Results for Point Group D15h



Symmetric powers of degenerate representation E'3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7 15C'2 σh 2S15 2(S15)13 2S5 2(S15)11 2S3 2(S5)3 2(S15)7 15σv
1 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 0 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 0
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 0 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 0
4 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 0 6 1.000 1.000 1.000 1.000 6 1.000 1.000 0
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1
7 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 0 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1
9 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 0 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1
11 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 0 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 0
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 0 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 0
14 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 0 16 1.000 1.000 1.000 1.000 16 1.000 1.000 0
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1
17 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 0 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1
19 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 0 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 0
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1


Decomposition to irreducible representations
Power
To
A'1 A'2 E'1 E'2 E'3 E'4 E'5 E'6 E'7 A''1 A''2 E''1 E''2 E''3 E''4 E''5 E''6 E''7
1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E'3
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'6
3 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 E'3⊕E'6
4 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'3⊕E'6
5 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'3⊕E'6
6 1 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕2E'3⊕E'6
7 1 1 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'3⊕2E'6
8 1 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 A'1⊕2E'3⊕2E'6
9 1 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'3⊕2E'6
10 2 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2A'1⊕A'2⊕2E'3⊕2E'6
11 1 1 0 0 3 0 0 2 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕3E'3⊕2E'6
12 2 1 0 0 2 0 0 3 0 0 0 0 0 0 0 0 0 0 2A'1⊕A'2⊕2E'3⊕3E'6
13 1 1 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕3E'3⊕3E'6
14 2 1 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 2A'1⊕A'2⊕3E'3⊕3E'6
15 2 2 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 2A'1⊕2A'2⊕3E'3⊕3E'6
16 2 1 0 0 4 0 0 3 0 0 0 0 0 0 0 0 0 0 2A'1⊕A'2⊕4E'3⊕3E'6
17 2 2 0 0 3 0 0 4 0 0 0 0 0 0 0 0 0 0 2A'1⊕2A'2⊕3E'3⊕4E'6
18 2 1 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 2A'1⊕A'2⊕4E'3⊕4E'6
19 2 2 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 2A'1⊕2A'2⊕4E'3⊕4E'6
20 3 2 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 3A'1⊕2A'2⊕4E'3⊕4E'6



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