Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 36 0 0 4
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 30 2 0 4



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 10 8 8 10 36
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 9 7 6 8 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 9
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 9 7 6 8 23 / 7
Quadratic (Raman) 9 7 6 8 30 / 0
IR + Raman 9 - 6 8 23 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 30 2 0 4
quadratic 2 465 17 15 23
cubic 3 4.960 32 0 72
quartic 4 40.920 152 120 256
quintic 5 278.256 272 0 680
sextic 6 1.623.160 952 680 1.904


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 9 7 6 8
quadratic 2 130 111 110 114
cubic 3 1.266 1.230 1.214 1.250
quartic 4 10.362 10.174 10.158 10.226
quintic 5 69.802 69.462 69.326 69.666
sextic 6 406.674 405.382 405.246 405.858


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