Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 21 -3 5 5
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 15 -1 5 5



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 7 2 6 6 21
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 6 1 4 4 15



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 6
Number of vibrational modes 15





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 6 1 4 4 14 / 1
Quadratic (Raman) 6 1 4 4 15 / 0
IR + Raman 6 - 4 4 14 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 15 -1 5 5
quadratic 2 120 8 20 20
cubic 3 680 -8 60 60
quartic 4 3.060 36 160 160
quintic 5 11.628 -36 376 376
sextic 6 38.760 120 820 820


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 6 1 4 4
quadratic 2 42 22 28 28
cubic 3 198 138 172 172
quartic 4 854 694 756 756
quintic 5 3.086 2.710 2.916 2.916
sextic 6 10.130 9.310 9.660 9.660


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