Reduction formula for point group C2v



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



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 46 32 39 39 156
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 45 31 37 37 150



Molecule Parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 45
Number of vibrational modes 150




Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 45 31 37 37 119 / 31
Quadratic (Raman) 45 31 37 37 150 / 0
IR + Raman 45 - 37 37 119 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order		 E C2 (z) v(xz) v(yz)
linear 1 150 2 14 14
quadratic 2 11.325 77 173 173
cubic 3 573.800 152 1.512 1.512
quartic 4 21.947.850 3.002 11.866 11.866
quintic 5 675.993.780 5.852 79.492 79.492
sextic 6 17.463.172.650 79.002 490.042 490.042


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 A1 A2 B1 B2
linear 1 45 31 37 37
quadratic 2 2.937 2.764 2.812 2.812
cubic 3 144.244 142.732 143.412 143.412
quartic 4 5.493.646 5.481.780 5.486.212 5.486.212
quintic 5 169.039.654 168.960.162 168.996.982 168.996.982
sextic 6 4.366.057.934 4.365.567.892 4.365.773.412 4.365.773.412


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