Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 216 0 0 8
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 210 2 0 8



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 56 52 52 56 216
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 55 50 51 54 210



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 55
Number of vibrational modes 210




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 55 50 51 54 105 / 105
Quadratic (Raman) 55 50 51 54 105 / 105
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 1 210 2 0 8
quadratic 2 22.155 107 105 137
cubic 3 1.565.620 212 0 928
quartic 4 83.369.265 5.777 5.565 9.117
quintic 5 3.568.204.542 11.342 0 54.120
sextic 6 127.860.662.755 209.827 198.485 397.333


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 55 50 51 54
quadratic 2 5.626 5.504 5.505 5.520
cubic 3 391.690 391.120 391.226 391.584
quartic 4 20.847.431 20.839.984 20.840.090 20.841.760
quintic 5 892.067.501 892.034.770 892.040.441 892.061.830
sextic 6 31.965.367.100 31.965.063.520 31.965.069.191 31.965.162.944


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