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<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"
cite="mid:BY5PR13MB3810B0B99C11635F66766757D3990@BY5PR13MB3810.namprd13.prod.outlook.com">
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">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>
<blockquote type="cite"
cite="mid:BY5PR13MB3810B0B99C11635F66766757D3990@BY5PR13MB3810.namprd13.prod.outlook.com">
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);"><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>
<blockquote type="cite"
cite="mid:BY5PR13MB3810B0B99C11635F66766757D3990@BY5PR13MB3810.namprd13.prod.outlook.com">
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);"><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="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>
<blockquote type="cite"
cite="mid:BY5PR13MB3810B0B99C11635F66766757D3990@BY5PR13MB3810.namprd13.prod.outlook.com">
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
case. outputirso:</div>
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
<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>
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
...</div>
<div style="font-family: Calibri, Helvetica, sans-serif;
font-size: 12pt; color: rgb(0, 0, 0);">
<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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