Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 12 -2 4 2
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 6 0 4 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 4 1 4 3 12
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 3 0 2 1 6



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 3
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 3 0 2 1 6 / 0
Quadratic (Raman) 3 0 2 1 6 / 0
IR + Raman 3 - 2 1 6 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 6 0 4 2
quadratic 2 21 3 11 5
cubic 3 56 0 24 8
quartic 4 126 6 46 14
quintic 5 252 0 80 20
sextic 6 462 10 130 30


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 3 0 2 1
quadratic 2 10 2 6 3
cubic 3 22 6 18 10
quartic 4 48 18 38 22
quintic 5 88 38 78 48
sextic 6 158 78 138 88


Literature




Character tables for chemically important point groups Character table for point group C2v Jacobs University Bremen

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