Results for Point Group C5h



Symmetric powers of degenerate representation E'1
Vibrational overtones


Characters of symmetric powers
Power
To		 E C5 (C5)2 (C5)3 (C5)4 σh S5 (S5)7 (S5)3 (S5)9
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		 A' E'1* E'2* A'' E''1* E''2*
1 0 1 0 0 0 0 E'1
2 1 0 1 0 0 0 A'⊕E'2
3 0 1 1 0 0 0 E'1⊕E'2
4 1 1 1 0 0 0 A'⊕E'1⊕E'2
5 2 1 1 0 0 0 2A'⊕E'1⊕E'2
6 1 2 1 0 0 0 A'⊕2E'1⊕E'2
7 2 1 2 0 0 0 2A'⊕E'1⊕2E'2
8 1 2 2 0 0 0 A'⊕2E'1⊕2E'2
9 2 2 2 0 0 0 2A'⊕2E'1⊕2E'2
10 3 2 2 0 0 0 3A'⊕2E'1⊕2E'2
11 2 3 2 0 0 0 2A'⊕3E'1⊕2E'2
12 3 2 3 0 0 0 3A'⊕2E'1⊕3E'2
13 2 3 3 0 0 0 2A'⊕3E'1⊕3E'2
14 3 3 3 0 0 0 3A'⊕3E'1⊕3E'2
15 4 3 3 0 0 0 4A'⊕3E'1⊕3E'2
16 3 4 3 0 0 0 3A'⊕4E'1⊕3E'2
17 4 3 4 0 0 0 4A'⊕3E'1⊕4E'2
18 3 4 4 0 0 0 3A'⊕4E'1⊕4E'2
19 4 4 4 0 0 0 4A'⊕4E'1⊕4E'2
20 5 4 4 0 0 0 5A'⊕4E'1⊕4E'2


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