Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 42 -2 -2 -2
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 36 0 0 0



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 9 11 11 11 42
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 9 9 9 9 36



Molecule Parameter
Number of Atoms (N) 14
Number of internal coordinates 36
Number of independant internal coordinates 9
Number of vibrational modes 36





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 9 9 9 9 27 / 9
Quadratic (Raman) 9 9 9 9 36 / 0
IR + Raman - 9 9 9 27 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 36 0 0 0
quadratic 2 666 18 18 18
cubic 3 8.436 0 0 0
quartic 4 82.251 171 171 171
quintic 5 658.008 0 0 0
sextic 6 4.496.388 1.140 1.140 1.140


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 9 9 9 9
quadratic 2 180 162 162 162
cubic 3 2.109 2.109 2.109 2.109
quartic 4 20.691 20.520 20.520 20.520
quintic 5 164.502 164.502 164.502 164.502
sextic 6 1.124.952 1.123.812 1.123.812 1.123.812


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