Reduction formula for point group C4h



Characters for molecular motions
Motion E C4(z) C2 (C4)3 i (S4)3 h S4
Cartesian 3N 24 0 0 0 0 0 8 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 18 -2 2 -2 0 0 8 0



Decomposition into Irreducible representations
Motion Ag Bg Eg Au Bu Eu Total
Cartesian 3N 4 4 2 2 2 4 18
Translation (x,y,z) 0 0 0 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 0 0 0 2
Vibration 3 4 1 1 2 3 14



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 3
Number of vibrational modes 14





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Eg Au Bu Eu Total
Linear (IR) 3 4 1 1 2 3 4 / 10
Quadratic (Raman) 3 4 1 1 2 3 8 / 6
IR + Raman - - - - 2 - 0* / 2
* 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 18 -2 2 -2 0 0 8 0
quadratic 2 171 3 11 3 9 1 41 1
cubic 3 1.140 -4 20 -4 0 0 160 0
quartic 4 5.985 9 65 9 45 5 525 5
quintic 5 26.334 -14 110 -14 0 0 1.512 0
sextic 6 100.947 19 275 19 165 5 3.941 5


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Bg Eg Au Bu Eu
linear 1 3 4 1 1 2 3
quadratic 2 30 28 16 17 16 24
cubic 3 164 166 120 124 126 160
quartic 4 831 824 680 686 684 800
quintic 5 3.491 3.498 3.089 3.113 3.120 3.467
sextic 6 13.172 13.160 12.112 12.143 12.136 13.056


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