Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 54 0 0 6
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 48 2 0 6



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 15 12 12 15 54
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 14 10 11 13 48



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 14
Number of vibrational modes 48





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 14 10 11 13 24 / 24
Quadratic (Raman) 14 10 11 13 24 / 24
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 48 2 0 6
quadratic 2 1.176 26 24 42
cubic 3 19.600 50 0 182
quartic 4 249.900 350 300 798
quintic 5 2.598.960 650 0 2.814
sextic 6 22.957.480 3.250 2.600 9.730


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 14 10 11 13
quadratic 2 317 283 284 292
cubic 3 4.958 4.842 4.867 4.933
quartic 4 62.837 62.263 62.288 62.512
quintic 5 650.606 648.874 649.199 650.281
sextic 6 5.743.265 5.736.775 5.737.100 5.740.340


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