Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 27 -1 3 3
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 21 1 3 3



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 8 5 7 7 27
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 7 4 5 5 21



Molecule Parameter
Number of Atoms (N) 9
Number of internal coordinates 21
Number of independant internal coordinates 7
Number of vibrational modes 21





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 7 4 5 5 17 / 4
Quadratic (Raman) 7 4 5 5 21 / 0
IR + Raman 7 - 5 5 17 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 21 1 3 3
quadratic 2 231 11 15 15
cubic 3 1.771 11 37 37
quartic 4 10.626 66 114 114
quintic 5 53.130 66 246 246
sextic 6 230.230 286 598 598


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 7 4 5 5
quadratic 2 68 53 55 55
cubic 3 464 427 440 440
quartic 4 2.730 2.616 2.640 2.640
quintic 5 13.422 13.176 13.266 13.266
sextic 6 57.928 57.330 57.486 57.486


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