Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 216 -8 72 8
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 210 -6 72 8



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 72 32 72 40 216
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 71 31 70 38 210



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 71
Number of vibrational modes 210





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 71 31 70 38 179 / 31
Quadratic (Raman) 71 31 70 38 210 / 0
IR + Raman 71 - 70 38 179 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 210 -6 72 8
quadratic 2 22.155 123 2.697 137
cubic 3 1.565.620 -668 69.792 928
quartic 4 83.369.265 7.521 1.399.197 9.117
quintic 5 3.568.204.542 -37.482 23.121.576 54.120
sextic 6 127.860.662.755 305.731 327.363.605 397.333


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 71 31 70 38
quadratic 2 6.278 4.861 6.148 4.868
cubic 3 408.918 373.558 408.788 374.356
quartic 4 21.196.275 20.492.118 21.187.956 20.492.916
quintic 5 897.835.689 886.247.841 897.827.370 886.293.642
sextic 6 32.047.182.356 31.883.301.887 32.046.830.824 31.883.347.688


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