Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 78 0 6 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 72 2 6 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 21 18 21 18 78
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 20 17 19 16 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 20
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 20 17 19 16 55 / 17
Quadratic (Raman) 20 17 19 16 72 / 0
IR + Raman 20 - 19 16 55 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 72 2 6 0
quadratic 2 2.628 38 54 36
cubic 3 64.824 74 254 0
quartic 4 1.215.450 740 1.380 666
quintic 5 18.474.840 1.406 5.466 0
sextic 6 237.093.780 9.842 22.946 8.436


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 20 17 19 16
quadratic 2 689 644 652 643
cubic 3 16.288 16.161 16.251 16.124
quartic 4 304.559 303.536 303.856 303.499
quintic 5 4.620.428 4.617.695 4.619.725 4.616.992
sextic 6 59.283.751 59.268.060 59.274.612 59.267.357


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