Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 42 -2 6 6
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 36 0 6 6



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 13 7 11 11 42
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 12 6 9 9 36



Molecule Parameter
Number of Atoms (N) 14
Number of internal coordinates 36
Number of independant internal coordinates 12
Number of vibrational modes 36





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 12 6 9 9 30 / 6
Quadratic (Raman) 12 6 9 9 36 / 0
IR + Raman 12 - 9 9 30 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 36 0 6 6
quadratic 2 666 18 36 36
cubic 3 8.436 0 146 146
quartic 4 82.251 171 561 561
quintic 5 658.008 0 1.812 1.812
sextic 6 4.496.388 1.140 5.552 5.552


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 12 6 9 9
quadratic 2 189 153 162 162
cubic 3 2.182 2.036 2.109 2.109
quartic 4 20.886 20.325 20.520 20.520
quintic 5 165.408 163.596 164.502 164.502
sextic 6 1.127.158 1.121.606 1.123.812 1.123.812


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