Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 78 0 0 26
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 72 2 0 26



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 26 13 13 26 78
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 25 11 12 24 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 25
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 25 11 12 24 36 / 36
Quadratic (Raman) 25 11 12 24 36 / 36
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 72 2 0 26
quadratic 2 2.628 38 36 374
cubic 3 64.824 74 0 3.874
quartic 4 1.215.450 740 666 32.100
quintic 5 18.474.840 1.406 0 225.030
sextic 6 237.093.780 9.842 8.436 1.381.730


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 25 11 12 24
quadratic 2 769 563 564 732
cubic 3 17.193 15.219 15.256 17.156
quartic 4 312.239 295.819 295.856 311.536
quintic 5 4.675.319 4.562.101 4.562.804 4.674.616
sextic 6 59.623.447 58.927.661 58.928.364 59.614.308


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