Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 90 -2 0 0
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 84 0 0 0



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 22 23 22 23 90
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 21 21 21 21 84



Molecule Parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 21
Number of vibrational modes 84




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 21 21 21 21 42 / 42
Quadratic (Raman) 21 21 21 21 42 / 42
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 84 0 0 0
quadratic 2 3.570 42 42 42
cubic 3 102.340 0 0 0
quartic 4 2.225.895 903 903 903
quintic 5 39.175.752 0 0 0
sextic 6 581.106.988 13.244 13.244 13.244


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 21 21 21 21
quadratic 2 924 882 882 882
cubic 3 25.585 25.585 25.585 25.585
quartic 4 557.151 556.248 556.248 556.248
quintic 5 9.793.938 9.793.938 9.793.938 9.793.938
sextic 6 145.286.680 145.273.436 145.273.436 145.273.436


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