Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 324 0 24 12
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 318 2 24 12



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 90 72 84 78 324
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 89 71 82 76 318



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 89
Number of vibrational modes 318





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 89 71 82 76 247 / 71
Quadratic (Raman) 89 71 82 76 318 / 0
IR + Raman 89 - 82 76 247 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 318 2 24 12
quadratic 2 50.721 161 447 231
cubic 3 5.410.240 320 6.128 2.200
quartic 4 434.171.760 13.040 72.528 25.080
quintic 5 27.960.661.344 25.760 741.552 201.432
sextic 6 1.505.215.602.352 708.400 6.858.544 1.748.824


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 89 71 82 76
quadratic 2 12.890 12.551 12.694 12.586
cubic 3 1.354.722 1.350.558 1.353.462 1.351.498
quartic 4 108.570.602 108.521.798 108.551.542 108.527.818
quintic 5 6.990.407.522 6.989.936.030 6.990.293.926 6.990.023.866
sextic 6 376.306.229.530 376.301.925.846 376.305.000.918 376.302.446.058


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