How to obtain the irreducible representations of the electronic bands ?

DLP

Hi,

I would like to obtain the irreducible representations of the eigenstates for a given crystal at each k-point. To do so, I am running properties with the following .d3 file:

NEWK
0 0
0 2
66 1
67 1
END

The output file (.outp) gives me the eigenvalues at each k-point with a label, for instance A'',A',E'',etc. In that same .outp file there is a list of character tables, which I assume that each character table corresponds to a k-point in order of appearance. However, the irreps that appear in the n-th character table do not correspond to the irreps that appear in the n-th set of eigenvalues, meaning that you can have an irrep labelled B3 in the eigenvalues but for the corresponding character table there is no B3 irrep. How can I identify what the irreps of the eigenstates actually are or how they transform under the symmetry operations of the little point group ?

GiacomoAmbrogio

Hi DLP,

NEWK
0 n

is used to specify an anisotropic shrinking factor. However in you input you are not providing the three parameters required for this, which makes the usage unclear.

Could you please attach the output file you are referring to, so that I can take a closer look?

DLP

Hi GiacomoAmbrogio ,

I have attached the properties output file below so you can take a look. If there is anything else you want to check let me know.

hBN.outp

The main issue that I have is that, for instance, the set of eigenvalues at K= 91 ( 10 10 0) (which starts at line 2396 of the file) has labels that corresponds to the irrep of each band at that k point. You will find that in that same file, there is a list of character tables. However, the labels of the irreps that appear in the last character table is not the same as the labels that appear in the last set of eigenvalues. In general it seems that the n-th character table that appears does not contain the same irreps as the n-th set of eigenvalues. In other words, I do not know to what k-point each character table is referring to in order to properly identify the irreps.

aerba

Hi,

The following keyword combination to be inserted in the third block of the .d12 CRYSTAL input file works for me on a 3D crystal (I have tried on ZnO as a test):

SETPRINT
2
47 10
66 10
KSYMMPRT

The keyword KSYMMPRT activates a printing level with character tables for the various k little groups. With SETPRINT you set other printing options: option 47 refers to KSYMMPRT while option 66 activates the printing of the eigenvalues. With 10 in both cases I am asking for detailed printing for the first 10 k points in the list. Just increase this parameter from 10 to X for detailed information on the first X k points.

At the end of the SCF, in the output file you will find detailed symmetry information. For ZnO, for instance:

+++ SYMMETRY ADAPTION OF THE BLOCH FUNCTIONS +++

 SYMMETRY INFORMATION:
 K-LITTLE GROUP: CLASS TABLE, CHARACTER TABLE.
 IRREP-(DIMENSION, NO. IRREDUCIBLE SETS)
 (P, D, RP, RD, STAND FOR PAIRING, DOUBLING, REAL PAIRING AND REAL DOUBLING
 OF THE IRREPS (SEE MANUAL))

 CLASS  | GROUP OPERATORS (SEE SYMMOPS KEYWORD)
 --------------------------------------------------------------------
 C2     |   2;
 C3     |   3;   4;
 C6     |   5;   6;
 SGV    |   7;   8;   9;
 SGV'   |  10;  12;  11;

 IRREP/CLA      E     C2     C3     C6    SGV   SGV'
 ---------------------------------------------------
  MULTIP |      1      1      2      2      3      3
 ---------------------------------------------------
    A    |   1.00   1.00   1.00   1.00   1.00   1.00
    B    |   1.00  -1.00   1.00  -1.00   1.00  -1.00
    E1   |   2.00  -2.00  -1.00   1.00   0.00   0.00
    E2   |   2.00   2.00  -1.00  -1.00   0.00   0.00

 A  -(1,  21); B  -(1,  21); E1 -(2,  15); E2 -(2,  15);


 CLASS  | GROUP OPERATORS (SEE SYMMOPS KEYWORD)
 --------------------------------------------------------------------
 C2     |   8;

 IRREP/CLA      E     C2
 -----------------------
  MULTIP |      1      1
 -----------------------
    A    |   1.00   1.00
    B    |   1.00  -1.00

 A  -(1,  72); B  -(1,  30);


[...]

And information about the eigenvalues at each k point with the associated irrep symmetry label:

 FINAL EIGENVALUES (A.U.)
  (LABELS REFER TO SYMMETRY CLASSIFICATION)

   1 (  0  0  0)
 -3.4563E+02(B  ) -3.4563E+02(A  ) -4.1575E+01(B  ) -4.1575E+01(A  ) -3.6643E+01(A  )
 -3.6643E+01(B  ) -3.6643E+01(E1 ) -3.6643E+01(E1 ) -3.6642E+01(E2 ) -3.6642E+01(E2 )
 -1.8704E+01(A  ) -1.8704E+01(B  ) -4.5481E+00(A  ) -4.5481E+00(B  ) -2.9815E+00(B  )
 -2.9814E+00(A  ) -2.9812E+00(E2 ) -2.9812E+00(E2 ) -2.9812E+00(E1 ) -2.9812E+00(E1 )
 -8.2115E-01(A  ) -7.9663E-01(B  ) -3.8298E-01(E1 ) -3.8298E-01(E1 ) -3.8023E-01(A  )
 -3.7674E-01(E2 ) -3.7674E-01(E2 ) -3.6589E-01(B  ) -3.4625E-01(E1 ) -3.4625E-01(E1 )
 -3.3970E-01(E2 ) -3.3970E-01(E2 ) -3.2752E-01(B  ) -2.0184E-01(E2 ) -2.0184E-01(E2 )
 -1.7704E-01(A  ) -1.7506E-01(E1 ) -1.7506E-01(E1 ) -1.3296E-01(A  )  2.8917E-02(B  )
  1.3748E-01(B  )  3.0394E-01(E1 )  3.0394E-01(E1 )  3.4544E-01(E2 )  3.4544E-01(E2 )
  3.5105E-01(A  )  7.3399E-01(A  )  7.9567E-01(B  )  7.9827E-01(E2 )  7.9827E-01(E2 )
  8.0430E-01(E1 )  8.0430E-01(E1 )  9.2452E-01(E1 )  9.2452E-01(E1 )  9.4481E-01(A  )
  1.0085E+00(E2 )  1.0085E+00(E2 )  1.0835E+00(B  )  1.1254E+00(A  )  1.4388E+00(E2 )
  1.4388E+00(E2 )  1.5197E+00(E1 )  1.5197E+00(E1 )  1.5953E+00(B  )  1.6980E+00(A  )
  1.9424E+00(B  )  2.1214E+00(B  )  2.4581E+00(E2 )  2.4581E+00(E2 )  2.6850E+00(A  )
  2.6884E+00(E1 )  2.6884E+00(E1 )  2.6992E+00(B  )  2.7357E+00(E1 )  2.7357E+00(E1 )
  2.7753E+00(E2 )  2.7753E+00(E2 )  3.0348E+00(E2 )  3.0348E+00(E2 )  3.1219E+00(E1 )
  3.1219E+00(E1 )  3.1318E+00(A  )  4.2450E+00(E2 )  4.2450E+00(E2 )  4.2830E+00(A  )
  4.4957E+00(E1 )  4.4957E+00(E1 )  4.5498E+00(E1 )  4.5498E+00(E1 )  4.7190E+00(B  )
  4.7730E+00(E2 )  4.7730E+00(E2 )  4.7949E+00(A  )  4.8374E+00(E2 )  4.8374E+00(E2 )
  4.8743E+00(B  )  5.0462E+00(E1 )  5.0462E+00(E1 )  5.4477E+00(A  )  5.8198E+00(B  )
  3.9355E+01(B  )  3.9424E+01(A  )

   2 (  1  0  0)
 -3.4563E+02(A  ) -3.4563E+02(A  ) -4.1575E+01(A  ) -4.1575E+01(A  ) -3.6643E+01(A  )
 -3.6643E+01(A  ) -3.6643E+01(B  ) -3.6642E+01(A  ) -3.6642E+01(B  ) -3.6642E+01(A  )
 -1.8704E+01(A  ) -1.8704E+01(A  ) -4.5481E+00(A  ) -4.5481E+00(A  ) -2.9815E+00(A  )
 -2.9814E+00(A  ) -2.9812E+00(A  ) -2.9812E+00(B  ) -2.9812E+00(A  ) -2.9812E+00(B  )
 -8.1833E-01(A  ) -7.9542E-01(A  ) -3.8502E-01(A  ) -3.8129E-01(B  ) -3.7873E-01(A  )
 -3.7647E-01(A  ) -3.7434E-01(B  ) -3.6339E-01(A  ) -3.4716E-01(A  ) -3.4630E-01(B  )
 -3.3948E-01(B  ) -3.3567E-01(A  ) -3.2769E-01(A  ) -2.2123E-01(A  ) -2.0904E-01(B  )
 -2.0238E-01(A  ) -1.8061E-01(A  ) -1.7889E-01(B  ) -9.9076E-02(A  )  5.0288E-02(A  )
  1.3868E-01(A  )  2.6653E-01(A  )  3.0802E-01(B  )  3.1234E-01(A  )  3.5046E-01(B  )
  3.5371E-01(A  )  7.3602E-01(A  )  7.7587E-01(B  )  7.9991E-01(A  )  8.0492E-01(A  )
  8.3924E-01(B  )  8.5620E-01(A  )  9.3227E-01(A  )  9.3403E-01(B  )  9.5348E-01(A  )
  9.9448E-01(A  )  1.0316E+00(B  )  1.1292E+00(A  )  1.1707E+00(A  )  1.3826E+00(A  )
  1.4008E+00(B  )  1.5217E+00(B  )  1.5347E+00(A  )  1.6362E+00(A  )  1.7168E+00(A  )
  1.9795E+00(A  )  2.1273E+00(A  )  2.4524E+00(B  )  2.4562E+00(A  )  2.6427E+00(A  )
  2.6752E+00(B  )  2.6832E+00(A  )  2.6862E+00(A  )  2.7057E+00(B  )  2.7063E+00(A  )
  2.7671E+00(B  )  2.7722E+00(A  )  2.9842E+00(A  )  3.0206E+00(B  )  3.0849E+00(A  )
  3.1311E+00(B  )  3.1382E+00(A  )  4.2311E+00(A  )  4.2454E+00(B  )  4.2544E+00(A  )
  4.4759E+00(B  )  4.4850E+00(A  )  4.5531E+00(B  )  4.5945E+00(A  )  4.6563E+00(A  )
  4.7965E+00(A  )  4.8056E+00(B  )  4.8150E+00(B  )  4.8262E+00(A  )  4.9013E+00(A  )
  4.9403E+00(A  )  5.0500E+00(B  )  5.0510E+00(A  )  5.5124E+00(A  )  5.8464E+00(A  )
  3.9366E+01(A  )  3.9416E+01(A  )

[...]

Hope this helps,

DLP

Hi aerba,

Thank you for your reply. The keyword combination needed to obtain the irreps is much clearer now. However, I am still unsure of the labels of the irreps. In the case in which the bulk ZnO you considered has a space group P6₃mc, the irreps of the point group at Γ ( C6v(6mm) ) are A1,A2,B1,B2,E1,E2 which does not correspond to the output you gave me. It might be that the bulk ZnO you considered has a different space group. Could you tell me the space group or check if the labels of the irreps are correct ?

aerba

Hi,

I used space group 186 for ZnO that corresponds to the one you mention. In the character table printed by CRYSTAL only those irreps that are actually used to build symmetry-adapted Bloch functions are shown. I have updated my original post above to show the irrep labels in the character tables, which match those found in the printing of the eigenvalues.

Hope this clarifies things,