Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 72 0 0 8
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 66 2 0 8



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 20 16 16 20 72
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 19 14 15 18 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 19
Number of vibrational modes 66




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 19 14 15 18 33 / 33
Quadratic (Raman) 19 14 15 18 33 / 33
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 66 2 0 8
quadratic 2 2.211 35 33 65
cubic 3 50.116 68 0 352
quartic 4 864.501 629 561 1.809
quintic 5 12.103.014 1.190 0 7.752
sextic 6 143.218.999 7.735 6.545 31.441


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 19 14 15 18
quadratic 2 586 536 537 552
cubic 3 12.634 12.424 12.458 12.600
quartic 4 216.875 215.656 215.690 216.280
quintic 5 3.027.989 3.023.518 3.024.113 3.027.394
sextic 6 35.816.180 35.796.592 35.797.187 35.809.040


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