Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 72 0 4 4
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 66 2 4 4



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 20 16 18 18 72
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 19 15 16 16 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 19
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 19 15 16 16 51 / 15
Quadratic (Raman) 19 15 16 16 66 / 0
IR + Raman 19 - 16 16 51 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 66 2 4 4
quadratic 2 2.211 35 41 41
cubic 3 50.116 68 144 144
quartic 4 864.501 629 841 841
quintic 5 12.103.014 1.190 2.660 2.660
sextic 6 143.218.999 7.735 11.585 11.585


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 19 15 16 16
quadratic 2 582 541 544 544
cubic 3 12.618 12.474 12.512 12.512
quartic 4 216.703 215.862 215.968 215.968
quintic 5 3.027.381 3.024.721 3.025.456 3.025.456
sextic 6 35.812.476 35.800.891 35.802.816 35.802.816


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