Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 78 -6 0 0
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 72 -4 0 0



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



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 17
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 17 19 17 19 36 / 36
Quadratic (Raman) 17 19 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 -4 0 0
quadratic 2 2.628 44 36 36
cubic 3 64.824 -156 0 0
quartic 4 1.215.450 970 666 666
quintic 5 18.474.840 -3.116 0 0
sextic 6 237.093.780 14.364 8.436 8.436


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 17 19 17 19
quadratic 2 686 646 650 646
cubic 3 16.167 16.245 16.167 16.245
quartic 4 304.438 303.620 303.772 303.620
quintic 5 4.617.931 4.619.489 4.617.931 4.619.489
sextic 6 59.281.254 59.269.854 59.272.818 59.269.854


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