Results for Point Group D12h



Symmetric powers of degenerate representation E1u
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C12 2C6 2C4 2C3 2(C12)5 C2 6C'2 6C''2 i 2(S12)5 2S3 2S4 2S6 2S12 σh v d
1 2 1.732 1 0 -1 -1.732 -2 0 0 -2 -1.732 -1 0 1 1.732 2 0 0
2 3 2.000 0 -1 0 2.000 3 1 1 3 2.000 0 -1 0 2.000 3 1 1
3 4 1.732 -1 0 1 -1.732 -4 0 0 -4 -1.732 1 0 -1 1.732 4 0 0
4 5 1.000 -1 1 -1 1.000 5 1 1 5 1.000 -1 1 -1 1.000 5 1 1
5 6 0.000 0 0 0 0.000 -6 0 0 -6 0.000 0 0 0 0.000 6 0 0
6 7 -1.000 1 -1 1 -1.000 7 1 1 7 -1.000 1 -1 1 -1.000 7 1 1
7 8 -1.732 1 0 -1 1.732 -8 0 0 -8 1.732 -1 0 1 -1.732 8 0 0
8 9 -2.000 0 1 0 -2.000 9 1 1 9 -2.000 0 1 0 -2.000 9 1 1
9 10 -1.732 -1 0 1 1.732 -10 0 0 -10 1.732 1 0 -1 -1.732 10 0 0
10 11 -1.000 -1 -1 -1 -1.000 11 1 1 11 -1.000 -1 -1 -1 -1.000 11 1 1
11 12 0.000 0 0 0 0.000 -12 0 0 -12 0.000 0 0 0 0.000 12 0 0
12 13 1.000 1 1 1 1.000 13 1 1 13 1.000 1 1 1 1.000 13 1 1
13 14 1.732 1 0 -1 -1.732 -14 0 0 -14 -1.732 -1 0 1 1.732 14 0 0
14 15 2.000 0 -1 0 2.000 15 1 1 15 2.000 0 -1 0 2.000 15 1 1
15 16 1.732 -1 0 1 -1.732 -16 0 0 -16 -1.732 1 0 -1 1.732 16 0 0
16 17 1.000 -1 1 -1 1.000 17 1 1 17 1.000 -1 1 -1 1.000 17 1 1
17 18 0.000 0 0 0 -0.000 -18 0 0 -18 -0.000 0 0 0 0.000 18 0 0
18 19 -1.000 1 -1 1 -1.000 19 1 1 19 -1.000 1 -1 1 -1.000 19 1 1
19 20 -1.732 1 0 -1 1.732 -20 0 0 -20 1.732 -1 0 1 -1.732 20 0 0
20 21 -2.000 0 1 0 -2.000 21 1 1 21 -2.000 0 1 0 -2.000 21 1 1


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



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