Reduction formula for point group C4v



Characters for molecular motions
Motion E 2C4 (z) C2 2v 2d
Cartesian 3N 156 0 0 4 14
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 150 -2 2 4 14



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 24 15 17 22 39 117
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 23 14 17 22 37 113



Molecule Parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 23
Number of vibrational modes 113





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 23 14 17 22 37 60 / 53
Quadratic (Raman) 23 14 17 22 37 99 / 14
IR + Raman 23 14 - - 37 60 / 14



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 2v 2d
linear 1 150 -2 2 4 14
quadratic 2 11.325 3 77 83 173
cubic 3 573.800 -4 152 312 1.512
quartic 4 21.947.850 42 3.002 3.466 11.866
quintic 5 675.993.780 -80 5.852 12.320 79.492
sextic 6 17.463.172.650 118 79.002 97.174 490.042


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 23 14 17 22 37
quadratic 2 1.490 1.362 1.402 1.447 2.812
cubic 3 72.199 71.287 71.445 72.045 143.412
quartic 4 2.747.700 2.740.034 2.741.746 2.745.946 5.486.212
quintic 5 84.522.887 84.476.981 84.483.181 84.516.767 168.996.982
sextic 6 2.183.053.290 2.182.759.682 2.182.808.210 2.183.004.644 4.365.773.412


Literature




Character tables for chemically important point groups Character table for point group C4v Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement