Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 18 0 2 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 12 2 2 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 5 4 5 4 18
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 4 3 3 2 12



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 4
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 4 3 3 2 9 / 3
Quadratic (Raman) 4 3 3 2 12 / 0
IR + Raman 4 - 3 2 9 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 12 2 2 0
quadratic 2 78 8 8 6
cubic 3 364 14 14 0
quartic 4 1.365 35 35 21
quintic 5 4.368 56 56 0
sextic 6 12.376 112 112 56


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 4 3 3 2
quadratic 2 25 18 18 17
cubic 3 98 91 91 84
quartic 4 364 336 336 329
quintic 5 1.120 1.092 1.092 1.064
sextic 6 3.164 3.080 3.080 3.052


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