Reduction formula for point group C4h



Characters for molecular motions
Motion E C4(z) C2 (C4)3 i (S4)3 h S4
Cartesian 3N 15 1 -1 1 -3 -1 5 -1
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 9 -1 1 -1 -3 -1 5 -1



Decomposition into Irreducible representations
Motion Ag Bg Eg Au Bu Eu Total
Cartesian 3N 2 2 1 2 1 3 11
Translation (x,y,z) 0 0 0 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 0 0 0 2
Vibration 1 2 0 1 1 2 7



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 1
Number of vibrational modes 7





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Eg Au Bu Eu Total
Linear (IR) 1 2 0 1 1 2 3 / 4
Quadratic (Raman) 1 2 0 1 1 2 3 / 4
IR + Raman - - - - 1 - 0* / 1
* 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 9 -1 1 -1 -3 -1 5 -1
quadratic 2 45 1 5 1 9 1 17 1
cubic 3 165 -1 5 -1 -19 -1 45 -1
quartic 4 495 3 15 3 39 3 103 3
quintic 5 1.287 -3 15 -3 -69 -3 211 -3
sextic 6 3.003 3 35 3 119 3 399 3


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Eg Au Bu Eu
linear 1 1 2 0 1 1 2
quadratic 2 10 9 4 3 3 6
cubic 3 24 25 12 18 18 28
quartic 4 83 80 52 46 46 68
quintic 5 179 182 124 145 145 194
sextic 6 446 443 336 315 315 406


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