Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 324 0 12 8
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 318 2 12 8



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 86 76 82 80 324
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 85 75 80 78 318



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 85
Number of vibrational modes 318





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 85 75 80 78 243 / 75
Quadratic (Raman) 85 75 80 78 318 / 0
IR + Raman 85 - 80 78 243 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 318 2 12 8
quadratic 2 50.721 161 231 191
cubic 3 5.410.240 320 2.200 1.360
quartic 4 434.171.760 13.040 25.080 18.000
quintic 5 27.960.661.344 25.760 201.432 116.112
sextic 6 1.505.215.602.352 708.400 1.748.824 1.120.816


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 85 75 80 78
quadratic 2 12.826 12.615 12.650 12.630
cubic 3 1.353.530 1.351.750 1.352.690 1.352.270
quartic 4 108.556.970 108.535.430 108.541.450 108.537.910
quintic 5 6.990.251.162 6.990.092.390 6.990.180.226 6.990.137.566
sextic 6 376.304.795.098 376.303.360.278 376.303.880.490 376.303.566.486


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