Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 216 0 0 72
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 210 2 0 72



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 72 36 36 72 216
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 71 34 35 70 210



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 71
Number of vibrational modes 210




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 71 34 35 70 105 / 105
Quadratic (Raman) 71 34 35 70 105 / 105
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 1 210 2 0 72
quadratic 2 22.155 107 105 2.697
cubic 3 1.565.620 212 0 69.792
quartic 4 83.369.265 5.777 5.565 1.399.197
quintic 5 3.568.204.542 11.342 0 23.121.576
sextic 6 127.860.662.755 209.827 198.485 327.363.605


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 71 34 35 70
quadratic 2 6.266 4.864 4.865 6.160
cubic 3 408.906 373.904 374.010 408.800
quartic 4 21.194.951 20.492.464 20.492.570 21.189.280
quintic 5 897.834.365 886.267.906 886.273.577 897.828.694
sextic 6 32.047.108.668 31.883.321.952 31.883.327.623 32.046.904.512


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