Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 60 0 8 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 54 2 8 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 17 13 17 13 60
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 16 12 15 11 54



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 16
Number of vibrational modes 54





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 16 12 15 11 42 / 12
Quadratic (Raman) 16 12 15 11 54 / 0
IR + Raman 16 - 15 11 42 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 54 2 8 0
quadratic 2 1.485 29 59 27
cubic 3 27.720 56 304 0
quartic 4 395.010 434 1.434 378
quintic 5 4.582.116 812 5.760 0
sextic 6 45.057.474 4.466 21.542 3.654


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 16 12 15 11
quadratic 2 400 357 372 356
cubic 3 7.020 6.868 6.992 6.840
quartic 4 99.314 98.408 98.908 98.380
quintic 5 1.147.172 1.144.292 1.146.766 1.143.886
sextic 6 11.271.784 11.259.186 11.267.724 11.258.780


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