Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 30 0 10 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 24 2 10 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 10 5 10 5 30
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 9 4 8 3 24



Molecule Parameter
Number of Atoms (N) 10
Number of internal coordinates 24
Number of independant internal coordinates 9
Number of vibrational modes 24





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 9 4 8 3 20 / 4
Quadratic (Raman) 9 4 8 3 24 / 0
IR + Raman 9 - 8 3 20 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 24 2 10 0
quadratic 2 300 14 62 12
cubic 3 2.600 26 290 0
quartic 4 17.550 104 1.128 78
quintic 5 98.280 182 3.822 0
sextic 6 475.020 546 11.634 364


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 9 4 8 3
quadratic 2 97 60 84 59
cubic 3 729 584 716 571
quartic 4 4.715 4.112 4.624 4.099
quintic 5 25.571 23.660 25.480 23.569
sextic 6 121.891 115.892 121.436 115.801


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