[Wien] Parity determination by group theory analysis question

[Paul Fons]

Hi,
	I have been using the irreducible representations calculated by irrep to determine the parity of the wavefunction for particular k-points for each band.  A typical case is shown below for the gamma point.    As I am solving the system without spin, each band is at least two-fold degenerate.  For most bands, for example the first band, the situation is clear as the irrep is G4+ that the parity is +.  This also follows from the character of the (I) class being the same dimension as the irrep.  I am a little more confused by what to do a band such as band 9 where there are two irreps spanning the same band, but presumably as the character of the (I) class is the same as that of the dimension of the irrep (and that both irreps are of the same parity, +) that the parity is again +.  The situation I am writing to ask about, however is that of band 63 which is four-fold degenerate and is composed of irreps of both parities.  How does one interpret the parity from the information below for band 63?  Thanks for any advice.




       The point group is D3d
       12 symmetry operations in  6 classes
       Table 55   on page  58 in Koster  et al [7]
       Table 42.4 on page 371 in Altmann et al [8]

                   E   2C3   3C2     I  2IC3  3IC2                                      
       G1+   A1g   1     1     1     1     1     1  
       G2+   A2g   1     1    -1     1     1    -1  
       G3+   Eg    2    -1     0     2    -1     0  
       G1-   A1u   1     1     1    -1    -1    -1  
       G2-   A2u   1     1    -1    -1    -1     1  
       G3-   Eu    2    -1     0    -2     1     0  
       --------------------------------------------
       G4+   E1/2g 2     1     0     2     1     0  
       G5+  1E3/2g 1    -1     i     1    -1     i  
       G6+  2E3/2g 1    -1    -i     1    -1    -i  
       G4-   E1/2u 2     1     0    -2    -1     0  
       G5-  1E3/2u 1    -1     i    -1     1    -i  
       G6-  2E3/2u 1    -1    -i    -1     1     i  


class, symmetry ops, exp(-i*k*taui)
   E   10             (+1.00+0.00i)
 2C3    2  7          (+1.00+0.00i)
 3C2    1  8  9       (+1.00+0.00i)
   I    3             (+1.00+0.00i)
2IC3    6 11          (+1.00+0.00i)
3IC2    4  5 12       (+1.00+0.00i)

bnd ndg  eigval     E         2C3         3C2           I        2IC3        3IC2   
  1  2 -7.239676 2.00+0.00i  1.00+0.00i  0.00-0.00i  2.00+0.00i  1.00-0.00i  0.00-0.00i =G4+ 
  3  2 -7.239533 2.00+0.00i  1.00+0.00i -0.00+0.00i -2.00+0.00i -1.00-0.00i  0.00-0.00i =G4- 
  5  2 -6.641446 2.00+0.00i  1.00+0.00i  0.00+0.00i  2.00-0.00i  1.00+0.00i  0.00+0.00i =G4+ 
  7  2 -6.641393 2.00-0.00i  1.00-0.00i -0.00-0.00i -2.00-0.00i -1.00+0.00i  0.00-0.00i =G4- 
  9  2 -6.641277 2.00+0.00i -2.00-0.00i -0.00+0.00i  2.00+0.00i -2.00-0.00i -0.00-0.00i =G5+ + G6+



 63  4 -1.880979 4.00-0.00i -4.00+0.00i  0.00-0.00i  0.00-0.00i -0.00+0.00i -0.00+0.00i =G5+ + G6+ + G5- + G6-  
 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20140604/f2549c6c/attachment.htm>