Results for Point Group D5d



Symmetric powers of degenerate representation E1g
Vibrational overtones


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


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


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