Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 72 0 0 24
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 66 2 0 24



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 24 12 12 24 72
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 23 10 11 22 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 23
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 23 10 11 22 33 / 33
Quadratic (Raman) 23 10 11 22 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 24
quadratic 2 2.211 35 33 321
cubic 3 50.116 68 0 3.104
quartic 4 864.501 629 561 24.081
quintic 5 12.103.014 1.190 0 158.424
sextic 6 143.218.999 7.735 6.545 914.641


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 23 10 11 22
quadratic 2 650 472 473 616
cubic 3 13.322 11.736 11.770 13.288
quartic 4 222.443 210.088 210.122 221.848
quintic 5 3.065.657 2.985.850 2.986.445 3.065.062
sextic 6 36.036.980 35.575.792 35.576.387 36.029.840


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