Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 36 0 12 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 30 2 12 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 12 6 12 6 36
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 11 5 10 4 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 11
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 11 5 10 4 25 / 5
Quadratic (Raman) 11 5 10 4 30 / 0
IR + Raman 11 - 10 4 25 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 30 2 12 0
quadratic 2 465 17 87 15
cubic 3 4.960 32 472 0
quartic 4 40.920 152 2.112 120
quintic 5 278.256 272 8.184 0
sextic 6 1.623.160 952 28.336 680


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 11 5 10 4
quadratic 2 146 95 130 94
cubic 3 1.366 1.130 1.350 1.114
quartic 4 10.826 9.710 10.690 9.694
quintic 5 71.678 67.586 71.542 67.450
sextic 6 413.282 398.774 412.466 398.638


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