 2. I plot the Wannier orbital WFs using
Xcrysden. I find that the 's' orbitals have the same sign on
both atoms, while 'px' orbitals have opposite sign on atom 1 and 2.</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">However, the "hopping"
matrix element between these orbitals seem to reveal that the 'px' orbitals on
atom 1 and 2 have the same sign (recall they are displaced from each other
along the x-direction). In particular:</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><atom1, s | H | atom2, px
> = +1.476</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><atom2, s | H | atom1, px
> = -1.476</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">found in the *_hr.dat file as:</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">0
0 0 1 12
1.476361 0.000002</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">0
0 0 10 3
-1.476345 0.000003</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">This pattern of signs for the
hopping is inconsistent with the signs of the wannier orbitals I observe using
XCrysDen</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">This leads to the question: can
the output of the code for the Hamiltonian use different signs for the orbitals
compared to the output of the code for the real space orbitals?</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"> </p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">The wannier90 input file is:</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><br></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">-----------------------------------------------------------------------------------------------------</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">num_bands
= 50</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">num_wann
= 18 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">spin
= up</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">bands_plot
= true</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">wannier_plot
= true</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">wannier_plot_supercell
= 5</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">#dis_win_max
= 85d0</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">dis_froz_max
= 30d0</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">dis_num_iter
= 0 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">num_iter
= 1000 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">dis_mix_ratio
= 1 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">write_hr
= true</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">begin
atoms_frac</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">Fe
0.0 0.0 0.0</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">Fe
0.5 0.5 0.5</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">end
atoms_frac</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">begin
unit_cell_cart</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">Bohr</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">5.4235
0. 0.</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">0.
5.4235 0.</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">0.
0. 5.4235</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">end
unit_cell_cart</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">begin
projections</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">f
= 0., 0., 0.: s;p;d</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">f
= 0.5, 0.5, 0.5: s;p;d</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">end
projections</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">bands_num_points
= 100 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">begin
kpoint_path</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">G
0.0000 0.0000 0.0000 H 0.500 -0.5000
-0.5000 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">H
0.500 -0.5000 -0.5000 P 0.7500 0.2500
-0.2500 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">P
0.7500 0.2500 -0.2500 N 0.5000 0.0000 -0.5000</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">end
kpoint_path</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">mp_grid
= 8 8 8</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">begin
kpoints</span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">
0.00000000 0.00000000 0.00000000 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">
</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas"> 0.00000000
0.00000000 0.12500000 </span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-family:Consolas">-------------------------------------------------------</span></p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">Best</p>
<p class="MsoNormal" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:Calibri,sans-serif">Fei</p><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><a name="SignatureSanitizer__MailAutoSig"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Dr. Fei Xue</span></a><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt"><span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Postdoctoral Research Associate<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">University of Maryland/National Institute
of Standards and Technology<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">100 Bureau Dr. Stop 8412<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">RM B231, Bldg. 216<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Gaithersburg, MD 20899-8412<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Phone: (301) 975-4360<span></span></span></p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Work Email: <a href="mailto:fei.xue@nist.gov" target="_blank">fei.xue@nist.gov</a><span></span></span></p><p>
</p><p class="MsoNormal" style="background-image:initial;background-position:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif;letter-spacing:0.15pt">Permanent Email: <a href="mailto:feixue@utexas.edu" target="_blank">feixue@utexas.edu</a><span></span></span></p><p><br></p><div><div><br><div><br></div></div></div></div></div></div></div></div></div></div></div></div></div>