Results for Point Group D10h



Symmetric powers of degenerate representation E3g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C10 2C5 2(C10)3 2(C5)2 C2 5C'2 5C''2 i 2(S5)3 2(S10)3 2S5 2S10 σh 5σd 5σv
1 2 -0.618 -1.618 1.618 0.618 -2 0 0 2 -0.618 -1.618 1.618 0.618 -2 0 0
2 3 -0.618 1.618 1.618 -0.618 3 1 1 3 -0.618 1.618 1.618 -0.618 3 1 1
3 4 1.000 -1.000 1.000 -1.000 -4 0 0 4 1.000 -1.000 1.000 -1.000 -4 0 0
4 5 0.000 0.000 0.000 -0.000 5 1 1 5 0.000 0.000 0.000 -0.000 5 1 1
5 6 -1.000 1.000 -1.000 1.000 -6 0 0 6 -1.000 1.000 -1.000 1.000 -6 0 0
6 7 0.618 -1.618 -1.618 0.618 7 1 1 7 0.618 -1.618 -1.618 0.618 7 1 1
7 8 0.618 1.618 -1.618 -0.618 -8 0 0 8 0.618 1.618 -1.618 -0.618 -8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9 1 1 9 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 0.000 -0.000 -0.000 -10 0 0 10 -0.000 0.000 -0.000 -0.000 -10 0 0
10 11 1.000 1.000 1.000 1.000 11 1 1 11 1.000 1.000 1.000 1.000 11 1 1
11 12 -0.618 -1.618 1.618 0.618 -12 0 0 12 -0.618 -1.618 1.618 0.618 -12 0 0
12 13 -0.618 1.618 1.618 -0.618 13 1 1 13 -0.618 1.618 1.618 -0.618 13 1 1
13 14 1.000 -1.000 1.000 -1.000 -14 0 0 14 1.000 -1.000 1.000 -1.000 -14 0 0
14 15 0.000 0.000 0.000 -0.000 15 1 1 15 0.000 0.000 0.000 -0.000 15 1 1
15 16 -1.000 1.000 -1.000 1.000 -16 0 0 16 -1.000 1.000 -1.000 1.000 -16 0 0
16 17 0.618 -1.618 -1.618 0.618 17 1 1 17 0.618 -1.618 -1.618 0.618 17 1 1
17 18 0.618 1.618 -1.618 -0.618 -18 0 0 18 0.618 1.618 -1.618 -0.618 -18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19 1 1 19 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 0.000 -0.000 -0.000 -20 0 0 20 -0.000 0.000 -0.000 -0.000 -20 0 0
20 21 1.000 1.000 1.000 1.000 21 1 1 21 1.000 1.000 1.000 1.000 21 1 1


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


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