Reduction formula for point group C3v



Characters for molecular motions
Motion E 2C3 (z) 3v
Cartesian 3N 60 0 4
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 54 0 4



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 12 8 20 40
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 11 7 18 36



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 11
Number of vibrational modes 36





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 11 7 18 29 / 7
Quadratic (Raman) 11 7 18 29 / 7
IR + Raman 11 7 18 29 / 7



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3v
linear 1 54 0 4
quadratic 2 1.485 0 35
cubic 3 27.720 18 120
quartic 4 395.010 0 610
quintic 5 4.582.116 0 1.856
sextic 6 45.057.474 171 7.134


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 11 7 18
quadratic 2 265 230 495
cubic 3 4.686 4.566 9.234
quartic 4 66.140 65.530 131.670
quintic 5 764.614 762.758 1.527.372
sextic 6 7.513.203 7.506.069 15.019.101


Literature




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

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