Reduction formula for point group Oh



Characters for molecular motions
Motion E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
Cartesian 3N 48 0 0 0 0 0 0 0 0 8
Translation 3 0 -1 1 -1 -3 -1 0 1 1
Rotation 3 0 -1 1 -1 3 1 0 -1 -1
Vibration 42 0 2 -2 2 0 0 0 0 8



Decomposition into Irreducible representations
Motion A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
Cartesian 3N 2 0 2 2 4 0 2 2 4 2 20
Translation 0 0 0 0 0 0 0 0 1 0 1
Rotation 0 0 0 1 0 0 0 0 0 0 1
Vibration 2 0 2 1 4 0 2 2 3 2 18



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 2
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
Linear (IR) 2 0 2 1 4 0 2 2 3 2 3 / 15
Quadratic (Raman) 2 0 2 1 4 0 2 2 3 2 8 / 10
IR + Raman - 0 - 1 - 0 2 2 - 2 0* / 7
* 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 42 0 2 -2 2 0 0 0 0 8
quadratic 2 903 0 23 3 23 21 1 0 21 53
cubic 3 13.244 14 44 -4 44 0 0 0 0 256
quartic 4 148.995 0 275 15 275 231 11 0 231 1.095
quintic 5 1.370.754 0 506 -26 506 0 0 0 0 4.056
sextic 6 10.737.573 105 2.277 37 2.277 1.771 11 7 1.771 13.803


Decomposition into Irreducible representations
Force field Tensor
Order
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
linear 1 2 0 2 1 4 0 2 2 3 2
quadratic 2 32 12 44 46 64 15 22 37 59 51
cubic 3 318 244 555 787 863 254 308 555 851 799
quartic 4 3.315 2.966 6.281 9.127 9.463 3.000 3.204 6.204 9.398 9.192
quintic 5 29.156 28.022 57.178 85.067 86.214 28.142 29.036 57.178 86.081 85.200
sextic 6 226.024 221.992 447.960 668.952 672.960 222.273 225.148 447.372 672.400 669.512


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