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Hi Gavin,</div>
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Thank you for your reply. I have another calculation with a different k-path but output file still contains "??" marks. I am also not sure if the complex numbers are the characters of the point group. Here are few bands at a general k-points which belongs to
C1 point group. This group has only unit operator, E. So, the character of E should be 1. But the numbers listed under operator E in the output file are clearly different, and doesn't look like due to rounding error. Maybe I misunderstood the output file. </div>
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<span>knum = 2 kname=<br>
</span>
<div>k = 0.000000 0.000000 0.225000<br>
</div>
<div><br>
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<div> The point group is C1<br>
</div>
<div> 1 symmetry operations in 1 classes<br>
</div>
<div><br>
</div>
<div> E
<br>
</div>
<div> G1 A1 1<br>
</div>
<div> --------------<br>
</div>
<div> G2 A1/2 1<br>
</div>
<span></span><br>
</div>
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<span>bnd ndg eigval E</span><br>
</div>
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<span>....</span></div>
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<span> 15 2 -4.673171 1.56-0.00i ??<br>
</span>
<div> 17 2 -4.673047 0.04+0.00i ??<br>
</div>
<div> 19 2 -4.673041 0.03-0.00i ??<br>
</div>
<div> 21 4 -4.672125 0.07-0.00i ??<br>
</div>
<span></span><br>
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Thanks,</div>
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Fhokrul</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Wien <wien-bounces@zeus.theochem.tuwien.ac.at> on behalf of Gavin Abo <gsabo@crimson.ua.edu><br>
<b>Sent:</b> Sunday, June 21, 2020 3:35 AM<br>
<b>To:</b> wien@zeus.theochem.tuwien.ac.at <wien@zeus.theochem.tuwien.ac.at><br>
<b>Subject:</b> Re: [Wien] Irrep output file</font>
<div> </div>
</div>
<div><font color="#0000ff">I'm not sure that I have the proper answers but given below is what I'm currently thinking they might be.</font><br>
<blockquote type="cite">
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I am trying to extract irreducible representation of eigenvalues. I have obtained the case.outputirso and case.irrepso files. But I am not sure if I understood these files correctly. The Ci point group has two irreducible representations as listed in the file
but many of the eigenstates are labelled by "??". Am I doing anything wrong?</div>
</blockquote>
<p><font color="#0000ff">The 3.99-0.00i 0.00+0.00i for band 109 for E and I values, respectively, look very close to 4.00+0.00i 0.00-0.00i for band 105. I wondering if perhaps there is some round off error where the ?? might indicate that the program was
not able to identify a irreducible representation label corresponding to </font>
<font color="#0000ff"><font color="#0000ff">3.99-0.00i 0.00+0.00i</font> (since it would need to be
</font><font color="#0000ff"><font color="#0000ff">4.00+0.00i 0.00-0.00 to have</font> G2+ + G2+ + G2- + G2-
</font><font color="#0000ff">in this case). I'm wondering if that would be effected by your k-mesh. Have you tried change it to see if the values change? There is also a tolerance value (TOL variable) in SRC_irrep/wrtir.f that looks like it could be adjusted.
Though, I would only fiddle with that as a last resort.<br>
</font></p>
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<span style="font-family:Calibri,Helvetica,sans-serif; background-color:rgb(255,255,255); display:inline!important"> The bands 105 -108 are </span><span style="color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif; font-size:12pt">four-fold degenerate
with irrep of the double group G2+, G2+,G2-,G2-, respectively, right? </span></div>
</blockquote>
<p><font color="#0000ff">I believe you are right about that.</font><br>
</p>
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<span style="color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif; font-size:12pt">Also, can anyone please clarify what are the complex numbers under operators E and I?
<br>
</span></div>
</blockquote>
<p><font color="#0000ff">Since in some point groups the characters can be complex [1], I guessing the developer for programming simplicity decided to output the results always in complex number notation even though in many cases it is only a real number. For
your calculation, it appears to be only be a real number as the imaginary part is zero (i.e., 0.00i).</font></p>
<p><font color="#0000ff">[1] <a class="x_moz-txt-link-freetext" href="https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.06%3A_Character_Tables#Irreducible_representations_with_complex_characters">
https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.06%3A_Character_Tables#Irreducible_representations_with_complex_characters</a></font><br>
</p>
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case. outputirso:</div>
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<span> The point group is Ci<br>
</span>
<div> 2 symmetry operations in 2 classes<br>
</div>
<div> Table 6 on page 32 in Koster et al [7]<br>
</div>
<div> Table 11.4 on page 138 in Altmann et al [8]<br>
</div>
<div><br>
</div>
<div> E I
<br>
</div>
<div> G1+ A1g 1 1<br>
</div>
<div> G1- A1u 1 -1<br>
</div>
<div> --------------------<br>
</div>
<div> G2+ A1/2g 1 1<br>
</div>
<div> G2- A1/2u 1 -1<br>
</div>
<div><br>
</div>
<div><br>
</div>
<div>class, symmetry ops, exp(-i*k*taui)<br>
</div>
<div> E 2 (+1.00 0.00i)<br>
</div>
<div> I 1 (+1.00 0.00i)<br>
</div>
<div><br>
</div>
<div>bnd ndg eigval E I<br>
</div>
<div> 1 2 -4.675588 1.99+0.00i -1.99-0.00i ??<br>
</div>
<div> 3 2 -4.675572 1.99-0.00i 1.99-0.00i ??<br>
</div>
<div> 5 2 -4.674606 1.98-0.00i -1.98+0.00i ??<br>
</div>
<span></span>...</div>
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...</div>
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<span> 97 4 -4.261267 3.97+0.00i -0.00-0.00i ??<br>
</span>
<div>101 4 -4.261167 3.99-0.00i 0.01+0.00i ??<br>
</div>
<div>105 4 -4.260795 4.00-0.00i 0.00+0.00i =G2+ + G2+ + G2- + G2-<br>
</div>
<div>109 4 -4.259344 3.99-0.00i 0.00+0.00i ??<br>
</div>
<div>113 4 -4.258747 4.00+0.00i 0.00-0.00i =G2+ + G2+ + G2- + G2-<br>
</div>
<div>117 4 -4.258715 4.00-0.00i 0.00+0.00i =G2+ + G2+ + G2- + G2-<br>
</div>
<div>121 4 -2.333313 3.90-0.00i -0.01-0.00i ??<br>
</div>
<div>125 4 -2.333098 4.00+0.00i -0.00-0.00i =G2+ + G2+ + G2- + G2-<br>
</div>
<div>129 4 -2.332321 3.93+0.00i -0.02+0.00i ??<br>
</div>
<div><br>
</div>
<div>The corresponding bands in the case.irrepso file:</div>
<div>....</div>
<div><span> 104 4 -4.261165 0 0 0 0 0 0 0 0<br>
</span>
<div> 105 4 -4.260795 2 1 2 1 -2 1 -2 1<br>
</div>
<div> 106 4 -4.260795 2 1 2 1 -2 1 -2 1<br>
</div>
<div> 107 4 -4.260791 2 1 2 1 -2 1 -2 1<br>
</div>
<div> 108 4 -4.260791 2 1 2 1 -2 1 -2 1<br>
</div>
<div> 109 4 -4.259344 0 0 0 0 0 0 0 0<br>
</div>
<div> 110 4 -4.259344 0 0 0 0 0 0 0 0<br>
</div>
<span></span>....</div>
<div><br>
</div>
<div>What are the numbers in column 4-7?</div>
</div>
</blockquote>
<p><font color="#0000ff">In case. outputirso for band 105, there is:</font></p>
<p><font color="#0000ff"><font color="#ff8000">G2+</font> + <font color="#008000">
G2+</font> + <font color="#ff00ff">G2-</font> + <font color="#804000">G2-</font></font></p>
<p><font color="#0000ff">In case.irrepso for band 105, there is:</font></p>
<p><font color="#0000ff"><font color="#ff8000">2 1 </font> <font color="#008000">
2 1</font> <font color="#ff00ff">-2 1</font> <font color="#804000"> -2 1</font></font><br>
</p>
<p><font color="#0000ff">The columns 4 & 5, 6 </font><font color="#0000ff"><font color="#0000ff">&</font> 7, 8
</font><font color="#0000ff"><font color="#0000ff">&</font> 9, and 10 </font><font color="#0000ff"><font color="#0000ff">&</font> 11 might correspond to irreducible representation numbers that correspond with the labels (e.g., G2+ with 2 1 and G2- with -2 1).</font><br>
</p>
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