Reduction formula for point group C2v



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



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 18 9 18 9 54
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 17 8 16 7 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 8 16 7 40 / 8
Quadratic (Raman) 17 8 16 7 48 / 0
IR + Raman 17 - 16 7 40 / 0



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


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


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