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 <[email protected]> on behalf of Gavin Abo
<[email protected]>
Sent: Sunday, June 21, 2020 3:35 AM
To: [email protected] <[email protected]>
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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