Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 18 -2 4 4
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 12 0 4 4



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 6 2 5 5 18
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 5 1 3 3 12



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 5
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 5 1 3 3 11 / 1
Quadratic (Raman) 5 1 3 3 12 / 0
IR + Raman 5 - 3 3 11 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 12 0 4 4
quadratic 2 78 6 14 14
cubic 3 364 0 36 36
quartic 4 1.365 21 85 85
quintic 5 4.368 0 176 176
sextic 6 12.376 56 344 344


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 5 1 3 3
quadratic 2 28 14 18 18
cubic 3 109 73 91 91
quartic 4 389 304 336 336
quintic 5 1.180 1.004 1.092 1.092
sextic 6 3.280 2.936 3.080 3.080


Literature




Character tables for chemically important point groups Character table for point group C2v Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement