Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 60 0 0 8
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 54 2 0 8



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 17 13 13 17 60
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 16 11 12 15 54



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 16
Number of vibrational modes 54





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 16 11 12 15 27 / 27
Quadratic (Raman) 16 11 12 15 27 / 27
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 54 2 0 8
quadratic 2 1.485 29 27 59
cubic 3 27.720 56 0 304
quartic 4 395.010 434 378 1.434
quintic 5 4.582.116 812 0 5.760
sextic 6 45.057.474 4.466 3.654 21.542


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 16 11 12 15
quadratic 2 400 356 357 372
cubic 3 7.020 6.840 6.868 6.992
quartic 4 99.314 98.380 98.408 98.908
quintic 5 1.147.172 1.143.886 1.144.292 1.146.766
sextic 6 11.271.784 11.258.780 11.259.186 11.267.724


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