Reduction formula for point group C4v



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



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 10 8 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 9 7 9 9 16 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 9
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 9 7 9 9 16 25 / 25
Quadratic (Raman) 9 7 9 9 16 43 / 7
IR + Raman 9 7 - - 16 25 / 7



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


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 9 7 9 9 16
quadratic 2 299 264 280 280 544
cubic 3 6.306 6.238 6.274 6.274 12.512
quartic 4 108.461 107.832 108.136 108.136 215.968
quintic 5 1.513.611 1.512.421 1.513.035 1.513.035 3.025.456
sextic 6 17.907.223 17.899.488 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