Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 78 0 26 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 72 2 26 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 26 13 26 13 78
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 25 12 24 11 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 25
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 25 12 24 11 60 / 12
Quadratic (Raman) 25 12 24 11 72 / 0
IR + Raman 25 - 24 11 60 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 72 2 26 0
quadratic 2 2.628 38 374 36
cubic 3 64.824 74 3.874 0
quartic 4 1.215.450 740 32.100 666
quintic 5 18.474.840 1.406 225.030 0
sextic 6 237.093.780 9.842 1.381.730 8.436


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 25 12 24 11
quadratic 2 769 564 732 563
cubic 3 17.193 15.256 17.156 15.219
quartic 4 312.239 295.856 311.536 295.819
quintic 5 4.675.319 4.562.804 4.674.616 4.562.101
sextic 6 59.623.447 58.928.364 59.614.308 58.927.661


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