Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 57 -3 9 9
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 51 -1 9 9



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 18 9 15 15 57
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 17 8 13 13 51



Molecule Parameter
Number of Atoms (N) 19
Number of internal coordinates 51
Number of independant internal coordinates 17
Number of vibrational modes 51





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 17 8 13 13 43 / 8
Quadratic (Raman) 17 8 13 13 51 / 0
IR + Raman 17 - 13 13 43 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 51 -1 9 9
quadratic 2 1.326 26 66 66
cubic 3 23.426 -26 354 354
quartic 4 316.251 351 1.671 1.671
quintic 5 3.478.761 -351 6.831 6.831
sextic 6 32.468.436 3.276 25.564 25.564


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 17 8 13 13
quadratic 2 371 305 325 325
cubic 3 6.027 5.673 5.863 5.863
quartic 4 79.986 78.315 78.975 78.975
quintic 5 873.018 866.187 869.778 869.778
sextic 6 8.130.710 8.105.146 8.116.290 8.116.290


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