Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 15 -3 -3 3
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 9 -1 -3 3



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 3 3 3 6 15
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 2 1 2 4 9



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 2
Number of vibrational modes 9





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 2 1 2 4 6 / 3
Quadratic (Raman) 2 1 2 4 3 / 6
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 9 -1 -3 3
quadratic 2 45 5 9 9
cubic 3 165 -5 -19 19
quartic 4 495 15 39 39
quintic 5 1.287 -15 -69 69
sextic 6 3.003 35 119 119


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 2 1 2 4
quadratic 2 17 10 8 10
cubic 3 40 33 40 52
quartic 4 147 120 108 120
quintic 5 318 291 318 360
sextic 6 819 742 700 742


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