Results for Point Group D15h



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


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