Reduction formula for point group Oh



Characters of input representation
E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
15 0 1 1 -1 -3 -1 0 5 3



Decomposition into Irreducible representations
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
1 0 1 0 1 0 0 0 2 1 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
Linear (IR) 1 0 1 0 1 0 0 0 2 1 2 / 4
Quadratic (Raman) 1 0 1 0 1 0 0 0 2 1 3 / 3
IR + Raman - 0 - 0 - 0 0 0 - 1 0* / 1
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
linear 1 15 0 1 1 -1 -3 -1 0 5 3
quadratic 2 120 0 8 0 8 12 0 0 20 12
cubic 3 680 5 8 0 -8 -28 0 -1 60 28
quartic 4 3.060 0 36 4 36 72 4 0 160 72
quintic 5 11.628 0 36 4 -36 -144 -4 0 376 144
sextic 6 38.760 15 120 0 120 300 0 3 820 300


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
linear 1 1 0 1 0 1 0 0 0 2 1
quadratic 2 7 2 9 4 9 1 2 3 8 7
cubic 3 22 13 33 33 42 9 14 20 51 46
quartic 4 92 63 155 171 196 50 59 109 199 190
quintic 5 283 238 521 674 719 207 232 439 776 747
sextic 6 928 823 1.742 2.330 2.435 737 782 1.513 2.470 2.425


Literature




Character tables for chemically important point groups Character table for point group Oh Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement