Results for Point Group D18h



Symmetric powers of degenerate representation E7u
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 d v
1 2 -1.532 0.347 1 -1.879 1.879 -1 -0.347 1.532 -2 0 0 -2 1.532 -0.347 -1 1.879 -1.879 1 0.347 -1.532 2 0 0
2 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3 1 1 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3 1 1
3 4 -0.532 -0.653 -1 -2.879 2.879 1 0.653 0.532 -4 0 0 -4 0.532 0.653 1 2.879 -2.879 -1 -0.653 -0.532 4 0 0
4 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5 1 1 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5 1 1
5 6 1.347 0.879 0 -2.532 2.532 0 -0.879 -1.347 -6 0 0 -6 -1.347 -0.879 0 2.532 -2.532 0 0.879 1.347 6 0 0
6 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7 1 1 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7 1 1
7 8 1.000 -1.000 1 -1.000 1.000 -1 1.000 -1.000 -8 0 0 -8 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000 8 0 0
8 9 0.000 0.000 0 0.000 -0.000 0 -0.000 -0.000 9 1 1 9 0.000 0.000 0 0.000 -0.000 0 -0.000 -0.000 9 1 1
9 10 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000 -10 0 0 -10 1.000 -1.000 1 -1.000 1.000 -1 1.000 -1.000 10 0 0
10 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11 1 1 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11 1 1
11 12 -1.347 -0.879 0 2.532 -2.532 0 0.879 1.347 -12 0 0 -12 1.347 0.879 0 -2.532 2.532 0 -0.879 -1.347 12 0 0
12 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13 1 1 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13 1 1
13 14 0.532 0.653 1 2.879 -2.879 -1 -0.653 -0.532 -14 0 0 -14 -0.532 -0.653 -1 -2.879 2.879 1 0.653 0.532 14 0 0
14 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15 1 1 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15 1 1
15 16 1.532 -0.347 -1 1.879 -1.879 1 0.347 -1.532 -16 0 0 -16 -1.532 0.347 1 -1.879 1.879 -1 -0.347 1.532 16 0 0
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 1 1 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 1 1
17 18 -0.000 0.000 0 0.000 0.000 0 0.000 -0.000 -18 0 0 -18 0.000 -0.000 0 -0.000 -0.000 0 -0.000 0.000 18 0 0
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1 1 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1 1
19 20 -1.532 0.347 1 -1.879 1.879 -1 -0.347 1.532 -20 0 0 -20 1.532 -0.347 -1 1.879 -1.879 1 0.347 -1.532 20 0 0
20 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 21 1 1 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 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 0 0 0 0 1 0 E7u
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 E3u⊕E7u
4 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕E8g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 E1u⊕E3u⊕E7u
6 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕E6g⊕E8g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 E1u⊕E3u⊕E5u⊕E7u
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E8g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 B1u⊕B2u⊕E1u⊕E3u⊕E5u⊕E7u
10 1 0 0 0 0 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E2g⊕E4g⊕E6g⊕E8g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 2 0 1 0 B1u⊕B2u⊕E1u⊕E3u⊕2E5u⊕E7u
12 1 0 0 0 0 2 0 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E2g⊕E4g⊕2E6g⊕E8g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 1 0 2 0 1 0 B1u⊕B2u⊕2E1u⊕E3u⊕2E5u⊕E7u
14 1 0 0 0 0 2 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E2g⊕E4g⊕2E6g⊕2E8g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 2 0 2 0 1 0 B1u⊕B2u⊕2E1u⊕2E3u⊕2E5u⊕E7u
16 1 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 2 0 2 0 2 0 B1u⊕B2u⊕2E1u⊕2E3u⊕2E5u⊕2E7u
18 2 1 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 2 0 2 0 3 0 B1u⊕B2u⊕2E1u⊕2E3u⊕2E5u⊕3E7u
20 2 1 0 0 0 2 0 3 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E2g⊕3E4g⊕2E6g⊕2E8g



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement