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Dear Hassan,
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<div>Each line in hr.dat refers to an element of H_{mn}(R) = <w_m(0)|H|w_n(R)>. The first three entries in each line give the translation vector R, the next two give the WF indices m and n, and the last two are the real and imaginary parts of the matrix element
itself. See the User Guide Sec. 8.18, for example. The order of the indices m and n are the same order in which the WFs appear at the end of the wannier90 output file (*.wout), so which atoms are referred to by a particular hopping matrix element with indices
m and n depends on where the wannier functions w_m and w_n are centred in the cell.</div>
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<div>Whilst the WFs themselves are orthogonal, you would not expect the matrix representation of the Hamiltonian in the WF basis to be diagonal in the m and n indices because the WFs are not eigenstates of H. The WFs are, however, localised, so you would expect
the matrix elements of H to reflect this.</div>
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<div>Hope this helps,</div>
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<div>Arash</div>
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<div>Dr Arash Mostofi — <a href="http://www.mostofigroup.org">www.mostofigroup.org</a></div>
<div>Imperial College London</div>
<div>Director, Thomas Young Centre @Imperial</div>
<div>Assistant Director, CDT in Theory & Simulation of Materials</div>
<div>Warden, Wilkinson & Weeks Hall</div>
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<div>On 14 Dec 2014, at 06:32, Hassan Tahini <<a href="mailto:hat343@gmail.com">hat343@gmail.com</a>> wrote:</div>
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<p class="MsoNormal">Dear All,</p>
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<p class="MsoNormal">We are having a problem interpreting the output of wannier_hr.dat. This file is supposed to contain the on-site energies and hopping elements from one orbital on one site to another.</p>
<p class="MsoNormal">We have a perovskite system (space group R-3c) with octahedral tilting and we are interested in the eg bands, we define our projections as:</p>
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<p class="MsoNormal">num_wann = 4 </p>
<p class="MsoNormal">num_bands = 144</p>
<p class="MsoNormal">begin projections</p>
<p class="MsoNormal">Mn:l=2,mr=1,4</p>
<p class="MsoNormal">end projections</p>
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<p class="MsoNormal">Part of the wannier90.up_hr.dat looks like this:</p>
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<p class="MsoNormal"> 0 0 0 1 1 11.382484 0.000000</p>
<p class="MsoNormal"> 0 0 0 2 1 -0.435842 0.000000</p>
<p class="MsoNormal"> 0 0 0 3 1 0.017151 0.000000</p>
<p class="MsoNormal"> 0 0 0 4 1 0.170537 0.000000</p>
<p class="MsoNormal"> 0 0 0 1 2 -0.435842 0.000000</p>
<p class="MsoNormal"> 0 0 0 2 2 11.966686 0.000000</p>
<p class="MsoNormal"> 0 0 0 3 2 -0.067861 0.000000</p>
<p class="MsoNormal"> 0 0 0 4 2 -0.613858 0.000000</p>
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<p class="MsoNormal">We are finding it difficult to interpret the above. Can we say for instance that there is “hopping” between the dz2 orbital on atom one to a dx2-y2 on the same atom (=-0.435 eV)? Or can we say that the hopping between dz2 on atom 1 to dx2-y2
on atom 2 is 0.17 eV? Shouldn't the hopping between orthogonal orbitals be equal to zero? Should we use different projection settings?</p>
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<p class="MsoNormal">Your help is highly appreciated.</p>
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<p class="MsoNormal">Hassan</p>
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<p class="MsoNormal">p.s. The band structure obtained with wannier90 looks just like the one we obtain from ab-initio calculations.</p>
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<b><font face="courier new, monospace">Dr Hassan A. Tahini</font></b>
<div><b><font face="courier new, monospace"><i>PhD</i>, <i>DIC</i></font></b>
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<div><font face="courier new, monospace" color="#ff9900"><i style="background-color:rgb(255,255,255)">Physical Sciences and Engineering,</i></font></div>
<div><i><font face="courier new, monospace" color="#ff9900">Computational Physics & Materials Science Group,</font></i></div>
<div><i style="font-family:'courier new',monospace;font-size:small"><font color="#ff9900">KAUST</font></i></div>
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