Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 78 -2 8 8
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 72 0 8 8



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 23 15 20 20 78
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 22 14 18 18 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 22
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 22 14 18 18 58 / 14
Quadratic (Raman) 22 14 18 18 72 / 0
IR + Raman 22 - 18 18 58 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 72 0 8 8
quadratic 2 2.628 36 68 68
cubic 3 64.824 0 376 376
quartic 4 1.215.450 666 2.010 2.010
quintic 5 18.474.840 0 8.856 8.856
sextic 6 237.093.780 8.436 37.268 37.268


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 22 14 18 18
quadratic 2 700 632 648 648
cubic 3 16.394 16.018 16.206 16.206
quartic 4 305.034 303.024 303.696 303.696
quintic 5 4.623.138 4.614.282 4.618.710 4.618.710
sextic 6 59.294.188 59.256.920 59.271.336 59.271.336


Literature




Character tables for chemically important point groups Character table for point group C2v Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement