Results for Point Group C12h



Symmetric powers of degenerate representation E1u
Vibrational overtones


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


Decomposition to irreducible representations
Power
To		 Ag Bg E1g* E2g* E3g* E4g* E5g* Au Bu E1u* E2u* E3u* E4u* E5u*
1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 E1u
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 0 0 0 0 0 0 0 1 0 1 0 0 E1u⊕E3u
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 0 0 0 0 0 0 0 0 1 0 1 0 1 E1u⊕E3u⊕E5u
6 1 2 0 1 0 1 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g
7 0 0 0 0 0 0 0 0 0 1 0 1 0 2 E1u⊕E3u⊕2E5u
8 1 2 0 1 0 2 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕2E4g
9 0 0 0 0 0 0 0 0 0 1 0 2 0 2 E1u⊕2E3u⊕2E5u
10 1 2 0 2 0 2 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g⊕2E4g
11 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2E1u⊕2E3u⊕2E5u
12 3 2 0 2 0 2 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕2E2g⊕2E4g
13 0 0 0 0 0 0 0 0 0 3 0 2 0 2 3E1u⊕2E3u⊕2E5u
14 3 2 0 3 0 2 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕3E2g⊕2E4g
15 0 0 0 0 0 0 0 0 0 3 0 3 0 2 3E1u⊕3E3u⊕2E5u
16 3 2 0 3 0 3 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕3E2g⊕3E4g
17 0 0 0 0 0 0 0 0 0 3 0 3 0 3 3E1u⊕3E3u⊕3E5u
18 3 4 0 3 0 3 0 0 0 0 0 0 0 0 3Ag⊕4Bg⊕3E2g⊕3E4g
19 0 0 0 0 0 0 0 0 0 3 0 3 0 4 3E1u⊕3E3u⊕4E5u
20 3 4 0 3 0 4 0 0 0 0 0 0 0 0 3Ag⊕4Bg⊕3E2g⊕4E4g


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