Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 12 0 0 4
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 6 2 0 4



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 4 2 2 4 12
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 3 0 1 2 6



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 3
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 3 0 1 2 3 / 3
Quadratic (Raman) 3 0 1 2 3 / 3
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 6 2 0 4
quadratic 2 21 5 3 11
cubic 3 56 8 0 24
quartic 4 126 14 6 46
quintic 5 252 20 0 80
sextic 6 462 30 10 130


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 3 0 1 2
quadratic 2 10 2 3 6
cubic 3 22 6 10 18
quartic 4 48 18 22 38
quintic 5 88 38 48 78
sextic 6 158 78 88 138


Literature




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

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