Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 78 0 0 6
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 72 2 0 6



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 21 18 18 21 78
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 20 16 17 19 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 20
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 20 16 17 19 36 / 36
Quadratic (Raman) 20 16 17 19 36 / 36
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 72 2 0 6
quadratic 2 2.628 38 36 54
cubic 3 64.824 74 0 254
quartic 4 1.215.450 740 666 1.380
quintic 5 18.474.840 1.406 0 5.466
sextic 6 237.093.780 9.842 8.436 22.946


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 20 16 17 19
quadratic 2 689 643 644 652
cubic 3 16.288 16.124 16.161 16.251
quartic 4 304.559 303.499 303.536 303.856
quintic 5 4.620.428 4.616.992 4.617.695 4.619.725
sextic 6 59.283.751 59.267.357 59.268.060 59.274.612


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