Reduction formula for point group C3v



Characters for molecular motions
Motion E 2C3 (z) 3v
Cartesian 3N 15 0 3
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 9 0 3



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 4 1 5 10
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 3 0 3 6



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 3
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 3 0 3 6 / 0
Quadratic (Raman) 3 0 3 6 / 0
IR + Raman 3 0 3 6 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3v
linear 1 9 0 3
quadratic 2 45 0 9
cubic 3 165 3 19
quartic 4 495 0 39
quintic 5 1.287 0 69
sextic 6 3.003 6 119


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 3 0 3
quadratic 2 12 3 15
cubic 3 38 19 54
quartic 4 102 63 165
quintic 5 249 180 429
sextic 6 562 443 999


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