Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 24 0 0 8
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 18 2 0 8



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 8 4 4 8 24
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 7 2 3 6 18



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 7
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 7 2 3 6 9 / 9
Quadratic (Raman) 7 2 3 6 9 / 9
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 18 2 0 8
quadratic 2 171 11 9 41
cubic 3 1.140 20 0 160
quartic 4 5.985 65 45 525
quintic 5 26.334 110 0 1.512
sextic 6 100.947 275 165 3.941


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 7 2 3 6
quadratic 2 58 32 33 48
cubic 3 330 240 250 320
quartic 4 1.655 1.360 1.370 1.600
quintic 5 6.989 6.178 6.233 6.934
sextic 6 26.332 24.224 24.279 26.112


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