Reduction formula for point group C4h



Characters for molecular motions
Motion E C4(z) C2 (C4)3 i (S4)3 h S4
Cartesian 3N 72 0 0 0 0 0 24 0
Translation (x,y,z) 3 1 -1 1 -3 -1 1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 1 3 1 -1 1
Vibration 66 -2 2 -2 0 0 24 0



Decomposition into Irreducible representations
Motion Ag Bg Eg Au Bu Eu Total
Cartesian 3N 12 12 6 6 6 12 54
Translation (x,y,z) 0 0 0 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 0 0 0 2
Vibration 11 12 5 5 6 11 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 11
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Eg Au Bu Eu Total
Linear (IR) 11 12 5 5 6 11 16 / 34
Quadratic (Raman) 11 12 5 5 6 11 28 / 22
IR + Raman - - - - 6 - 0* / 6
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4(z) C2 (C4)3 i (S4)3 h S4
linear 1 66 -2 2 -2 0 0 24 0
quadratic 2 2.211 3 35 3 33 1 321 1
cubic 3 50.116 -4 68 -4 0 0 3.104 0
quartic 4 864.501 21 629 21 561 17 24.081 17
quintic 5 12.103.014 -38 1.190 -38 0 0 158.424 0
sextic 6 143.218.999 55 7.735 55 6.545 17 914.641 17


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Eg Au Bu Eu
linear 1 11 12 5 5 6 11
quadratic 2 326 324 236 237 236 308
cubic 3 6.660 6.662 5.868 5.884 5.886 6.644
quartic 4 111.231 111.212 105.044 105.062 105.060 110.924
quintic 5 1.532.819 1.532.838 1.492.925 1.493.213 1.493.232 1.532.531
sextic 6 18.018.508 18.018.472 17.787.896 17.788.203 17.788.184 18.014.920


Literature




Character tables for chemically important point groups Character table for point group C4h Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement