Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 216 -8 0 0
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 210 -6 0 0



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



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 51
Number of vibrational modes 210




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 51 54 51 54 105 / 105
Quadratic (Raman) 51 54 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 -6 0 0
quadratic 2 22.155 123 105 105
cubic 3 1.565.620 -668 0 0
quartic 4 83.369.265 7.521 5.565 5.565
quintic 5 3.568.204.542 -37.482 0 0
sextic 6 127.860.662.755 305.731 198.485 198.485


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 51 54 51 54
quadratic 2 5.622 5.508 5.517 5.508
cubic 3 391.238 391.572 391.238 391.572
quartic 4 20.846.979 20.840.436 20.841.414 20.840.436
quintic 5 892.041.765 892.060.506 892.041.765 892.060.506
sextic 6 31.965.341.364 31.965.089.256 31.965.142.879 31.965.089.256


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