Reduction formula for point group D2d



Characters for molecular motions
Motion E 2S4 C2 (z) 2C'2 2d
Cartesian 3N 72 0 0 -4 4
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 66 0 2 -2 4



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 9 9 7 11 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 7 10 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 7 10 16 26 / 24
Quadratic (Raman) 9 8 7 10 16 42 / 8
IR + Raman - 8 - 10 16 26 / 8



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2S4 C2 (z) 2C'2 2d
linear 1 66 0 2 -2 4
quadratic 2 2.211 1 35 35 41
cubic 3 50.116 0 68 -68 144
quartic 4 864.501 17 629 629 841
quintic 5 12.103.014 0 1.190 -1.190 2.660
sextic 6 143.218.999 17 7.735 7.735 11.585


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 9 8 7 10 16
quadratic 2 300 262 279 282 544
cubic 3 6.292 6.254 6.220 6.326 12.512
quartic 4 108.513 107.778 108.084 108.190 215.968
quintic 5 1.513.393 1.512.658 1.512.063 1.513.988 3.025.456
sextic 6 17.908.176 17.898.516 17.902.375 17.904.300 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