Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 54 -2 18 2
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 48 0 18 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 18 8 18 10 54
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 17 7 16 8 48



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 17
Number of vibrational modes 48





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 17 7 16 8 41 / 7
Quadratic (Raman) 17 7 16 8 48 / 0
IR + Raman 17 - 16 8 41 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 48 0 18 2
quadratic 2 1.176 24 186 26
cubic 3 19.600 0 1.410 50
quartic 4 249.900 300 8.670 350
quintic 5 2.598.960 0 45.594 650
sextic 6 22.957.480 2.600 211.922 3.250


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 17 7 16 8
quadratic 2 353 247 328 248
cubic 3 5.265 4.535 5.240 4.560
quartic 4 64.805 60.295 64.480 60.320
quintic 5 661.301 638.179 660.976 638.504
sextic 6 5.793.813 5.686.227 5.790.888 5.686.552


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