Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 48 0 16 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 42 2 16 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 16 8 16 8 48
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 15 7 14 6 42



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 15
Number of vibrational modes 42





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 15 7 14 6 35 / 7
Quadratic (Raman) 15 7 14 6 42 / 0
IR + Raman 15 - 14 6 35 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 42 2 16 0
quadratic 2 903 23 149 21
cubic 3 13.244 44 1.024 0
quartic 4 148.995 275 5.735 231
quintic 5 1.370.754 506 27.568 0
sextic 6 10.737.573 2.277 117.483 1.771


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 15 7 14 6
quadratic 2 274 189 252 188
cubic 3 3.578 3.066 3.556 3.044
quartic 4 38.809 35.826 38.556 35.804
quintic 5 349.707 335.923 349.454 335.670
sextic 6 2.714.776 2.655.149 2.712.752 2.654.896


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