Results for Point Group D18h



Symmetric powers of degenerate representation E3u
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C18 2C9 2C6 2(C9)2 2(C18)5 2C3 2(C18)7 2(C9)4 C2 9C'2 9C''2 i 2(S9)5 2(S18)7 2S3 2(S18)5 2(S9)7 2S6 2S9 2S18 σh 9σd 9σv
1 2 1.000 -1.000 -2 -1.000 1.000 2 1.000 -1.000 -2 0 0 -2 -1.000 1.000 2 1.000 -1.000 -2 -1.000 1.000 2 0 0
2 3 0.000 0.000 3 0.000 0.000 3 0.000 0.000 3 1 1 3 0.000 0.000 3 0.000 0.000 3 0.000 0.000 3 1 1
3 4 -1.000 1.000 -4 1.000 -1.000 4 -1.000 1.000 -4 0 0 -4 1.000 -1.000 4 -1.000 1.000 -4 1.000 -1.000 4 0 0
4 5 -1.000 -1.000 5 -1.000 -1.000 5 -1.000 -1.000 5 1 1 5 -1.000 -1.000 5 -1.000 -1.000 5 -1.000 -1.000 5 1 1
5 6 0.000 0.000 -6 0.000 0.000 6 0.000 0.000 -6 0 0 -6 0.000 0.000 6 0.000 0.000 -6 0.000 0.000 6 0 0
6 7 1.000 1.000 7 1.000 1.000 7 1.000 1.000 7 1 1 7 1.000 1.000 7 1.000 1.000 7 1.000 1.000 7 1 1
7 8 1.000 -1.000 -8 -1.000 1.000 8 1.000 -1.000 -8 0 0 -8 -1.000 1.000 8 1.000 -1.000 -8 -1.000 1.000 8 0 0
8 9 0.000 0.000 9 0.000 0.000 9 0.000 0.000 9 1 1 9 0.000 0.000 9 0.000 0.000 9 0.000 0.000 9 1 1
9 10 -1.000 1.000 -10 1.000 -1.000 10 -1.000 1.000 -10 0 0 -10 1.000 -1.000 10 -1.000 1.000 -10 1.000 -1.000 10 0 0
10 11 -1.000 -1.000 11 -1.000 -1.000 11 -1.000 -1.000 11 1 1 11 -1.000 -1.000 11 -1.000 -1.000 11 -1.000 -1.000 11 1 1
11 12 0.000 0.000 -12 0.000 0.000 12 0.000 0.000 -12 0 0 -12 0.000 0.000 12 0.000 0.000 -12 0.000 0.000 12 0 0
12 13 1.000 1.000 13 1.000 1.000 13 1.000 1.000 13 1 1 13 1.000 1.000 13 1.000 1.000 13 1.000 1.000 13 1 1
13 14 1.000 -1.000 -14 -1.000 1.000 14 1.000 -1.000 -14 0 0 -14 -1.000 1.000 14 1.000 -1.000 -14 -1.000 1.000 14 0 0
14 15 0.000 0.000 15 0.000 0.000 15 0.000 0.000 15 1 1 15 0.000 0.000 15 0.000 0.000 15 0.000 0.000 15 1 1
15 16 -1.000 1.000 -16 1.000 -1.000 16 -1.000 1.000 -16 0 0 -16 1.000 -1.000 16 -1.000 1.000 -16 1.000 -1.000 16 0 0
16 17 -1.000 -1.000 17 -1.000 -1.000 17 -1.000 -1.000 17 1 1 17 -1.000 -1.000 17 -1.000 -1.000 17 -1.000 -1.000 17 1 1
17 18 0.000 0.000 -18 0.000 0.000 18 0.000 0.000 -18 0 0 -18 0.000 0.000 18 0.000 0.000 -18 0.000 0.000 18 0 0
18 19 1.000 1.000 19 1.000 1.000 19 1.000 1.000 19 1 1 19 1.000 1.000 19 1.000 1.000 19 1.000 1.000 19 1 1
19 20 1.000 -1.000 -20 -1.000 1.000 20 1.000 -1.000 -20 0 0 -20 -1.000 1.000 20 1.000 -1.000 -20 -1.000 1.000 20 0 0
20 21 0.000 0.000 21 0.000 0.000 21 0.000 0.000 21 1 1 21 0.000 0.000 21 0.000 0.000 21 0.000 0.000 21 1 1


Decomposition to irreducible representations
Power
To		 A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u E8u
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 E3u
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E6g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 B1u⊕B2u⊕E3u
4 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E6g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 2 0 0 0 0 0 B1u⊕B2u⊕2E3u
6 2 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E6g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 3 0 0 0 0 0 B1u⊕B2u⊕3E3u
8 2 1 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E6g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 3 0 0 0 0 0 2B1u⊕2B2u⊕3E3u
10 2 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E6g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 4 0 0 0 0 0 2B1u⊕2B2u⊕4E3u
12 3 2 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4E6g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 5 0 0 0 0 0 2B1u⊕2B2u⊕5E3u
14 3 2 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕5E6g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 5 0 0 0 0 0 3B1u⊕3B2u⊕5E3u
16 3 2 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕6E6g
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 6 0 0 0 0 0 3B1u⊕3B2u⊕6E3u
18 4 3 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕6E6g
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 7 0 0 0 0 0 3B1u⊕3B2u⊕7E3u
20 4 3 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕7E6g


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