Results for Point Group S10



Symmetric powers of degenerate representation E1g
Vibrational overtones


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


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



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