Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 30 0 0 10
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 24 2 0 10



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 10 5 5 10 30
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 9 3 4 8 24



Molecule Parameter
Number of Atoms (N) 10
Number of internal coordinates 24
Number of independant internal coordinates 9
Number of vibrational modes 24





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 9 3 4 8 12 / 12
Quadratic (Raman) 9 3 4 8 12 / 12
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 24 2 0 10
quadratic 2 300 14 12 62
cubic 3 2.600 26 0 290
quartic 4 17.550 104 78 1.128
quintic 5 98.280 182 0 3.822
sextic 6 475.020 546 364 11.634


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 9 3 4 8
quadratic 2 97 59 60 84
cubic 3 729 571 584 716
quartic 4 4.715 4.099 4.112 4.624
quintic 5 25.571 23.569 23.660 25.480
sextic 6 121.891 115.801 115.892 121.436


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