[Wien] Irrep output file

[Md. Fhokrul Islam]

Hi Gavin,

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.


knum =  2    kname=
k = 0.000000 0.000000 0.225000

       The point group is C1
       1 symmetry operations in  1 classes

                         E
       G1    A1     1
       --------------
       G2    A1/2  1

bnd ndg      eigval         E
....
 15    2    -4.673171   1.56-0.00i  ??
 17    2    -4.673047   0.04+0.00i ??
 19    2    -4.673041   0.03-0.00i  ??
 21    4    -4.672125   0.07-0.00i  ??


Thanks,
Fhokrul
________________________________
From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of Gavin Abo <gsabo at crimson.ua.edu>
Sent: Sunday, June 21, 2020 3:35 AM
To: wien at zeus.theochem.tuwien.ac.at <wien at zeus.theochem.tuwien.ac.at>
Subject: Re: [Wien] Irrep output file

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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