Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 18 -2 0 0
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 12 0 0 0



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 4 5 4 5 18
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 3 3 3 3 12



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 3
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 3 3 3 3 6 / 6
Quadratic (Raman) 3 3 3 3 6 / 6
IR + Raman - - - - 0* / 0
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) i h
linear 1 12 0 0 0
quadratic 2 78 6 6 6
cubic 3 364 0 0 0
quartic 4 1.365 21 21 21
quintic 5 4.368 0 0 0
sextic 6 12.376 56 56 56


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 3 3 3 3
quadratic 2 24 18 18 18
cubic 3 91 91 91 91
quartic 4 357 336 336 336
quintic 5 1.092 1.092 1.092 1.092
sextic 6 3.136 3.080 3.080 3.080


Literature




Character tables for chemically important point groups Character table for point group C2h Constructor University Bremen

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