Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 72 -4 0 4
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 66 -2 0 4



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 18 18 16 20 72
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 17 16 15 18 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 17
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 17 16 15 18 33 / 33
Quadratic (Raman) 17 16 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 4
quadratic 2 2.211 35 33 41
cubic 3 50.116 -68 0 144
quartic 4 864.501 629 561 841
quintic 5 12.103.014 -1.190 0 2.660
sextic 6 143.218.999 7.735 6.545 11.585


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Au Bu
linear 1 17 16 15 18
quadratic 2 580 542 543 546
cubic 3 12.548 12.510 12.476 12.582
quartic 4 216.633 215.898 215.932 216.038
quintic 5 3.026.121 3.025.386 3.024.791 3.026.716
sextic 6 35.811.216 35.801.556 35.802.151 35.804.076


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