[Wien] Irrep output file

[Gavin Abo]

I'm not sure that I have the proper answers but given below is what I'm 
currently thinking they might be.
> 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?

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 3.99-0.00i  0.00+0.00i (since it 
would need to be 4.00+0.00i 0.00-0.00 to have G2+ + G2+ + G2- + G2- 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.

>  The bands 105 -108 are four-fold degenerate with irrep of the double 
> group G2+, G2+,G2-,G2-, respectively, right?

I believe you are right about that.

> Also, can anyone please clarify what are the complex numbers under 
> operators E and I?

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).

[1] 
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

> case. outputirso:
>
>        The point group is Ci
>        2 symmetry operations in  2 classes
>        Table  6   on page  32 in Koster  et al [7]
>        Table 11.4 on page 138 in Altmann et al [8]
>
>                            E     I
>        G1+   A1g    1     1
>        G1-    A1u    1    -1
>        --------------------
>        G2+  A1/2g  1     1
>        G2-   A1/2u  1    -1
>
>
> class, symmetry ops, exp(-i*k*taui)
>    E    2             (+1.00 0.00i)
>     I    1             (+1.00 0.00i)
>
> bnd ndg  eigval     E                   I
>   1  2 -4.675588 1.99+0.00i -1.99-0.00i  ??
>   3  2 -4.675572 1.99-0.00i   1.99-0.00i  ??
>   5  2 -4.674606 1.98-0.00i  -1.98+0.00i ??
> ...
> ...
>  97  4 -4.261267 3.97+0.00i -0.00-0.00i  ??
> 101  4 -4.261167 3.99-0.00i  0.01+0.00i  ??
> 105  4 -4.260795 4.00-0.00i  0.00+0.00i =G2+ + G2+ + G2- + G2-
> 109  4 -4.259344 3.99-0.00i  0.00+0.00i ??
> 113  4 -4.258747 4.00+0.00i  0.00-0.00i =G2+ + G2+ + G2- + G2-
> 117  4 -4.258715 4.00-0.00i  0.00+0.00i =G2+ + G2+ + G2- + G2-
> 121  4 -2.333313 3.90-0.00i -0.01-0.00i ??
> 125  4 -2.333098 4.00+0.00i -0.00-0.00i =G2+ + G2+ + G2- + G2-
> 129  4 -2.332321 3.93+0.00i -0.02+0.00i ??
>
> The corresponding bands in the case.irrepso file:
> ....
>        104         4  -4.261165    0  0    0  0    0  0    0  0
>        105         4  -4.260795    2  1    2  1   -2  1 -2  1
>        106         4  -4.260795    2  1    2  1   -2  1 -2  1
>        107         4  -4.260791    2  1    2  1   -2  1 -2  1
>        108         4  -4.260791    2  1    2  1   -2  1 -2  1
>        109         4  -4.259344    0  0    0  0    0  0  0  0
>        110         4  -4.259344    0  0    0  0    0  0  0  0
> ....
>
> What are the numbers in column 4-7?

In case. outputirso for band 105, there is:

G2+ + G2+ + G2- + G2-

In case.irrepso for band 105, there is:

2  1 2  1 -2  1 -2  1

The columns 4 & 5, 6 & 7, 8 & 9, and 10 & 11 might correspond to 
irreducible representation numbers that correspond with the labels 
(e.g., G2+ with 2 1 and G2- with -2 1).

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