Reduction formula for point group C3v



Characters for molecular motions
Motion E 2C3 (z) 3v
Cartesian 3N 18 0 4
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 12 0 4



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 5 1 6 12
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 4 0 4 8



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 4
Number of vibrational modes 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 4 0 4 8 / 0
Quadratic (Raman) 4 0 4 8 / 0
IR + Raman 4 0 4 8 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3v
linear 1 12 0 4
quadratic 2 78 0 14
cubic 3 364 4 36
quartic 4 1.365 0 85
quintic 5 4.368 0 176
sextic 6 12.376 10 344


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 4 0 4
quadratic 2 20 6 26
cubic 3 80 44 120
quartic 4 270 185 455
quintic 5 816 640 1.456
sextic 6 2.238 1.894 4.122


Literature




Character tables for chemically important point groups Character table for point group C3v Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement