Reduction formula for point group D2d



Characters for molecular motions
Motion E 2S4 C2 (z) 2C'2 2d
Cartesian 3N 72 0 0 -2 2
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 66 0 2 0 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 9 9 8 10 18 54
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 9 8 8 9 16 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 9
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 9 8 8 9 16 25 / 25
Quadratic (Raman) 9 8 8 9 16 42 / 8
IR + Raman - 8 - 9 16 25 / 8



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2S4 C2 (z) 2C'2 2d
linear 1 66 0 2 0 2
quadratic 2 2.211 1 35 33 35
cubic 3 50.116 0 68 0 68
quartic 4 864.501 17 629 561 629
quintic 5 12.103.014 0 1.190 0 1.190
sextic 6 143.218.999 17 7.735 6.545 7.735


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 9 8 8 9 16
quadratic 2 298 264 280 281 544
cubic 3 6.290 6.256 6.256 6.290 12.512
quartic 4 108.443 107.848 108.120 108.154 215.968
quintic 5 1.513.323 1.512.728 1.512.728 1.513.323 3.025.456
sextic 6 17.906.916 17.899.776 17.903.040 17.903.635 35.802.816


Literature




Character tables for chemically important point groups Character table for point group D2d Constructor University Bremen

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