Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 144 0 0 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 138 2 0 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 36 36 36 36 144
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 35 35 34 34 138



Molecule Parameter
Number of Atoms (N) 48
Number of internal coordinates 138
Number of independant internal coordinates 35
Number of vibrational modes 138





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 35 35 34 34 103 / 35
Quadratic (Raman) 35 35 34 34 138 / 0
IR + Raman 35 - 34 34 103 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 138 2 0 0
quadratic 2 9.591 71 69 69
cubic 3 447.580 140 0 0
quartic 4 15.777.195 2.555 2.415 2.415
quintic 5 448.072.338 4.970 0 0
sextic 6 10.679.057.389 62.125 57.155 57.155


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 35 35 34 34
quadratic 2 2.450 2.381 2.380 2.380
cubic 3 111.930 111.930 111.860 111.860
quartic 4 3.946.145 3.943.730 3.943.660 3.943.660
quintic 5 112.019.327 112.019.327 112.016.842 112.016.842
sextic 6 2.669.808.456 2.669.751.301 2.669.748.816 2.669.748.816


Literature




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

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