Results for Point Group D15h



Symmetric powers of degenerate representation E''7
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 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 0 -2 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 0
2 3 2.827 2.338 1.618 0.791 0 -0.618 -0.956 1 3 2.827 2.338 1.618 0.791 0 -0.618 -0.956 1
3 4 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 0 -4 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 0
4 5 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 1 5 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 1
5 6 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 0 -6 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 0
6 7 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 1 7 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 1
7 8 -4.783 -0.511 1.618 0.547 -1 -0.618 0.747 0 -8 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 0
8 9 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 1 9 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 1
9 10 -4.165 -2.129 -0.000 1.165 1 0.000 -0.871 0 -10 4.165 2.129 0.000 -1.165 -1 -0.000 0.871 0
10 11 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 1 11 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 1
11 12 -2.827 -2.338 -1.618 -0.791 0 0.618 0.956 0 -12 2.827 2.338 1.618 0.791 0 -0.618 -0.956 0
12 13 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 1 13 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 1
13 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 0 -14 1.000 1.000 1.000 1.000 1 1.000 1.000 0
14 15 -0.000 -0.000 -0.000 -0.000 0 0.000 -0.000 1 15 -0.000 -0.000 -0.000 -0.000 0 0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 1 1.000 1.000 0 -16 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 0
16 17 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 1 17 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 1
17 18 2.827 2.338 1.618 0.791 0 -0.618 -0.956 0 -18 -2.827 -2.338 -1.618 -0.791 0 0.618 0.956 0
18 19 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 1 19 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 1
19 20 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 0 -20 -4.165 -2.129 0.000 1.165 1 -0.000 -0.871 0
20 21 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 1 21 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E''7
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 E''6⊕E''7
4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 E''5⊕E''6⊕E''7
6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 E''4⊕E''5⊕E''6⊕E''7
8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 E''3⊕E''4⊕E''5⊕E''6⊕E''7
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
12 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
13 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
14 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
15 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 A''1⊕A''2⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
16 1 0 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕2E'7
17 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 A''1⊕A''2⊕2E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
18 1 0 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕2E'6⊕2E'7
19 0 0 0 0 0 0 0 0 0 1 1 2 2 1 1 1 1 1 A''1⊕A''2⊕2E''1⊕2E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
20 1 0 1 1 1 1 2 2 2 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕2E'6⊕2E'7


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