Reduction formula for point group C4v



Characters for molecular motions
Motion E 2C4 (z) C2 2v 2d
Cartesian 3N 24 0 0 4 0
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 18 -2 2 4 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 4 2 4 2 6 18
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 3 1 4 2 4 14



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 3
Number of vibrational modes 14





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 3 1 4 2 4 7 / 7
Quadratic (Raman) 3 1 4 2 4 13 / 1
IR + Raman 3 1 - - 4 7 / 1



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 2v 2d
linear 1 18 -2 2 4 0
quadratic 2 171 3 11 17 9
cubic 3 1.140 -4 20 48 0
quartic 4 5.985 9 65 133 45
quintic 5 26.334 -14 110 308 0
sextic 6 100.947 19 275 693 165


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 3 1 4 2 4
quadratic 2 30 17 24 20 40
cubic 3 156 132 158 134 280
quartic 4 803 714 776 732 1.480
quintic 5 3.379 3.225 3.386 3.232 6.556
sextic 6 12.872 12.443 12.780 12.516 25.168


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