Reduction formula for point group C2v



Characters for molecular motions
Motion E C2 (z) v(xz) v(yz)
Cartesian 3N 72 0 4 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 66 2 4 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 19 17 19 17 72
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 18 16 17 15 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 18
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 18 16 17 15 50 / 16
Quadratic (Raman) 18 16 17 15 66 / 0
IR + Raman 18 - 17 15 50 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) v(xz) v(yz)
linear 1 66 2 4 0
quadratic 2 2.211 35 41 33
cubic 3 50.116 68 144 0
quartic 4 864.501 629 841 561
quintic 5 12.103.014 1.190 2.660 0
sextic 6 143.218.999 7.735 11.585 6.545


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 18 16 17 15
quadratic 2 580 543 546 542
cubic 3 12.582 12.510 12.548 12.476
quartic 4 216.633 215.932 216.038 215.898
quintic 5 3.026.716 3.025.386 3.026.121 3.024.791
sextic 6 35.811.216 35.802.151 35.804.076 35.801.556


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