Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 48 0 0 16
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 42 2 0 16



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 16 8 8 16 48
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 15 6 7 14 42



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 15
Number of vibrational modes 42





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 15 6 7 14 21 / 21
Quadratic (Raman) 15 6 7 14 21 / 21
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 42 2 0 16
quadratic 2 903 23 21 149
cubic 3 13.244 44 0 1.024
quartic 4 148.995 275 231 5.735
quintic 5 1.370.754 506 0 27.568
sextic 6 10.737.573 2.277 1.771 117.483


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 15 6 7 14
quadratic 2 274 188 189 252
cubic 3 3.578 3.044 3.066 3.556
quartic 4 38.809 35.804 35.826 38.556
quintic 5 349.707 335.670 335.923 349.454
sextic 6 2.714.776 2.654.896 2.655.149 2.712.752


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