Reduction formula for point group C3



Characters for molecular motions
Motion E C3 (C3)2
Cartesian 3N 90 0 0
Translation (x,y,z) 3 0 0
Rotation (Rx,Ry,Rz) 3 0 0
Vibration 84 0 0



Decomposition into Irreducible representations
Motion A E Total
Cartesian 3N 30 30 60
Translation (x,y,z) 1 1 2
Rotation (Rx,Ry,Rz) 1 1 2
Vibration 28 28 56



Molecule Parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 28
Number of vibrational modes 56





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E Total
Linear (IR) 28 28 56 / 0
Quadratic (Raman) 28 28 56 / 0
IR + Raman 28 28 56 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3 (C3)2
linear 1 84 0 0
quadratic 2 3.570 0 0
cubic 3 102.340 28 28
quartic 4 2.225.895 0 0
quintic 5 39.175.752 0 0
sextic 6 581.106.988 406 406


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A E
linear 1 28 28
quadratic 2 1.190 1.190
cubic 3 34.132 34.104
quartic 4 741.965 741.965
quintic 5 13.058.584 13.058.584
sextic 6 193.702.600 193.702.194


Literature




Character tables for chemically important point groups Character table for point group C3 Constructor University Bremen

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