Reduction formula for point group C4v



Characters for molecular motions
Motion E 2C4 (z) C2 2v 2d
Cartesian 3N 72 0 0 4 4
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 66 -2 2 4 4



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 11 7 9 9 18 54
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 10 6 9 9 16 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 10
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 10 6 9 9 16 26 / 24
Quadratic (Raman) 10 6 9 9 16 44 / 6
IR + Raman 10 6 - - 16 26 / 6



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 2v 2d
linear 1 66 -2 2 4 4
quadratic 2 2.211 3 35 41 41
cubic 3 50.116 -4 68 144 144
quartic 4 864.501 21 629 841 841
quintic 5 12.103.014 -38 1.190 2.660 2.660
sextic 6 143.218.999 55 7.735 11.585 11.585


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 10 6 9 9 16
quadratic 2 302 261 280 280 544
cubic 3 6.344 6.200 6.274 6.274 12.512
quartic 4 108.567 107.726 108.136 108.136 215.968
quintic 5 1.514.346 1.511.686 1.513.035 1.513.035 3.025.456
sextic 6 17.909.148 17.897.563 17.903.328 17.903.328 35.802.816


Literature




Character tables for chemically important point groups Character table for point group C4v Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement