Reduction formula for point group C3



Characters for molecular motions
Motion E C3 (C3)2
Cartesian 3N 54 0 0
Translation (x,y,z) 3 0 0
Rotation (Rx,Ry,Rz) 3 0 0
Vibration 48 0 0



Decomposition into Irreducible representations
Motion A E Total
Cartesian 3N 18 18 36
Translation (x,y,z) 1 1 2
Rotation (Rx,Ry,Rz) 1 1 2
Vibration 16 16 32



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 16
Number of vibrational modes 32





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E Total
Linear (IR) 16 16 32 / 0
Quadratic (Raman) 16 16 32 / 0
IR + Raman 16 16 32 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3 (C3)2
linear 1 48 0 0
quadratic 2 1.176 0 0
cubic 3 19.600 16 16
quartic 4 249.900 0 0
quintic 5 2.598.960 0 0
sextic 6 22.957.480 136 136


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A E
linear 1 16 16
quadratic 2 392 392
cubic 3 6.544 6.528
quartic 4 83.300 83.300
quintic 5 866.320 866.320
sextic 6 7.652.584 7.652.448


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