Results for Point Group D20h



Symmetric powers of degenerate representation E1g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C20 2C10 2(C20)3 2C5 2C4 2(C10)3 2(C20)7 2(C5)2 2(C20)9 C2 10C'2 10C''2 i 2(S20)9 2(S5)3 2(S20)7 2(S10)3 2S4 2S5 2(S20)3 2S10 2S20 σh 10σv 10σd
1 2 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -2 0 0 2 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -2 0 0
2 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3 1 1 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3 1 1
3 4 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -4 0 0 4 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -4 0 0
4 5 3.236 0.000 -1.236 -0.000 1 0.000 -1.236 -0.000 3.236 5 1 1 5 3.236 0.000 -1.236 -0.000 1 0.000 -1.236 -0.000 3.236 5 1 1
5 6 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -6 0 0 6 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -6 0 0
6 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7 1 1 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7 1 1
7 8 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -8 0 0 8 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -8 0 0
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1 1 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1 1
9 10 0.000 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 -0.000 -10 0 0 10 0.000 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 -0.000 -10 0 0
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 1 1 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 1 1
11 12 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -12 0 0 12 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -12 0 0
12 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13 1 1 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13 1 1
13 14 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -14 0 0 14 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -14 0 0
14 15 -3.236 0.000 1.236 -0.000 -1 0.000 1.236 -0.000 -3.236 15 1 1 15 -3.236 0.000 1.236 -0.000 -1 0.000 1.236 -0.000 -3.236 15 1 1
15 16 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -16 0 0 16 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -16 0 0
16 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17 1 1 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17 1 1
17 18 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -18 0 0 18 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 1 1 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 0.000 -20 0 0 20 -0.000 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 0.000 -20 0 0
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1 1 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To		 A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g E9g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u E8u E9u
1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g
5 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g
7 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E8g
9 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g⊕E9g
10 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕E4g⊕E6g⊕E8g
11 0 0 0 0 1 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g⊕2E9g
12 1 0 1 1 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕E4g⊕E6g⊕2E8g
13 0 0 0 0 1 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕2E7g⊕2E9g
14 1 0 1 1 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕E4g⊕2E6g⊕2E8g
15 0 0 0 0 1 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕2E5g⊕2E7g⊕2E9g
16 1 0 1 1 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕2E4g⊕2E6g⊕2E8g
17 0 0 0 0 1 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕2E3g⊕2E5g⊕2E7g⊕2E9g
18 1 0 1 1 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕2E7g⊕2E9g
20 2 1 1 1 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕2E2g⊕2E4g⊕2E6g⊕2E8g


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