Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 21 -1 7 1
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 15 1 7 1



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 7 3 7 4 21
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 6 2 5 2 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 2 5 2 13 / 2
Quadratic (Raman) 6 2 5 2 15 / 0
IR + Raman 6 - 5 2 13 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 15 1 7 1
quadratic 2 120 8 32 8
cubic 3 680 8 112 8
quartic 4 3.060 36 332 36
quintic 5 11.628 36 868 36
sextic 6 38.760 120 2.064 120


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 6 2 5 2
quadratic 2 42 22 34 22
cubic 3 202 142 194 142
quartic 4 866 682 830 682
quintic 5 3.142 2.690 3.106 2.690
sextic 6 10.266 9.174 10.146 9.174


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