Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 180 0 0 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 174 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 45 45 45 45 180
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 45 43 43 43 174



Molecule Parameter
Number of Atoms (N) 60
Number of internal coordinates 174
Number of independant internal coordinates 45
Number of vibrational modes 174




Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 45 43 43 43 129 / 45
Quadratic (Raman) 45 43 43 43 174 / 0
IR + Raman - 43 43 43 129 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order		 E C2 (z) C2 (y) C2 (x)
linear 1 174 2 2 2
quadratic 2 15.225 89 89 89
cubic 3 893.200 176 176 176
quartic 4 39.524.100 4.004 4.004 4.004
quintic 5 1.407.057.960 7.832 7.832 7.832
sextic 6 41.977.229.140 121.396 121.396 121.396


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 A B1 B2 B3
linear 1 45 43 43 43
quadratic 2 3.873 3.784 3.784 3.784
cubic 3 223.432 223.256 223.256 223.256
quartic 4 9.884.028 9.880.024 9.880.024 9.880.024
quintic 5 351.770.364 351.762.532 351.762.532 351.762.532
sextic 6 10.494.398.332 10.494.276.936 10.494.276.936 10.494.276.936


Literature



Character tables for chemically important point groups Character table for point group D2 Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement