Results for Point Group D4h



Symmetric powers of degenerate representation Eu
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C4 C2 2C'2 2C''2 i 2S4 σh 2σv 2σd
1 2 0 -2 0 0 -2 0 2 0 0
2 3 -1 3 1 1 3 -1 3 1 1
3 4 0 -4 0 0 -4 0 4 0 0
4 5 1 5 1 1 5 1 5 1 1
5 6 0 -6 0 0 -6 0 6 0 0
6 7 -1 7 1 1 7 -1 7 1 1
7 8 0 -8 0 0 -8 0 8 0 0
8 9 1 9 1 1 9 1 9 1 1
9 10 0 -10 0 0 -10 0 10 0 0
10 11 -1 11 1 1 11 -1 11 1 1
11 12 0 -12 0 0 -12 0 12 0 0
12 13 1 13 1 1 13 1 13 1 1
13 14 0 -14 0 0 -14 0 14 0 0
14 15 -1 15 1 1 15 -1 15 1 1
15 16 0 -16 0 0 -16 0 16 0 0
16 17 1 17 1 1 17 1 17 1 1
17 18 0 -18 0 0 -18 0 18 0 0
18 19 -1 19 1 1 19 -1 19 1 1
19 20 0 -20 0 0 -20 0 20 0 0
20 21 1 21 1 1 21 1 21 1 1


Decomposition to irreducible representations
Power
To		 A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
1 0 0 0 0 0 0 0 0 0 1 Eu
2 1 0 1 1 0 0 0 0 0 0 A1g⊕B1g⊕B2g
3 0 0 0 0 0 0 0 0 0 2 2Eu
4 2 1 1 1 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g
5 0 0 0 0 0 0 0 0 0 3 3Eu
6 2 1 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g
7 0 0 0 0 0 0 0 0 0 4 4Eu
8 3 2 2 2 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g
9 0 0 0 0 0 0 0 0 0 5 5Eu
10 3 2 3 3 0 0 0 0 0 0 3A1g⊕2A2g⊕3B1g⊕3B2g
11 0 0 0 0 0 0 0 0 0 6 6Eu
12 4 3 3 3 0 0 0 0 0 0 4A1g⊕3A2g⊕3B1g⊕3B2g
13 0 0 0 0 0 0 0 0 0 7 7Eu
14 4 3 4 4 0 0 0 0 0 0 4A1g⊕3A2g⊕4B1g⊕4B2g
15 0 0 0 0 0 0 0 0 0 8 8Eu
16 5 4 4 4 0 0 0 0 0 0 5A1g⊕4A2g⊕4B1g⊕4B2g
17 0 0 0 0 0 0 0 0 0 9 9Eu
18 5 4 5 5 0 0 0 0 0 0 5A1g⊕4A2g⊕5B1g⊕5B2g
19 0 0 0 0 0 0 0 0 0 10 10Eu
20 6 5 5 5 0 0 0 0 0 0 6A1g⊕5A2g⊕5B1g⊕5B2g


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement