Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 72 -2 24 2
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 66 0 24 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 24 11 24 13 72
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 23 10 22 11 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 23
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 23 10 22 11 56 / 10
Quadratic (Raman) 23 10 22 11 66 / 0
IR + Raman 23 - 22 11 56 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 66 0 24 2
quadratic 2 2.211 33 321 35
cubic 3 50.116 0 3.104 68
quartic 4 864.501 561 24.081 629
quintic 5 12.103.014 0 158.424 1.190
sextic 6 143.218.999 6.545 914.641 7.735


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 23 10 22 11
quadratic 2 650 472 616 473
cubic 3 13.322 11.736 13.288 11.770
quartic 4 222.443 210.088 221.848 210.122
quintic 5 3.065.657 2.985.850 3.065.062 2.986.445
sextic 6 36.036.980 35.575.792 36.029.840 35.576.387


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