Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 21 -1 -3 3
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 15 1 -3 3



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 5 4 5 7 21
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 4 2 4 5 15



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 4
Number of vibrational modes 15





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 4 2 4 5 9 / 6
Quadratic (Raman) 4 2 4 5 6 / 9
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 15 1 -3 3
quadratic 2 120 8 12 12
cubic 3 680 8 -28 28
quartic 4 3.060 36 72 72
quintic 5 11.628 36 -144 144
sextic 6 38.760 120 300 300


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 4 2 4 5
quadratic 2 38 28 26 28
cubic 3 172 154 172 182
quartic 4 810 756 738 756
quintic 5 2.916 2.826 2.916 2.970
sextic 6 9.870 9.660 9.570 9.660


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